diff --git a/CHANGELOG.md b/CHANGELOG.md
new file mode 100644
--- /dev/null
+++ b/CHANGELOG.md
@@ -0,0 +1,1837 @@
+## [v1.5.1](https://github.com/diagrams/diagrams-lib/tree/v1.5.1) (2025-12-02)
+
+- New `Semigroup` instance for located lines (i.e. `Located (Trail'
+  Line v n)`), which adds an extra segment from the end of the first
+  to the start of the second.
+
+## [v1.5.0.1](https://github.com/diagrams/diagrams-lib/tree/v1.5.0.1) (2025-08-25)
+
+- Fix bug in `bezierFindRoot` that caused diagrams to hang when
+  computing the trace of certain degenerate Bezier curves.  See
+  https://github.com/diagrams/diagrams-contrib/issues/91 .
+
+## [v1.5-r2](https://github.com/diagrams/diagrams-lib/tree/v1.5-r2) (2025-06-12)
+
+- Allow `optparse-applicative-0.19`
+
+## [v1.5-r1](https://github.com/diagrams/diagrams-lib/tree/v1.5-r1) (2025-05-17)
+
+- Allow `monoid-extras-0.7`
+
+## [v1.5](https://github.com/diagrams/diagrams-lib/tree/v1.5) (2025-02-13)
+
+- Allow `base-4.21` and test on GHC 9.12
+- Remove looped compilation mode options ([#372](https://github.com/diagrams/diagrams-lib/pull/372))
+    - This allows us to remove the `fsnotify` dependency, which in
+      turn allows compiling diagrams to Wasm.
+    - To recover similar functionality (automatically recompiling
+      every time a source file changes), try an external tool like
+      `ghcid` or `ghciwatch`, or, more generically, `entr`.
+
+## [v1.4.7](https://github.com/diagrams/diagrams-lib/tree/v1.4.7) (2024-10-26)
+
+- Switch to `data-default-0.8` instead of `data-default-class`
+
+## [v1.4.6.2-r3](https://github.com/diagrams/diagrams-lib/tree/v1.4.6.2-r3) (2024-08-23)
+
+- Allow `hashable-1.5`
+
+## [v1.4.6.2-r2](https://github.com/diagrams/diagrams-lib/tree/v1.4.6.2-r2) (2024-07-01)
+
+- Allow `tasty-quickcheck-0.11`
+
+## [v1.4.6.2-r1](https://github.com/diagrams/diagrams-lib/tree/v1.4.6.2-r1) (2024-05-01)
+
+- Allow `base-4.21` (GHC 9.10), `containers-0.7`, `lens-5.3`, and `filepath-1.5`
+
+## [v1.4.6.2](https://github.com/diagrams/diagrams-lib/tree/v1.4.6.2) (2024-05-01)
+
+- Support for `linear-1.23`.  This version of `linear` introduces a
+  breaking change, so add an internal compatibility module that allows
+  diagrams to work with any version of `linear` both before and after
+  the change.
+
+## [v1.4.6.1](https://github.com/diagrams/diagrams-lib/tree/v1.4.6.1) (2024-02-26)
+
+- Fix compilation on BSD ([#367](https://github.com/diagrams/diagrams-lib/pull/367), thanks to Finn Espen Gundersen)
+
+## [v1.4.6-r4](https://github.com/diagrams/diagrams-lib/tree/v1.4.6-r4) (2024-01-11)
+
+- Allow `base-4.19` and test with GHC 9.8
+- Allow `text-2.1`
+
+## [v1.4.6-r3](https://github.com/diagrams/diagrams-lib/tree/v1.4.6-r3) (2023-09-14)
+
+- Allow `tasty-1.5`
+
+## [v1.4.6-r2](https://github.com/diagrams/diagrams-lib/tree/v1.4.6-r2) (2023-08-16)
+
+- Allow `bytestring-0.12` and `deepseq-1.5`
+
+## [v1.4.6-r1](https://github.com/diagrams/diagrams-lib/tree/v1.4.6-r1) (2023-05-25)
+
+- Allow `optparse-applicative-0.18`
+
+## [v1.4.6](https://github.com/diagrams/diagrams-lib/tree/v1.4.5.3) (2023-05-15)
+
+- Allow `base-4.18`; test with GHC 9.6 (thanks to @sergv)
+- Fix some warnings (thanks to @sergv)
+
+## [v1.4.5.3](https://github.com/diagrams/diagrams-lib/tree/v1.4.5.3) (2022-09-19)
+
+- Update to `fsnotify-0.4`
+
+- Revisions:
+  - r1: require `lens-5.1`
+  - r2: allow `mtl-2.3`
+  - r3 (3 Dec 2022): allow `linear-1.22`
+
+## [v1.4.5.2](https://github.com/diagrams/diagrams-lib/tree/v1.4.5.2) (2022-09-14)
+
+- Fix build with `transformers-0.6`
+- Fix some deprecation warnings
+
+## [v1.4.5.1-r3](https://github.com/diagrams/diagrams-lib/tree/v1.4.5.1-r3) (2022-08-27)
+
+- Allow `base-4.17` and `lens-5.2`; test with GHC 9.4
+
+## [v1.4.5.1-r2](https://github.com/diagrams/diagrams-lib/tree/v1.4.5.1-r2) (2022-02-01)
+
+- Allow `optparse-applicative-0.17`
+
+## [v1.4.5.1-r1](https://github.com/diagrams/diagrams-lib/tree/v1.4.5.1-r1) (2022-01-08)
+
+- Allow `text-2.0`
+
+## [v1.4.5.1](https://github.com/diagrams/diagrams-lib/tree/v1.4.5.1) (2021-12-17)
+
+- Bug fix: make things compile again under versions of `lens` before 5.1.
+
+## [v1.4.5](https://github.com/diagrams/diagrams-lib/tree/v1.4.5) (2021-12-16)
+
+- Allow `base-4.16` (tested with GHC 9.2.1)
+- Allow `semigroups-0.20`, `lens-5.1`, `hashable-1.4`,
+  `transformers-0.6`
+- Add `Eq` instance for `SizeSpec`
+
+## [v1.4.4-r1](https://github.com/diagrams/diagrams-lib/tree/v1.4.4-r1) (2021-06-05)
+
+- Bumps to dependency upper bounds:
+    - Allow `tasty-1.4`
+    - Allow `bytestring-0.11`
+
+## [v1.4.4](https://github.com/diagrams/diagrams-lib/tree/v1.4.4) (2021-05-24)
+
+- Bumps to upper bounds, to allow building with:
+    - `base-4.15` (tested with GHC 9.0.1)
+    - `optparse-applicative` (tested with GHC 8.8.4 & 8.10.2)
+
+- Updated use of Kinds thoughout the package
+
+- Drop support for GHC 8.2 or earlier
+
+## [v1.4.3](https://github.com/diagrams/diagrams-lib/tree/v1.4.3) (2019-11-06)
+
+- Bumps to upper bounds, to allow building with:
+    - `base-4.13` (tested with GHC 8.8.1)
+    - `intervals-0.9`
+    - `semigroups-0.19`
+    - `hashable-1.3`
+- Many bug fixes, including
+    - [#313](https://github.com/diagrams/diagrams-lib/issues/313) (`combineBoundaries`)
+    - [#322](https://github.com/diagrams/diagrams-lib/issues/322), [#329](https://github.com/diagrams/diagrams-lib/issues/329) (`section`)
+    - [#325](https://github.com/diagrams/diagrams-lib/pull/325)
+      (Bezier/Bezier intersection)
+    - [#339](https://github.com/diagrams/diagrams-lib/pull/339) (`perspectiveZ1`)
+- Added derived `Eq` and `Ord` instances for `FixedSegment`
+
+## [v1.4.2.3](https://github.com/diagrams/diagrams-lib/tree/v1.4.2.3) (2018-06-11)
+
+- Bug fix for `extrudeEnvelope` and friends ([#316](https://github.com/diagrams/diagrams-lib/issues/316))
+
+## [v1.4.2.2](https://github.com/diagrams/diagrams-lib/tree/v1.4.2.2) (2018-05-08)
+
+- Fixes for GHC < 8.0
+
+## [v1.4.2.1](https://github.com/diagrams/diagrams-lib/tree/v1.4.2.1) (2018-04-13)
+
+- Allow `base-4.11` (GHC 8.4)
+- Allow `tasty-quickcheck-0.10`
+- Bug fix for `Diagrams.TwoD.Offset.capArc` ([#310](https://github.com/diagrams/diagrams-lib/pull/310))
+
+## [v1.4.2-r1](https://github.com/diagrams/diagrams-lib/tree/v1.4.2-r1) (2017-12-20)
+
+Hackage revision to allow `tasty-1.0` in the test suite.
+
+## [v1.4.2](https://github.com/diagrams/diagrams-lib/tree/v1.4.2) (2017-12-20)
+
+- New functions:
+    - `boxGrid`, for computing a grid of regularly spaced points.
+    - `scalingRotationTo` and `scaleRotateTo`, for affine conformal 2D
+      transformations.
+- Documentation fixes:
+    - `dirBetween`
+    - `PolyOrientation`
+- Upper bound updates: allow `tasty-0.12`, `tasty-quickcheck-0.9`,
+  `tasty-hunit-0.10`, `optparse-applicative-0.14`
+- Test with GHC 8.2.2
+
+## [v1.4.1.2](https://github.com/diagrams/diagrams-lib/tree/v1.4.1.2) (2017-06-10)
+
+- Fix test suite compilation failure [#299](https://github.com/diagrams/diagrams-lib/issues/299).
+
+## [v1.4.1.1](https://github.com/diagrams/diagrams-lib/tree/v1.4.1.1) (2017-06-06)
+
+- Fix `Diagrams.Points.centroid` to make it total.
+- Fix bug in `Diagrams.Transform.Matrix.fromMatWithInv` (and hence
+  also related functions which called it, such as `fromMat22` and
+  `fromMat33`).
+
+## [v1.4.1](https://github.com/diagrams/diagrams-lib/tree/v1.4.1) (2017-05-28)
+
+- New functions `embeddedImage` and `loadImageEmbBS` for loading
+  images.
+- Fix [#289](https://github.com/diagrams/diagrams-lib/issues/289)
+  which could have caused strange behavior in looped compilation mode
+  on 32-bit platforms.
+- Allow `intervals-0.8` and `directory-1.3`.
+- Minor fixes to compile with GHC 8.2.
+
+## [v1.4.0.1](https://github.com/diagrams/diagrams-lib/tree/v1.4.0.1) (2016-11-07)
+
+- Fix test suite compilation problem ([#286](https://github.com/diagrams/diagrams-lib/issues/286))
+
+## [v1.4](https://github.com/diagrams/diagrams-lib/tree/v1.4) (2016-10-26)
+
+* **New features**
+
+    - New `mkText'` function, which allows making a text primitive
+      without recommending a fill colour or font size so users can
+      recommend their own (*e.g.* using the `recommendFontSize`
+      function).
+
+    - New functions `reflectXY` and `reflectionXY`
+
+    - New `composeAligned` combinator for doing composition under an
+      alignment while leaving the local origin unaffected.
+
+    - Add `_LocLoop` and `_LocLine` prisms
+
+    - New `bspline` function for creating uniform cubic B-splines
+
+    - New 3D features:
+        - New `Skinned` class
+        - Improved handling of 3D primitives
+        - CSG
+
+    - New standard attributes for separate fill and stroke opacity
+      (see
+      [#248](https://github.com/diagrams/diagrams-lib/issues/248)).
+
+    - New `HasQuery` class for things which can be spatially queried
+      for values from some monoid.
+
+    - New function `inquire` for testing whether a given point is
+      inside a diagram.
+
+    - New font weights: `bolder`, `lighter`, `thinWeight`,
+      `ultraLight`, `light`, `mediumWeight`, `heavy`, `semiBold`,
+      `ultraBold`.  Note that currently only the SVG backend deals
+      with the new weights.
+
+    - Export `GetSegmentCodomain` and update documentation
+
+    - Improved performance of 2D rotations
+
+* **New instances**
+
+    - `Alignable` instance for `Located`
+
+    - `ToPath` instances for lines and loops
+
+    - `Serialize` instances for `Trail`, `Path`, `Located`, `SegTree`,
+      `Segment`
+
+    - `Generic` instances for `Path`, `Located`
+
+    - `Action` instance for `Angle`: angles act by rotation.
+
+* **API changes**
+
+    - `snugBL`, `snugBR`, `snugTR` and `snugBR` are deprecated.
+      These functions were unintuitive, ad-hoc, and not particularly useful,
+      especially since e.g. `snugL` and `snugB` do not commute. You
+      can use something like `snugB . snugL` directly, or use `snug`
+      with a direction vector.  See
+      [#250](https://github.com/diagrams/diagrams-lib/issues/250) for
+      more details.
+
+* **Dependency/version changes**
+
+    - upgrade `fsnotify` and drop dependency on deprecated
+      `system-filepath`
+    - Allow `lens-4.15`
+    - Many other bumped upper bounds, see release notes for minor releases
+      below
+
+* **Bug fixes**
+
+    - fix `orientPoints` function, which was previously generating NaN
+      values with lists of only one or two
+      points. ([#210](https://github.com/diagrams/diagrams-lib/issues/210))
+
+    - Broken offset joins with non-vertices in loops ([#263](https://github.com/diagrams/diagrams-lib/issues/263))
+
+    - Properly transform arrow shaft styles ([#274](https://github.com/diagrams/diagrams-lib/issues/274))
+
+    - Fix sign error in `reflectionAbout`
+
+## [v1.3.1.4](https://github.com/diagrams/diagrams-lib/tree/v1.3.1.4) (2016-08-16) (16 August 2016)
+
+- allow `optparse-applicative-0.13`
+
+## [v1.3.1.3](https://github.com/diagrams/diagrams-lib/tree/v1.3.1.3) (2016-06-05)
+
+- allow `base-4.9`
+- allow `data-default-class-0.1`
+- test with GHC 8.0.1
+
+[Full Changelog](https://github.com/diagrams/diagrams-lib/compare/v1.3.1.2...v1.3.1.3)
+
+## [v1.3.1.2](https://github.com/diagrams/diagrams-lib/tree/v1.3.1.2) (2016-05-01)
+
+- allow `lens-4.14`
+
+[Full Changelog](https://github.com/diagrams/diagrams-lib/compare/v1.3.1.1...v1.3.1.2)
+
+## [v1.3.1.2](https://github.com/diagrams/diagrams-lib/tree/v1.3.1.2) (2016-02-19)
+
+  - allow `unordered-containers-0.2.*`
+
+[Full Changelog](https://github.com/diagrams/diagrams-lib/compare/v1.3.1.0...v1.3.1.1)
+
+## [v1.3.1.0](https://github.com/diagrams/diagrams-lib/tree/v1.3.1.0) (2016-02-14)
+
+- improve path offset calculations
+
+[Full Changelog](https://github.com/diagrams/diagrams-lib/compare/v1.3.0.9...v1.3.1.0)
+
+## [v1.3.0.9](https://github.com/diagrams/diagrams-lib/tree/v1.3.0.9) (2016-01-14)
+
+- allow `unordered-containers-0.2.6`
+
+[Full Changelog](https://github.com/diagrams/diagrams-lib/compare/v1.3.0.8...v1.3.0.9)
+
+## [v1.3.0.8](https://github.com/diagrams/diagrams-lib/tree/v1.3.0.8) (2015-11-10)
+
+- allow `semigroups-0.18`
+
+[Full Changelog](https://github.com/diagrams/diagrams-lib/compare/v1.3.0.7...v1.3.0.8)
+
+## [v1.3.0.7](https://github.com/diagrams/diagrams-lib/tree/v1.3.0.7) (2015-10-08) ##
+
+- Add `LambdaCase` extension to `.cabal` file, so `cabal` correctly
+  reports that `diagrams-lib` does not build on `GHC-7.4`.
+
+[Full Changelog](https://github.com/diagrams/diagrams-lib/compare/v1.3.0.6...v1.3.0.7)
+
+## [v1.3.0.6](https://github.com/diagrams/diagrams-lib/tree/v1.3.0.6) (2015-09-29) ##
+
+- Allow `optparse-applicative-0.12`
+
+[Full Changelog](https://github.com/diagrams/diagrams-lib/compare/v1.3.0.5...v1.3.0.6)
+
+## [v1.3.0.5](https://github.com/diagrams/diagrams-lib/tree/v1.3.0.5) (2015-09-18) ##
+
+- Fix compilation problem with `lens-4.13`
+
+[Full Changelog](https://github.com/diagrams/diagrams-lib/compare/v1.3.0.4...v1.3.0.5)
+
+## [v1.3.0.4](https://github.com/diagrams/diagrams-lib/tree/v1.3.0.4) (2015-09-17) ##
+
+**Dependency/version changes**
+
+- Allow `lens-1.13`
+- Allow `semigroups-0.17`
+- Require `linear-1.20`
+
+## [v1.3.0.3](https://github.com/diagrams/diagrams-lib/tree/v1.3.0.3) (2015-08-10)
+
+**Dependency/version changes**
+
+- Drop dependency on deprecated `system-filepath` package
+- Require `fsnotify-0.2.1`
+
+## [v1.3.0.2](https://github.com/diagrams/diagrams-lib/tree/v1.3.0.2) (2015-07-19)
+
+[Full Changelog](https://github.com/diagrams/diagrams-lib/compare/v1.3.0.1...v1.3.0.2)
+
+## [v1.3.0.1](https://github.com/diagrams/diagrams-lib/tree/v1.3.0.1) (2015-05-26)
+
+[Full Changelog](https://github.com/diagrams/diagrams-lib/compare/v1.3...v1.3.0.1)
+
+## [v1.3](https://github.com/diagrams/diagrams-lib/tree/v1.3) (2015-04-19)
+
+**New features**
+
+- Native image type that backends can specify.
+
+- Affine maps between spaces for path-like objects. A new
+  `Diagrams.ThreeD.Projections` has some helper functions for
+  orthographic and perspective projections.
+
+- Intersections for path-like objects using Bézier clipping.
+
+- Helper functions in `Diagrams.Matrix` for converting between
+  transforms and matrices.
+
+- New `Diagrams` module that only exports functions defined in
+  diagrams.
+
+- New `Direction` type. `Direction` is a vector that's forgot it's
+  magnitude. Some functions have changed their type from `R2` to
+  `Direction V2 n` to make it clear that magnitude has no effect.
+
+- Use the [`fsnotify`](https://hackage.haskell.org/package/fsnotify)
+  package for command line looping. Command line looping now works
+  on Windows.
+
+- `groupOpacity` function added for lowering the opacity of a
+  diagram as a whole.
+
+- New `ToPath` class for converting path-like things to a `Path`.
+
+**New instances**
+
+- `Each` instances for `BoundingBox`, `Offset`, `Segment`,
+  `FixedSegment` and `Path`.
+
+- `Reversing` instances for `Offset`, `Segment`, `FixedSegment`,
+  `Trail` and `Path`.
+
+- `AsEmpty` instances for `BoundingBox`, `Trail` and `Path`.
+
+- `Cons` and `Snoc` instances for `Path` and `Line`.
+
+- New `Show` instances for `Angle`, `Segment`, `SomeColor`, `Trail'`
+  and `at`.
+
+- `Tangent` instance for `(FixedSegment v n)`.
+
+- `Ord` instances for `LineMiterLimit`, `LineJoin` and `LineCap`.
+
+**New helper functions**
+
+- `_Line` and `_Loop` prisms.
+
+- Style lenses: `_fontSize`, `_lineWidth`, `_fillTexture`,
+  `_lineTexture`, `_opacity`, `_font`, `_lineCap`, `_lineJoin`
+  `_dashing`.
+
+- `_SomeColor` iso and `_AC` prism onto an `AlphaColour`.
+
+- `atPoints` function to zip points with diagrams.
+
+**API changes**
+
+- `Diagram` type synonym now only takes a backend token: `Diagram B`
+
+- Types that previously had a `v` variable now have `v` and `n`.
+
+- `Control.Lens` and `Data.Default.Class` are now exported from from
+  `Diagrams.Prelude`
+
+- `Measure` has a new internal representation. `Local`, `Global`,
+  `Normalized`, and `Output` have been renamed to `local`, `global`,
+  `normalized` and `output` respectivly.
+
+- `SizeSpec2D` has moved to `SizeSpec v n` in `Diagrams.SizeSpec`.
+  `Dims, Height, Width and `Absolute` have moved to `dims2D`,
+  `mkHeight`, `mkWidth` and `absolute` respectively.
+
+- `Color` instances for `Colour` and `AlphaColour` are limited to
+  `Double` for better type inference.
+
+- `under` has been renamed to `underT`. New `transformed`,
+  `translated`, `movedTo`, `movedFrom` and `rotated` isomorphisms to
+  use with lens's `under` function.
+
+- `stroke` is now polymorphic. Use `strokePath` or `strokeP` to get
+  old `stroke` behaviour.
+
+- `angleBetween` now works for any vector space, which means the
+  angle is always positive. The old behaviour can be retrieved from
+  `signedAngleBetween`
+
+- `arc` now takes a starting `Direction` and a sweep `Angle`.
+  `arcCW` and `arcCCW` take a start and finish `Direction`.
+
+**Dependency/version changes**
+
+- use `linear` instead of `vector-space`
+
+**Closed issues:**
+
+- Perspective deformation of square vertices yields extra point [\#244](https://github.com/diagrams/diagrams-lib/issues/244)
+
+- Local fontsize renders inconsistentl on diffrent backends [\#243](https://github.com/diagrams/diagrams-lib/issues/243)
+
+- Factor out Diagrams.Solve into a package? [\#235](https://github.com/diagrams/diagrams-lib/issues/235)
+
+**Merged pull requests:**
+
+- add pathPoints and pathVertices' functions [\#245](https://github.com/diagrams/diagrams-lib/pull/245) ([byorgey](https://github.com/byorgey))
+
+- New loop [\#242](https://github.com/diagrams/diagrams-lib/pull/242) ([cchalmers](https://github.com/cchalmers))
+
+- Pre 1.3 [\#241](https://github.com/diagrams/diagrams-lib/pull/241) ([cchalmers](https://github.com/cchalmers))
+
+- Update CubicSpline.hs [\#240](https://github.com/diagrams/diagrams-lib/pull/240) ([fryguybob](https://github.com/fryguybob))
+
+- updated changes for GHC-7.10 [\#239](https://github.com/diagrams/diagrams-lib/pull/239) ([bergey](https://github.com/bergey))
+
+- split out new package diagrams-solve [\#237](https://github.com/diagrams/diagrams-lib/pull/237) ([byorgey](https://github.com/byorgey))
+
+- Lens style [\#236](https://github.com/diagrams/diagrams-lib/pull/236) ([cchalmers](https://github.com/cchalmers))
+
+- Half-dart arrowheads [\#234](https://github.com/diagrams/diagrams-lib/pull/234) ([byorgey](https://github.com/byorgey))
+
+- TwoD.Points: Needs TypeFamilies [\#233](https://github.com/diagrams/diagrams-lib/pull/233) ([bgamari](https://github.com/bgamari))
+
+- Projections [\#229](https://github.com/diagrams/diagrams-lib/pull/229) ([cchalmers](https://github.com/cchalmers))
+
+## [1.2.0.9]() (2 April 2015)
+
+ - allow `lens-4.9`
+
+ - allow `vector-space-0.10`
+
+## [v1.2.0.8](https://github.com/diagrams/diagrams-lib/tree/v1.2.0.8) (2015-01-13)
+
+[Full Changelog](https://github.com/diagrams/diagrams-lib/compare/v1.2.0.7...v1.2.0.8)
+
+**Merged pull requests:**
+
+- typo in haddocks [\#232](https://github.com/diagrams/diagrams-lib/pull/232) ([ggreif](https://github.com/ggreif))
+
+- Update diagrams-lib.cabal : bumping JuicyPixels dependency [\#230](https://github.com/diagrams/diagrams-lib/pull/230) ([Twinside](https://github.com/Twinside))
+
+## [v1.2.0.7](https://github.com/diagrams/diagrams-lib/tree/v1.2.0.7) (2014-12-07)
+
+[Full Changelog](https://github.com/diagrams/diagrams-lib/compare/v1.2.0.6...v1.2.0.7)
+
+## [v1.2.0.6](https://github.com/diagrams/diagrams-lib/tree/v1.2.0.6) (2014-12-04)
+
+[Full Changelog](https://github.com/diagrams/diagrams-lib/compare/v1.2.0.5...v1.2.0.6)
+
+**Merged pull requests:**
+
+- Minor changes in documentation about Polygons. [\#228](https://github.com/diagrams/diagrams-lib/pull/228) ([alexDarcy](https://github.com/alexDarcy))
+
+## [v1.2.0.5](https://github.com/diagrams/diagrams-lib/tree/v1.2.0.5) (2014-11-17)
+
+[Full Changelog](https://github.com/diagrams/diagrams-lib/compare/v1.2.0.4...v1.2.0.5)
+
+**Implemented enhancements:**
+
+- Path/trail intersection [\#209](https://github.com/diagrams/diagrams-lib/issues/209)
+
+- Turn R2 into D2 \(Generalize R2 to any numeric type\) [\#50](https://github.com/diagrams/diagrams-lib/issues/50)
+
+**Fixed bugs:**
+
+- `Sectionable` instance for `SegTree` is not a linear reparameterization. [\#217](https://github.com/diagrams/diagrams-lib/issues/217)
+
+**Closed issues:**
+
+- bezierFromSweep very slow? [\#227](https://github.com/diagrams/diagrams-lib/issues/227)
+
+- All lines render at same width [\#222](https://github.com/diagrams/diagrams-lib/issues/222)
+
+- numerically stable cubic rootfinder [\#204](https://github.com/diagrams/diagrams-lib/issues/204)
+
+**Merged pull requests:**
+
+- Intersections [\#226](https://github.com/diagrams/diagrams-lib/pull/226) ([cchalmers](https://github.com/cchalmers))
+
+- Linear update [\#225](https://github.com/diagrams/diagrams-lib/pull/225) ([cchalmers](https://github.com/cchalmers))
+
+- Add arcCCW and friends.  Fix offset joins. [\#221](https://github.com/diagrams/diagrams-lib/pull/221) ([fryguybob](https://github.com/fryguybob))
+
+- Reparameterize section [\#220](https://github.com/diagrams/diagrams-lib/pull/220) ([fryguybob](https://github.com/fryguybob))
+
+- Diagram b v n to QDiagram b v n Any [\#219](https://github.com/diagrams/diagrams-lib/pull/219) ([jeffreyrosenbluth](https://github.com/jeffreyrosenbluth))
+
+- New stuff [\#218](https://github.com/diagrams/diagrams-lib/pull/218) ([cchalmers](https://github.com/cchalmers))
+
+- Linear [\#215](https://github.com/diagrams/diagrams-lib/pull/215) ([cchalmers](https://github.com/cchalmers))
+
+## [v1.2.0.4](https://github.com/diagrams/diagrams-lib/tree/v1.2.0.4) (2014-10-08)
+
+[Full Changelog](https://github.com/diagrams/diagrams-lib/compare/v1.2.0.3...v1.2.0.4)
+
+**Merged pull requests:**
+
+- add semi-portable looping using fsnotify [\#213](https://github.com/diagrams/diagrams-lib/pull/213) ([bergey](https://github.com/bergey))
+
+## [v1.2.0.3](https://github.com/diagrams/diagrams-lib/tree/v1.2.0.3) (2014-09-07)
+
+[Full Changelog](https://github.com/diagrams/diagrams-lib/compare/v1.2.0.2...v1.2.0.3)
+
+**Closed issues:**
+
+- arrowFromLocatedTrail function [\#205](https://github.com/diagrams/diagrams-lib/issues/205)
+
+**Merged pull requests:**
+
+- Added `arrowFromLocatedTrail` [\#206](https://github.com/diagrams/diagrams-lib/pull/206) ([pnutus](https://github.com/pnutus))
+
+## [v1.2.0.2](https://github.com/diagrams/diagrams-lib/tree/v1.2.0.2) (2014-08-22)
+
+[Full Changelog](https://github.com/diagrams/diagrams-lib/compare/v1.2.0.1...v1.2.0.2)
+
+**Implemented enhancements:**
+
+- Generalize Angle class? [\#38](https://github.com/diagrams/diagrams-lib/issues/38)
+
+**Fixed bugs:**
+
+- --selection and --src both use -s abbreviation [\#172](https://github.com/diagrams/diagrams-lib/issues/172)
+
+**Closed issues:**
+
+- Spike arrowhead and tail render with oversized joint [\#203](https://github.com/diagrams/diagrams-lib/issues/203)
+
+**Merged pull requests:**
+
+- Enable compilation with GHC HEAD \(v7.9\) [\#211](https://github.com/diagrams/diagrams-lib/pull/211) ([ggreif](https://github.com/ggreif))
+
+- cli-options [\#200](https://github.com/diagrams/diagrams-lib/pull/200) ([bergey](https://github.com/bergey))
+
+- Add Native images to Diagrams.TwoD.Image [\#199](https://github.com/diagrams/diagrams-lib/pull/199) ([taruti](https://github.com/taruti))
+
+- add atPoints, deprecate decorateFoo [\#198](https://github.com/diagrams/diagrams-lib/pull/198) ([jeffreyrosenbluth](https://github.com/jeffreyrosenbluth))
+
+- Add bg' [\#197](https://github.com/diagrams/diagrams-lib/pull/197) ([jeffreyrosenbluth](https://github.com/jeffreyrosenbluth))
+
+- add convenience synonyms \[hv\]sep for \[hv\]cat' \(with & sep .~ x\) [\#196](https://github.com/diagrams/diagrams-lib/pull/196) ([byorgey](https://github.com/byorgey))
+
+- Vertices [\#192](https://github.com/diagrams/diagrams-lib/pull/192) ([jeffreyrosenbluth](https://github.com/jeffreyrosenbluth))
+
+- Direction type [\#186](https://github.com/diagrams/diagrams-lib/pull/186) ([bergey](https://github.com/bergey))
+
+## [v1.2.0.1](https://github.com/diagrams/diagrams-lib/tree/v1.2.0.1) (2014-06-04)
+
+[Full Changelog](https://github.com/diagrams/diagrams-lib/compare/v1.2...v1.2.0.1)
+
+**Closed issues:**
+
+- Local headLength / headGaps act like Output [\#193](https://github.com/diagrams/diagrams-lib/issues/193)
+
+**Merged pull requests:**
+
+- transform Local Measure in arrow styles [\#194](https://github.com/diagrams/diagrams-lib/pull/194) ([bergey](https://github.com/bergey))
+
+## [v1.2](https://github.com/diagrams/diagrams-lib/tree/v1.2) (2014-06-02)
+
+[Full Changelog](https://github.com/diagrams/diagrams-lib/compare/v1.1.0.4...v1.2)
+
+**New features**
+
+- Several attributes (such as line width, dashing size, arrowhead
+  size, and font size) that formerly had a value of type `Double`
+  now have the more general type `Measure R2`. This allows the
+  attributes to be specified relative to one of four measurement
+  frames: `Local`, `Global`, `Normalized`, and `Output`.
+
+- New DSL for specifying measurements.
+
+- New synonyms for specifying measurements, *e.g.* `thin`,
+  `thick`, and `medium`, `large`.
+
+- Support for radial and linear gradients for fills and strokes.
+
+- New `DImage` type that supports both embedded and external images in
+  Backends that support them.
+
+- New `lengths` Traversal for setting `headLength` and `tailLength`
+  simultaneously.
+
+- `Frustrum` and `Box` shapes added to `Diagrams.ThreeD.Shapes`.
+
+- New function `quartForm` to find roots of quartic polynomials.
+
+- New Lenses for polar coordinates.
+
+- New trig functions, `sinA`, `atanA`, etc. which take `Angle` as
+  input or output.
+
+**New instances**
+
+- `Transformable` instances for `LineWidth`, `Dashing`,
+  `LineTexture`, and  `FillTexture`.
+
+**API changes**
+
+- `FillColor` and `LineColor` attributes have been replaced with
+  the more general `FillTexture` and `LineTexture`. Use the `solid`
+  function to convert a color to a texture.
+
+- The size of arrow heads and tails is now specified in terms of
+  length instead of the radius of their circumcircle.
+
+- Gaps at the ends of arrows are now specified using `Measure R2`.
+
+- The `gap` traversal has been replaced by `gaps` for consistency
+  in naming, though `gap` is still provided for backwards compatibility.
+
+- `fontSize` now takes a value of type `Measure R2`.
+
+- Get rid of (bitrotted) `Show` backend.
+
+- Functions in `TwoD.Adjust` now return the adjustment
+  transformation itself in addition to the resized `Diagram` and
+  `Options` record; this can be used, *e.g.* to convert screen
+  coordinates back into diagram coordinates.
+
+- Export `pathLocSegments`.
+
+- The `avgScale` function has been moved to `Diagrams.Core`.
+
+- The `Angle` definition and related functions (*e.g.*
+  `angleBetween`) have moved to a separate module, `Diagrams.Angle`.
+
+- A separate `Diagrams.TwoD.Attributes` module now contains most
+  of the attributes that require 2D transformation instances.
+
+- The `splitColorFills` function has been replaced by `splitTextureFills`.
+
+**Dependency/version changes**
+
+- Allow `semigroups-0.15`
+
+- Allow `opt-parse-applicative-0.9.0
+
+- Allow `lens-4.2`
+
+**Implemented enhancements:**
+
+- 'image' should be in IO [\#29](https://github.com/diagrams/diagrams-lib/issues/29)
+
+- Add gradient support [\#9](https://github.com/diagrams/diagrams-lib/issues/9)
+
+**Closed issues:**
+
+- fails to build against HP [\#190](https://github.com/diagrams/diagrams-lib/issues/190)
+
+- text does not scale [\#179](https://github.com/diagrams/diagrams-lib/issues/179)
+
+- Please add support for latest version of intervals library [\#170](https://github.com/diagrams/diagrams-lib/issues/170)
+
+- presence of arrowHead can tilt connection sideways [\#162](https://github.com/diagrams/diagrams-lib/issues/162)
+
+**Merged pull requests:**
+
+- Quartic formula, no obvious bugs [\#187](https://github.com/diagrams/diagrams-lib/pull/187) ([Mathnerd314](https://github.com/Mathnerd314))
+
+- Arrow length [\#185](https://github.com/diagrams/diagrams-lib/pull/185) ([jeffreyrosenbluth](https://github.com/jeffreyrosenbluth))
+
+- fix handling of text scaling [\#182](https://github.com/diagrams/diagrams-lib/pull/182) ([byorgey](https://github.com/byorgey))
+
+- Texture [\#181](https://github.com/diagrams/diagrams-lib/pull/181) ([jeffreyrosenbluth](https://github.com/jeffreyrosenbluth))
+
+- arrow envelopes [\#180](https://github.com/diagrams/diagrams-lib/pull/180) ([jeffreyrosenbluth](https://github.com/jeffreyrosenbluth))
+
+- make headSize and tailSize back into ArrowOpts fields [\#177](https://github.com/diagrams/diagrams-lib/pull/177) ([byorgey](https://github.com/byorgey))
+
+- updated the upper bounds of the .cabal constraints for 'semigroups' package [\#176](https://github.com/diagrams/diagrams-lib/pull/176) ([zgredzik](https://github.com/zgredzik))
+
+- Image2 [\#174](https://github.com/diagrams/diagrams-lib/pull/174) ([jeffreyrosenbluth](https://github.com/jeffreyrosenbluth))
+
+- Image [\#173](https://github.com/diagrams/diagrams-lib/pull/173) ([jeffreyrosenbluth](https://github.com/jeffreyrosenbluth))
+
+- Preliminary implementation of Measure [\#159](https://github.com/diagrams/diagrams-lib/pull/159) ([jeffreyrosenbluth](https://github.com/jeffreyrosenbluth))
+
+- Gradient [\#136](https://github.com/diagrams/diagrams-lib/pull/136) ([jeffreyrosenbluth](https://github.com/jeffreyrosenbluth))
+
+## [v1.1.0.7]() (2014-05-15)
+
+- Allow `semigroups-0.14`
+
+## [v1.1.0.6]() (2014-04-10)
+
+- Allow `semigroups-0.13`
+
+## [v1.1.0.4](https://github.com/diagrams/diagrams-lib/tree/v1.1.0.4) (2014-04-04)
+
+[Full Changelog](https://github.com/diagrams/diagrams-lib/compare/v1.1.0.2...v1.1.0.4)
+
+**Merged pull requests:**
+
+- Updates to work with `Backend` redesign [\#171](https://github.com/diagrams/diagrams-lib/pull/171) ([byorgey](https://github.com/byorgey))
+
+- Rework of units [\#169](https://github.com/diagrams/diagrams-lib/pull/169) ([byorgey](https://github.com/byorgey))
+
+- Make Diagrams.Transform.under more polymorphic [\#168](https://github.com/diagrams/diagrams-lib/pull/168) ([FlorentBecker](https://github.com/FlorentBecker))
+
+## [v1.1.0.3]() (2014-03-19)
+
+- Allow `lens-4.1`
+
+## [v1.1.0.2](https://github.com/diagrams/diagrams-lib/tree/v1.1.0.2) (2014-03-19)
+
+[Full Changelog](https://github.com/diagrams/diagrams-lib/compare/v1.1.0.1...v1.1.0.2)
+
+**Merged pull requests:**
+
+- move avgScale to core [\#167](https://github.com/diagrams/diagrams-lib/pull/167) ([jeffreyrosenbluth](https://github.com/jeffreyrosenbluth))
+
+- 3d color & lighting, more solids, Angle utilities [\#166](https://github.com/diagrams/diagrams-lib/pull/166) ([bergey](https://github.com/bergey))
+
+- Added bothSize function, lineHead and lineTail [\#165](https://github.com/diagrams/diagrams-lib/pull/165) ([jeffreyrosenbluth](https://github.com/jeffreyrosenbluth))
+
+## [v1.1.0.1](https://github.com/diagrams/diagrams-lib/tree/v1.1.0.1) (2014-03-09)
+
+[Full Changelog](https://github.com/diagrams/diagrams-lib/compare/v1.1...v1.1.0.1)
+
+- Depend on `hashable` package, and add `Hashable` instance for
+  `SizeSpec2D`.
+
+  Technically, the PVP specifies that adding a new instance
+  requires a major version bump.  However, I highly doubt anyone
+  was making their own orphan `Hashable` instances before.  Feel
+  free to yell at Brent if this breaks your build.
+
+## [v1.1](https://github.com/diagrams/diagrams-lib/tree/v1.1) (2014-03-09)
+
+[Full Changelog](https://github.com/diagrams/diagrams-lib/compare/v1.0.1...v1.1)
+
+**New features**
+
+- Support for `Deformation`s, arbitrary (non-affine)
+  transformations on objects such as points, paths, and located
+  trails (though not on diagrams).
+
+- New functions `clipTo`, which clips a diagram's envelope and
+  trace along with its visual representation, and `clipped`, which
+  clips the diagram's visual representation but replaces its
+  envelope and trace with those of the clipping path.
+
+- New `arrowV` function, for creating an arrow with the direction
+  and magnitude of a given vector.
+
+- `gap` traversal, for setting the head and tail gaps of an arrow
+  simultaneously.
+
+- Generalized types for `centerXY` and `snugXY`, based on new
+  `basis` function from `diagrams-core
+
+- New 3D `Transform`s, alignment, and 3D-specific `Prelude`.
+
+- New `frame` function similar to `pad`, but increases the envelope
+  of a diagram by an amount specified in local units in every direction
+  irrespective of the local origin.
+
+- New `splitFills` function for pushing fill attributes down to
+  subtrees containing only loops (mostly of relevance only to
+  backend implementors).
+
+**New instances**
+
+- `Typeable` instances for all data types that are used as diagram
+  primitives.
+
+- `Sectionable` instance for `FixedSegment`.
+
+**API changes**
+
+- `Angle` is now a type, rather than a class.  It uses a single
+  internal representation for angles, and lenses `turn`, `rad,`
+  and `deg` are supplied for constructing (using `@@`) and viewing
+  (using `^.`) `Angle`s in various units.  In addition, the `Num`
+  instance for `Angle` has been removed, eliminating a class of
+  errors where a bare number is interpreted in units other than
+  what you expect.
+
+- Removed `Num` instance for angles.
+
+**Dependency/version changes**
+
+- Require `lens >= 4.0`.
+
+- Allow `array-0.5`.
+
+- Allow `hashable-1.1`.
+
+- Remove `NumInstances` dependency.
+
+**Bug fixes**
+
+- Exclude joins in offsets on close segments (#160).
+
+- Exclude extra segment when joining loops in offset (#155).
+
+**Performance improvements**
+
+- `colorToSRGBA` function now avoids expensive matrix operations,
+  offering dramatic speedups in rendering diagrams with many color
+  attributes.
+
+**Implemented enhancements:**
+
+- Better color model in 3D [\#121](https://github.com/diagrams/diagrams-lib/issues/121)
+
+- Projective/perspective transforms for points and paths [\#108](https://github.com/diagrams/diagrams-lib/issues/108)
+
+- clipTo function [\#35](https://github.com/diagrams/diagrams-lib/issues/35)
+
+**Fixed bugs:**
+
+- Offset Bug [\#155](https://github.com/diagrams/diagrams-lib/issues/155)
+
+**Closed issues:**
+
+- Expand of an expand [\#160](https://github.com/diagrams/diagrams-lib/issues/160)
+
+**Merged pull requests:**
+
+- fix doc for === and ||| [\#164](https://github.com/diagrams/diagrams-lib/pull/164) ([denys-duchier](https://github.com/denys-duchier))
+
+- Split fills [\#161](https://github.com/diagrams/diagrams-lib/pull/161) ([byorgey](https://github.com/byorgey))
+
+- Exclude extra segment when joining loops in offset. Fixes \#155. [\#158](https://github.com/diagrams/diagrams-lib/pull/158) ([fryguybob](https://github.com/fryguybob))
+
+- added basis, generalized `centerXY` and `snugXY` [\#157](https://github.com/diagrams/diagrams-lib/pull/157) ([jeffreyrosenbluth](https://github.com/jeffreyrosenbluth))
+
+- derive Typeable for all data types used in Prims [\#156](https://github.com/diagrams/diagrams-lib/pull/156) ([byorgey](https://github.com/byorgey))
+
+- Lens4 [\#154](https://github.com/diagrams/diagrams-lib/pull/154) ([bergey](https://github.com/bergey))
+
+- removed NumInstances dependency [\#153](https://github.com/diagrams/diagrams-lib/pull/153) ([jeffreyrosenbluth](https://github.com/jeffreyrosenbluth))
+
+- Remove Num instance for Angle [\#150](https://github.com/diagrams/diagrams-lib/pull/150) ([bergey](https://github.com/bergey))
+
+- Change internal color representation to SRGBA [\#149](https://github.com/diagrams/diagrams-lib/pull/149) ([jeffreyrosenbluth](https://github.com/jeffreyrosenbluth))
+
+- Projections - non-affine transformations [\#148](https://github.com/diagrams/diagrams-lib/pull/148) ([bergey](https://github.com/bergey))
+
+## [v1.0.1](https://github.com/diagrams/diagrams-lib/tree/v1.0.1) (2014-01-26)
+
+[Full Changelog](https://github.com/diagrams/diagrams-lib/compare/v1.0.0.1...v1.0.1)
+
+**Implemented enhancements:**
+
+- Module for generating nice colors/color schemes [\#77](https://github.com/diagrams/diagrams-lib/issues/77)
+
+**Closed issues:**
+
+- "Maybe.fromJust: Nothing" error when connecting translated small diagram [\#147](https://github.com/diagrams/diagrams-lib/issues/147)
+
+**Merged pull requests:**
+
+- Add Hashable instance for SizeSpec2D [\#146](https://github.com/diagrams/diagrams-lib/pull/146) ([byorgey](https://github.com/byorgey))
+
+- return list of traces [\#145](https://github.com/diagrams/diagrams-lib/pull/145) ([jeffreyrosenbluth](https://github.com/jeffreyrosenbluth))
+
+- added clipTo [\#144](https://github.com/diagrams/diagrams-lib/pull/144) ([jeffreyrosenbluth](https://github.com/jeffreyrosenbluth))
+
+- Unified angle type [\#140](https://github.com/diagrams/diagrams-lib/pull/140) ([bergey](https://github.com/bergey))
+
+## [v1.0.0.1](https://github.com/diagrams/diagrams-lib/tree/v1.0.0.1) (2013-11-28)
+
+[Full Changelog](https://github.com/diagrams/diagrams-lib/compare/v1.0...v1.0.0.1)
+
+## [v1.0](https://github.com/diagrams/diagrams-lib/tree/v1.0) (2013-11-25)
+
+[Full Changelog](https://github.com/diagrams/diagrams-lib/compare/v0.7.1.1...v1.0)
+
+**New features**
+
+- New modules `Diagrams.TwoD.Arrow` and `Diagrams.TwoD.Arrowheads`
+  for creating arrows.
+
+- New module `Diagrams.Backend.CmdLine`, providing a flexible
+  framework for creating command-line-driven diagram rendering executables.
+
+- New functions in `Diagrams.Offset`: `offsetTrail` and
+  `offsetPath` for one-sided offsets of trails and paths;
+  `expandTrail` and `expandPath` for "stroking" trails and paths,
+  computing a path whose fill corresponds to the stroke of the
+  given trail or path.
+
+- New module `Diagrams.Tangent` for computing tangent and normal
+  vectors of segments, trails, and paths.
+
+- New functions in `Diagrams.Align` to allow diagrams to be aligned by `Trace`
+  called `snug`, `snugBy` and `snugCenter`
+  and the ability to define other boundary functions for alignment. Functions
+  `snugL`, `snugR`, etc. are included in `TwoD.Align`.
+
+- Lenses from `Control.Lens` are now used consistently for record fields
+  throughout the library.
+
+- New function `angleRatio` for calculating the ratio between two angles.
+
+- Restricted identity functions `asTurn`, `asRad`, and `asDeg` for
+  resolving type ambiguity
+
+- New miter limit attribute.
+
+- New function `annularWedge` in `TwoD.Arc`
+
+- New `avgScale` utility in `TwoD.Transform`, for backends which
+  cannot fully implement freezing of line width
+
+- New function `heptagon`, a vast improvement over the linguistic
+  frankenstein `septagon`.
+
+- New function `lookupName` (re-exported from `diagrams-core`) for
+  simple lookups of named subdiagrams
+
+- New function `angleBetween` to calculate the angle between two
+  vectors.
+
+- New function `arcBetween` to draw an arc between two given
+  points.
+
+- A bunch of new modules containing types, primitives and
+  utilities for constructing 3D diagrams: `Diagrams.ThreeD.Align`,
+  `.Camera`, `.Light`, `.Shapes`, `.Transform`, `.Types`, and
+  `.Vector`.  This is still a "feature preview" (in particular,
+  appropriate 3D backends are still under construction).
+
+**New instances**
+
+- `AdditiveGroup` and `VectorSpace` instances for `Turn`, `Rad`, `Deg`
+
+- `Alignable` instance for `(->) e`
+
+- `Default` instances for `FillRule`, `FillRuleA`, `LineJoin`,
+    `LineCap`, `FillColor`
+
+- `Show` instances for `FillRule`, `FillRuleA`
+
+**API changes**
+
+- `e` no longer exported from `Diagrams.Prelude`.
+
+- `Diagrams.BoundingBox` is no longer exported from `Diagrams.Prelude`.
+
+- Re-export `Diagrams.Core.pointDiagram` from `Diagrams.Prelude`.
+
+- Added `fromAlphaColour` method to `Color` class.
+
+- `&` renamed to `^&`
+
+- Stop re-exporting `tan`, `over`, and `both` from `Data.Colour`.
+
+- New coordinate lenses `_x`, `_y`, and `_z` for `R2`, `P2`, `R3`, `P3`
+
+- Export `fullTurn` from `Diagrams.Prelude`.
+
+- `Codomain (Located a)` is now `Point (Codomain a)` instead of
+  `Located (Codomain a)`.
+
+- Export `domainBounds` from `Diagrams.Parametric`.
+
+- Adjusting functionality moved from `Diagrams.Parametric` to its
+  own module, `Diagrams.Parametric.Adjust`.
+
+- Rename `strokeT` (and primed variant) to `strokeTrail`; rename
+  `strokeLocT` to `strokeLocTrail`.
+
+- `ScaleInv` is now in its own module, `Diagrams.TwoD.Transform.ScaleInv`.
+
+- Re-export `Image` type (but not constructor) from `Diagrams.TwoD`
+
+- Removed `Floating` and `RealFloat` instances for `Turn` and `Deg`
+
+- `offsetSegment` now returns a `Located` instead of a tuple.
+
+- Removed `Num` and `Fractional` instances for `R2`.
+
+**Dependency/version changes**
+
+- Remove `newtype` dependency
+
+- New dependencies on `lens`, `tagged`, `optparse-applicative`,
+  `filepath`, `safe`, `vector-space-points`, `MemoTrie`
+
+- Depend on `intervals >= 0.3 && < 0.5`.
+
+**Bug fixes**
+
+- Depend on `intervals 0.3`, which allows diagrams to build on
+  Windows, by evading a GHCi linker bug which affects the FFI use in
+  previous versions of intervals ([diagrams-contrib#14](https://github.com/diagrams/diagrams-contrib/issues/14))
+
+- Use point envelope at the origin for text objects instead of an
+  empty envelope
+  ([#115](https://github.com/diagrams/diagrams-lib/issues/115),
+  [#116](https://github.com/diagrams/diagrams-lib/issues/116)).
+
+- Adjusting the end of a trail now works correctly ([#95](https://github.com/diagrams/diagrams-lib/issues/95)).
+
+- Only look for miter join on corners in `Diagrams.TwoD.Offset` ([#118](https://github.com/diagrams/diagrams-lib/issues/118)).
+
+- `wedge` from `Diagrams.TwoD.Arc` is now a Loop ([#99](https://github.com/diagrams/diagrams-lib/issues/99))
+
+- Arrows do not behave correctly under scaling [\#112](https://github.com/diagrams/diagrams-lib/issues/112)
+
+**Performance improvements**
+
+- `R2` is now strict and `UNPACK`ed
+
+- Add strictness to `Offset`, `Segment`, `OffsetEnvelope`, and `SizeSpec2D`.
+
+- Make `getEnvelope` calculation for `Segment` more efficient by
+  floating divisions out of the inner calculation.
+
+- Use a specialized `HasTrie` instance for `R2`.
+
+
+**Closed issues:**
+
+- diagrams-lib-0.7.1.1 fails to build with ghc-7.7 \(-HEAD\) [\#128](https://github.com/diagrams/diagrams-lib/issues/128)
+
+- Arrow misses target [\#126](https://github.com/diagrams/diagrams-lib/issues/126)
+
+**Merged pull requests:**
+
+- Lenses for setting arrow head, tail, and shaft colors [\#138](https://github.com/diagrams/diagrams-lib/pull/138) ([byorgey](https://github.com/byorgey))
+
+- Delayed subtrees [\#137](https://github.com/diagrams/diagrams-lib/pull/137) ([byorgey](https://github.com/byorgey))
+
+- Add helpers for common optparse-applicative backend command line. [\#135](https://github.com/diagrams/diagrams-lib/pull/135) ([fryguybob](https://github.com/fryguybob))
+
+- add located lens for access into Located things [\#134](https://github.com/diagrams/diagrams-lib/pull/134) ([byorgey](https://github.com/byorgey))
+
+- add b-\>a instance for Alignable [\#133](https://github.com/diagrams/diagrams-lib/pull/133) ([cscheid](https://github.com/cscheid))
+
+- Strictness optimizations [\#132](https://github.com/diagrams/diagrams-lib/pull/132) ([JohnLato](https://github.com/JohnLato))
+
+- Lens [\#131](https://github.com/diagrams/diagrams-lib/pull/131) ([jeffreyrosenbluth](https://github.com/jeffreyrosenbluth))
+
+- 3D scaling, alignment, coordinate lenses [\#129](https://github.com/diagrams/diagrams-lib/pull/129) ([bergey](https://github.com/bergey))
+
+- correctly \(?\) compute shaftScale by solving a quadratic [\#127](https://github.com/diagrams/diagrams-lib/pull/127) ([byorgey](https://github.com/byorgey))
+
+- calculate arrow shaftScale using projection of ends onto shaft offset [\#125](https://github.com/diagrams/diagrams-lib/pull/125) ([bergey](https://github.com/bergey))
+
+- Convert from newtype to lens [\#124](https://github.com/diagrams/diagrams-lib/pull/124) ([byorgey](https://github.com/byorgey))
+
+- Version bump on lens [\#123](https://github.com/diagrams/diagrams-lib/pull/123) ([haasn](https://github.com/haasn))
+
+## [v0.7.1.1](https://github.com/diagrams/diagrams-lib/tree/v0.7.1.1) (2013-09-27)
+
+[Full Changelog](https://github.com/diagrams/diagrams-lib/compare/v0.7.1...v0.7.1.1)
+
+**Implemented enhancements:**
+
+- Use a point envelope for built-in text objects [\#116](https://github.com/diagrams/diagrams-lib/issues/116)
+
+- implement rotations in 3D [\#86](https://github.com/diagrams/diagrams-lib/issues/86)
+
+- Control over boundary conditions on cubic splines. [\#32](https://github.com/diagrams/diagrams-lib/issues/32)
+
+**Fixed bugs:**
+
+- diagrams with empty envelopes are not properly separated by struts [\#115](https://github.com/diagrams/diagrams-lib/issues/115)
+
+**Closed issues:**
+
+- calculate ratio between two angles [\#109](https://github.com/diagrams/diagrams-lib/issues/109)
+
+- Add primitives for arrows [\#73](https://github.com/diagrams/diagrams-lib/issues/73)
+
+**Merged pull requests:**
+
+- Three d render [\#114](https://github.com/diagrams/diagrams-lib/pull/114) ([bergey](https://github.com/bergey))
+
+- API for computing tangent and normal vectors to segments and trails [\#113](https://github.com/diagrams/diagrams-lib/pull/113) ([byorgey](https://github.com/byorgey))
+
+- change default styles for arrows [\#111](https://github.com/diagrams/diagrams-lib/pull/111) ([byorgey](https://github.com/byorgey))
+
+- 3D utility functions [\#107](https://github.com/diagrams/diagrams-lib/pull/107) ([bergey](https://github.com/bergey))
+
+## [v0.7.1](https://github.com/diagrams/diagrams-lib/tree/v0.7.1) (2013-09-11)
+
+**New features**
+
+- New standard miter limit attribute
+
+- New functions `lineColorA`, `lineWidthA`, `lineMiterLimitA`,
+  `fontSizeA` for directly applying attribute values
+
+- `setDefault2DAttributes` now sets default line cap (butt), line
+  join (miter), and miter limit (10) attributes
+
+**New instances**
+
+- `Data.Default` instances for
+
+- `LineCap`
+
+- `LineJoin`
+
+- `LineMiterLimit`
+
+- `LineWidth`
+
+- `LineColor`
+
+- `FontSize`
+
+[Full Changelog](https://github.com/diagrams/diagrams-lib/compare/v0.7...v0.7.1)
+
+**Implemented enhancements:**
+
+- Path expansion. [\#55](https://github.com/diagrams/diagrams-lib/issues/55)
+
+- way to move diagrams closer together [\#18](https://github.com/diagrams/diagrams-lib/issues/18)
+
+**Fixed bugs:**
+
+- wedge should be closed [\#99](https://github.com/diagrams/diagrams-lib/issues/99)
+
+- Adjusting trail from the end has no effect [\#95](https://github.com/diagrams/diagrams-lib/issues/95)
+
+**Merged pull requests:**
+
+- Add offsetTrail and expandTrail. [\#103](https://github.com/diagrams/diagrams-lib/pull/103) ([fryguybob](https://github.com/fryguybob))
+
+- change Codomain of Located to Point \(Codomain a\) [\#102](https://github.com/diagrams/diagrams-lib/pull/102) ([byorgey](https://github.com/byorgey))
+
+- Default and Show instances for FillRule and FillRuleA [\#100](https://github.com/diagrams/diagrams-lib/pull/100) ([jbracker](https://github.com/jbracker))
+
+- Changes required due to the introduction of Roles in GHC [\#98](https://github.com/diagrams/diagrams-lib/pull/98) ([co-dan](https://github.com/co-dan))
+
+- removed default implementation of reverseDomain [\#97](https://github.com/diagrams/diagrams-lib/pull/97) ([jeffreyrosenbluth](https://github.com/jeffreyrosenbluth))
+
+- fixed issue \#95 [\#96](https://github.com/diagrams/diagrams-lib/pull/96) ([jeffreyrosenbluth](https://github.com/jeffreyrosenbluth))
+
+## [v0.7](https://github.com/diagrams/diagrams-lib/tree/v0.7) (2013-08-09)
+
+[Full Changelog](https://github.com/diagrams/diagrams-lib/compare/v0.6.0.3...v0.7)
+
+**New features**
+
+- New module `Diagrams.TwoD.Curvature`, for computing the
+  curvature of 2D segments at any given point.
+
+- New module `Diagrams.Offset`, containing an `offsetSegment`
+  function that builds a trail a fixed distance from the original
+  segment.  This is a precursor to planned functions `offsetTrail`
+  and `offsetPath`.
+
+- New function `Diagrams.TwoD.Transform.onBasis`, for extracting a
+  matrix representation of a 2D transformation
+
+- New functions `extrudeEnvelope` and `intrudeEnvelope`, for
+  extending or shrinking an envelope only in a certain direction.
+
+- Generalize the `Color` class to absolute colors.
+  This addresses concerns raised in issue #66 by letting the backend
+  choose which color space to render `Color` instances to. Functions are
+  provided for backwards compatibility with the old semantics.
+
+- New function `scaleInvPrim` for creating a diagram from a single
+  scale-invariant primitive.
+
+- New module `Diagrams.Parametric`, containing a collection of
+  classes abstracting over "parametric" things: `Parametric`,
+  `DomainBounds`, `EndValues`, `Sectionable`, and `HasArcLength`,
+  with instances for segments, trails, and related things.
+
+- A big refactoring of segments and trails:
+
+  - Segments can now be either "closed" or "open".
+
+  - There are now two types of trails: "lines" (which travel
+    from point A to point B) or "loops" (closed curves which end
+      where they started). `Trail` is now a wrapper type which can
+      contain both loops and lines.
+
+  - There is a new `Located` wrapper type for adding locations to
+    translation-invariant things.  `Path`s now consist of a
+    collection of `Located Trail`s.
+
+  - The `PathLike` class is now renamed to `TrailLike`; the
+    `trailLike` function takes a `Located Trail` as input.
+
+- New convenience functions `boundaryFrom` and `boundaryFromMay`,
+  for computing boundaries of subdiagrams.
+
+- Re-export from `diagrams-lib` a lot of things defined in
+  `diagrams-core`, to make them easier for users to find.  Several
+  new modules have been created as a result: `Diagrams.Query`,
+  `Diagrams.Envelope`, `Diagrams.Trace`, and `Diagrams.Names`.
+
+- Export the `centroid` function from `Diagrams.Prelude`.
+
+- `triangle` is now a synonym for `eqTriangle`.
+
+**New instances**
+
+- `IsPrim` instances for `Path`, `Ellipsoid`, `Image`, `Text`, and
+  `ScaleInv`
+
+- `Eq`, `Ord`, and `Show` instances for `SizeSpec2D`
+
+**API changes**
+
+- `CircleFrac` has been renamed `Turn` (though `CircleFrac` is
+  retained as a deprecated synonym).
+
+- `Diagrams.Coordinates` is no longer exported from
+  `Diagrams.Prelude`.  This is for compatibility with `lens`, as `(&)`
+  is a rather important lens operator and clashes with
+  `Diagrams.Coordinates`.  Users who want the `Coordinates` stuff can import
+  `Diagrams.Coordinates` explicitly.
+
+**Dependency/version changes**
+
+- allow `base-4.7`
+
+- upgrade to `monoid-extras-0.3`
+
+- depend on `data-default-class` instead of `data-default`
+
+- Tested with GHC 7.7.
+
+**Bug fixes**
+
+- Added a special case that was a not handled properly by the
+  quadratic solver, resulting in bogus envelopes in certain cases
+  (#88).
+
+- Import only `Data.NumInstances.Tuple` instead of
+  `Data.NumInstances`. Previously, `Diagrams.Prelude` exported
+  `Eq`, `Show`, and `Num` instances for functions and tuples; now
+  it only exports tuple instances. Users wishing to use
+  `Diagrams.CubicSpline` with a vector space built over functions (!?)
+  can import `Data.NumInstances.Function` themselves. (#48)
+
+- Do scaling on a `Path` *before* constructing a `TrailLike` in
+      `rect` (#43)
+
+**Implemented enhancements:**
+
+- Split PathLike, Trail, and Path into separate modules [\#25](https://github.com/diagrams/diagrams-lib/issues/25)
+
+- Add support for path-oriented diagrams. [\#13](https://github.com/diagrams/diagrams-lib/issues/13)
+
+**Fixed bugs:**
+
+- Wrong envelope for cubic segment [\#88](https://github.com/diagrams/diagrams-lib/issues/88)
+
+- Fix documentation of beside, \(===\), and \(|||\) re: monoidal semantics [\#83](https://github.com/diagrams/diagrams-lib/issues/83)
+
+- reverseTrail should not generate extra segments for closed trails [\#24](https://github.com/diagrams/diagrams-lib/issues/24)
+
+**Closed issues:**
+
+- Test issue [\#91](https://github.com/diagrams/diagrams-lib/issues/91)
+
+**Merged pull requests:**
+
+- Add parametric generalizations for segments, trails, Located, etc. [\#92](https://github.com/diagrams/diagrams-lib/pull/92) ([byorgey](https://github.com/byorgey))
+
+- Adding type signature so it compiles with GHC7.7 [\#90](https://github.com/diagrams/diagrams-lib/pull/90) ([co-dan](https://github.com/co-dan))
+
+- bug fix: add special case for b==0 to quadform solver [\#89](https://github.com/diagrams/diagrams-lib/pull/89) ([byorgey](https://github.com/byorgey))
+
+- Big refactoring of segments and trails. [\#87](https://github.com/diagrams/diagrams-lib/pull/87) ([byorgey](https://github.com/byorgey))
+
+- Stop exporting Diagrams.Coordinates from Diagrams.Prelude [\#82](https://github.com/diagrams/diagrams-lib/pull/82) ([byorgey](https://github.com/byorgey))
+
+- Generalization of R2 to D2 a [\#65](https://github.com/diagrams/diagrams-lib/pull/65) ([jbracker](https://github.com/jbracker))
+
+## [v0.6.0.3](https://github.com/diagrams/diagrams-lib/tree/v0.6.0.3) (2013-05-04)
+
+[Full Changelog](https://github.com/diagrams/diagrams-lib/compare/v0.6.0.2...v0.6.0.3)
+
+**Closed issues:**
+
+- Offset [\#80](https://github.com/diagrams/diagrams-lib/issues/80)
+
+**Merged pull requests:**
+
+- Added offsetSegment function [\#79](https://github.com/diagrams/diagrams-lib/pull/79) ([fryguybob](https://github.com/fryguybob))
+
+- Working on adding curvature. [\#74](https://github.com/diagrams/diagrams-lib/pull/74) ([fryguybob](https://github.com/fryguybob))
+
+- New `scaleInvPrim` function [\#71](https://github.com/diagrams/diagrams-lib/pull/71) ([byorgey](https://github.com/byorgey))
+
+## [v0.6.0.2](https://github.com/diagrams/diagrams-lib/tree/v0.6.0.2) (2013-03-29)
+
+[Full Changelog](https://github.com/diagrams/diagrams-lib/compare/types-generalized...v0.6.0.2)
+
+**Implemented enhancements:**
+
+- Don't export Eq and Show instances for functions from Diagrams.Prelude [\#48](https://github.com/diagrams/diagrams-lib/issues/48)
+
+**Closed issues:**
+
+- radius is wrong [\#75](https://github.com/diagrams/diagrams-lib/issues/75)
+
+**Merged pull requests:**
+
+- Matrix basis rep [\#78](https://github.com/diagrams/diagrams-lib/pull/78) ([bergey](https://github.com/bergey))
+
+## [types-generalized](https://github.com/diagrams/diagrams-lib/tree/types-generalized) (2013-02-13)
+
+[Full Changelog](https://github.com/diagrams/diagrams-lib/compare/v0.6.0.1...types-generalized)
+
+## [v0.6.0.1](https://github.com/diagrams/diagrams-lib/tree/v0.6.0.1) (2013-01-07)
+
+[Full Changelog](https://github.com/diagrams/diagrams-lib/compare/v0.6...v0.6.0.1)
+
+**Fixed bugs:**
+
+- text on zero width rect leads to nans [\#51](https://github.com/diagrams/diagrams-lib/issues/51)
+
+- wrong result when using `beside` with circle and vector \(1 & \(-1\)\) [\#46](https://github.com/diagrams/diagrams-lib/issues/46)
+
+- Handle `rect` with zero arguments. [\#43](https://github.com/diagrams/diagrams-lib/issues/43)
+
+**Closed issues:**
+
+- Generalization of color space used in rendering [\#66](https://github.com/diagrams/diagrams-lib/issues/66)
+
+**Merged pull requests:**
+
+- do scaling on a Path before constructing PathLike in 'rect' \(fixes \#43\) [\#70](https://github.com/diagrams/diagrams-lib/pull/70) ([byorgey](https://github.com/byorgey))
+
+## [v0.6](https://github.com/diagrams/diagrams-lib/tree/v0.6) (2012-12-12)
+
+[Full Changelog](https://github.com/diagrams/diagrams-lib/compare/0_5_0_1...v0.6)
+
+**New features**
+
+- `boundingRect` function for constructing a bounding rectangle
+
+- `bg` function for "setting the background color" (*i.e.* placing
+  atop a colored bounding rectangle)
+
+- New functions `setDefault2DAttributes` and `adjustDiaSize2D`.
+  `adjustDia2D` does both --- so the behavior of `adjustDia2D` has
+  not changed, but it is now possible to apply just one of the two
+  adjustments using the new functions.
+
+- `Diagrams.TwoD.Transform` now exports a `ScaleInv` type for creating
+  scale-invariant objects, which are only affected by rotational
+  and translational components of transformations.
+
+- The new `Diagrams.Coordinates` module provides nicer syntax for
+  constructing and pattern-matching point and vector literals.
+
+- New `fromFixedSeg` function in `Diagrams.Segment`, which
+  decomposes a `FixedSegment` into a starting point and a `Segment`.
+
+- New `withTrace` function for setting the `Trace` of a diagram.
+
+- Three new size-related functions:
+
+    - New `sized` function for scaling an object to a particular size.
+      One particularly nice use of this is to obviate the need to keep
+      fiddling with the line width to get diagrams to "look right";
+      just set the line width relative to some arbitrary scale
+      (*e.g.* assuming the final diagram will fit into a 1x1 box) and
+      then apply `sized` to the final diagram to make it that given
+      arbitrary size.  It can also be used for easily making something
+      (a diagram, path, trail, ...) the same size as something else,
+      with the help of the new `sizeSpec2D` function.
+
+    - New `sizedAs` function, for setting the size of some object to
+      be "the same as" some other object.
+
+    - New `sizeSpec2D` function for conveniently calculating the size
+      of an object as a `SizeSpec2D` value (for use with the new `sized`
+      funtion).
+
+- New `extrudeEnvelope` and `intrudeEnvelope` functions for
+  modifying envelopes in a single direction only, as well as new
+  functions `extrude{Left,Right,Bottom,Top}` specializing
+  `extrudeEnvelope` to 2D.
+
+- `arcCW` draws clockwise arcs; `arc'` draws arcs counterclockwise
+  or clockwise as the radius is positive or negative,
+  respectively.
+
+- fill color attribute is generalized to support "recommended" and
+  "committed" colors; text objects use a recommended fill color of
+  black.
+
+**New instances**
+
+- The `Show` instance for `R2` now produces something like `2 & 6`
+  instead of `R2 { unR2 = (2,6) }`.  The `Read` instance has also
+  been changed to match, so `read . show = id`.
+
+- `Enveloped` instance for `FixedSegment`
+
+- `Traced` instances for `Segment`, `FixedSegment`, `Trail`, and `Path`
+
+- New derived `Eq` instances for `LineCapA`, `LineJoinA`, `Dashing`,
+  `DashingA`, `FillRule`, `Font`, `FontSize`, `FontSlant`, `FontSlantA`,
+  `FontWeight`, and `FontWeightA`
+
+- `Renderable Ellipsoid NullBackend` instance
+
+**API changes**
+
+- `Data.Colour` (minus `atop` and `AffineSpace`) is now re-exported
+  from Diagrams.Prelude for convenience.
+
+- The `beneath` function is now infixl 6.
+
+- The `BoundingBox` module has had a complete overhaul.  There is
+  now a special empty bounding box, and bounding boxes are an
+  instance of `Monoid`.
+
+- The type of `withEnvelope` has been slightly generalized.
+
+- `Diagrams.TwoD.Adjust.adjustSize` is now deprecated; it has been
+  renamed and moved to `Diagrams.TwoD.Size.requiredScaleT`.
+
+- `expandPath` has been renamed to `scalePath`.
+
+**Dependency/version changes**
+
+- Allow `data-default` 0.4 and 0.5
+
+- Allow `base`-4.6
+
+- Allow `containers`-0.5
+
+**Bug fixes**
+
+- `arc` and `arcT` functions now always produce counterclockwise arcs,
+  as claimed.
+
+**Implemented enhancements:**
+
+- Enhancements for `arc`s. [\#54](https://github.com/diagrams/diagrams-lib/issues/54)
+
+- align and friends should be in terms of a new 'Alignable' class instead of 'Boundable' [\#31](https://github.com/diagrams/diagrams-lib/issues/31)
+
+- Tools for more accurate boundary calculations in common cases [\#30](https://github.com/diagrams/diagrams-lib/issues/30)
+
+- Reimplement Diagrams.TwoD.Ellipse in terms of Diagrams.TwoD.Arc [\#27](https://github.com/diagrams/diagrams-lib/issues/27)
+
+- Function to convert angles into 2D unit vectors [\#23](https://github.com/diagrams/diagrams-lib/issues/23)
+
+- 2D specialization of 'beside' which takes an angle instead of a vector [\#22](https://github.com/diagrams/diagrams-lib/issues/22)
+
+- Generalize showOrigin function [\#21](https://github.com/diagrams/diagrams-lib/issues/21)
+
+- Add generic 'extent' and 'breadth' ? functions [\#20](https://github.com/diagrams/diagrams-lib/issues/20)
+
+- Add shearing transformations to standard library [\#19](https://github.com/diagrams/diagrams-lib/issues/19)
+
+- Add support for text [\#15](https://github.com/diagrams/diagrams-lib/issues/15)
+
+- Allow the user to choose the fill rule used for paths when stroking [\#14](https://github.com/diagrams/diagrams-lib/issues/14)
+
+- Image primitives [\#10](https://github.com/diagrams/diagrams-lib/issues/10)
+
+- Merge polygon code from Dmitry Olshansky [\#4](https://github.com/diagrams/diagrams-lib/issues/4)
+
+**Fixed bugs:**
+
+- Enhancements for `arc`s. [\#54](https://github.com/diagrams/diagrams-lib/issues/54)
+
+- boundingBox computes incorrect bounding box for transformed diagrams [\#39](https://github.com/diagrams/diagrams-lib/issues/39)
+
+- hcat is really \*terrible\* performance-wise [\#28](https://github.com/diagrams/diagrams-lib/issues/28)
+
+- stroke sets the fill rule attribute to a default value, so it can't be changed later [\#26](https://github.com/diagrams/diagrams-lib/issues/26)
+
+- Text alignment should be with respect to descent and ascent lines rather than text bounding box [\#17](https://github.com/diagrams/diagrams-lib/issues/17)
+
+- incorrect bounds for Bezier segments [\#11](https://github.com/diagrams/diagrams-lib/issues/11)
+
+- More combinators in D.Combinators [\#5](https://github.com/diagrams/diagrams-lib/issues/5)
+
+**Merged pull requests:**
+
+- clean up and fix bugs with ScaleInv wrapper [\#69](https://github.com/diagrams/diagrams-lib/pull/69) ([byorgey](https://github.com/byorgey))
+
+- Patch proposal for generalized Color [\#67](https://github.com/diagrams/diagrams-lib/pull/67) ([haasn](https://github.com/haasn))
+
+- Renamed `expandPath` to `scalePath` to make room [\#61](https://github.com/diagrams/diagrams-lib/pull/61) ([fryguybob](https://github.com/fryguybob))
+
+- Envelope deformation [\#60](https://github.com/diagrams/diagrams-lib/pull/60) ([mgsloan](https://github.com/mgsloan))
+
+- Added `Eq` instances for some data structures. [\#59](https://github.com/diagrams/diagrams-lib/pull/59) ([fryguybob](https://github.com/fryguybob))
+
+- More involved diameter benchmark + better implementation [\#58](https://github.com/diagrams/diagrams-lib/pull/58) ([mgsloan](https://github.com/mgsloan))
+
+- Add NullBackend for Ellipsoid [\#57](https://github.com/diagrams/diagrams-lib/pull/57) ([mgsloan](https://github.com/mgsloan))
+
+- Fixed `arc` and `arcT` so they are always CCW. [\#56](https://github.com/diagrams/diagrams-lib/pull/56) ([fryguybob](https://github.com/fryguybob))
+
+- new sized, sizedAs, and sizeSpec2D functions [\#52](https://github.com/diagrams/diagrams-lib/pull/52) ([byorgey](https://github.com/byorgey))
+
+- Update to track with diagrams-core renaming, and a better Show instance for R2 [\#47](https://github.com/diagrams/diagrams-lib/pull/47) ([byorgey](https://github.com/byorgey))
+
+- Minor tweaks due to monoid-extra and dual-tree changes [\#45](https://github.com/diagrams/diagrams-lib/pull/45) ([byorgey](https://github.com/byorgey))
+
+- split out default attribute setting and size adjustment into separate functions [\#42](https://github.com/diagrams/diagrams-lib/pull/42) ([byorgey](https://github.com/byorgey))
+
+- make beneath infixl 6 [\#41](https://github.com/diagrams/diagrams-lib/pull/41) ([byorgey](https://github.com/byorgey))
+
+- scale invariant [\#3](https://github.com/diagrams/diagrams-lib/pull/3) ([ludflu](https://github.com/ludflu))
+
+- BoundingBox is now Monoidal [\#2](https://github.com/diagrams/diagrams-lib/pull/2) ([mgsloan](https://github.com/mgsloan))
+
+- New module enabling nice syntax for constructing and pattern-matching literal points and vectors [\#1](https://github.com/diagrams/diagrams-lib/pull/1) ([byorgey](https://github.com/byorgey))
+
+## [v0.5.0.1](https://github.com/diagrams/diagrams-lib/tree/0_5_0_1) (2012-07-24)
+
+[Full Changelog](https://github.com/diagrams/diagrams-lib/compare/0_5...0_5_0_1)
+
+## [v0.5](https://github.com/diagrams/diagrams-lib/tree/0_5) (2012-03-09)
+
+[Full Changelog](https://github.com/diagrams/diagrams-lib/compare/0_4...0_5)
+
+**New features**
+- `mkSizeSpec` function for constructing a `SizeSpec2D` from two `Maybe Double`s
+
+- `beneath` as convenient synonym for `flip atop`
+
+- Improvements and extensions to rounded rectangles by Peter Hall:
+
+    + `roundedRect'` allows rounded rectangles with a different radius
+      specified for each corner
+
+    + both `roundedRect'` and `roundedRect` now allow negative radii,
+      resulting in "inverted" circular corners
+
+- [\#64](http://code.google.com/p/diagrams/issues/detail?id=64): New `Alignable` class for things that can be aligned.
+
+- `explodeTrail` and `explodePath` have been generalized to return any
+  `PathLike` type.
+
+- New path functions `pathCentroid` (compute the centroid of a
+  path's vertices) and `expandPath` (scale a path about its centroid).
+
+- Generalized `centroid` function now exported from new module
+  `Diagrams.Points`.
+
+- Initial (experimental) support for animation:
+
+    + `Animation` and `QAnimation` defined as synonyms for `Active`
+      diagrams (see `active` package)
+
+    + Instances for `Active`: `V`, `HasOrigin`, `Transformable`,
+      `HasStyle`, `PathLike`, `Juxtaposable`, `Alignable`
+
+    + `animEnvelope` and `animRect` functions for automatic bounding of
+      animations
+
+- `addClosingSegment` function for making the implicit closing
+  segment of a closed trail explicit
+
+- Improvements to `BoundingBox` module from Michael Sloan: querying
+  of `BoundingBox` bounds, corners, extents, and transformation of
+  objects to fit within a given box.
+
+- Text alignment options from Michael Sloan
+
+- `view` function for restricting a diagram's envelope to a
+  rectangular region.
+
+- `iterateN` function for iterating a finite number of times
+
+- `atAngle` for placing two diagrams next to each other along a
+  specified angle.
+
+- `padX` and `padY` functions for padding in the X- and Y-directions
+  independently.
+
+
+- generalized `showOrigin` function from Ian Ross
+
+- [\#40](http://code.google.com/p/diagrams/issues/detail?id=40): add shears to `Diagrams.TwoD.Transform`
+
+**Performance improvements**
+
+- Use a balanced folding scheme for `cat'`, reducing time in some
+  cases from \\(O(n^2)\\) to \\(O(n \\log n)\\)
+
+- More efficient implementation of `beside`
+
+**New instances**
+
+- `Alignable` instances for `QDiagram`, `Path`, `Envelope`, `Active`, `Set`,
+  `Map`, `[]`
+
+- `Renderable` instances for `NullBackend` (`Trail`, `Path`, `Segment`,
+  `Image`, `Text`)
+
+- Instances for `Active`: `V`, `HasOrigin`, `Transformable`,
+  `HasStyle`, `PathLike`, `Juxtaposable`, `Alignable`
+
+**API changes**
+
+- `R2` used to be a synonym for `(Double, Double)` but is now
+  abstract. To convert between pairs of `Doubles` and `R2`, use the
+  new functions `r2` and `unr2`.  There are two reasons for this
+  change:
+      1. to allow for future changes to the implementation of `R2`;
+      2. `(Double, Double)` was an awkward special case getting in the
+       way of useful tuple instances for classes like `HasOrigin`,
+       `Enveloped`, and so on.
+
+- `circlePath` has been removed; its functionality has been
+  subsumed by `circle`.
+
+- `adjustSegment` now takes an extra tolerance option.
+
+- Ellipses are now represented using Bezier approximations rather
+  than a separate special type.
+
+- `BoundingBox` no longer has a `Transformable` instance; the old
+  instance was misleading at best.
+
+- Change semantics of `beside` (hence also `(|||)` and `(===)`) so the
+  result's origin is the same as that of the first argument.
+
+- `adjustDia2D` now takes a `SizeSpec2D`.
+
+- `beside` and related functions are now implemented in terms of
+  `juxtapose`.
+
+- Instead of taking an `R2`, `roundedRect` now takes a pair of
+  `Double`s, to be more consistent with `rect`.
+
+**Dependency/version changes**
+
+- Support for GHC 7.4.1:
+
+    + depend on `colour` >= 2.3.2
+
+    + update `base` and `array` upper bounds
+
+- bump `vector-space` upper bound
+
+**Bug fixes**
+
+- Avoid scale by zero error in `showOrigin`.
+- Base `adjustDia2D` translation on output size rather than diagram size.
+
+## [v0.4.0.1] () (30 October 2011)
+------------------------
+
+- bump `data-default` dependency to allow version 0.3
+
+## [v0.4]() (23 October 2011)
+--------------------
+
+**documentation fixes**
+
+**New functions and primitives**
+
++ `wedge` shape primitive
+
++ `fromDirection` function for converting angles to 2D unit vectors;
+
+  inverse function `direction` generalized to return any Angle type
++ New functions for computing and adjusting segment lengths
+
++ `scaleUToX` and `scaleUToY` for doing uniform scales
+  resulting in a desired width or height.
+
++ `circlePath`, `reversePath`, `decoratePath`
+
+
+**New features**
+
++ Completely new and improved polygon generation API
+
++ Cubic splines
+
++ User-controllable path fill rules
+
+**Bug fixes**
+
++ fix incorrect corner case in arc generation
+
++ fix incorrect `reverseTrail` function
+
+## [v0.3]() (18 June 2011)
+-----------------
+
+**New features**
+
++ new customizable `stroke'` function which lets you assign names to
+  path vertices
+
++ `circle` and `square` functions now take a size argument
+
++ function for adjusting 2D diagrams to requested size abstracted
+  from cairo backend
+
++ generalize `PathLike` class to include an instance for diagrams,
+  and collapse things like `polygon`/`polygonPath` into a single
+  polymorphic function
+
++ basic text support
+
++ basic support for external images
+
++ very sketchy initial proof-of-concept library of 3D primitives.
+  See also diagrams-povray package.
+
+**Bug fixes**
+
++ Issue 32 (`mempty` not behaving correctly within concatenations)
+
+## [v0.2]() (3 June 2011)
+----------------
+
+**New functions and primitives**
+
++ `scaleToX` and `scaleToY` for scaling to an absolute width/height
+
++ `reverseTrail`
+
++ new `Angle` class and ability to use radians, degrees, or circle fractions
+  for specifying angles
+
++ `rotateAbout` and `reflectAbout` transformations based on new conjugation functions
+
++ `rect` and `roundedRect` primitives
+
++ `explodeTrail`/`Path` for breaking trails and paths into individual segments
+
+**New features**
+
++ opacity attribute
+
++ support for path clipping
+
+* **New modules**
+    + `Diagrams.BoundingBox`
+
+**Fixes and updates**
+
+
++ `withBounds` now properly uses the new bounds instead of just combining
+      them with the old
+
+## [v0.1.1]() (18 May 2011)
+------------------
+
+* minor documentation fixes
+
+* link to new website
+
+## [v0.1]() [17 May 2011]
+----------------
+
+* initial preview release
+
+\* *This Change Log was automatically generated by (and then edited by hand) [github_changelog_generator](https://github.com/skywinder/Github-Changelog-Generator)*
diff --git a/CHANGES.markdown b/CHANGES.markdown
deleted file mode 100644
--- a/CHANGES.markdown
+++ /dev/null
@@ -1,754 +0,0 @@
-1.2.0.9 (2 April 2015)
-----------------------
-
- - allow `lens-4.9`
- - allow `vector-space-0.10`
-
-1.2.0.8 (13 Jan 2015)
----------------------
-
-- Allow `vector-space-0.9`
-- Allow `lens-4.7`
-
-1.2.0.7 (07 Dec 2014)
----------------------
-
-- Allow `JuicyPixels-3.2`
-
-1.2.0.6 (04 Dec 2014)
----------------------
-
-- Allow `semigroups-0.16`
-
-1.2.0.5 (17 November 2014)
---------------------------
-
-- Allow `lens-4.6`
-
-1.2.0.4 (8 October 2014)
-------------------------
-
-- Allow and require `optparse-applicative-0.11`
-
-1.2.0.3 (7 September 2014)
---------------------------
-
-- Allow `optparse-applicative-0.10`
-
-1.2.0.2 (22 August 2014)
-------------------------
-
-- Allow `lens-4.4`
-
-1.2.0.1 (4 June 2014)
----------------------
-
-- Bug fix: arrow head and tail length and gaps specified with `Local`
-  now work correctly ([#193](https://github.com/diagrams/diagrams-lib/issues/193)).
-
-1.2 (27 May 2014)
------------------
-
-* **New features**
-
-    - Several attributes (such as line width, dashing size, arrowhead
-      size, and font size) that formerly had a value of type `Double`
-      now have the more general type `Measure R2`. This allows the
-      attributes to be specified relative to one of four measurement
-      frames: `Local`, `Global`, `Normalized`, and `Output`.
-
-    - New DSL for specifying measurements.
-
-    - New synonyms for specifying measurements, *e.g.* `thin`,
-      `thick`, and `medium`, `large`.
-
-    - Support for radial and linear gradients for fills and strokes.
-
-    - New `DImage` type that supports both embedded and external images in
-      Backends that support them.
-
-    - New `lengths` Traversal for setting `headLength` and `tailLength`
-      simultaneously.
-
-    - `Frustrum` and `Box` shapes added to `Diagrams.ThreeD.Shapes`.
-
-    - New function `quartForm` to find roots of quartic polynomials.
-
-    - New Lenses for polar coordinates.
-
-    - New trig functions, `sinA`, `atanA`, etc. which take `Angle` as
-      input or output.
-
-* **New instances**
-
-    - `Transformable` instances for `LineWidth`, `Dashing`,
-      `LineTexture`, and  `FillTexture`.
-
-* **API changes**
-
-    - `FillColor` and `LineColor` attributes have been replaced with
-      the more general `FillTexture` and `LineTexture`. Use the `solid`
-      function to convert a color to a texture.
-
-    - The size of arrow heads and tails is now specified in terms of
-      length instead of the radius of their circumcircle.
-
-    - Gaps at the ends of arrows are now specified using `Measure R2`.
-
-    - The `gap` traversal has been replaced by `gaps` for consistency
-      in naming, though `gap` is still provided for backwards compatibility.
-
-    - `fontSize` now takes a value of type `Measure R2`.
-
-    - Get rid of (bitrotted) `Show` backend.
-
-    - Functions in `TwoD.Adjust` now return the adjustment
-      transformation itself in addition to the resized `Diagram` and
-      `Options` record; this can be used, *e.g.* to convert screen
-      coordinates back into diagram coordinates.
-
-    - Export `pathLocSegments`.
-
-    - The `avgScale` function has been moved to `Diagrams.Core`.
-
-    - The `Angle` definition and related functions (*e.g.*
-      `angleBetween`) have moved to a separate module, `Diagrams.Angle`.
-
-    - A separate `Diagrams.TwoD.Attributes` module now contains most
-      of the attributes that require 2D transformation instances.
-
-    - The `splitColorFills` function has been replaced by `splitTextureFills`.
-
-* **Dependency/version changes**
-
-  - Allow `semigroups-0.15`
-
-  - Allow `opt-parse-applicative-0.9.0
-
-  - Allow `lens-4.2`
-
-1.1.0.7 (15 May 2014)
-------------------------
-
-    - Allow `semigroups-0.14`
-
-1.1.0.6 (10 April 2014)
-------------------------
-
-    - Allow `semigroups-0.13`
-
-1.1.0.4 (4 April 2014)
-----------------------
-
-  - Require `intervals-0.7`
-  - Give `connectOutside` a reasonable behavior even when one or both
-    endpoints has no trace
-
-1.1.0.3 (19 March 2014)
-----------------------
-
-  - Allow `lens-4.1`
-
-1.1.0.2 (18 March 2014)
------------------------
-
-  - Allow `optparse-applicative-0.8`
-
-1.1.0.1 (9 March 2014)
-----------------------
-
-  - Allow `vector-space-points-0.2`
-
-1.1 (8 March 2014)
-------------------
-
-* **New features**
-
-    - Support for `Deformation`s, arbitrary (non-affine)
-      transformations on objects such as points, paths, and located
-      trails (though not on diagrams).
-
-    - New functions `clipTo`, which clips a diagram's envelope and
-      trace along with its visual representation, and `clipped`, which
-      clips the diagram's visual representation but replaces its
-      envelope and trace with those of the clipping path.
-
-    - New `arrowV` function, for creating an arrow with the direction
-      and magnitude of a given vector.
-
-    - `gap` traversal, for setting the head and tail gaps of an arrow
-      simultaneously.
-
-    - Generalized types for `centerXY` and `snugXY`, based on new
-      `basis` function from `diagrams-core
-
-    - New 3D `Transform`s, alignment, and 3D-specific `Prelude`.
-
-    - New `frame` function similar to `pad`, but increases the envelope
-      of a diagram by an amount specified in local units in every direction
-      irrespective of the local origin.
-
-    - New `splitFills` function for pushing fill attributes down to
-      subtrees containing only loops (mostly of relevance only to
-      backend implementors).
-
-* **New instances**
-
-    - `Typeable` instances for all data types that are used as diagram
-      primitives.
-    - `Sectionable` instance for `FixedSegment`.
-
-* **API changes**
-
-    - `Angle` is now a type, rather than a class.  It uses a single
-      internal representation for angles, and lenses `turn`, `rad,`
-      and `deg` are supplied for constructing (using `@@`) and viewing
-      (using `^.`) `Angle`s in various units.  In addition, the `Num`
-      instance for `Angle` has been removed, eliminating a class of
-      errors where a bare number is interpreted in units other than
-      what you expect.
-
-    - Removed `Num` instance for angles.
-
-* **Dependency/version changes**
-
-    - Require `lens >= 4.0`.
-	- Allow `array-0.5`.
-	- Allow `hashable-1.1`.
-	- Remove `NumInstances` dependency.
-
-* **Bug fixes**
-
-    - Exclude joins in offsets on close segments (#160).
-    - Exclude extra segment when joining loops in offset (#155).
-
-* **Performance improvements**
-
-    - `colorToSRGBA` function now avoids expensive matrix operations,
-      offering dramatic speedups in rendering diagrams with many color
-      attributes.
-
-1.0.1 (26 January 2014)
------------------------
-
-    - Depend on `hashable` package, and add `Hashable` instance for
-      `SizeSpec2D`.
-
-      Technically, the PVP specifies that adding a new instance
-      requires a major version bump.  However, I highly doubt anyone
-      was making their own orphan `Hashable` instances before.  Feel
-      free to yell at Brent if this breaks your build.
-
-1.0.0.1 (28 November 2013)
---------------------------
-
-    - Allow semigroups-0.12
-
-1.0 (25 November 2013)
-----------------------
-
-* **New features**
-
-    - New modules `Diagrams.TwoD.Arrow` and `Diagrams.TwoD.Arrowheads`
-      for creating arrows.
-    - New module `Diagrams.Backend.CmdLine`, providing a flexible
-      framework for creating command-line-driven diagram rendering executables.
-    - New functions in `Diagrams.Offset`: `offsetTrail` and
-      `offsetPath` for one-sided offsets of trails and paths;
-      `expandTrail` and `expandPath` for "stroking" trails and paths,
-      computing a path whose fill corresponds to the stroke of the
-      given trail or path.
-    - New module `Diagrams.Tangent` for computing tangent and normal
-      vectors of segments, trails, and paths.
-    - New functions in `Diagrams.Align` to allow diagrams to be aligned by `Trace`
-      called `snug`, `snugBy` and `snugCenter`
-      and the ability to define other boundary functions for alignment. Functions
-      `snugL`, `snugR`, etc. are included in `TwoD.Align`.
-    - Lenses from `Control.Lens` are now used consistently for record fields
-      throughout the library.
-    - New function `angleRatio` for calculating the ratio between two angles.
-    - Restricted identity functions `asTurn`, `asRad`, and `asDeg` for
-      resolving type ambiguity
-    - New miter limit attribute.
-    - New function `annularWedge` in `TwoD.Arc`
-    - New `avgScale` utility in `TwoD.Transform`, for backends which
-      cannot fully implement freezing of line width
-    - New function `heptagon`, a vast improvement over the linguistic
-      frankenstein `septagon`.
-    - New function `lookupName` (re-exported from `diagrams-core`) for
-      simple lookups of named subdiagrams
-    - New function `angleBetween` to calculate the angle between two
-      vectors.
-    - New function `arcBetween` to draw an arc between two given
-      points.
-    - A bunch of new modules containing types, primitives and
-      utilities for constructing 3D diagrams: `Diagrams.ThreeD.Align`,
-      `.Camera`, `.Light`, `.Shapes`, `.Transform`, `.Types`, and
-      `.Vector`.  This is still a "feature preview" (in particular,
-      appropriate 3D backends are still under construction).
-
-* **New instances**
-
-    - `AdditiveGroup` and `VectorSpace` instances for `Turn`, `Rad`, `Deg`
-    - `Alignable` instance for `(->) e`
-	- `Default` instances for `FillRule`, `FillRuleA`, `LineJoin`,
-      `LineCap`, `FillColor`
-	- `Show` instances for `FillRule`, `FillRuleA`
-
-* **API changes**
-
-    - `e` no longer exported from `Diagrams.Prelude`.
-    - `Diagrams.BoundingBox` is no longer exported from `Diagrams.Prelude`.
-    - Re-export `Diagrams.Core.pointDiagram` from `Diagrams.Prelude`.
-    - Added `fromAlphaColour` method to `Color` class.
-    - `&` renamed to `^&`
-    - Stop re-exporting `tan`, `over`, and `both` from `Data.Colour`.
-	- New coordinate lenses `_x`, `_y`, and `_z` for `R2`, `P2`, `R3`, `P3`
-    - Export `fullTurn` from `Diagrams.Prelude`.
-    - `Codomain (Located a)` is now `Point (Codomain a)` instead of
-      `Located (Codomain a)`.
-	- Export `domainBounds` from `Diagrams.Parametric`.
-	- Adjusting functionality moved from `Diagrams.Parametric` to its
-      own module, `Diagrams.Parametric.Adjust`.
-    - Rename `strokeT` (and primed variant) to `strokeTrail`; rename
-      `strokeLocT` to `strokeLocTrail`.
-    - `ScaleInv` is now in its own module, `Diagrams.TwoD.Transform.ScaleInv`.
-	- Re-export `Image` type (but not constructor) from `Diagrams.TwoD`
-    - Removed `Floating` and `RealFloat` instances for `Turn` and `Deg`
-    - `offsetSegment` now returns a `Located` instead of a tuple.
-    - Removed `Num` and `Fractional` instances for `R2`.
-
-* **Dependency/version changes**
-
-    - Remove `newtype` dependency
-    - New dependencies on `lens`, `tagged`, `optparse-applicative`,
-      `filepath`, `safe`, `vector-space-points`, `MemoTrie`
-    - Depend on `intervals >= 0.3 && < 0.5`.
-
-* **Bug fixes**
-
-    - Depend on `intervals 0.3`, which allows diagrams to build on
-      Windows, by evading a GHCi linker bug which affects the FFI use in
-      previous versions of intervals ([diagrams-contrib#14](https://github.com/diagrams/diagrams-contrib/issues/14))
-
-    - Use point envelope at the origin for text objects instead of an
-      empty envelope
-      ([#115](https://github.com/diagrams/diagrams-lib/issues/115),
-      [#116](https://github.com/diagrams/diagrams-lib/issues/116)).
-    - Adjusting the end of a trail now works correctly ([#95](https://github.com/diagrams/diagrams-lib/issues/95)).
-    - Only look for miter join on corners in `Diagrams.TwoD.Offset` ([#118](https://github.com/diagrams/diagrams-lib/issues/118)).
-    - `wedge` from `Diagrams.TwoD.Arc` is now a Loop ([#99](https://github.com/diagrams/diagrams-lib/issues/99))
-
-* **Performance improvements**
-
-    - `R2` is now strict and `UNPACK`ed
-    - Add strictness to `Offset`, `Segment`, `OffsetEnvelope`, and `SizeSpec2D`.
-	- Make `getEnvelope` calculation for `Segment` more efficient by
-      floating divisions out of the inner calculation.
-    - Use a specialized `HasTrie` instance for `R2`.
-
-0.7.1.1 (27 September 2013)
----------------------------
-
-* allow semigroups-0.11
-
-0.7.1 (11 September 2013)
--------------------------
-
-* **New features**
-
-    - New standard miter limit attribute
-    - New functions `lineColorA`, `lineWidthA`, `lineMiterLimitA`,
-      `fontSizeA` for directly applying attribute values
-    - `setDefault2DAttributes` now sets default line cap (butt), line
-      join (miter), and miter limit (10) attributes
-
-* **New instances**
-
-    - `Data.Default` instances for
-        - `LineCap`
-	- `LineJoin`
-	- `LineMiterLimit`
-	- `LineWidth`
-	- `LineColor`
-	- `FontSize`
-
-0.7 (9 August 2013)
--------------------
-
-* **New features**
-
-    - New module `Diagrams.TwoD.Curvature`, for computing the
-      curvature of 2D segments at any given point.
-    - New module `Diagrams.Offset`, containing an `offsetSegment`
-      function that builds a trail a fixed distance from the original
-      segment.  This is a precursor to planned functions `offsetTrail`
-      and `offsetPath`.
-    - New function `Diagrams.TwoD.Transform.onBasis`, for extracting a
-      matrix representation of a 2D transformation
-    - New functions `extrudeEnvelope` and `intrudeEnvelope`, for
-      extending or shrinking an envelope only in a certain direction.
-    - Generalize the `Color` class to absolute colors.
-      This addresses concerns raised in issue #66 by letting the backend
-      choose which color space to render `Color` instances to. Functions are
-      provided for backwards compatibility with the old semantics.
-    - New function `scaleInvPrim` for creating a diagram from a single
-      scale-invariant primitive.
-    - New module `Diagrams.Parametric`, containing a collection of
-      classes abstracting over "parametric" things: `Parametric`,
-      `DomainBounds`, `EndValues`, `Sectionable`, and `HasArcLength`,
-      with instances for segments, trails, and related things.
-    - A big refactoring of segments and trails:
-        - Segments can now be either "closed" or "open".
-        - There are now two types of trails: "lines" (which travel
-          from point A to point B) or "loops" (closed curves which end
-          where they started). `Trail` is now a wrapper type which can
-          contain both loops and lines.
-        - There is a new `Located` wrapper type for adding locations to
-          translation-invariant things.  `Path`s now consist of a
-          collection of `Located Trail`s.
-        - The `PathLike` class is now renamed to `TrailLike`; the
-          `trailLike` function takes a `Located Trail` as input.
-    - New convenience functions `boundaryFrom` and `boundaryFromMay`,
-      for computing boundaries of subdiagrams.
-    - Re-export from `diagrams-lib` a lot of things defined in
-      `diagrams-core`, to make them easier for users to find.  Several
-      new modules have been created as a result: `Diagrams.Query`,
-      `Diagrams.Envelope`, `Diagrams.Trace`, and `Diagrams.Names`.
-    - Export the `centroid` function from `Diagrams.Prelude`.
-    - `triangle` is now a synonym for `eqTriangle`.
-
-* **New instances**
-
-    - `IsPrim` instances for `Path`, `Ellipsoid`, `Image`, `Text`, and
-      `ScaleInv`
-    - `Eq`, `Ord`, and `Show` instances for `SizeSpec2D`
-
-* **API changes**
-
-    - `CircleFrac` has been renamed `Turn` (though `CircleFrac` is
-      retained as a deprecated synonym).
-    - `Diagrams.Coordinates` is no longer exported from
-      `Diagrams.Prelude`.  This is for compatibility with `lens`, as `(&)`
-      is a rather important lens operator and clashes with
-      `Diagrams.Coordinates`.  Users who want the `Coordinates` stuff can import
-      `Diagrams.Coordinates` explicitly.
-
-* **Dependency/version changes**
-
-    - allow `base-4.7`
-    - upgrade to `monoid-extras-0.3`
-    - depend on `data-default-class` instead of `data-default`
-    - Tested with GHC 7.7.
-
-* **Bug fixes**
-
-    - Added a special case that was a not handled properly by the
-      quadratic solver, resulting in bogus envelopes in certain cases
-      (#88).
-    - Import only `Data.NumInstances.Tuple` instead of
-      `Data.NumInstances`. Previously, `Diagrams.Prelude` exported
-      `Eq`, `Show`, and `Num` instances for functions and tuples; now
-      it only exports tuple instances. Users wishing to use
-      `Diagrams.CubicSpline` with a vector space built over functions (!?)
-      can import `Data.NumInstances.Function` themselves. (#48)
-    - Do scaling on a `Path` *before* constructing a `TrailLike` in
-      `rect` (#43)
-
-0.6.0.3 (4 May 2013)
---------------------
-
-* bump upper bound to allow `NumInstances-1.3`
-
-0.6.0.2 (28 March 2013)
------------------------
-
-* bump upper bound to allow `NumInstances-1.2`
-
-* Quadratic solver is now more numerically stable, getting rid of some
-  incorrect behavior of `juxtapose`
-  ([\#46](https://github.com/diagrams/diagrams-lib/issues/46))
-
-0.6.0.1: 7 January 2013
------------------------
-
-* allow `semigroups-0.9`
-
-0.6: 11 December 2012
----------------------
-
-* **New features**
-
-    - `boundingRect` function for constructing a bounding rectangle
-
-    - `bg` function for "setting the background color" (*i.e.* placing
-      atop a colored bounding rectangle)
-
-    - New functions `setDefault2DAttributes` and `adjustDiaSize2D`.
-      `adjustDia2D` does both --- so the behavior of `adjustDia2D` has
-      not changed, but it is now possible to apply just one of the two
-      adjustments using the new functions.
-
-    - `Diagrams.TwoD.Transform` now exports a `ScaleInv` type for creating
-      scale-invariant objects, which are only affected by rotational
-      and translational components of transformations.
-
-    - The new `Diagrams.Coordinates` module provides nicer syntax for
-      constructing and pattern-matching point and vector literals.
-
-    - New `fromFixedSeg` function in `Diagrams.Segment`, which
-      decomposes a `FixedSegment` into a starting point and a `Segment`.
-
-    - New `withTrace` function for setting the `Trace` of a diagram.
-
-    - Three new size-related functions:
-
-        - New `sized` function for scaling an object to a particular size.
-          One particularly nice use of this is to obviate the need to keep
-          fiddling with the line width to get diagrams to "look right";
-          just set the line width relative to some arbitrary scale
-          (*e.g.* assuming the final diagram will fit into a 1x1 box) and
-          then apply `sized` to the final diagram to make it that given
-          arbitrary size.  It can also be used for easily making something
-          (a diagram, path, trail, ...) the same size as something else,
-          with the help of the new `sizeSpec2D` function.
-
-        - New `sizedAs` function, for setting the size of some object to
-          be "the same as" some other object.
-
-        - New `sizeSpec2D` function for conveniently calculating the size
-          of an object as a `SizeSpec2D` value (for use with the new `sized`
-          funtion).
-
-    - New `extrudeEnvelope` and `intrudeEnvelope` functions for
-      modifying envelopes in a single direction only, as well as new
-      functions `extrude{Left,Right,Bottom,Top}` specializing
-      `extrudeEnvelope` to 2D.
-
-    - `arcCW` draws clockwise arcs; `arc'` draws arcs counterclockwise
-      or clockwise as the radius is positive or negative,
-      respectively.
-
-    - fill color attribute is generalized to support "recommended" and
-      "committed" colors; text objects use a recommended fill color of
-      black.
-
-* **New instances**
-
-    - The `Show` instance for `R2` now produces something like `2 & 6`
-      instead of `R2 { unR2 = (2,6) }`.  The `Read` instance has also
-      been changed to match, so `read . show = id`.
-
-    - `Enveloped` instance for `FixedSegment`
-
-    - `Traced` instances for `Segment`, `FixedSegment`, `Trail`, and `Path`
-
-    - New derived `Eq` instances for `LineCapA`, `LineJoinA`, `Dashing`,
-      `DashingA`, `FillRule`, `Font`, `FontSize`, `FontSlant`, `FontSlantA`,
-      `FontWeight`, and `FontWeightA`
-
-    - `Renderable Ellipsoid NullBackend` instance
-
-* **API changes**
-
-    - `Data.Colour` (minus `atop` and `AffineSpace`) is now re-exported
-      from Diagrams.Prelude for convenience.
-
-    - The `beneath` function is now infixl 6.
-
-    - The `BoundingBox` module has had a complete overhaul.  There is
-      now a special empty bounding box, and bounding boxes are an
-      instance of `Monoid`.
-
-    - The type of `withEnvelope` has been slightly generalized.
-
-    - `Diagrams.TwoD.Adjust.adjustSize` is now deprecated; it has been
-      renamed and moved to `Diagrams.TwoD.Size.requiredScaleT`.
-
-    - `expandPath` has been renamed to `scalePath`.
-
-* **Dependency/version changes**
-
-    - Allow `data-default` 0.4 and 0.5
-    - Allow `base`-4.6
-    - Allow `containers`-0.5
-
-* **Bug fixes**
-
-    - `arc` and `arcT` functions now always produce counterclockwise arcs,
-      as claimed.
-
-0.5: 9 March 2012
------------------
-
-* **New features**
-    - `mkSizeSpec` function for constructing a `SizeSpec2D` from two `Maybe Double`s
-    - `beneath` as convenient synonym for `flip atop`
-    - Improvements and extensions to rounded rectangles by Peter Hall:
-        + `roundedRect'` allows rounded rectangles with a different radius
-          specified for each corner
-        + both `roundedRect'` and `roundedRect` now allow negative radii,
-          resulting in "inverted" circular corners
-    - [\#64](http://code.google.com/p/diagrams/issues/detail?id=64): New `Alignable` class for things that can be aligned.
-    - `explodeTrail` and `explodePath` have been generalized to return any
-      `PathLike` type.
-    - New path functions `pathCentroid` (compute the centroid of a
-      path's vertices) and `expandPath` (scale a path about its centroid).
-    - Generalized `centroid` function now exported from new module
-      `Diagrams.Points`.
-    - Initial (experimental) support for animation:
-        + `Animation` and `QAnimation` defined as synonyms for `Active`
-          diagrams (see `active` package)
-        + Instances for `Active`: `V`, `HasOrigin`, `Transformable`,
-          `HasStyle`, `PathLike`, `Juxtaposable`, `Alignable`
-        + `animEnvelope` and `animRect` functions for automatic bounding of
-          animations
-    - `addClosingSegment` function for making the implicit closing
-      segment of a closed trail explicit
-    - Improvements to `BoundingBox` module from Michael Sloan: querying
-      of `BoundingBox` bounds, corners, extents, and transformation of
-      objects to fit within a given box.
-    - Text alignment options from Michael Sloan
-    - `view` function for restricting a diagram's envelope to a
-      rectangular region.
-    - `iterateN` function for iterating a finite number of times
-    - `atAngle` for placing two diagrams next to each other along a
-      specified angle.
-    - `padX` and `padY` functions for padding in the X- and Y-directions
-      independently.
-    - generalized `showOrigin` function from Ian Ross
-    - [\#40](http://code.google.com/p/diagrams/issues/detail?id=40): add shears to `Diagrams.TwoD.Transform`
-
-* **Performance improvements**
-    - Use a balanced folding scheme for `cat'`, reducing time in some
-      cases from \\(O(n^2)\\) to \\(O(n \\log n)\\)
-    - More efficient implementation of `beside`
-
-* **New instances**
-    - `Alignable` instances for `QDiagram`, `Path`, `Envelope`, `Active`, `Set`,
-      `Map`, `[]`
-    - `Renderable` instances for `NullBackend` (`Trail`, `Path`, `Segment`,
-      `Image`, `Text`)
-    - Instances for `Active`: `V`, `HasOrigin`, `Transformable`,
-      `HasStyle`, `PathLike`, `Juxtaposable`, `Alignable`
-
-* **API changes**
-    - `R2` used to be a synonym for `(Double, Double)` but is now
-      abstract. To convert between pairs of `Doubles` and `R2`, use the
-      new functions `r2` and `unr2`.  There are two reasons for this
-      change:
-          1. to allow for future changes to the implementation of `R2`;
-          2. `(Double, Double)` was an awkward special case getting in the
-           way of useful tuple instances for classes like `HasOrigin`,
-           `Enveloped`, and so on.
-    - `circlePath` has been removed; its functionality has been
-      subsumed by `circle`.
-    - `adjustSegment` now takes an extra tolerance option.
-    - Ellipses are now represented using Bezier approximations rather
-      than a separate special type.
-    - `BoundingBox` no longer has a `Transformable` instance; the old
-      instance was misleading at best.
-    - Change semantics of `beside` (hence also `(|||)` and `(===)`) so the
-      result's origin is the same as that of the first argument.
-    - `adjustDia2D` now takes a `SizeSpec2D`.
-    - `beside` and related functions are now implemented in terms of
-      `juxtapose`.
-    - Instead of taking an `R2`, `roundedRect` now takes a pair of
-      `Double`s, to be more consistent with `rect`.
-
-* **Dependency/version changes**
-    - Support for GHC 7.4.1:
-        + depend on `colour` >= 2.3.2
-        + update `base` and `array` upper bounds
-    - bump `vector-space` upper bound
-
-* **Bug fixes**
-    - Avoid scale by zero error in `showOrigin`.
-    - Base `adjustDia2D` translation on output size rather than diagram size.
-
-0.4.0.1: 30 October 2011
-------------------------
-
-* bump `data-default` dependency to allow version 0.3
-
-0.4: 23 October 2011
---------------------
-
-* **documentation fixes**
-
-* **New functions and primitives**
-
-    + `wedge` shape primitive
-    + `fromDirection` function for converting angles to 2D unit vectors;
-      inverse function `direction` generalized to return any Angle type
-    + New functions for computing and adjusting segment lengths
-    + `scaleUToX` and `scaleUToY` for doing uniform scales
-      resulting in a desired width or height.
-    + `circlePath`, `reversePath`, `decoratePath`
-
-* **New features**
-
-    + Completely new and improved polygon generation API
-    + Cubic splines
-    + User-controllable path fill rules
-
-* **Bug fixes**
-
-    + fix incorrect corner case in arc generation
-    + fix incorrect `reverseTrail` function
-
-0.3: 18 June 2011
------------------
-
-* **New features**
-    + new customizable `stroke'` function which lets you assign names to
-      path vertices
-    + `circle` and `square` functions now take a size argument
-    + function for adjusting 2D diagrams to requested size abstracted
-      from cairo backend
-    + generalize `PathLike` class to include an instance for diagrams,
-      and collapse things like `polygon`/`polygonPath` into a single
-      polymorphic function
-    + basic text support
-    + basic support for external images
-    + very sketchy initial proof-of-concept library of 3D primitives.
-      See also diagrams-povray package.
-
-* **Bug fixes**
-    + Issue 32 (`mempty` not behaving correctly within concatenations)
-
-0.2: 3 June 2011
-----------------
-
-* **documentation fixes**
-
-* **New functions and primitives**
-    + `scaleToX` and `scaleToY` for scaling to an absolute width/height
-    + `reverseTrail`
-    + new `Angle` class and ability to use radians, degrees, or circle fractions
-      for specifying angles
-    + `rotateAbout` and `reflectAbout` transformations based on new conjugation functions
-    + `rect` and `roundedRect` primitives
-    + `explodeTrail`/`Path` for breaking trails and paths into individual segments
-
-* **New features**
-    + opacity attribute
-    + support for path clipping
-
-* **New modules**
-    + `Diagrams.BoundingBox`
-
-* **Fixes and updates**
-    + `withBounds` now properly uses the new bounds instead of just combining
-      them with the old
-
-0.1.1: 18 May 2011
-------------------
-
-* minor documentation fixes
-* link to new website
-
-0.1: 17 May 2011
-----------------
-
-* initial preview release
diff --git a/LICENSE b/LICENSE
--- a/LICENSE
+++ b/LICENSE
@@ -1,21 +1,35 @@
-Copyright (c) 2011-2014 diagrams-lib team:
+Copyright (c) 2011-2016 diagrams-lib team:
 
+  Florent Becker <florent.becker@univ-orleans.fr>
   Jan Bracker <jan.bracker@googlemail.com>
   Daniel Bergey <bergey@alum.mit.edu>
+  Vincent Berthoux <vincent.berthoux@gmail.com>
+  Christopher Chalmers <c.chalmers@me.com>
+  Michael Chavinda <mchavinda@colgate.edu>
   Denys Duchier <denys.duchier@univ-orleans.fr>
   Daniil Frumin <difrumin@gmail.com>
+  Ben Gamari <ben@smart-cactus.org>
+  Allan Gardner <allanegardner@gmail.com>
+  Pontus Granström <pnutus@gmail.com>
+  Gabor Greif <ggreif@gmail.com>
   Niklas Haas <nand@lavabit.com>
   Peter Hall <peter.hall@memorphic.com>
+  Dashiell Halpern
   Claude Heiland-Allen <claudiusmaximus@goto10.org>
   Deepak Jois <deepak.jois@gmail.com>
+  Sidharth Kapur <sidharthkapur1@gmail.com>
+  Taru Karttunen <taruti@taruti.net>
   John Lato <jwlato@tsurucapital.com>
+  Konrad Madej <kdmadej@gmail.com>
   Chris Mears <chris@cmears.id.au>
+  Alexis Praga <praga@cerfacs.fr>
   Jeffrey Rosenbluth <jeffrey.rosenbluth@gmail.com>
   Ian Ross <ian@skybluetrades.net>
   Carlos Scheidegger <cscheid@research.att.com>
   Michael Sloan <mgsloan@gmail.com>
   Jim Snavely <ludflu@gmail.com>
   Kanchalai Suveepattananont <ksuvee@seas.upenn.edu>
+  Robert Vollmert <rfvollmert@gmail.com>
   Scott Walck <walck@lvc.edu>
   Ryan Yates <fryguybob@gmail.com>
   Brent Yorgey <byorgey@cis.upenn.edu>
diff --git a/README.markdown b/README.markdown
--- a/README.markdown
+++ b/README.markdown
@@ -1,4 +1,4 @@
-[![Build Status](https://secure.travis-ci.org/diagrams/diagrams-lib.png)](http://travis-ci.org/diagrams/diagrams-lib)
+[![Build Status](https://github.com/diagrams/diagrams-lib/actions/workflows/haskell-ci.yml/badge.svg)](https://github.com/diagrams/diagrams-lib/actions/workflows/haskell-ci.yml)
 
 The standard library for
 [diagrams](http://projects.haskell.org/diagrams/), a Haskell embedded
diff --git a/Setup.hs b/Setup.hs
--- a/Setup.hs
+++ b/Setup.hs
@@ -1,2 +1,2 @@
-import Distribution.Simple
+import           Distribution.Simple
 main = defaultMain
diff --git a/diagrams-lib.cabal b/diagrams-lib.cabal
--- a/diagrams-lib.cabal
+++ b/diagrams-lib.cabal
@@ -1,5 +1,5 @@
 Name:                diagrams-lib
-Version:             1.2.0.9
+Version:             1.5.1
 Synopsis:            Embedded domain-specific language for declarative graphics
 Description:         Diagrams is a flexible, extensible EDSL for creating
                      graphics of many types.  Graphics can be created
@@ -7,8 +7,10 @@
                      multiple backends.  diagrams-lib provides a
                      standard library of primitives and operations for
                      creating diagrams.  To get started using it, see
-                     "Diagrams.Prelude".
-Homepage:            http://projects.haskell.org/diagrams
+                     the "Diagrams" module, and refer to the tutorials and
+                     documentation on the diagrams website,
+                     <http://diagrams.github.io>.
+Homepage:            http://diagrams.github.io
 License:             BSD3
 License-file:        LICENSE
 Author:              Brent Yorgey
@@ -16,103 +18,165 @@
 Bug-reports:         http://github.com/diagrams/diagrams-lib/issues
 Category:            Graphics
 Build-type:          Simple
-Cabal-version:       >=1.10
-Extra-source-files:  CHANGES.markdown, README.markdown, diagrams/*.svg
-Extra-doc-files:     diagrams/*.svg
-Tested-with:         GHC == 7.4.2, GHC == 7.6.3, GHC == 7.8.1
+Cabal-version:       1.18
+Extra-source-files:  diagrams/*.svg
+Extra-doc-files:     CHANGELOG.md, README.markdown, diagrams/*.svg
+Tested-with:         GHC ==8.4.4 || ==8.6.5 || ==8.8.4 || ==8.10.7 || ==9.0.2 || ==9.2.8 || ==9.4.8 || ==9.6.6 || ==9.8.2 || ==9.10.1 || ==9.12.1
 Source-repository head
   type:     git
   location: http://github.com/diagrams/diagrams-lib.git
 
 Library
-  Exposed-modules:     Diagrams.Prelude,
-                       Diagrams.Prelude.ThreeD,
+  Exposed-modules:     Diagrams,
+                       Diagrams.Prelude,
                        Diagrams.Align,
                        Diagrams.Angle,
-                       Diagrams.Combinators,
-                       Diagrams.Coordinates,
+                       Diagrams.Animation,
+                       Diagrams.Animation.Active,
                        Diagrams.Attributes,
                        Diagrams.Attributes.Compile,
-                       Diagrams.Points,
+                       Diagrams.Backend.CmdLine,
+                       Diagrams.BoundingBox,
+                       Diagrams.Combinators,
+                       Diagrams.Coordinates,
+                       Diagrams.CubicSpline,
+                       Diagrams.CubicSpline.Boehm,
+                       Diagrams.CubicSpline.Internal,
+                       Diagrams.Deform
+                       Diagrams.Direction,
+                       Diagrams.Envelope,
+                       Diagrams.LinearMap,
                        Diagrams.Located,
+                       Diagrams.Names,
                        Diagrams.Parametric,
                        Diagrams.Parametric.Adjust,
+                       Diagrams.Path,
+                       Diagrams.Points,
+                       Diagrams.Query,
                        Diagrams.Segment,
+                       Diagrams.Size,
+                       Diagrams.Tangent,
+                       Diagrams.ThreeD,
+                       Diagrams.ThreeD.Align,
+                       Diagrams.ThreeD.Attributes,
+                       Diagrams.ThreeD.Camera,
+                       Diagrams.ThreeD.Deform,
+                       Diagrams.ThreeD.Light,
+                       Diagrams.ThreeD.Shapes,
+                       Diagrams.ThreeD.Size,
+                       Diagrams.ThreeD.Transform,
+                       Diagrams.ThreeD.Projection,
+                       Diagrams.ThreeD.Types,
+                       Diagrams.ThreeD.Vector,
+                       Diagrams.Trace,
                        Diagrams.Trail,
                        Diagrams.TrailLike,
-                       Diagrams.Path,
-                       Diagrams.CubicSpline,
-                       Diagrams.CubicSpline.Internal,
-                       Diagrams.Solve,
-                       Diagrams.Tangent,
                        Diagrams.Transform,
-                       Diagrams.Deform
-                       Diagrams.BoundingBox,
-                       Diagrams.Names,
-                       Diagrams.Envelope,
-                       Diagrams.Trace,
-                       Diagrams.Query,
+                       Diagrams.Transform.ScaleInv,
+                       Diagrams.Transform.Matrix,
                        Diagrams.TwoD,
-                       Diagrams.TwoD.Types,
+                       Diagrams.TwoD.Adjust,
                        Diagrams.TwoD.Align,
+                       Diagrams.TwoD.Arc,
                        Diagrams.TwoD.Arrow,
                        Diagrams.TwoD.Arrowheads,
                        Diagrams.TwoD.Attributes,
                        Diagrams.TwoD.Combinators,
+                       Diagrams.TwoD.Curvature,
                        Diagrams.TwoD.Deform,
-                       Diagrams.TwoD.Transform,
-                       Diagrams.TwoD.Transform.ScaleInv,
                        Diagrams.TwoD.Ellipse,
-                       Diagrams.TwoD.Arc,
-                       Diagrams.TwoD.Segment,
-                       Diagrams.TwoD.Curvature,
+                       Diagrams.TwoD.Image,
+                       Diagrams.TwoD.Model,
                        Diagrams.TwoD.Offset,
                        Diagrams.TwoD.Path,
+                       Diagrams.TwoD.Points,
                        Diagrams.TwoD.Polygons,
-                       Diagrams.TwoD.Shapes,
-                       Diagrams.TwoD.Vector,
+                       Diagrams.TwoD.Segment,
+                       Diagrams.TwoD.Segment.Bernstein,
                        Diagrams.TwoD.Size,
-                       Diagrams.TwoD.Model,
+                       Diagrams.TwoD.Shapes,
                        Diagrams.TwoD.Text,
-                       Diagrams.TwoD.Image,
-                       Diagrams.TwoD.Adjust,
-                       Diagrams.ThreeD.Align,
-                       Diagrams.ThreeD.Attributes,
-                       Diagrams.ThreeD.Camera,
-                       Diagrams.ThreeD.Deform,
-                       Diagrams.ThreeD.Light,
-                       Diagrams.ThreeD.Shapes,
-                       Diagrams.ThreeD.Transform,
-                       Diagrams.ThreeD.Types,
-                       Diagrams.ThreeD.Vector,
-                       Diagrams.ThreeD,
-                       Diagrams.Animation,
-                       Diagrams.Animation.Active,
-                       Diagrams.Util,
-                       Diagrams.Backend.CmdLine
-  Build-depends:       base >= 4.2 && < 4.8,
-                       containers >= 0.3 && < 0.6,
+                       Diagrams.TwoD.Transform,
+                       Diagrams.TwoD.Types,
+                       Diagrams.TwoD.Vector,
+                       Diagrams.Util
+  other-modules:       Linear.Vector.Compat
+  Build-depends:       base >= 4.9 && < 4.22,
+                       containers >= 0.3 && < 0.8,
                        array >= 0.3 && < 0.6,
-                       semigroups >= 0.3.4 && < 0.17,
-                       monoid-extras >= 0.3 && < 0.4,
+                       semigroups >= 0.3.4 && < 0.21,
+                       monoid-extras >= 0.6 && < 0.8,
                        dual-tree >= 0.2 && < 0.3,
-                       diagrams-core >= 1.2 && < 1.3,
-                       active >= 0.1 && < 0.2,
-                       vector-space >= 0.7.7 && < 0.11,
-                       vector-space-points >= 0.1.2 && < 0.3,
-                       MemoTrie >= 0.6 && < 0.7,
+                       diagrams-core >= 1.4 && < 1.6,
+                       diagrams-solve >= 0.1 && < 0.2,
+                       active >= 0.2 && < 0.3,
                        colour >= 2.3.2 && < 2.4,
-                       data-default-class < 0.1,
+                       data-default >= 0.8 && < 0.9,
                        fingertree >= 0.1 && < 0.2,
-                       intervals >= 0.7 && < 0.8,
-                       lens >= 4.0 && < 4.10,
-                       tagged >= 0.7,
-                       optparse-applicative >= 0.11 && < 0.12,
-                       filepath,
-                       JuicyPixels >= 3.1.5 && < 3.3,
-                       hashable >= 1.1 && < 1.3
-  if impl(ghc < 7.6)
-    Build-depends: ghc-prim
+                       intervals >= 0.7 && < 0.10,
+                       lens >= 5.1 && < 5.4,
+                       tagged >= 0.7 && < 0.9,
+                       optparse-applicative >= 0.11 && < 0.20,
+                       filepath >= 1.4 && < 1.6,
+                       JuicyPixels >= 3.3.4 && < 3.4,
+                       hashable >= 1.1 && < 1.6,
+                       linear >= 1.20.1 && < 1.24,
+                       adjunctions >= 4.0 && < 5.0,
+                       distributive >=0.2.2 && < 1.0,
+                       process >= 1.1 && < 1.7,
+                       directory >= 1.2 && < 1.4,
+                       unordered-containers >= 0.2 && < 0.3,
+                       text >= 0.7.1 && < 2.2,
+                       mtl >= 2.0 && < 2.3 || >= 2.3.1 && < 2.4,
+                       transformers >= 0.3.0 && < 0.7.0,
+                       profunctors >= 5.0 && < 6.0,
+                       exceptions >= 0.6 && < 1.0,
+                       cereal >=0.4.1.1 && <0.6,
+                       bytestring >=0.9 && <0.13,
+                       fail >= 4.9.0.0 && <4.10
   Hs-source-dirs:      src
   ghc-options: -Wall
   default-language:    Haskell2010
+  other-extensions: BangPatterns, CPP, DefaultSignatures, DeriveDataTypeable,
+    DeriveFunctor, DeriveGeneric, EmptyDataDecls, ExistentialQuantification,
+    GADTs, GeneralizedNewtypeDeriving, NoMonomorphismRestriction, Rank2Types,
+    RankNTypes, ScopedTypeVariables, StandaloneDeriving, TemplateHaskell,
+    TypeOperators, TypeSynonymInstances, UndecidableInstances, ViewPatterns,
+    LambdaCase
+
+test-suite tests
+  type: exitcode-stdio-1.0
+  main-is: Test.hs
+  other-modules: Diagrams.Test.Direction
+               , Diagrams.Test.Trail
+               , Diagrams.Test.Transform
+               , Diagrams.Test.Transform.Matrix
+               , Diagrams.Test.TwoD.Offset
+               , Diagrams.Test.TwoD.Segment
+               , Diagrams.Test.TwoD
+               , Diagrams.Test.Angle
+               , Instances
+  hs-source-dirs: test
+  build-depends:       base,
+                       tasty >= 0.10 && < 1.6,
+                       tasty-hunit >= 0.9.2 && < 0.11,
+                       tasty-quickcheck >= 0.8 && < 0.12,
+                       QuickCheck >= 2.7,
+                       deepseq >= 1.3 && < 1.6,
+                       diagrams-lib,
+                       lens,
+                       distributive,
+                       numeric-extras,
+                       diagrams-solve
+  default-language:    Haskell2010
+
+benchmark benchmarks
+  type: exitcode-stdio-1.0
+  main-is:Speed.hs
+  hs-source-dirs:test
+  default-language: Haskell2010
+  build-depends:
+    base < 5,
+    criterion,
+    diagrams-core,
+    diagrams-lib
diff --git a/diagrams/src_Diagrams_Combinators_alignedEx1.svg b/diagrams/src_Diagrams_Combinators_alignedEx1.svg
new file mode 100644
--- /dev/null
+++ b/diagrams/src_Diagrams_Combinators_alignedEx1.svg
@@ -0,0 +1,1 @@
+<svg xmlns="http://www.w3.org/2000/svg" height="151.7241" stroke-opacity="1" viewBox="0 0 400 152" font-size="1" width="400.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.9854108192823033" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 393.1034,34.4828 c 0.0000,-15.2354 -12.3508,-27.5862 -27.5862 -27.5862c -15.2354,-0.0000 -27.5862,12.3508 -27.5862 27.5862c -0.0000,15.2354 12.3508,27.5862 27.5862 27.5862c 15.2354,0.0000 27.5862,-12.3508 27.5862 -27.5862Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.9854108192823033" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 310.3448,75.8621 c 0.0000,-38.0886 -30.8769,-68.9655 -68.9655 -68.9655c -38.0886,-0.0000 -68.9655,30.8769 -68.9655 68.9655c -0.0000,38.0886 30.8769,68.9655 68.9655 68.9655c 38.0886,0.0000 68.9655,-30.8769 68.9655 -68.9655Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.9854108192823033" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 144.8276,48.2759 c 0.0000,-22.8532 -18.5261,-41.3793 -41.3793 -41.3793c -22.8532,-0.0000 -41.3793,18.5261 -41.3793 41.3793c -0.0000,22.8532 18.5261,41.3793 41.3793 41.3793c 22.8532,0.0000 41.3793,-18.5261 41.3793 -41.3793Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.9854108192823033" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 34.4828,20.6897 c 0.0000,-7.6177 -6.1754,-13.7931 -13.7931 -13.7931c -7.6177,-0.0000 -13.7931,6.1754 -13.7931 13.7931c -0.0000,7.6177 6.1754,13.7931 13.7931 13.7931c 7.6177,0.0000 13.7931,-6.1754 13.7931 -13.7931Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(255,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 28.4138,20.6897 c 0.0000,-4.2659 -3.4582,-7.7241 -7.7241 -7.7241c -4.2659,-0.0000 -7.7241,3.4582 -7.7241 7.7241c -0.0000,4.2659 3.4582,7.7241 7.7241 7.7241c 4.2659,0.0000 7.7241,-3.4582 7.7241 -7.7241Z"/></g></svg>
diff --git a/diagrams/src_Diagrams_Combinators_alignedEx2.svg b/diagrams/src_Diagrams_Combinators_alignedEx2.svg
new file mode 100644
--- /dev/null
+++ b/diagrams/src_Diagrams_Combinators_alignedEx2.svg
@@ -0,0 +1,1 @@
+<svg xmlns="http://www.w3.org/2000/svg" height="400.0000" stroke-opacity="1" viewBox="0 0 400 400" font-size="1" width="400.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.5999999999999999" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 256.1849,297.9712 l 56.1849,-172.9194 l -147.0940,-106.8700 l -147.0940,106.8700 l 56.1849,172.9194 Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.5999999999999999" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 200.0000,175.6410 l -90.9091,-157.4592 l -90.9091,157.4592 Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.5999999999999999" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 200.0000,200.0000 l -0.0000,-181.8182 h -181.8182 l -0.0000,181.8182 Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.5999999999999999" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 381.8182,200.0000 c 0.0000,-100.4154 -81.4028,-181.8182 -181.8182 -181.8182c -100.4154,-0.0000 -181.8182,81.4028 -181.8182 181.8182c -0.0000,100.4154 81.4028,181.8182 181.8182 181.8182c 100.4154,0.0000 181.8182,-81.4028 181.8182 -181.8182Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(255,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 207.2727,200.0000 c 0.0000,-4.0166 -3.2561,-7.2727 -7.2727 -7.2727c -4.0166,-0.0000 -7.2727,3.2561 -7.2727 7.2727c -0.0000,4.0166 3.2561,7.2727 7.2727 7.2727c 4.0166,0.0000 7.2727,-3.2561 7.2727 -7.2727Z"/></g></svg>
diff --git a/diagrams/src_Diagrams_Combinators_appendsEx.svg b/diagrams/src_Diagrams_Combinators_appendsEx.svg
--- a/diagrams/src_Diagrams_Combinators_appendsEx.svg
+++ b/diagrams/src_Diagrams_Combinators_appendsEx.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="200.0" height="182.15600114617723" font-size="1" viewBox="0 0 200 182" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="0.7634783583493163" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><g><g><path d="M 160.6111204622467,143.5731526092298 c 0.0,-16.735901510024043 -13.567128793006255,-30.3030303030303 -30.303030303030294 -30.3030303030303c -16.735901510024043,-1.024778410754815e-15 -30.3030303030303,13.567128793006253 -30.3030303030303 30.30303030303029c -2.04955682150963e-15,16.735901510024043 13.567128793006251,30.3030303030303 30.303030303030287 30.3030303030303c 16.735901510024043,3.0743352322644448e-15 30.3030303030303,-13.56712879300625 30.303030303030308 -30.30303030303029Z" /></g><g><path d="M 99.99494014381385,143.57315260922977 c 0.0,-16.735901510024043 -13.567128793006255,-30.3030303030303 -30.303030303030294 -30.3030303030303c -16.735901510024043,-1.024778410754815e-15 -30.3030303030303,13.567128793006253 -30.3030303030303 30.30303030303029c -2.04955682150963e-15,16.735901510024043 13.567128793006251,30.3030303030303 30.303030303030287 30.3030303030303c 16.735901510024043,3.0743352322644448e-15 30.3030303030303,-13.56712879300625 30.303030303030308 -30.30303030303029Z" /></g><g><path d="M 69.6969696969697,91.07800057308859 c 0.0,-16.735901510024043 -13.567128793006255,-30.3030303030303 -30.303030303030294 -30.3030303030303c -16.735901510024043,-1.024778410754815e-15 -30.3030303030303,13.567128793006253 -30.3030303030303 30.30303030303029c -2.04955682150963e-15,16.735901510024043 13.567128793006251,30.3030303030303 30.303030303030287 30.3030303030303c 16.735901510024043,3.0743352322644448e-15 30.3030303030303,-13.56712879300625 30.303030303030308 -30.30303030303029Z" /></g><g><path d="M 99.99494014381389,38.58284853694745 c 0.0,-16.735901510024043 -13.567128793006255,-30.3030303030303 -30.303030303030294 -30.3030303030303c -16.735901510024043,-1.024778410754815e-15 -30.3030303030303,13.567128793006253 -30.3030303030303 30.30303030303029c -2.04955682150963e-15,16.735901510024043 13.567128793006251,30.3030303030303 30.303030303030287 30.3030303030303c 16.735901510024043,3.0743352322644448e-15 30.3030303030303,-13.56712879300625 30.303030303030308 -30.30303030303029Z" /></g><g><path d="M 160.61112046224676,38.58284853694746 c 0.0,-16.735901510024043 -13.567128793006255,-30.3030303030303 -30.303030303030294 -30.3030303030303c -16.735901510024043,-1.024778410754815e-15 -30.3030303030303,13.567128793006253 -30.3030303030303 30.30303030303029c -2.04955682150963e-15,16.735901510024043 13.567128793006251,30.3030303030303 30.303030303030287 30.3030303030303c 16.735901510024043,3.0743352322644448e-15 30.3030303030303,-13.56712879300625 30.303030303030308 -30.30303030303029Z" /></g><g><path d="M 190.9090909090909,91.07800057308862 c 0.0,-16.735901510024043 -13.567128793006255,-30.3030303030303 -30.303030303030294 -30.3030303030303c -16.735901510024043,-1.024778410754815e-15 -30.3030303030303,13.567128793006253 -30.3030303030303 30.30303030303029c -2.04955682150963e-15,16.735901510024043 13.567128793006251,30.3030303030303 30.303030303030287 30.3030303030303c 16.735901510024043,3.0743352322644448e-15 30.3030303030303,-13.56712879300625 30.303030303030308 -30.30303030303029Z" /></g><g><path d="M 130.3030303030303,91.07800057308862 c 0.0,-16.735901510024043 -13.567128793006255,-30.3030303030303 -30.303030303030294 -30.3030303030303c -16.735901510024043,-1.024778410754815e-15 -30.3030303030303,13.567128793006253 -30.3030303030303 30.30303030303029c -2.04955682150963e-15,16.735901510024043 13.567128793006251,30.3030303030303 30.303030303030287 30.3030303030303c 16.735901510024043,3.0743352322644448e-15 30.3030303030303,-13.56712879300625 30.303030303030308 -30.30303030303029Z" /></g></g></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="182.1560" stroke-opacity="1" viewBox="0 0 200 182" font-size="1" width="200.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.7634783583493163" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 160.6111,143.5732 c 0.0000,-16.7359 -13.5671,-30.3030 -30.3030 -30.3030c -16.7359,-0.0000 -30.3030,13.5671 -30.3030 30.3030c -0.0000,16.7359 13.5671,30.3030 30.3030 30.3030c 16.7359,0.0000 30.3030,-13.5671 30.3030 -30.3030Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.7634783583493163" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 99.9949,143.5732 c 0.0000,-16.7359 -13.5671,-30.3030 -30.3030 -30.3030c -16.7359,-0.0000 -30.3030,13.5671 -30.3030 30.3030c -0.0000,16.7359 13.5671,30.3030 30.3030 30.3030c 16.7359,0.0000 30.3030,-13.5671 30.3030 -30.3030Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.7634783583493163" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 69.6970,91.0780 c 0.0000,-16.7359 -13.5671,-30.3030 -30.3030 -30.3030c -16.7359,-0.0000 -30.3030,13.5671 -30.3030 30.3030c -0.0000,16.7359 13.5671,30.3030 30.3030 30.3030c 16.7359,0.0000 30.3030,-13.5671 30.3030 -30.3030Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.7634783583493163" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 99.9949,38.5828 c 0.0000,-16.7359 -13.5671,-30.3030 -30.3030 -30.3030c -16.7359,-0.0000 -30.3030,13.5671 -30.3030 30.3030c -0.0000,16.7359 13.5671,30.3030 30.3030 30.3030c 16.7359,0.0000 30.3030,-13.5671 30.3030 -30.3030Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.7634783583493163" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 160.6111,38.5828 c 0.0000,-16.7359 -13.5671,-30.3030 -30.3030 -30.3030c -16.7359,-0.0000 -30.3030,13.5671 -30.3030 30.3030c -0.0000,16.7359 13.5671,30.3030 30.3030 30.3030c 16.7359,0.0000 30.3030,-13.5671 30.3030 -30.3030Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.7634783583493163" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 190.9091,91.0780 c 0.0000,-16.7359 -13.5671,-30.3030 -30.3030 -30.3030c -16.7359,-0.0000 -30.3030,13.5671 -30.3030 30.3030c -0.0000,16.7359 13.5671,30.3030 30.3030 30.3030c 16.7359,0.0000 30.3030,-13.5671 30.3030 -30.3030Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.7634783583493163" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 130.3030,91.0780 c 0.0000,-16.7359 -13.5671,-30.3030 -30.3030 -30.3030c -16.7359,-0.0000 -30.3030,13.5671 -30.3030 30.3030c -0.0000,16.7359 13.5671,30.3030 30.3030 30.3030c 16.7359,0.0000 30.3030,-13.5671 30.3030 -30.3030Z"/></g></svg>
diff --git a/diagrams/src_Diagrams_Combinators_besideEx.svg b/diagrams/src_Diagrams_Combinators_besideEx.svg
--- a/diagrams/src_Diagrams_Combinators_besideEx.svg
+++ b/diagrams/src_Diagrams_Combinators_besideEx.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="169.72067997066802" height="200.0" font-size="1" viewBox="0 0 170 200" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="0.7369573772655632" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><g><g fill="rgb(128,0,128)" fill-opacity="1.0"><g fill="rgb(128,0,128)" fill-opacity="1.0"><g fill="rgb(128,0,128)" fill-opacity="1.0"><path d="M 162.00610360836492,68.63383995200215 c 0.0,-32.884652674811015 -26.658278186282047,-59.54293086109307 -59.542930861093055 -59.54293086109307c -32.884652674811015,-2.0136042319639878e-15 -59.54293086109307,26.658278186282043 -59.54293086109307 59.54293086109305c -4.0272084639279756e-15,32.884652674811015 26.65827818628204,59.54293086109307 59.54293086109304 59.54293086109307c 32.884652674811015,6.0408126958919634e-15 59.54293086109307,-26.658278186282036 59.54293086109308 -59.54293086109305Z" /></g></g></g><g fill="rgb(255,165,0)" fill-opacity="1.0"><g fill="rgb(255,165,0)" fill-opacity="1.0"><g fill="rgb(255,165,0)" fill-opacity="1.0"><path d="M 87.10515084376053,151.2138036683622 c 0.0,-21.923101783207343 -17.772185457521363,-39.69528724072871 -39.6952872407287 -39.69528724072871c -21.923101783207343,-1.342402821309325e-15 -39.69528724072871,17.77218545752136 -39.69528724072871 39.695287240728696c -2.68480564261865e-15,21.923101783207343 17.77218545752136,39.69528724072871 39.695287240728696 39.69528724072871c 21.923101783207343,4.0272084639279756e-15 39.69528724072871,-17.772185457521356 39.69528724072871 -39.695287240728696Z" /></g></g></g><g fill="rgb(255,0,0)" fill-opacity="1.0" stroke-width="0.0"><g fill="rgb(255,0,0)" fill-opacity="1.0"><g fill="rgb(255,0,0)" fill-opacity="1.0"><path d="M 51.04622723939545,151.2138036683622 c 0.0,-2.0083081812028856 -1.628055455160751,-3.6363636363636367 -3.6363636363636362 -3.6363636363636367c -2.0083081812028856,-1.2297340929057781e-16 -3.6363636363636367,1.6280554551607507 -3.6363636363636367 3.636363636363636c -2.4594681858115563e-16,2.0083081812028856 1.6280554551607507,3.6363636363636367 3.6363636363636354 3.6363636363636367c 2.0083081812028856,3.689202278717335e-16 3.6363636363636367,-1.6280554551607502 3.636363636363638 -3.636363636363636Z" /></g></g></g></g></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="200.0000" stroke-opacity="1" viewBox="0 0 170 200" font-size="1" width="169.7207" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.7369573772655632" fill="rgb(128,0,128)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 162.0061,68.6338 c 0.0000,-32.8847 -26.6583,-59.5429 -59.5429 -59.5429c -32.8847,-0.0000 -59.5429,26.6583 -59.5429 59.5429c -0.0000,32.8847 26.6583,59.5429 59.5429 59.5429c 32.8847,0.0000 59.5429,-26.6583 59.5429 -59.5429Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.7369573772655632" fill="rgb(255,165,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 87.1052,151.2138 c 0.0000,-21.9231 -17.7722,-39.6953 -39.6953 -39.6953c -21.9231,-0.0000 -39.6953,17.7722 -39.6953 39.6953c -0.0000,21.9231 17.7722,39.6953 39.6953 39.6953c 21.9231,0.0000 39.6953,-17.7722 39.6953 -39.6953Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(255,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 51.0462,151.2138 c 0.0000,-2.0083 -1.6281,-3.6364 -3.6364 -3.6364c -2.0083,-0.0000 -3.6364,1.6281 -3.6364 3.6364c -0.0000,2.0083 1.6281,3.6364 3.6364 3.6364c 2.0083,0.0000 3.6364,-1.6281 3.6364 -3.6364Z"/></g></svg>
diff --git a/diagrams/src_Diagrams_Combinators_positionEx.svg b/diagrams/src_Diagrams_Combinators_positionEx.svg
--- a/diagrams/src_Diagrams_Combinators_positionEx.svg
+++ b/diagrams/src_Diagrams_Combinators_positionEx.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="204.25531914893568" height="300.0" font-size="1" viewBox="0 0 204 300" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="0.9901643964084406" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 204.25531914893565,6.3829787234042215 c 0.0,-3.525221807430585 -2.857756915973649,-6.382978723404235 -6.382978723404233 -6.382978723404235c -3.525221807430585,-2.1585758013771565e-16 -6.382978723404235,2.8577569159736487 -6.382978723404235 6.382978723404233c -4.317151602754313e-16,3.525221807430585 2.8577569159736482,6.382978723404235 6.382978723404232 6.382978723404235c 3.525221807430585,6.47572740413147e-16 6.382978723404235,-2.857756915973648 6.382978723404236 -6.382978723404233Z" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 197.87234042553143,43.40425531914886 c 0.0,-3.525221807430585 -2.857756915973649,-6.382978723404235 -6.382978723404233 -6.382978723404235c -3.525221807430585,-2.1585758013771565e-16 -6.382978723404235,2.8577569159736487 -6.382978723404235 6.382978723404233c -4.317151602754313e-16,3.525221807430585 2.8577569159736482,6.382978723404235 6.382978723404232 6.382978723404235c 3.525221807430585,6.47572740413147e-16 6.382978723404235,-2.857756915973648 6.382978723404236 -6.382978723404233Z" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 191.48936170212718,77.87234042553186 c 0.0,-3.525221807430585 -2.857756915973649,-6.382978723404235 -6.382978723404233 -6.382978723404235c -3.525221807430585,-2.1585758013771565e-16 -6.382978723404235,2.8577569159736487 -6.382978723404235 6.382978723404233c -4.317151602754313e-16,3.525221807430585 2.8577569159736482,6.382978723404235 6.382978723404232 6.382978723404235c 3.525221807430585,6.47572740413147e-16 6.382978723404235,-2.857756915973648 6.382978723404236 -6.382978723404233Z" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 185.10638297872293,109.78723404255311 c 0.0,-3.525221807430585 -2.857756915973649,-6.382978723404235 -6.382978723404233 -6.382978723404235c -3.525221807430585,-2.1585758013771565e-16 -6.382978723404235,2.8577569159736487 -6.382978723404235 6.382978723404233c -4.317151602754313e-16,3.525221807430585 2.8577569159736482,6.382978723404235 6.382978723404232 6.382978723404235c 3.525221807430585,6.47572740413147e-16 6.382978723404235,-2.857756915973648 6.382978723404236 -6.382978723404233Z" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 178.7234042553187,139.14893617021266 c 0.0,-3.525221807430585 -2.857756915973649,-6.382978723404235 -6.382978723404233 -6.382978723404235c -3.525221807430585,-2.1585758013771565e-16 -6.382978723404235,2.8577569159736487 -6.382978723404235 6.382978723404233c -4.317151602754313e-16,3.525221807430585 2.8577569159736482,6.382978723404235 6.382978723404232 6.382978723404235c 3.525221807430585,6.47572740413147e-16 6.382978723404235,-2.857756915973648 6.382978723404236 -6.382978723404233Z" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 172.34042553191446,165.95744680851053 c 0.0,-3.525221807430585 -2.857756915973649,-6.382978723404235 -6.382978723404233 -6.382978723404235c -3.525221807430585,-2.1585758013771565e-16 -6.382978723404235,2.8577569159736487 -6.382978723404235 6.382978723404233c -4.317151602754313e-16,3.525221807430585 2.8577569159736482,6.382978723404235 6.382978723404232 6.382978723404235c 3.525221807430585,6.47572740413147e-16 6.382978723404235,-2.857756915973648 6.382978723404236 -6.382978723404233Z" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 165.9574468085102,190.2127659574467 c 0.0,-3.525221807430585 -2.857756915973649,-6.382978723404235 -6.382978723404233 -6.382978723404235c -3.525221807430585,-2.1585758013771565e-16 -6.382978723404235,2.8577569159736487 -6.382978723404235 6.382978723404233c -4.317151602754313e-16,3.525221807430585 2.8577569159736482,6.382978723404235 6.382978723404232 6.382978723404235c 3.525221807430585,6.47572740413147e-16 6.382978723404235,-2.857756915973648 6.382978723404236 -6.382978723404233Z" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 159.574468085106,211.91489361702116 c 0.0,-3.525221807430585 -2.857756915973649,-6.382978723404235 -6.382978723404233 -6.382978723404235c -3.525221807430585,-2.1585758013771565e-16 -6.382978723404235,2.8577569159736487 -6.382978723404235 6.382978723404233c -4.317151602754313e-16,3.525221807430585 2.8577569159736482,6.382978723404235 6.382978723404232 6.382978723404235c 3.525221807430585,6.47572740413147e-16 6.382978723404235,-2.857756915973648 6.382978723404236 -6.382978723404233Z" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 153.19148936170174,231.06382978723394 c 0.0,-3.525221807430585 -2.857756915973649,-6.382978723404235 -6.382978723404233 -6.382978723404235c -3.525221807430585,-2.1585758013771565e-16 -6.382978723404235,2.8577569159736487 -6.382978723404235 6.382978723404233c -4.317151602754313e-16,3.525221807430585 2.8577569159736482,6.382978723404235 6.382978723404232 6.382978723404235c 3.525221807430585,6.47572740413147e-16 6.382978723404235,-2.857756915973648 6.382978723404236 -6.382978723404233Z" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 146.8085106382975,247.659574468085 c 0.0,-3.525221807430585 -2.857756915973649,-6.382978723404235 -6.382978723404233 -6.382978723404235c -3.525221807430585,-2.1585758013771565e-16 -6.382978723404235,2.8577569159736487 -6.382978723404235 6.382978723404233c -4.317151602754313e-16,3.525221807430585 2.8577569159736482,6.382978723404235 6.382978723404232 6.382978723404235c 3.525221807430585,6.47572740413147e-16 6.382978723404235,-2.857756915973648 6.382978723404236 -6.382978723404233Z" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 140.42553191489327,261.7021276595744 c 0.0,-3.525221807430585 -2.857756915973649,-6.382978723404235 -6.382978723404233 -6.382978723404235c -3.525221807430585,-2.1585758013771565e-16 -6.382978723404235,2.8577569159736487 -6.382978723404235 6.382978723404233c -4.317151602754313e-16,3.525221807430585 2.8577569159736482,6.382978723404235 6.382978723404232 6.382978723404235c 3.525221807430585,6.47572740413147e-16 6.382978723404235,-2.857756915973648 6.382978723404236 -6.382978723404233Z" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 134.04255319148902,273.19148936170205 c 0.0,-3.525221807430585 -2.857756915973649,-6.382978723404235 -6.382978723404233 -6.382978723404235c -3.525221807430585,-2.1585758013771565e-16 -6.382978723404235,2.8577569159736487 -6.382978723404235 6.382978723404233c -4.317151602754313e-16,3.525221807430585 2.8577569159736482,6.382978723404235 6.382978723404232 6.382978723404235c 3.525221807430585,6.47572740413147e-16 6.382978723404235,-2.857756915973648 6.382978723404236 -6.382978723404233Z" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 127.6595744680848,282.12765957446805 c 0.0,-3.525221807430585 -2.857756915973649,-6.382978723404235 -6.382978723404233 -6.382978723404235c -3.525221807430585,-2.1585758013771565e-16 -6.382978723404235,2.8577569159736487 -6.382978723404235 6.382978723404233c -4.317151602754313e-16,3.525221807430585 2.8577569159736482,6.382978723404235 6.382978723404232 6.382978723404235c 3.525221807430585,6.47572740413147e-16 6.382978723404235,-2.857756915973648 6.382978723404236 -6.382978723404233Z" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 121.27659574468056,288.51063829787233 c 0.0,-3.525221807430585 -2.857756915973649,-6.382978723404235 -6.382978723404233 -6.382978723404235c -3.525221807430585,-2.1585758013771565e-16 -6.382978723404235,2.8577569159736487 -6.382978723404235 6.382978723404233c -4.317151602754313e-16,3.525221807430585 2.8577569159736482,6.382978723404235 6.382978723404232 6.382978723404235c 3.525221807430585,6.47572740413147e-16 6.382978723404235,-2.857756915973648 6.382978723404236 -6.382978723404233Z" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 114.89361702127631,292.3404255319149 c 0.0,-3.525221807430585 -2.857756915973649,-6.382978723404235 -6.382978723404233 -6.382978723404235c -3.525221807430585,-2.1585758013771565e-16 -6.382978723404235,2.8577569159736487 -6.382978723404235 6.382978723404233c -4.317151602754313e-16,3.525221807430585 2.8577569159736482,6.382978723404235 6.382978723404232 6.382978723404235c 3.525221807430585,6.47572740413147e-16 6.382978723404235,-2.857756915973648 6.382978723404236 -6.382978723404233Z" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 108.51063829787208,293.6170212765958 c 0.0,-3.525221807430585 -2.857756915973649,-6.382978723404235 -6.382978723404233 -6.382978723404235c -3.525221807430585,-2.1585758013771565e-16 -6.382978723404235,2.8577569159736487 -6.382978723404235 6.382978723404233c -4.317151602754313e-16,3.525221807430585 2.8577569159736482,6.382978723404235 6.382978723404232 6.382978723404235c 3.525221807430585,6.47572740413147e-16 6.382978723404235,-2.857756915973648 6.382978723404236 -6.382978723404233Z" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 102.12765957446784,292.34042553191495 c 0.0,-3.525221807430585 -2.857756915973649,-6.382978723404235 -6.382978723404233 -6.382978723404235c -3.525221807430585,-2.1585758013771565e-16 -6.382978723404235,2.8577569159736487 -6.382978723404235 6.382978723404233c -4.317151602754313e-16,3.525221807430585 2.8577569159736482,6.382978723404235 6.382978723404232 6.382978723404235c 3.525221807430585,6.47572740413147e-16 6.382978723404235,-2.857756915973648 6.382978723404236 -6.382978723404233Z" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 95.74468085106359,288.51063829787245 c 0.0,-3.525221807430585 -2.857756915973649,-6.382978723404235 -6.382978723404233 -6.382978723404235c -3.525221807430585,-2.1585758013771565e-16 -6.382978723404235,2.8577569159736487 -6.382978723404235 6.382978723404233c -4.317151602754313e-16,3.525221807430585 2.8577569159736482,6.382978723404235 6.382978723404232 6.382978723404235c 3.525221807430585,6.47572740413147e-16 6.382978723404235,-2.857756915973648 6.382978723404236 -6.382978723404233Z" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 89.36170212765936,282.1276595744682 c 0.0,-3.525221807430585 -2.857756915973649,-6.382978723404235 -6.382978723404233 -6.382978723404235c -3.525221807430585,-2.1585758013771565e-16 -6.382978723404235,2.8577569159736487 -6.382978723404235 6.382978723404233c -4.317151602754313e-16,3.525221807430585 2.8577569159736482,6.382978723404235 6.382978723404232 6.382978723404235c 3.525221807430585,6.47572740413147e-16 6.382978723404235,-2.857756915973648 6.382978723404236 -6.382978723404233Z" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 82.97872340425512,273.19148936170234 c 0.0,-3.525221807430585 -2.857756915973649,-6.382978723404235 -6.382978723404233 -6.382978723404235c -3.525221807430585,-2.1585758013771565e-16 -6.382978723404235,2.8577569159736487 -6.382978723404235 6.382978723404233c -4.317151602754313e-16,3.525221807430585 2.8577569159736482,6.382978723404235 6.382978723404232 6.382978723404235c 3.525221807430585,6.47572740413147e-16 6.382978723404235,-2.857756915973648 6.382978723404236 -6.382978723404233Z" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 76.59574468085087,261.7021276595747 c 0.0,-3.525221807430585 -2.857756915973649,-6.382978723404235 -6.382978723404233 -6.382978723404235c -3.525221807430585,-2.1585758013771565e-16 -6.382978723404235,2.8577569159736487 -6.382978723404235 6.382978723404233c -4.317151602754313e-16,3.525221807430585 2.8577569159736482,6.382978723404235 6.382978723404232 6.382978723404235c 3.525221807430585,6.47572740413147e-16 6.382978723404235,-2.857756915973648 6.382978723404236 -6.382978723404233Z" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 70.21276595744663,247.65957446808542 c 0.0,-3.525221807430585 -2.857756915973649,-6.382978723404235 -6.382978723404233 -6.382978723404235c -3.525221807430585,-2.1585758013771565e-16 -6.382978723404235,2.8577569159736487 -6.382978723404235 6.382978723404233c -4.317151602754313e-16,3.525221807430585 2.8577569159736482,6.382978723404235 6.382978723404232 6.382978723404235c 3.525221807430585,6.47572740413147e-16 6.382978723404235,-2.857756915973648 6.382978723404236 -6.382978723404233Z" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 63.8297872340424,231.0638297872344 c 0.0,-3.525221807430585 -2.857756915973649,-6.382978723404235 -6.382978723404233 -6.382978723404235c -3.525221807430585,-2.1585758013771565e-16 -6.382978723404235,2.8577569159736487 -6.382978723404235 6.382978723404233c -4.317151602754313e-16,3.525221807430585 2.8577569159736482,6.382978723404235 6.382978723404232 6.382978723404235c 3.525221807430585,6.47572740413147e-16 6.382978723404235,-2.857756915973648 6.382978723404236 -6.382978723404233Z" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 57.44680851063816,211.9148936170217 c 0.0,-3.525221807430585 -2.857756915973649,-6.382978723404235 -6.382978723404233 -6.382978723404235c -3.525221807430585,-2.1585758013771565e-16 -6.382978723404235,2.8577569159736487 -6.382978723404235 6.382978723404233c -4.317151602754313e-16,3.525221807430585 2.8577569159736482,6.382978723404235 6.382978723404232 6.382978723404235c 3.525221807430585,6.47572740413147e-16 6.382978723404235,-2.857756915973648 6.382978723404236 -6.382978723404233Z" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 51.06382978723392,190.2127659574473 c 0.0,-3.525221807430585 -2.857756915973649,-6.382978723404235 -6.382978723404233 -6.382978723404235c -3.525221807430585,-2.1585758013771565e-16 -6.382978723404235,2.8577569159736487 -6.382978723404235 6.382978723404233c -4.317151602754313e-16,3.525221807430585 2.8577569159736482,6.382978723404235 6.382978723404232 6.382978723404235c 3.525221807430585,6.47572740413147e-16 6.382978723404235,-2.857756915973648 6.382978723404236 -6.382978723404233Z" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 44.68085106382968,165.9574468085112 c 0.0,-3.525221807430585 -2.857756915973649,-6.382978723404235 -6.382978723404233 -6.382978723404235c -3.525221807430585,-2.1585758013771565e-16 -6.382978723404235,2.8577569159736487 -6.382978723404235 6.382978723404233c -4.317151602754313e-16,3.525221807430585 2.8577569159736482,6.382978723404235 6.382978723404232 6.382978723404235c 3.525221807430585,6.47572740413147e-16 6.382978723404235,-2.857756915973648 6.382978723404236 -6.382978723404233Z" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 38.29787234042544,139.1489361702134 c 0.0,-3.525221807430585 -2.857756915973649,-6.382978723404235 -6.382978723404233 -6.382978723404235c -3.525221807430585,-2.1585758013771565e-16 -6.382978723404235,2.8577569159736487 -6.382978723404235 6.382978723404233c -4.317151602754313e-16,3.525221807430585 2.8577569159736482,6.382978723404235 6.382978723404232 6.382978723404235c 3.525221807430585,6.47572740413147e-16 6.382978723404235,-2.857756915973648 6.382978723404236 -6.382978723404233Z" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 31.914893617021193,109.78723404255393 c 0.0,-3.525221807430585 -2.857756915973649,-6.382978723404235 -6.382978723404233 -6.382978723404235c -3.525221807430585,-2.1585758013771565e-16 -6.382978723404235,2.8577569159736487 -6.382978723404235 6.382978723404233c -4.317151602754313e-16,3.525221807430585 2.8577569159736482,6.382978723404235 6.382978723404232 6.382978723404235c 3.525221807430585,6.47572740413147e-16 6.382978723404235,-2.857756915973648 6.382978723404236 -6.382978723404233Z" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 25.531914893616957,77.87234042553271 c 0.0,-3.525221807430585 -2.857756915973649,-6.382978723404235 -6.382978723404233 -6.382978723404235c -3.525221807430585,-2.1585758013771565e-16 -6.382978723404235,2.8577569159736487 -6.382978723404235 6.382978723404233c -4.317151602754313e-16,3.525221807430585 2.8577569159736482,6.382978723404235 6.382978723404232 6.382978723404235c 3.525221807430585,6.47572740413147e-16 6.382978723404235,-2.857756915973648 6.382978723404236 -6.382978723404233Z" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 19.14893617021272,43.404255319149826 c 0.0,-3.525221807430585 -2.857756915973649,-6.382978723404235 -6.382978723404233 -6.382978723404235c -3.525221807430585,-2.1585758013771565e-16 -6.382978723404235,2.8577569159736487 -6.382978723404235 6.382978723404233c -4.317151602754313e-16,3.525221807430585 2.8577569159736482,6.382978723404235 6.382978723404232 6.382978723404235c 3.525221807430585,6.47572740413147e-16 6.382978723404235,-2.857756915973648 6.382978723404236 -6.382978723404233Z" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 12.765957446808471,6.382978723405245 c 0.0,-3.525221807430585 -2.857756915973649,-6.382978723404235 -6.382978723404233 -6.382978723404235c -3.525221807430585,-2.1585758013771565e-16 -6.382978723404235,2.8577569159736487 -6.382978723404235 6.382978723404233c -4.317151602754313e-16,3.525221807430585 2.8577569159736482,6.382978723404235 6.382978723404232 6.382978723404235c 3.525221807430585,6.47572740413147e-16 6.382978723404235,-2.857756915973648 6.382978723404236 -6.382978723404233Z" /></g></g></g></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="300.0000" stroke-opacity="1" viewBox="0 0 204 300" font-size="1" width="204.2553" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.9901643964084406" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 204.2553,6.3830 c 0.0000,-3.5252 -2.8578,-6.3830 -6.3830 -6.3830c -3.5252,-0.0000 -6.3830,2.8578 -6.3830 6.3830c -0.0000,3.5252 2.8578,6.3830 6.3830 6.3830c 3.5252,0.0000 6.3830,-2.8578 6.3830 -6.3830Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.9901643964084406" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 197.8723,43.4043 c 0.0000,-3.5252 -2.8578,-6.3830 -6.3830 -6.3830c -3.5252,-0.0000 -6.3830,2.8578 -6.3830 6.3830c -0.0000,3.5252 2.8578,6.3830 6.3830 6.3830c 3.5252,0.0000 6.3830,-2.8578 6.3830 -6.3830Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.9901643964084406" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 191.4894,77.8723 c 0.0000,-3.5252 -2.8578,-6.3830 -6.3830 -6.3830c -3.5252,-0.0000 -6.3830,2.8578 -6.3830 6.3830c -0.0000,3.5252 2.8578,6.3830 6.3830 6.3830c 3.5252,0.0000 6.3830,-2.8578 6.3830 -6.3830Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.9901643964084406" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 185.1064,109.7872 c 0.0000,-3.5252 -2.8578,-6.3830 -6.3830 -6.3830c -3.5252,-0.0000 -6.3830,2.8578 -6.3830 6.3830c -0.0000,3.5252 2.8578,6.3830 6.3830 6.3830c 3.5252,0.0000 6.3830,-2.8578 6.3830 -6.3830Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.9901643964084406" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 178.7234,139.1489 c 0.0000,-3.5252 -2.8578,-6.3830 -6.3830 -6.3830c -3.5252,-0.0000 -6.3830,2.8578 -6.3830 6.3830c -0.0000,3.5252 2.8578,6.3830 6.3830 6.3830c 3.5252,0.0000 6.3830,-2.8578 6.3830 -6.3830Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.9901643964084406" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 172.3404,165.9574 c 0.0000,-3.5252 -2.8578,-6.3830 -6.3830 -6.3830c -3.5252,-0.0000 -6.3830,2.8578 -6.3830 6.3830c -0.0000,3.5252 2.8578,6.3830 6.3830 6.3830c 3.5252,0.0000 6.3830,-2.8578 6.3830 -6.3830Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.9901643964084406" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 165.9574,190.2128 c 0.0000,-3.5252 -2.8578,-6.3830 -6.3830 -6.3830c -3.5252,-0.0000 -6.3830,2.8578 -6.3830 6.3830c -0.0000,3.5252 2.8578,6.3830 6.3830 6.3830c 3.5252,0.0000 6.3830,-2.8578 6.3830 -6.3830Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.9901643964084406" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 159.5745,211.9149 c 0.0000,-3.5252 -2.8578,-6.3830 -6.3830 -6.3830c -3.5252,-0.0000 -6.3830,2.8578 -6.3830 6.3830c -0.0000,3.5252 2.8578,6.3830 6.3830 6.3830c 3.5252,0.0000 6.3830,-2.8578 6.3830 -6.3830Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.9901643964084406" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 153.1915,231.0638 c 0.0000,-3.5252 -2.8578,-6.3830 -6.3830 -6.3830c -3.5252,-0.0000 -6.3830,2.8578 -6.3830 6.3830c -0.0000,3.5252 2.8578,6.3830 6.3830 6.3830c 3.5252,0.0000 6.3830,-2.8578 6.3830 -6.3830Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.9901643964084406" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 146.8085,247.6596 c 0.0000,-3.5252 -2.8578,-6.3830 -6.3830 -6.3830c -3.5252,-0.0000 -6.3830,2.8578 -6.3830 6.3830c -0.0000,3.5252 2.8578,6.3830 6.3830 6.3830c 3.5252,0.0000 6.3830,-2.8578 6.3830 -6.3830Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.9901643964084406" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 140.4255,261.7021 c 0.0000,-3.5252 -2.8578,-6.3830 -6.3830 -6.3830c -3.5252,-0.0000 -6.3830,2.8578 -6.3830 6.3830c -0.0000,3.5252 2.8578,6.3830 6.3830 6.3830c 3.5252,0.0000 6.3830,-2.8578 6.3830 -6.3830Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.9901643964084406" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 134.0426,273.1915 c 0.0000,-3.5252 -2.8578,-6.3830 -6.3830 -6.3830c -3.5252,-0.0000 -6.3830,2.8578 -6.3830 6.3830c -0.0000,3.5252 2.8578,6.3830 6.3830 6.3830c 3.5252,0.0000 6.3830,-2.8578 6.3830 -6.3830Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.9901643964084406" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 127.6596,282.1277 c 0.0000,-3.5252 -2.8578,-6.3830 -6.3830 -6.3830c -3.5252,-0.0000 -6.3830,2.8578 -6.3830 6.3830c -0.0000,3.5252 2.8578,6.3830 6.3830 6.3830c 3.5252,0.0000 6.3830,-2.8578 6.3830 -6.3830Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.9901643964084406" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 121.2766,288.5106 c 0.0000,-3.5252 -2.8578,-6.3830 -6.3830 -6.3830c -3.5252,-0.0000 -6.3830,2.8578 -6.3830 6.3830c -0.0000,3.5252 2.8578,6.3830 6.3830 6.3830c 3.5252,0.0000 6.3830,-2.8578 6.3830 -6.3830Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.9901643964084406" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 114.8936,292.3404 c 0.0000,-3.5252 -2.8578,-6.3830 -6.3830 -6.3830c -3.5252,-0.0000 -6.3830,2.8578 -6.3830 6.3830c -0.0000,3.5252 2.8578,6.3830 6.3830 6.3830c 3.5252,0.0000 6.3830,-2.8578 6.3830 -6.3830Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.9901643964084406" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 108.5106,293.6170 c 0.0000,-3.5252 -2.8578,-6.3830 -6.3830 -6.3830c -3.5252,-0.0000 -6.3830,2.8578 -6.3830 6.3830c -0.0000,3.5252 2.8578,6.3830 6.3830 6.3830c 3.5252,0.0000 6.3830,-2.8578 6.3830 -6.3830Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.9901643964084406" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 102.1277,292.3404 c 0.0000,-3.5252 -2.8578,-6.3830 -6.3830 -6.3830c -3.5252,-0.0000 -6.3830,2.8578 -6.3830 6.3830c -0.0000,3.5252 2.8578,6.3830 6.3830 6.3830c 3.5252,0.0000 6.3830,-2.8578 6.3830 -6.3830Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.9901643964084406" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 95.7447,288.5106 c 0.0000,-3.5252 -2.8578,-6.3830 -6.3830 -6.3830c -3.5252,-0.0000 -6.3830,2.8578 -6.3830 6.3830c -0.0000,3.5252 2.8578,6.3830 6.3830 6.3830c 3.5252,0.0000 6.3830,-2.8578 6.3830 -6.3830Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.9901643964084406" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 89.3617,282.1277 c 0.0000,-3.5252 -2.8578,-6.3830 -6.3830 -6.3830c -3.5252,-0.0000 -6.3830,2.8578 -6.3830 6.3830c -0.0000,3.5252 2.8578,6.3830 6.3830 6.3830c 3.5252,0.0000 6.3830,-2.8578 6.3830 -6.3830Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.9901643964084406" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 82.9787,273.1915 c 0.0000,-3.5252 -2.8578,-6.3830 -6.3830 -6.3830c -3.5252,-0.0000 -6.3830,2.8578 -6.3830 6.3830c -0.0000,3.5252 2.8578,6.3830 6.3830 6.3830c 3.5252,0.0000 6.3830,-2.8578 6.3830 -6.3830Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.9901643964084406" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 76.5957,261.7021 c 0.0000,-3.5252 -2.8578,-6.3830 -6.3830 -6.3830c -3.5252,-0.0000 -6.3830,2.8578 -6.3830 6.3830c -0.0000,3.5252 2.8578,6.3830 6.3830 6.3830c 3.5252,0.0000 6.3830,-2.8578 6.3830 -6.3830Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.9901643964084406" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 70.2128,247.6596 c 0.0000,-3.5252 -2.8578,-6.3830 -6.3830 -6.3830c -3.5252,-0.0000 -6.3830,2.8578 -6.3830 6.3830c -0.0000,3.5252 2.8578,6.3830 6.3830 6.3830c 3.5252,0.0000 6.3830,-2.8578 6.3830 -6.3830Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.9901643964084406" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 63.8298,231.0638 c 0.0000,-3.5252 -2.8578,-6.3830 -6.3830 -6.3830c -3.5252,-0.0000 -6.3830,2.8578 -6.3830 6.3830c -0.0000,3.5252 2.8578,6.3830 6.3830 6.3830c 3.5252,0.0000 6.3830,-2.8578 6.3830 -6.3830Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.9901643964084406" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 57.4468,211.9149 c 0.0000,-3.5252 -2.8578,-6.3830 -6.3830 -6.3830c -3.5252,-0.0000 -6.3830,2.8578 -6.3830 6.3830c -0.0000,3.5252 2.8578,6.3830 6.3830 6.3830c 3.5252,0.0000 6.3830,-2.8578 6.3830 -6.3830Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.9901643964084406" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 51.0638,190.2128 c 0.0000,-3.5252 -2.8578,-6.3830 -6.3830 -6.3830c -3.5252,-0.0000 -6.3830,2.8578 -6.3830 6.3830c -0.0000,3.5252 2.8578,6.3830 6.3830 6.3830c 3.5252,0.0000 6.3830,-2.8578 6.3830 -6.3830Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.9901643964084406" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 44.6809,165.9574 c 0.0000,-3.5252 -2.8578,-6.3830 -6.3830 -6.3830c -3.5252,-0.0000 -6.3830,2.8578 -6.3830 6.3830c -0.0000,3.5252 2.8578,6.3830 6.3830 6.3830c 3.5252,0.0000 6.3830,-2.8578 6.3830 -6.3830Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.9901643964084406" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 38.2979,139.1489 c 0.0000,-3.5252 -2.8578,-6.3830 -6.3830 -6.3830c -3.5252,-0.0000 -6.3830,2.8578 -6.3830 6.3830c -0.0000,3.5252 2.8578,6.3830 6.3830 6.3830c 3.5252,0.0000 6.3830,-2.8578 6.3830 -6.3830Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.9901643964084406" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 31.9149,109.7872 c 0.0000,-3.5252 -2.8578,-6.3830 -6.3830 -6.3830c -3.5252,-0.0000 -6.3830,2.8578 -6.3830 6.3830c -0.0000,3.5252 2.8578,6.3830 6.3830 6.3830c 3.5252,0.0000 6.3830,-2.8578 6.3830 -6.3830Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.9901643964084406" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 25.5319,77.8723 c 0.0000,-3.5252 -2.8578,-6.3830 -6.3830 -6.3830c -3.5252,-0.0000 -6.3830,2.8578 -6.3830 6.3830c -0.0000,3.5252 2.8578,6.3830 6.3830 6.3830c 3.5252,0.0000 6.3830,-2.8578 6.3830 -6.3830Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.9901643964084406" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 19.1489,43.4043 c 0.0000,-3.5252 -2.8578,-6.3830 -6.3830 -6.3830c -3.5252,-0.0000 -6.3830,2.8578 -6.3830 6.3830c -0.0000,3.5252 2.8578,6.3830 6.3830 6.3830c 3.5252,0.0000 6.3830,-2.8578 6.3830 -6.3830Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.9901643964084406" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 12.7660,6.3830 c 0.0000,-3.5252 -2.8578,-6.3830 -6.3830 -6.3830c -3.5252,-0.0000 -6.3830,2.8578 -6.3830 6.3830c -0.0000,3.5252 2.8578,6.3830 6.3830 6.3830c 3.5252,0.0000 6.3830,-2.8578 6.3830 -6.3830Z"/></g></svg>
diff --git a/diagrams/src_Diagrams_Combinators_strutEx.svg b/diagrams/src_Diagrams_Combinators_strutEx.svg
--- a/diagrams/src_Diagrams_Combinators_strutEx.svg
+++ b/diagrams/src_Diagrams_Combinators_strutEx.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="300.0" height="119.99999999999999" font-size="1" viewBox="0 0 300 120" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="0.758946638440411" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><g><g><path d="M 286.3636363636364,60.0 c 0.0,-30.12462271804328 -24.42083182741126,-54.54545454545455 -54.54545454545453 -54.54545454545455c -30.12462271804328,-1.844601139358667e-15 -54.54545454545455,24.42083182741126 -54.54545454545455 54.545454545454525c -3.689202278717334e-15,30.12462271804328 24.420831827411256,54.54545454545455 54.545454545454525 54.54545454545455c 30.12462271804328,5.533803418076001e-15 54.54545454545455,-24.420831827411252 54.545454545454554 -54.545454545454525Z" /></g><g></g><g><path d="M 122.72727272727272,60.0 c 0.0,-30.12462271804328 -24.42083182741126,-54.54545454545455 -54.54545454545453 -54.54545454545455c -30.12462271804328,-1.844601139358667e-15 -54.54545454545455,24.42083182741126 -54.54545454545455 54.545454545454525c -3.689202278717334e-15,30.12462271804328 24.420831827411256,54.54545454545455 54.545454545454525 54.54545454545455c 30.12462271804328,5.533803418076001e-15 54.54545454545455,-24.420831827411252 54.545454545454554 -54.545454545454525Z" /></g></g></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="120.0000" stroke-opacity="1" viewBox="0 0 300 120" font-size="1" width="300.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.758946638440411" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 286.3636,60.0000 c 0.0000,-30.1246 -24.4208,-54.5455 -54.5455 -54.5455c -30.1246,-0.0000 -54.5455,24.4208 -54.5455 54.5455c -0.0000,30.1246 24.4208,54.5455 54.5455 54.5455c 30.1246,0.0000 54.5455,-24.4208 54.5455 -54.5455Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.758946638440411" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 122.7273,60.0000 c 0.0000,-30.1246 -24.4208,-54.5455 -54.5455 -54.5455c -30.1246,-0.0000 -54.5455,24.4208 -54.5455 54.5455c -0.0000,30.1246 24.4208,54.5455 54.5455 54.5455c 30.1246,0.0000 54.5455,-24.4208 54.5455 -54.5455Z"/></g></svg>
diff --git a/diagrams/src_Diagrams_Combinators_withEnvelopeEx.svg b/diagrams/src_Diagrams_Combinators_withEnvelopeEx.svg
--- a/diagrams/src_Diagrams_Combinators_withEnvelopeEx.svg
+++ b/diagrams/src_Diagrams_Combinators_withEnvelopeEx.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="300.0" height="166.66666666666669" font-size="1" viewBox="0 0 300 167" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="0.894427190999916" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><g><g><g fill="rgb(0,0,255)" fill-opacity="1.0"><g fill="rgb(0,0,255)" fill-opacity="1.0"><g fill="rgb(0,0,255)" fill-opacity="1.0"><g fill="rgb(0,0,255)" fill-opacity="1.0"></g><g fill="rgb(0,0,255)" fill-opacity="1.0"><g fill="rgb(0,0,255)" fill-opacity="1.0"></g><g fill="rgb(0,0,255)" fill-opacity="1.0"><g fill="rgb(0,0,255)" fill-opacity="1.0"><path d="M 261.11111111111114,138.8888888888889 l -1.2335811384723963e-14,-111.11111111111113 h -111.11111111111113 l -1.2335811384723963e-14,111.11111111111113 Z" /></g><g fill="rgb(0,0,255)" fill-opacity="1.0"></g></g></g></g></g></g><g stroke="rgb(255,255,255)" stroke-opacity="1.0" stroke-dasharray="5.555555555555557,5.555555555555557" stroke-dashoffset="0.0"><path d="M 250.0,83.33333333333334 c 0.0,-24.545988881368604 -19.898455563075846,-44.44444444444446 -44.44444444444445 -44.44444444444446c -24.545988881368604,-1.503008335773729e-15 -44.44444444444446,19.898455563075846 -44.44444444444446 44.44444444444444c -3.006016671547458e-15,24.545988881368604 19.898455563075842,44.44444444444446 44.444444444444436 44.44444444444446c 24.545988881368604,4.509025007321188e-15 44.44444444444446,-19.89845556307584 44.44444444444448 -44.44444444444444Z" /></g></g><g fill="rgb(0,128,0)" fill-opacity="1.0"><g fill="rgb(0,128,0)" fill-opacity="1.0"><g fill="rgb(0,128,0)" fill-opacity="1.0"><path d="M 161.11111111111111,83.33333333333334 c 0.0,-30.68248610171075 -24.873069453844806,-55.555555555555564 -55.55555555555555 -55.555555555555564c -30.68248610171075,-1.878760419717161e-15 -55.555555555555564,24.873069453844803 -55.555555555555564 55.55555555555554c -3.757520839434322e-15,30.68248610171075 24.8730694538448,55.555555555555564 55.55555555555554 55.555555555555564c 30.68248610171075,5.636281259151484e-15 55.555555555555564,-24.873069453844796 55.55555555555557 -55.55555555555554Z" /></g></g></g></g></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="166.6667" stroke-opacity="1" viewBox="0 0 300 167" font-size="1" width="300.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.8944271909999159" fill="rgb(0,0,255)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 261.1111,138.8889 l -0.0000,-111.1111 h -111.1111 l -0.0000,111.1111 Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(255,255,255)" stroke-width="0.8944271909999159" fill="rgb(0,0,0)" stroke-dashoffset="0.0" stroke-linecap="butt" stroke-miterlimit="10.0" stroke-dasharray="5.555555555555557,5.555555555555557"><path d="M 250.0000,83.3333 c 0.0000,-24.5460 -19.8985,-44.4444 -44.4444 -44.4444c -24.5460,-0.0000 -44.4444,19.8985 -44.4444 44.4444c -0.0000,24.5460 19.8985,44.4444 44.4444 44.4444c 24.5460,0.0000 44.4444,-19.8985 44.4444 -44.4444Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.8944271909999159" fill="rgb(0,128,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 161.1111,83.3333 c 0.0000,-30.6825 -24.8731,-55.5556 -55.5556 -55.5556c -30.6825,-0.0000 -55.5556,24.8731 -55.5556 55.5556c -0.0000,30.6825 24.8731,55.5556 55.5556 55.5556c 30.6825,0.0000 55.5556,-24.8731 55.5556 -55.5556Z"/></g></svg>
diff --git a/diagrams/src_Diagrams_CubicSpline_Boehm_bsplineEx.svg b/diagrams/src_Diagrams_CubicSpline_Boehm_bsplineEx.svg
new file mode 100644
--- /dev/null
+++ b/diagrams/src_Diagrams_CubicSpline_Boehm_bsplineEx.svg
@@ -0,0 +1,1 @@
+<svg xmlns="http://www.w3.org/2000/svg" height="184.6154" stroke-opacity="1" viewBox="0 0 300 185" font-size="1" width="300.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.9413574486632834" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 135.5769,106.7308 c 0.0000,-0.0000 0.0000,-0.0000 9.6154 -14.4231c 9.6154,-14.4231 28.8462,-43.2692 52.8846 -33.6538c 24.0385,9.6154 52.8846,57.6923 24.0385 67.3077c -28.8462,9.6154 -115.3846,-19.2308 -139.4231 -43.2692c -24.0385,-24.0385 14.4231,-43.2692 33.6538 -52.8846c 19.2308,-9.6154 19.2308,-9.6154 19.2308 -9.6154"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,255)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 141.3462,20.1923 c 0.0000,-3.1863 -2.5830,-5.7692 -5.7692 -5.7692c -3.1863,-0.0000 -5.7692,2.5830 -5.7692 5.7692c -0.0000,3.1863 2.5830,5.7692 5.7692 5.7692c 3.1863,0.0000 5.7692,-2.5830 5.7692 -5.7692Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,255)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 25.9615,77.8846 c 0.0000,-3.1863 -2.5830,-5.7692 -5.7692 -5.7692c -3.1863,-0.0000 -5.7692,2.5830 -5.7692 5.7692c -0.0000,3.1863 2.5830,5.7692 5.7692 5.7692c 3.1863,0.0000 5.7692,-2.5830 5.7692 -5.7692Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,255)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 285.5769,164.4231 c 0.0000,-3.1863 -2.5830,-5.7692 -5.7692 -5.7692c -3.1863,-0.0000 -5.7692,2.5830 -5.7692 5.7692c -0.0000,3.1863 2.5830,5.7692 5.7692 5.7692c 3.1863,0.0000 5.7692,-2.5830 5.7692 -5.7692Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,255)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 199.0385,20.1923 c 0.0000,-3.1863 -2.5830,-5.7692 -5.7692 -5.7692c -3.1863,-0.0000 -5.7692,2.5830 -5.7692 5.7692c -0.0000,3.1863 2.5830,5.7692 5.7692 5.7692c 3.1863,0.0000 5.7692,-2.5830 5.7692 -5.7692Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,255)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 141.3462,106.7308 c 0.0000,-3.1863 -2.5830,-5.7692 -5.7692 -5.7692c -3.1863,-0.0000 -5.7692,2.5830 -5.7692 5.7692c -0.0000,3.1863 2.5830,5.7692 5.7692 5.7692c 3.1863,0.0000 5.7692,-2.5830 5.7692 -5.7692Z"/></g></svg>
diff --git a/diagrams/src_Diagrams_CubicSpline_cubicSplineEx.svg b/diagrams/src_Diagrams_CubicSpline_cubicSplineEx.svg
--- a/diagrams/src_Diagrams_CubicSpline_cubicSplineEx.svg
+++ b/diagrams/src_Diagrams_CubicSpline_cubicSplineEx.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="600.0" height="150.9864382575878" font-size="1" viewBox="0 0 600 151" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="1.2039392872038202" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><g><g><path d="M 434.12540826428113,88.50749970338121 c -6.894535367777746,-6.894535367777746 6.894535367777746,-85.03260286925885 50.559926030370136 -75.83988904555518c 43.66539066259239,9.192713823703665 117.20710125222166,105.7162089725921 75.8398890455552 126.39981507592529c -41.36721220666647,20.68360610333324 -197.64334720962873,-34.472676838888724 -227.51966713666556 -75.8398890455552c -29.876319927036917,-41.36721220666648 66.64717522185153,-68.94535367777745 101.1198520607403 -50.55992603037012c 34.47267683888874,18.385427647407315 6.894535367777746,82.73442441333296 -7.105427357601002e-14 75.83988904555521Z" /><g fill="rgb(0,0,255)" fill-opacity="1.0" stroke-width="0.0"><g fill="rgb(0,0,255)" fill-opacity="1.0"><g fill="rgb(0,0,255)" fill-opacity="1.0"><path d="M 439.18140086731813,12.667610657826017 c 0.0,-2.7923476099146396 -2.263644993122374,-5.055992603037014 -5.055992603037013 -5.055992603037014c -2.7923476099146396,-1.7098197812943627e-16 -5.055992603037014,2.2636449931223734 -5.055992603037014 5.055992603037012c -3.4196395625887253e-16,2.7923476099146396 2.2636449931223734,5.055992603037014 5.055992603037011 5.055992603037014c 2.7923476099146396,5.129459343883088e-16 5.055992603037014,-2.263644993122373 5.055992603037017 -5.055992603037012Z" /></g></g></g><g fill="rgb(0,0,255)" fill-opacity="1.0" stroke-width="0.0"><g fill="rgb(0,0,255)" fill-opacity="1.0"><g fill="rgb(0,0,255)" fill-opacity="1.0"><path d="M 338.0615488065779,63.227536688196146 c 0.0,-2.7923476099146396 -2.263644993122374,-5.055992603037014 -5.055992603037013 -5.055992603037014c -2.7923476099146396,-1.7098197812943627e-16 -5.055992603037014,2.2636449931223734 -5.055992603037014 5.055992603037012c -3.4196395625887253e-16,2.7923476099146396 2.2636449931223734,5.055992603037014 5.055992603037011 5.055992603037014c 2.7923476099146396,5.129459343883088e-16 5.055992603037014,-2.263644993122373 5.055992603037017 -5.055992603037012Z" /></g></g></g><g fill="rgb(0,0,255)" fill-opacity="1.0" stroke-width="0.0"><g fill="rgb(0,0,255)" fill-opacity="1.0"><g fill="rgb(0,0,255)" fill-opacity="1.0"><path d="M 565.5812159432435,139.06742573375135 c 0.0,-2.7923476099146396 -2.263644993122374,-5.055992603037014 -5.055992603037013 -5.055992603037014c -2.7923476099146396,-1.7098197812943627e-16 -5.055992603037014,2.2636449931223734 -5.055992603037014 5.055992603037012c -3.4196395625887253e-16,2.7923476099146396 2.2636449931223734,5.055992603037014 5.055992603037011 5.055992603037014c 2.7923476099146396,5.129459343883088e-16 5.055992603037014,-2.263644993122373 5.055992603037017 -5.055992603037012Z" /></g></g></g><g fill="rgb(0,0,255)" fill-opacity="1.0" stroke-width="0.0"><g fill="rgb(0,0,255)" fill-opacity="1.0"><g fill="rgb(0,0,255)" fill-opacity="1.0"><path d="M 489.7413268976883,12.667610657826017 c 0.0,-2.7923476099146396 -2.263644993122374,-5.055992603037014 -5.055992603037013 -5.055992603037014c -2.7923476099146396,-1.7098197812943627e-16 -5.055992603037014,2.2636449931223734 -5.055992603037014 5.055992603037012c -3.4196395625887253e-16,2.7923476099146396 2.2636449931223734,5.055992603037014 5.055992603037011 5.055992603037014c 2.7923476099146396,5.129459343883088e-16 5.055992603037014,-2.263644993122373 5.055992603037017 -5.055992603037012Z" /></g></g></g><g fill="rgb(0,0,255)" fill-opacity="1.0" stroke-width="0.0"><g fill="rgb(0,0,255)" fill-opacity="1.0"><g fill="rgb(0,0,255)" fill-opacity="1.0"><path d="M 439.18140086731813,88.50749970338121 c 0.0,-2.7923476099146396 -2.263644993122374,-5.055992603037014 -5.055992603037013 -5.055992603037014c -2.7923476099146396,-1.7098197812943627e-16 -5.055992603037014,2.2636449931223734 -5.055992603037014 5.055992603037012c -3.4196395625887253e-16,2.7923476099146396 2.2636449931223734,5.055992603037014 5.055992603037011 5.055992603037014c 2.7923476099146396,5.129459343883088e-16 5.055992603037014,-2.263644993122373 5.055992603037017 -5.055992603037012Z" /></g></g></g></g><g></g><path d="M 139.89139549241958,88.50749970338121 c 5.417134931825375,-48.3027864754429 10.83426986365075,-96.6055729508858 50.559926030370136 -75.8398890455552c 39.72565616671939,20.765683905330597 113.75983356833281,110.59983819143467 75.83988904555518 126.39981507592535c -37.9199445227776,15.799976884490668 -187.79401096994619,-42.43422363263207 -227.51966713666562 -75.83988904555518c -39.72565616671941,-33.40566541292313 30.69709794701043,-41.98279572164664 101.11985206074027 -50.559926030370136" /><g fill="rgb(0,0,255)" fill-opacity="1.0" stroke-width="0.0"><g fill="rgb(0,0,255)" fill-opacity="1.0"><g fill="rgb(0,0,255)" fill-opacity="1.0"><path d="M 144.9473880954566,12.667610657826017 c 0.0,-2.7923476099146396 -2.263644993122374,-5.055992603037014 -5.055992603037013 -5.055992603037014c -2.7923476099146396,-1.7098197812943627e-16 -5.055992603037014,2.2636449931223734 -5.055992603037014 5.055992603037012c -3.4196395625887253e-16,2.7923476099146396 2.2636449931223734,5.055992603037014 5.055992603037011 5.055992603037014c 2.7923476099146396,5.129459343883088e-16 5.055992603037014,-2.263644993122373 5.055992603037017 -5.055992603037012Z" /></g></g></g><g fill="rgb(0,0,255)" fill-opacity="1.0" stroke-width="0.0"><g fill="rgb(0,0,255)" fill-opacity="1.0"><g fill="rgb(0,0,255)" fill-opacity="1.0"><path d="M 43.82753603471632,63.227536688196146 c 0.0,-2.7923476099146396 -2.263644993122374,-5.055992603037014 -5.055992603037013 -5.055992603037014c -2.7923476099146396,-1.7098197812943627e-16 -5.055992603037014,2.2636449931223734 -5.055992603037014 5.055992603037012c -3.4196395625887253e-16,2.7923476099146396 2.2636449931223734,5.055992603037014 5.055992603037011 5.055992603037014c 2.7923476099146396,5.129459343883088e-16 5.055992603037014,-2.263644993122373 5.055992603037017 -5.055992603037012Z" /></g></g></g><g fill="rgb(0,0,255)" fill-opacity="1.0" stroke-width="0.0"><g fill="rgb(0,0,255)" fill-opacity="1.0"><g fill="rgb(0,0,255)" fill-opacity="1.0"><path d="M 271.3472031713819,139.06742573375135 c 0.0,-2.7923476099146396 -2.263644993122374,-5.055992603037014 -5.055992603037013 -5.055992603037014c -2.7923476099146396,-1.7098197812943627e-16 -5.055992603037014,2.2636449931223734 -5.055992603037014 5.055992603037012c -3.4196395625887253e-16,2.7923476099146396 2.2636449931223734,5.055992603037014 5.055992603037011 5.055992603037014c 2.7923476099146396,5.129459343883088e-16 5.055992603037014,-2.263644993122373 5.055992603037017 -5.055992603037012Z" /></g></g></g><g fill="rgb(0,0,255)" fill-opacity="1.0" stroke-width="0.0"><g fill="rgb(0,0,255)" fill-opacity="1.0"><g fill="rgb(0,0,255)" fill-opacity="1.0"><path d="M 195.50731412582675,12.667610657826017 c 0.0,-2.7923476099146396 -2.263644993122374,-5.055992603037014 -5.055992603037013 -5.055992603037014c -2.7923476099146396,-1.7098197812943627e-16 -5.055992603037014,2.2636449931223734 -5.055992603037014 5.055992603037012c -3.4196395625887253e-16,2.7923476099146396 2.2636449931223734,5.055992603037014 5.055992603037011 5.055992603037014c 2.7923476099146396,5.129459343883088e-16 5.055992603037014,-2.263644993122373 5.055992603037017 -5.055992603037012Z" /></g></g></g><g fill="rgb(0,0,255)" fill-opacity="1.0" stroke-width="0.0"><g fill="rgb(0,0,255)" fill-opacity="1.0"><g fill="rgb(0,0,255)" fill-opacity="1.0"><path d="M 144.9473880954566,88.50749970338121 c 0.0,-2.7923476099146396 -2.263644993122374,-5.055992603037014 -5.055992603037013 -5.055992603037014c -2.7923476099146396,-1.7098197812943627e-16 -5.055992603037014,2.2636449931223734 -5.055992603037014 5.055992603037012c -3.4196395625887253e-16,2.7923476099146396 2.2636449931223734,5.055992603037014 5.055992603037011 5.055992603037014c 2.7923476099146396,5.129459343883088e-16 5.055992603037014,-2.263644993122373 5.055992603037017 -5.055992603037012Z" /></g></g></g></g></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="150.9864" stroke-opacity="1" viewBox="0 0 600 151" font-size="1" width="600.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.2039392872038202" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 434.1254,88.5075 c -6.8945,-6.8945 6.8945,-85.0326 50.5599 -75.8399c 43.6654,9.1927 117.2071,105.7162 75.8399 126.3998c -41.3672,20.6836 -197.6433,-34.4727 -227.5197 -75.8399c -29.8763,-41.3672 66.6472,-68.9454 101.1199 -50.5599c 34.4727,18.3854 6.8945,82.7344 -0.0000 75.8399Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,255)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 439.1814,12.6676 c 0.0000,-2.7923 -2.2636,-5.0560 -5.0560 -5.0560c -2.7923,-0.0000 -5.0560,2.2636 -5.0560 5.0560c -0.0000,2.7923 2.2636,5.0560 5.0560 5.0560c 2.7923,0.0000 5.0560,-2.2636 5.0560 -5.0560Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,255)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 338.0615,63.2275 c 0.0000,-2.7923 -2.2636,-5.0560 -5.0560 -5.0560c -2.7923,-0.0000 -5.0560,2.2636 -5.0560 5.0560c -0.0000,2.7923 2.2636,5.0560 5.0560 5.0560c 2.7923,0.0000 5.0560,-2.2636 5.0560 -5.0560Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,255)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 565.5812,139.0674 c 0.0000,-2.7923 -2.2636,-5.0560 -5.0560 -5.0560c -2.7923,-0.0000 -5.0560,2.2636 -5.0560 5.0560c -0.0000,2.7923 2.2636,5.0560 5.0560 5.0560c 2.7923,0.0000 5.0560,-2.2636 5.0560 -5.0560Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,255)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 489.7413,12.6676 c 0.0000,-2.7923 -2.2636,-5.0560 -5.0560 -5.0560c -2.7923,-0.0000 -5.0560,2.2636 -5.0560 5.0560c -0.0000,2.7923 2.2636,5.0560 5.0560 5.0560c 2.7923,0.0000 5.0560,-2.2636 5.0560 -5.0560Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,255)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 439.1814,88.5075 c 0.0000,-2.7923 -2.2636,-5.0560 -5.0560 -5.0560c -2.7923,-0.0000 -5.0560,2.2636 -5.0560 5.0560c -0.0000,2.7923 2.2636,5.0560 5.0560 5.0560c 2.7923,0.0000 5.0560,-2.2636 5.0560 -5.0560Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.2039392872038202" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 139.8914,88.5075 c 5.4171,-48.3028 10.8343,-96.6056 50.5599 -75.8399c 39.7257,20.7657 113.7598,110.5998 75.8399 126.3998c -37.9199,15.8000 -187.7940,-42.4342 -227.5197 -75.8399c -39.7257,-33.4057 30.6971,-41.9828 101.1199 -50.5599"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,255)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 144.9474,12.6676 c 0.0000,-2.7923 -2.2636,-5.0560 -5.0560 -5.0560c -2.7923,-0.0000 -5.0560,2.2636 -5.0560 5.0560c -0.0000,2.7923 2.2636,5.0560 5.0560 5.0560c 2.7923,0.0000 5.0560,-2.2636 5.0560 -5.0560Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,255)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 43.8275,63.2275 c 0.0000,-2.7923 -2.2636,-5.0560 -5.0560 -5.0560c -2.7923,-0.0000 -5.0560,2.2636 -5.0560 5.0560c -0.0000,2.7923 2.2636,5.0560 5.0560 5.0560c 2.7923,0.0000 5.0560,-2.2636 5.0560 -5.0560Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,255)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 271.3472,139.0674 c 0.0000,-2.7923 -2.2636,-5.0560 -5.0560 -5.0560c -2.7923,-0.0000 -5.0560,2.2636 -5.0560 5.0560c -0.0000,2.7923 2.2636,5.0560 5.0560 5.0560c 2.7923,0.0000 5.0560,-2.2636 5.0560 -5.0560Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,255)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 195.5073,12.6676 c 0.0000,-2.7923 -2.2636,-5.0560 -5.0560 -5.0560c -2.7923,-0.0000 -5.0560,2.2636 -5.0560 5.0560c -0.0000,2.7923 2.2636,5.0560 5.0560 5.0560c 2.7923,0.0000 5.0560,-2.2636 5.0560 -5.0560Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,255)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 144.9474,88.5075 c 0.0000,-2.7923 -2.2636,-5.0560 -5.0560 -5.0560c -2.7923,-0.0000 -5.0560,2.2636 -5.0560 5.0560c -0.0000,2.7923 2.2636,5.0560 5.0560 5.0560c 2.7923,0.0000 5.0560,-2.2636 5.0560 -5.0560Z"/></g></svg>
diff --git a/diagrams/src_Diagrams_TrailLike_explodeTrailEx.svg b/diagrams/src_Diagrams_TrailLike_explodeTrailEx.svg
--- a/diagrams/src_Diagrams_TrailLike_explodeTrailEx.svg
+++ b/diagrams/src_Diagrams_TrailLike_explodeTrailEx.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="300.0" height="285.3169548885461" font-size="1" viewBox="0 0 300 285" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="1.1702655183611206" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><g><g stroke="rgb(0,0,255)" stroke-opacity="1.0"><path d="M 65.72263789774158,272.34800239361215 l 168.5547242045168,-1.871333357211977e-14 " /></g><g stroke="rgb(255,0,0)" stroke-opacity="1.0"><path d="M 13.636363636363626,112.04293358657401 l 52.086274261377966,160.30506880703814 " /></g><g stroke="rgb(255,255,0)" stroke-opacity="1.0"><path d="M 150.0,12.968952494933887 l -136.36363636363637,99.0739810916401 " /></g><g stroke="rgb(0,128,0)" stroke-opacity="1.0"><path d="M 286.3636363636364,112.04293358657402 l -136.36363636363635,-99.07398109164014 " /></g><g stroke="rgb(255,165,0)" stroke-opacity="1.0"><path d="M 234.2773621022584,272.34800239361215 l 52.086274261377966,-160.30506880703814 " /></g></g></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="285.3170" stroke-opacity="1" viewBox="0 0 300 285" font-size="1" width="300.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,255)" stroke-width="1.17026551836112" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 65.7226,272.3480 l 168.5547,-0.0000 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(255,0,0)" stroke-width="1.17026551836112" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 13.6364,112.0429 l 52.0863,160.3051 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(255,255,0)" stroke-width="1.17026551836112" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 150.0000,12.9690 l -136.3636,99.0740 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,128,0)" stroke-width="1.17026551836112" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 286.3636,112.0429 l -136.3636,-99.0740 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(255,165,0)" stroke-width="1.17026551836112" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 234.2774,272.3480 l 52.0863,-160.3051 "/></g></svg>
diff --git a/diagrams/src_Diagrams_TrailLike_fromOffsetsEx.svg b/diagrams/src_Diagrams_TrailLike_fromOffsetsEx.svg
--- a/diagrams/src_Diagrams_TrailLike_fromOffsetsEx.svg
+++ b/diagrams/src_Diagrams_TrailLike_fromOffsetsEx.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="300.0" height="86.60254037844385" font-size="1" viewBox="0 0 300 87" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="0.644741959094125" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><g><path d="M 13.636363636363626,82.66606127033276 h 90.9090909090909 l 45.45454545454546,-78.72958216222169 l 45.45454545454546,78.72958216222169 h 90.9090909090909 " /></g></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="86.6025" stroke-opacity="1" viewBox="0 0 300 87" font-size="1" width="300.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.644741959094125" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 13.6364,82.6661 h 90.9091 l 45.4545,-78.7296 l 45.4545,78.7296 h 90.9091 "/></g></svg>
diff --git a/diagrams/src_Diagrams_TrailLike_fromSegmentsEx.svg b/diagrams/src_Diagrams_TrailLike_fromSegmentsEx.svg
--- a/diagrams/src_Diagrams_TrailLike_fromSegmentsEx.svg
+++ b/diagrams/src_Diagrams_TrailLike_fromSegmentsEx.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="247.48737341529161" height="200.00000000000003" font-size="1" viewBox="0 0 247 200" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="0.8899211172508118" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><g><path d="M 11.249426064331445,190.90909090909093 l 128.564869306645,-128.564869306645 c 128.564869306645,-128.564869306645 128.564869306645,0.0 0.0 128.564869306645h -128.564869306645 " /></g></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="200.0000" stroke-opacity="1" viewBox="0 0 247 200" font-size="1" width="247.4874" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.8899211172508118" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 11.2494,190.9091 l 128.5649,-128.5649 c 128.5649,-128.5649 128.5649,-0.0000 0.0000 128.5649h -128.5649 "/></g></svg>
diff --git a/diagrams/src_Diagrams_TrailLike_fromVerticesEx.svg b/diagrams/src_Diagrams_TrailLike_fromVerticesEx.svg
--- a/diagrams/src_Diagrams_TrailLike_fromVerticesEx.svg
+++ b/diagrams/src_Diagrams_TrailLike_fromVerticesEx.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="300.0" height="305.0220318351292" font-size="1" viewBox="0 0 300 305" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="1.21000237719131" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><g><path d="M 198.02231959365204,226.8357137585907 l 52.57961880085914,-15.539610741748685 l 35.761697969125166,-48.197675766316436 l -52.84137502819749,-45.52029976131276 l 1.4689477105917228,-54.80819289004408 l -34.78774118767253,-48.905296788481024 l -59.62126060155821,36.18858783527575 l -51.671759188017134,-18.33371532625888 l -57.261704414941406,17.972540121134063 l 15.9934095243195,67.88607704837416 l -33.40385114728599,43.47733367835122 l -0.601938394511168,60.012937447513 l 69.50573128358397,5.767315143513668 l 31.02704382385218,45.20418527970044 l 56.88968602799999,19.11749498615032 Z" /></g></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="305.0220" stroke-opacity="1" viewBox="0 0 300 305" font-size="1" width="300.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.2100023771913093" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 198.0223,226.8357 l 52.5796,-15.5396 l 35.7617,-48.1977 l -52.8414,-45.5203 l 1.4689,-54.8082 l -34.7877,-48.9053 l -59.6213,36.1886 l -51.6718,-18.3337 l -57.2617,17.9725 l 15.9934,67.8861 l -33.4039,43.4773 l -0.6019,60.0129 l 69.5057,5.7673 l 31.0270,45.2042 l 56.8897,19.1175 Z"/></g></svg>
diff --git a/diagrams/src_Diagrams_TrailLike_twiddleEx.svg b/diagrams/src_Diagrams_TrailLike_twiddleEx.svg
--- a/diagrams/src_Diagrams_TrailLike_twiddleEx.svg
+++ b/diagrams/src_Diagrams_TrailLike_twiddleEx.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="300.0" height="259.80762113533166" font-size="1" viewBox="0 0 300 260" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="1.1167258309225196" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><g><path d="M 81.81818181818174,247.99818381099834 h 0.0 " /><path d="M 81.81818181818174,247.99818381099834 l -68.18181818181809,-118.09437324333258 " /><path d="M 81.81818181818174,247.99818381099834 l 1.3625464393126918e-13,-236.18874648666508 " /><path d="M 81.81818181818174,247.99818381099834 l 136.36363636363646,-236.188746486665 " /><path d="M 81.81818181818174,247.99818381099834 l 204.5454545454546,-118.09437324333246 " /><path d="M 81.81818181818174,247.99818381099834 l 136.3636363636364,4.5418214643756395e-14 " /><path d="M 13.636363636363654,129.90381056766577 l 68.18181818181809,118.09437324333258 " /><path d="M 13.636363636363654,129.90381056766577 h 0.0 " /><path d="M 13.636363636363654,129.90381056766577 l 68.18181818181822,-118.09437324333248 " /><path d="M 13.636363636363654,129.90381056766577 l 204.54545454545456,-118.09437324333243 " /><path d="M 13.636363636363654,129.90381056766577 l 272.7272727272727,1.2111523905001706e-13 " /><path d="M 13.636363636363654,129.90381056766577 l 204.54545454545445,118.09437324333263 " /><path d="M 81.81818181818187,11.809437324333274 l -1.3625464393126918e-13,236.18874648666508 " /><path d="M 81.81818181818187,11.809437324333274 l -68.18181818181822,118.09437324333248 " /><path d="M 81.81818181818187,11.809437324333274 h 0.0 " /><path d="M 81.81818181818187,11.809437324333274 l 136.36363636363632,6.055761952500853e-14 " /><path d="M 81.81818181818187,11.809437324333274 l 204.54545454545445,118.09437324333261 " /><path d="M 81.81818181818187,11.809437324333274 l 136.36363636363626,236.1887464866651 " /><path d="M 218.1818181818182,11.80943732433333 l -136.36363636363646,236.188746486665 " /><path d="M 218.1818181818182,11.80943732433333 l -204.54545454545456,118.09437324333243 " /><path d="M 218.1818181818182,11.80943732433333 l -136.36363636363632,-6.055761952500853e-14 " /><path d="M 218.1818181818182,11.80943732433333 h 0.0 " /><path d="M 218.1818181818182,11.80943732433333 l 68.18181818181813,118.09437324333256 " /><path d="M 218.1818181818182,11.80943732433333 l -7.569702440626067e-14,236.18874648666505 " /><path d="M 286.3636363636363,129.9038105676659 l -204.5454545454546,118.09437324333246 " /><path d="M 286.3636363636363,129.9038105676659 l -272.7272727272727,-1.2111523905001706e-13 " /><path d="M 286.3636363636363,129.9038105676659 l -204.54545454545445,-118.09437324333261 " /><path d="M 286.3636363636363,129.9038105676659 l -68.18181818181813,-118.09437324333256 " /><path d="M 286.3636363636363,129.9038105676659 h 0.0 " /><path d="M 286.3636363636363,129.9038105676659 l -68.1818181818182,118.0943732433325 " /><path d="M 218.18181818181813,247.9981838109984 l -136.3636363636364,-4.5418214643756395e-14 " /><path d="M 218.18181818181813,247.9981838109984 l -204.54545454545445,-118.09437324333263 " /><path d="M 218.18181818181813,247.9981838109984 l -136.36363636363626,-236.1887464866651 " /><path d="M 218.18181818181813,247.9981838109984 l 7.569702440626067e-14,-236.18874648666505 " /><path d="M 218.18181818181813,247.9981838109984 l 68.1818181818182,-118.0943732433325 " /><path d="M 218.18181818181813,247.9981838109984 h 0.0 " /></g></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="259.8076" stroke-opacity="1" viewBox="0 0 300 260" font-size="1" width="300.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.1167258309225196" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 81.8182,247.9982 h 0.0000 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.1167258309225196" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 81.8182,247.9982 l -68.1818,-118.0944 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.1167258309225196" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 81.8182,247.9982 l 0.0000,-236.1887 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.1167258309225196" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 81.8182,247.9982 l 136.3636,-236.1887 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.1167258309225196" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 81.8182,247.9982 l 204.5455,-118.0944 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.1167258309225196" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 81.8182,247.9982 l 136.3636,0.0000 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.1167258309225196" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 13.6364,129.9038 l 68.1818,118.0944 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.1167258309225196" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 13.6364,129.9038 h 0.0000 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.1167258309225196" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 13.6364,129.9038 l 68.1818,-118.0944 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.1167258309225196" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 13.6364,129.9038 l 204.5455,-118.0944 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.1167258309225196" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 13.6364,129.9038 l 272.7273,0.0000 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.1167258309225196" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 13.6364,129.9038 l 204.5455,118.0944 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.1167258309225196" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 81.8182,11.8094 l -0.0000,236.1887 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.1167258309225196" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 81.8182,11.8094 l -68.1818,118.0944 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.1167258309225196" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 81.8182,11.8094 h 0.0000 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.1167258309225196" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 81.8182,11.8094 l 136.3636,0.0000 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.1167258309225196" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 81.8182,11.8094 l 204.5455,118.0944 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.1167258309225196" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 81.8182,11.8094 l 136.3636,236.1887 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.1167258309225196" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 218.1818,11.8094 l -136.3636,236.1887 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.1167258309225196" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 218.1818,11.8094 l -204.5455,118.0944 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.1167258309225196" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 218.1818,11.8094 l -136.3636,-0.0000 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.1167258309225196" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 218.1818,11.8094 h 0.0000 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.1167258309225196" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 218.1818,11.8094 l 68.1818,118.0944 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.1167258309225196" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 218.1818,11.8094 l -0.0000,236.1887 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.1167258309225196" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 286.3636,129.9038 l -204.5455,118.0944 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.1167258309225196" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 286.3636,129.9038 l -272.7273,-0.0000 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.1167258309225196" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 286.3636,129.9038 l -204.5455,-118.0944 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.1167258309225196" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 286.3636,129.9038 l -68.1818,-118.0944 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.1167258309225196" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 286.3636,129.9038 h 0.0000 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.1167258309225196" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 286.3636,129.9038 l -68.1818,118.0944 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.1167258309225196" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 218.1818,247.9982 l -136.3636,-0.0000 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.1167258309225196" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 218.1818,247.9982 l -204.5455,-118.0944 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.1167258309225196" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 218.1818,247.9982 l -136.3636,-236.1887 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.1167258309225196" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 218.1818,247.9982 l 0.0000,-236.1887 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.1167258309225196" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 218.1818,247.9982 l 68.1818,-118.0944 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.1167258309225196" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 218.1818,247.9982 h 0.0000 "/></g></svg>
diff --git a/diagrams/src_Diagrams_Trail_closeLineEx.svg b/diagrams/src_Diagrams_Trail_closeLineEx.svg
--- a/diagrams/src_Diagrams_Trail_closeLineEx.svg
+++ b/diagrams/src_Diagrams_Trail_closeLineEx.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="500.0" height="68.18181818181819" font-size="1" viewBox="0 0 500 68" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="0.7385489458759964" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><g><g><path d="M 394.6280991735537,3.099173553719009 l 82.64462809917356,41.32231404958678 l -123.96694214876034,20.66115702479339 l -82.64462809917356,-41.32231404958678 l 41.32231404958678,-20.66115702479339 Z" /></g><path d="M 146.69421487603304,3.099173553719009 l 82.64462809917356,41.32231404958678 l -123.96694214876034,20.66115702479339 l -82.64462809917356,-41.32231404958678 l 41.32231404958678,-20.66115702479339 " /></g></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="68.1818" stroke-opacity="1" viewBox="0 0 500 68" font-size="1" width="500.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.7385489458759964" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 394.6281,3.0992 l 82.6446,41.3223 l -123.9669,20.6612 l -82.6446,-41.3223 l 41.3223,-20.6612 Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.7385489458759964" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 146.6942,3.0992 l 82.6446,41.3223 l -123.9669,20.6612 l -82.6446,-41.3223 l 41.3223,-20.6612 "/></g></svg>
diff --git a/diagrams/src_Diagrams_Trail_glueLineEx.svg b/diagrams/src_Diagrams_Trail_glueLineEx.svg
--- a/diagrams/src_Diagrams_Trail_glueLineEx.svg
+++ b/diagrams/src_Diagrams_Trail_glueLineEx.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="500.0" height="68.18181818181819" font-size="1" viewBox="0 0 500 68" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="0.7385489458759964" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><g><path d="M 384.297520661157,0.0 l 82.64462809917354,41.32231404958677 l -123.96694214876032,20.661157024793386 l -82.64462809917354,-41.32231404958677 Z" /></g><path d="M 136.36363636363637,0.0 l 82.64462809917354,41.32231404958677 l -123.96694214876032,20.661157024793386 l -82.64462809917354,-41.32231404958677 l 41.32231404958677,-20.661157024793386 " /></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="68.1818" stroke-opacity="1" viewBox="0 0 500 68" font-size="1" width="500.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.7385489458759964" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 384.2975,0.0000 l 82.6446,41.3223 l -123.9669,20.6612 l -82.6446,-41.3223 Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.7385489458759964" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 136.3636,0.0000 l 82.6446,41.3223 l -123.9669,20.6612 l -82.6446,-41.3223 l 41.3223,-20.6612 "/></g></svg>
diff --git a/diagrams/src_Diagrams_Trail_lineFromOffsetsEx.svg b/diagrams/src_Diagrams_Trail_lineFromOffsetsEx.svg
--- a/diagrams/src_Diagrams_Trail_lineFromOffsetsEx.svg
+++ b/diagrams/src_Diagrams_Trail_lineFromOffsetsEx.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="300.0" height="50.0" font-size="1" viewBox="0 0 300 50" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="0.5" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><path d="M 0.0,50.0 l 100.0,-50.0 l 100.0,50.0 l 100.0,-25.0 " /></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="50.0000" stroke-opacity="1" viewBox="0 0 300 50" font-size="1" width="300.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.5" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 0.0000,50.0000 l 100.0000,-50.0000 l 100.0000,50.0000 l 100.0000,-25.0000 "/></g></svg>
diff --git a/diagrams/src_Diagrams_Trail_lineFromVerticesEx.svg b/diagrams/src_Diagrams_Trail_lineFromVerticesEx.svg
--- a/diagrams/src_Diagrams_Trail_lineFromVerticesEx.svg
+++ b/diagrams/src_Diagrams_Trail_lineFromVerticesEx.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="300.0" height="120.00000000000001" font-size="1" viewBox="0 0 300 120" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="0.7589466384404111" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><g><path d="M 13.636363636363626,114.54545454545456 v -54.54545454545455 l 54.54545454545455,-54.54545454545455 l 218.1818181818182,54.54545454545455 " /></g></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="120.0000" stroke-opacity="1" viewBox="0 0 300 120" font-size="1" width="300.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.7589466384404111" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 13.6364,114.5455 v -54.5455 l 54.5455,-54.5455 l 218.1818,54.5455 "/></g></svg>
diff --git a/diagrams/src_Diagrams_Trail_trailOffsetEx.svg b/diagrams/src_Diagrams_Trail_trailOffsetEx.svg
--- a/diagrams/src_Diagrams_Trail_trailOffsetEx.svg
+++ b/diagrams/src_Diagrams_Trail_trailOffsetEx.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="300.0" height="90.00000000000001" font-size="1" viewBox="0 0 300 90" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="0.6572670690061994" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><g><g stroke="rgb(255,0,0)" stroke-opacity="1.0"><path d="M 177.27272727272728,4.090909090909101 h -109.0909090909091 " /></g><path d="M 177.27272727272728,4.090909090909101 l 109.0909090909091,54.54545454545455 l -163.63636363636363,27.272727272727273 l -109.0909090909091,-54.54545454545455 l 54.54545454545455,-27.272727272727273 " /></g></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="90.0000" stroke-opacity="1" viewBox="0 0 300 90" font-size="1" width="300.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(255,0,0)" stroke-width="0.6572670690061994" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 177.2727,4.0909 h -109.0909 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.6572670690061994" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 177.2727,4.0909 l 109.0909,54.5455 l -163.6364,27.2727 l -109.0909,-54.5455 l 54.5455,-27.2727 "/></g></svg>
diff --git a/diagrams/src_Diagrams_TwoD_Arc_annularWedgeEx.svg b/diagrams/src_Diagrams_TwoD_Arc_annularWedgeEx.svg
--- a/diagrams/src_Diagrams_TwoD_Arc_annularWedgeEx.svg
+++ b/diagrams/src_Diagrams_TwoD_Arc_annularWedgeEx.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="400.0" height="178.54130895779457" font-size="1" viewBox="0 0 400 179" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="1.0689548060277785" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><g fill="rgb(0,0,255)" fill-opacity="1.0"><g fill="rgb(0,0,255)" fill-opacity="1.0"><g fill="rgb(0,0,255)" fill-opacity="1.0"><g><g fill="rgb(0,0,255)" fill-opacity="1.0"><g fill="rgb(0,0,255)" fill-opacity="1.0"><path d="M 364.6026155171688,49.10118238914234 l 17.215566301012974,-17.21556630101297 c -31.692982425834614,-31.692982425834618 -83.0774595809185,-31.692982425834632 -114.77044200675311 -1.8020020547460663e-14c -31.692982425834618,31.692982425834614 -31.692982425834632,83.0774595809185 -2.7030030821190994e-14 114.77044200675311c 31.69298242583461,31.69298242583462 83.07745958091849,31.692982425834636 114.77044200675309 3.6040041094921325e-14l -17.215566301012966,-17.215566301012974 c -22.185087698084224,22.185087698084217 -58.154221706642936,22.18508769808421 -80.33930940472716 -2.5228028766444926e-14c -22.185087698084224,-22.185087698084224 -22.185087698084214,-58.15422170664295 1.8921021574833692e-14 -80.33930940472717c 22.185087698084224,-22.185087698084228 58.15422170664295,-22.185087698084217 80.3393094047272 1.4210854715202004e-14Z" /></g></g></g><g fill="rgb(0,0,255)" fill-opacity="1.0"><g><g fill="rgb(0,0,255)" fill-opacity="1.0"><g fill="rgb(0,0,255)" fill-opacity="1.0"><path d="M 196.76242196124196,65.05772234978109 l 5.938102119434486,-56.49726773069128 c -22.87402851921224,-2.4041572749570763 -45.693919553281,5.0104747879005584 -62.78626916472949 20.400495504601384l 38.01228629587615,42.21692087747031 c 5.127704883434549,-4.617006215010248 11.973672193655174,-6.841395833867538 18.83588074941885 -6.120148651380411Z" /></g></g></g><g fill="rgb(0,0,255)" fill-opacity="1.0"><path d="M 58.75929709319445,89.27083709150592 h 40.57747891137626 c 0.0,-44.820645578667474 -36.33431224408504,-81.15495782275252 -81.15495782275251 -81.15495782275252l -2.4846539833143083e-15,40.57747891137626 c 22.41032278933373,0.0 40.577478911376254,18.167156122042524 40.57747891137625 40.57747891137626Z" /></g></g></g></g></g></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="178.5413" stroke-opacity="1" viewBox="0 0 400 179" font-size="1" width="400.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="1.0689548060277785" fill="rgb(0,0,255)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 364.6026,49.1012 l 17.2156,-17.2156 c -31.6930,-31.6930 -83.0775,-31.6930 -114.7704 -0.0000c -31.6930,31.6930 -31.6930,83.0775 -0.0000 114.7704c 31.6930,31.6930 83.0775,31.6930 114.7704 0.0000l -17.2156,-17.2156 c -22.1851,22.1851 -58.1542,22.1851 -80.3393 -0.0000c -22.1851,-22.1851 -22.1851,-58.1542 0.0000 -80.3393c 22.1851,-22.1851 58.1542,-22.1851 80.3393 -0.0000Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="1.0689548060277785" fill="rgb(0,0,255)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 196.7624,65.0577 l 5.9381,-56.4973 c -22.8740,-2.4042 -45.6939,5.0105 -62.7863 20.4005l 38.0123,42.2169 c 5.1277,-4.6170 11.9737,-6.8414 18.8359 -6.1201Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="1.0689548060277785" fill="rgb(0,0,255)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 58.7593,89.2708 h 40.5775 c 0.0000,-44.8206 -36.3343,-81.1550 -81.1550 -81.1550l -0.0000,40.5775 c 22.4103,0.0000 40.5775,18.1672 40.5775 40.5775Z"/></g></svg>
diff --git a/diagrams/src_Diagrams_TwoD_Arc_arc'Ex.svg b/diagrams/src_Diagrams_TwoD_Arc_arc'Ex.svg
--- a/diagrams/src_Diagrams_TwoD_Arc_arc'Ex.svg
+++ b/diagrams/src_Diagrams_TwoD_Arc_arc'Ex.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="300.0" height="299.99999999999994" font-size="1" viewBox="0 0 300 300" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="1.2" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><g><path d="M 286.3636363636364,177.27272727272728 c 0.0,-90.37386815412985 -73.2624954822338,-163.63636363636365 -163.63636363636363 -163.63636363636365" /><path d="M 231.8181818181818,177.27272727272728 c 0.0,60.24924543608655 -48.84166365482254,109.09090909090907 -109.09090909090911 109.09090909090905c -60.24924543608655,0.0 -109.09090909090907,-48.84166365482254 -109.09090909090907 -109.09090909090911c 0.0,-60.24924543608655 48.84166365482254,-109.09090909090907 109.09090909090911 -109.09090909090907" /><path d="M 177.27272727272725,177.27272727272728 c 0.0,-30.124622718043284 -24.420831827411263,-54.545454545454554 -54.54545454545454 -54.545454545454554" /></g></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="300.0000" stroke-opacity="1" viewBox="0 0 300 300" font-size="1" width="300.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.2" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 286.3636,286.3636 c 0.0000,-150.6231 -122.1042,-272.7273 -272.7273 -272.7273"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.2" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 195.4545,286.3636 c 0.0000,-100.4154 -81.4028,-181.8182 -181.8182 -181.8182"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.2" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 104.5455,286.3636 c 0.0000,-50.2077 -40.7014,-90.9091 -90.9091 -90.9091"/></g></svg>
diff --git a/diagrams/src_Diagrams_TwoD_Arc_arcBetweenEx.svg b/diagrams/src_Diagrams_TwoD_Arc_arcBetweenEx.svg
--- a/diagrams/src_Diagrams_TwoD_Arc_arcBetweenEx.svg
+++ b/diagrams/src_Diagrams_TwoD_Arc_arcBetweenEx.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="300.0" height="150.0" font-size="1" viewBox="0 0 300 150" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="0.8485281374238571" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><g><path d="M 13.636363636364111,143.18181818181793 c 71.7376874363651,-76.52462512726947 168.46496016363756,-124.88826149090566 272.7272727272722 -136.36363636363595" /><path d="M 13.636363636364266,143.1818181818181 c 82.05066190000052,-61.353221654543866 174.4142982636367,-107.53503983636188 272.72727272727207 -136.363636363636" /><path d="M 13.636363636364166,143.18181818181804 l 272.72727272727207,-136.36363636363603 " /><path d="M 13.636363636363624,143.1818181818182 c 98.31297446363554,-28.82859652727414 190.67661082727207,-75.01041470909239 272.72727272727275 -136.36363636363635" /><path d="M 13.636363636364058,143.1818181818181 c 104.26231256363465,-11.475374872730281 200.9895852909071,-59.83901123636646 272.7272727272722 -136.36363636363592" /></g></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="150.0000" stroke-opacity="1" viewBox="0 0 300 150" font-size="1" width="300.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.8485281374238577" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 13.6364,143.1818 c 71.7377,-76.5246 168.4650,-124.8883 272.7273 -136.3636"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.8485281374238577" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 13.6364,143.1818 c 82.0507,-61.3532 174.4143,-107.5350 272.7273 -136.3636"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.8485281374238577" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 13.6364,143.1818 l 272.7273,-136.3636 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.8485281374238577" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 13.6364,143.1818 c 98.3130,-28.8286 190.6766,-75.0104 272.7273 -136.3636"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.8485281374238577" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 13.6364,143.1818 c 104.2623,-11.4754 200.9896,-59.8390 272.7273 -136.3636"/></g></svg>
diff --git a/diagrams/src_Diagrams_TwoD_Arc_wedgeEx.svg b/diagrams/src_Diagrams_TwoD_Arc_wedgeEx.svg
--- a/diagrams/src_Diagrams_TwoD_Arc_wedgeEx.svg
+++ b/diagrams/src_Diagrams_TwoD_Arc_wedgeEx.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="400.0" height="178.54130895779457" font-size="1" viewBox="0 0 400 179" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="1.0689548060277785" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><g fill="rgb(0,0,255)" fill-opacity="1.0"><g fill="rgb(0,0,255)" fill-opacity="1.0"><g fill="rgb(0,0,255)" fill-opacity="1.0"><g><g fill="rgb(0,0,255)" fill-opacity="1.0"><g fill="rgb(0,0,255)" fill-opacity="1.0"><path d="M 324.43296081480526,89.27083709150592 l 57.385221003376564,-57.38522100337656 c -31.692982425834614,-31.692982425834618 -83.0774595809185,-31.692982425834632 -114.77044200675311 -1.8020020547460663e-14c -31.692982425834618,31.692982425834614 -31.692982425834632,83.0774595809185 -2.7030030821190994e-14 114.77044200675311c 31.69298242583461,31.69298242583462 83.07745958091849,31.692982425834636 114.77044200675309 3.6040041094921325e-14Z" /></g></g></g><g fill="rgb(0,0,255)" fill-opacity="1.0"><g><g fill="rgb(0,0,255)" fill-opacity="1.0"><g fill="rgb(0,0,255)" fill-opacity="1.0"><path d="M 194.21752105291293,89.27083709150592 l 8.483003027763553,-80.71038247241611 c -22.87402851921224,-2.4041572749570763 -45.693919553281,5.0104747879005584 -62.78626916472949 20.400495504601384Z" /></g></g></g><g fill="rgb(0,0,255)" fill-opacity="1.0"><path d="M 18.181818181818187,89.27083709150592 h 81.15495782275252 c 0.0,-44.820645578667474 -36.33431224408504,-81.15495782275252 -81.15495782275251 -81.15495782275252Z" /></g></g></g></g></g></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="178.5413" stroke-opacity="1" viewBox="0 0 400 179" font-size="1" width="400.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="1.0689548060277785" fill="rgb(0,0,255)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 324.4330,89.2708 l 57.3852,-57.3852 c -31.6930,-31.6930 -83.0775,-31.6930 -114.7704 -0.0000c -31.6930,31.6930 -31.6930,83.0775 -0.0000 114.7704c 31.6930,31.6930 83.0775,31.6930 114.7704 0.0000Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="1.0689548060277785" fill="rgb(0,0,255)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 194.2175,89.2708 l 8.4830,-80.7104 c -22.8740,-2.4042 -45.6939,5.0105 -62.7863 20.4005Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="1.0689548060277785" fill="rgb(0,0,255)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 18.1818,89.2708 h 81.1550 c 0.0000,-44.8206 -36.3343,-81.1550 -81.1550 -81.1550Z"/></g></svg>
diff --git a/diagrams/src_Diagrams_TwoD_Arrow_example1.svg b/diagrams/src_Diagrams_TwoD_Arrow_example1.svg
--- a/diagrams/src_Diagrams_TwoD_Arrow_example1.svg
+++ b/diagrams/src_Diagrams_TwoD_Arrow_example1.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="499.99999999999994" height="142.85714285714286" font-size="1" viewBox="0 0 500 143" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="1.0690449676496976" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><g><g stroke="rgb(169,169,169)" stroke-opacity="1.0" stroke-width="5.345224838248488"><path d="M 461.03896103896096,136.36363636363637 l -1.4418480839287746e-14,-129.87012987012986 h -129.87012987012986 l -1.4418480839287746e-14,129.87012987012986 Z" /><g fill="rgb(255,0,0)" fill-opacity="1.0" stroke-width="0.0"><g fill="rgb(255,0,0)" fill-opacity="1.0"><g fill="rgb(255,0,0)" fill-opacity="1.0"><path d="M 398.70129870129864,71.42857142857143 c 0.0,-1.4345058437163465 -1.1628967536862505,-2.5974025974025974 -2.597402597402597 -2.5974025974025974c -1.4345058437163465,-8.783814949326985e-17 -2.5974025974025974,1.1628967536862502 -2.5974025974025974 2.5974025974025965c -1.756762989865397e-16,1.4345058437163465 1.1628967536862502,2.5974025974025974 2.597402597402596 2.5974025974025974c 1.4345058437163465,2.6351444847980957e-16 2.5974025974025974,-1.16289675368625 2.5974025974025987 -2.5974025974025965Z" /></g></g></g></g></g><g></g><g stroke="rgb(169,169,169)" stroke-opacity="1.0" stroke-width="5.345224838248488"><path d="M 136.36363636363632,136.36363636363637 l -1.4418480839287746e-14,-129.87012987012986 h -129.87012987012986 l -1.4418480839287746e-14,129.87012987012986 Z" /><g fill="rgb(255,0,0)" fill-opacity="1.0" stroke-width="0.0"><g fill="rgb(255,0,0)" fill-opacity="1.0"><g fill="rgb(255,0,0)" fill-opacity="1.0"><path d="M 74.02597402597398,71.42857142857143 c 0.0,-1.4345058437163465 -1.1628967536862505,-2.5974025974025974 -2.597402597402597 -2.5974025974025974c -1.4345058437163465,-8.783814949326985e-17 -2.5974025974025974,1.1628967536862502 -2.5974025974025974 2.5974025974025965c -1.756762989865397e-16,1.4345058437163465 1.1628967536862502,2.5974025974025974 2.597402597402596 2.5974025974025974c 1.4345058437163465,2.6351444847980957e-16 2.5974025974025974,-1.16289675368625 2.5974025974025987 -2.5974025974025965Z" /></g></g></g></g><g><g><g><path d="M 89.9819766975543,73.83089383093066 c 61.406842947188636,7.951049003214775 122.81368589437727,15.90209800642955 138.71310687684397 10.954204913391047c 15.89942098246672,-4.947893093038505 -13.70857999978851,-22.794728282330297 2.1908409826782096 -27.742621375368802c 15.89942098246672,-4.947893093038505 77.30626392965536,3.0031559101762695 138.71310687684394 10.954204913391044" /></g><g stroke-width="0.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 89.9819766975543,73.83089383093066 l -6.420476687285677e-2,0.49586061338928916 l -0.47159146753799513,-6.106236191164162e-2 l 0.5357962344108519,-0.43479825147764756 l -0.4073867006651384,-0.5569229753009308 l 0.47159146753799513,6.106236191164162e-2 l -6.420476687285677e-2,0.49586061338928916 Z" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 89.9819766975543,73.83089383093066 l -9.81976544020477,7.968732456689302 l -19.326463821857203,-2.5024191691242024 l 10.592823993079056,-7.868635689924334 l -8.239407860814753,-10.307060971598373 l 19.326463821857203,2.5024191691242024 l 7.466349307940467,10.206964204833405 Z" /></g></g></g></g><g stroke-width="0.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 396.103896103896,71.42857142857143 l -32.982355078418344,6.185770522810794 l 6.7381797601759725,-9.583905225546857 l -4.075015142080604,-10.984013721974463 Z" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 369.8597207856536,68.03043672583537 l -0.26068935173322666,-3.375444349141672e-2 l -6.420476687285682e-2,0.49586061338928916 l 0.32489411860608347,-0.46210616989787245 l -0.26068935173322666,-3.375444349141672e-2 l 6.420476687285682e-2,-0.49586061338928916 Z" /></g></g></g></g></g></g></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="142.8571" stroke-opacity="1" viewBox="0 0 500 143" font-size="1" width="500.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(169,169,169)" stroke-width="5.345224838248488" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 461.0390,136.3636 l -0.0000,-129.8701 h -129.8701 l -0.0000,129.8701 Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(169,169,169)" stroke-width="0.0" fill="rgb(255,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 398.7013,71.4286 c 0.0000,-1.4345 -1.1629,-2.5974 -2.5974 -2.5974c -1.4345,-0.0000 -2.5974,1.1629 -2.5974 2.5974c -0.0000,1.4345 1.1629,2.5974 2.5974 2.5974c 1.4345,0.0000 2.5974,-1.1629 2.5974 -2.5974Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(169,169,169)" stroke-width="5.345224838248488" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 136.3636,136.3636 l -0.0000,-129.8701 h -129.8701 l -0.0000,129.8701 Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(169,169,169)" stroke-width="0.0" fill="rgb(255,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 74.0260,71.4286 c 0.0000,-1.4345 -1.1629,-2.5974 -2.5974 -2.5974c -1.4345,-0.0000 -2.5974,1.1629 -2.5974 2.5974c -0.0000,1.4345 1.1629,2.5974 2.5974 2.5974c 1.4345,0.0000 2.5974,-1.1629 2.5974 -2.5974Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.0690449676496976" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 89.9820,73.8309 c 61.4068,7.9510 122.8137,15.9021 138.7131 10.9542c 15.8994,-4.9479 -13.7086,-22.7947 2.1908 -27.7426c 15.8994,-4.9479 77.3063,3.0032 138.7131 10.9542"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 89.9820,73.8309 l -7.4663,-10.2070 l -19.3265,-2.5024 l 8.2394,10.3071 l -10.5928,7.8686 l 19.3265,2.5024 l 9.8198,-7.9687 Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 89.9820,73.8309 l 0.0686,-0.5301 l -0.5042,-0.0653 l 0.4355,0.5954 l -0.5728,0.4648 l 0.5042,0.0653 l 0.0686,-0.5301 Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 396.1039,71.4286 l -30.2984,-14.3723 l 4.0722,10.9765 l -6.7336,9.5773 Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 369.8777,68.0328 l -0.2787,-0.0361 l 0.0686,-0.5301 l 0.2101,0.5662 l -0.2787,-0.0361 l -0.0686,0.5301 Z"/></g></svg>
diff --git a/diagrams/src_Diagrams_TwoD_Arrow_example2.svg b/diagrams/src_Diagrams_TwoD_Arrow_example2.svg
--- a/diagrams/src_Diagrams_TwoD_Arrow_example2.svg
+++ b/diagrams/src_Diagrams_TwoD_Arrow_example2.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="500.0" height="191.60937134592436" font-size="1" viewBox="0 0 500 192" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="1.238093280317519" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><g><g><g><g><path d="M 92.8160519668354,95.80468567296218 l 2.89201135554859e-15,47.23012965962302 " /></g><g stroke-width="0.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="" /></g></g></g></g><g stroke-width="0.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 92.8160519668354,153.86813153536352 l -4.14210333348447,-12.748083238743886 l 4.142103333484469,2.1776325920251587 l 4.142103333484469,-2.1776325920251596 Z" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 92.8160519668354,143.29768088864478 l -1.6095873091721878e-17,-0.26286555605956674 l -0.5,3.061616997868383e-17 l 0.5,0.2628655560595667 l -1.6095873091721878e-17,-0.26286555605956674 l 0.5,-3.061616997868383e-17 Z" /></g></g></g></g></g></g><g><g stroke="rgb(169,169,169)" stroke-opacity="1.0" stroke-width="6.190466401587595"><path d="M 477.2727272727272,124.83640860416281 l -1.2892674897102844e-14,-58.063445862401316 l -41.05705630836196,-41.05705630836195 l -58.063445862401316,9.337314240960074e-15 l -41.05705630836195,41.05705630836196 l 5.781953584817304e-15,58.063445862401316 l 41.05705630836196,41.05705630836196 l 58.063445862401316,-2.2265929286745346e-15 Z" /></g><g fill="rgb(255,0,0)" fill-opacity="1.0" stroke-width="0.0"><g fill="rgb(255,0,0)" fill-opacity="1.0"><g fill="rgb(255,0,0)" fill-opacity="1.0"><path d="M 409.98749920274713,95.80468567296218 c 0.0,-1.5483585563307023 -1.2551926132518025,-2.803551169582505 -2.803551169582504 -2.803551169582505c -1.5483585563307023,-9.480961749714055e-17 -2.803551169582505,1.2551926132518023 -2.803551169582505 2.803551169582504c -1.896192349942811e-16,1.5483585563307023 1.255192613251802,2.803551169582505 2.8035511695825037 2.803551169582505c 1.5483585563307023,2.844288524914217e-16 2.803551169582505,-1.255192613251802 2.8035511695825055 -2.803551169582504Z" /></g></g></g></g><g></g><g stroke="rgb(169,169,169)" stroke-opacity="1.0" stroke-width="6.190466401587595"><path d="M 162.904831206398,124.83640860416281 l -1.2892674897102844e-14,-58.063445862401316 l -41.05705630836196,-41.05705630836195 l -58.063445862401316,9.337314240960074e-15 l -41.05705630836195,41.05705630836196 l 5.781953584817304e-15,58.063445862401316 l 41.05705630836196,41.05705630836196 l 58.063445862401316,-2.2265929286745346e-15 Z" /></g><g fill="rgb(255,0,0)" fill-opacity="1.0" stroke-width="0.0"><g fill="rgb(255,0,0)" fill-opacity="1.0"><g fill="rgb(255,0,0)" fill-opacity="1.0"><path d="M 95.61960313641791,95.80468567296218 c 0.0,-1.5483585563307023 -1.2551926132518025,-2.803551169582505 -2.803551169582504 -2.803551169582505c -1.5483585563307023,-9.480961749714055e-17 -2.803551169582505,1.2551926132518023 -2.803551169582505 2.803551169582504c -1.896192349942811e-16,1.5483585563307023 1.255192613251802,2.803551169582505 2.8035511695825037 2.803551169582505c 1.5483585563307023,2.844288524914217e-16 2.803551169582505,-1.255192613251802 2.8035511695825055 -2.803551169582504Z" /></g></g></g><g><g><g><path d="M 92.8160519668354,95.80468567296218 h 292.70126366077255 " /></g><g stroke-width="0.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="" /></g></g></g></g><g stroke-width="0.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 407.18394803316454,95.80468567296218 l -25.81318531625282,8.387212331760587 l 4.4094184667558025,-8.387212331760587 l -4.4094184667558025,-8.387212331760587 Z" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 385.78018118366754,95.80468567296218 h -0.26286555605956674 v 0.5 l 0.26286555605956674,-0.5 h -0.26286555605956674 v -0.5 Z" /></g></g></g></g></g></g><g><g><g><path d="M 162.90483120639794,124.83640860416287 l 152.52370518164744,-2.4886480444135933e-14 " /></g><g stroke-width="0.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="" /></g></g></g></g><g stroke-width="0.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 337.095168793602,124.83640860416284 l -25.81318531625282,8.38721233176059 l 4.409418466755801,-8.387212331760587 l -4.409418466755804,-8.387212331760587 Z" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 315.691401944105,124.83640860416284 l -0.26286555605956674,4.2890372434385847e-17 l 8.15823363800974e-17,0.5 l 0.2628655560595667,-0.5 l -0.26286555605956674,4.2890372434385847e-17 l -8.15823363800974e-17,-0.5 Z" /></g></g></g></g></g></g></g></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="191.6094" stroke-opacity="1" viewBox="0 0 500 192" font-size="1" width="500.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.238093280317519" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 92.8161,95.8047 l 0.0000,47.2301 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 92.8161,153.8681 l 4.1176,-12.6726 l -4.1176,2.1647 l -4.1176,-2.1647 Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 92.8161,143.3603 l -0.0000,-0.3255 l 0.6190,-0.0000 l -0.6190,0.3255 l -0.0000,-0.3255 l -0.6190,0.0000 Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(169,169,169)" stroke-width="6.190466401587595" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 477.2727,124.8364 l -0.0000,-58.0634 l -41.0571,-41.0571 l -58.0634,0.0000 l -41.0571,41.0571 l 0.0000,58.0634 l 41.0571,41.0571 l 58.0634,-0.0000 Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(255,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 409.9875,95.8047 c 0.0000,-1.5484 -1.2552,-2.8036 -2.8036 -2.8036c -1.5484,-0.0000 -2.8036,1.2552 -2.8036 2.8036c -0.0000,1.5484 1.2552,2.8036 2.8036 2.8036c 1.5484,0.0000 2.8036,-1.2552 2.8036 -2.8036Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(169,169,169)" stroke-width="6.190466401587595" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 162.9048,124.8364 l -0.0000,-58.0634 l -41.0571,-41.0571 l -58.0634,0.0000 l -41.0571,41.0571 l 0.0000,58.0634 l 41.0571,41.0571 l 58.0634,-0.0000 Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(255,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 95.6196,95.8047 c 0.0000,-1.5484 -1.2552,-2.8036 -2.8036 -2.8036c -1.5484,-0.0000 -2.8036,1.2552 -2.8036 2.8036c -0.0000,1.5484 1.2552,2.8036 2.8036 2.8036c 1.5484,0.0000 2.8036,-1.2552 2.8036 -2.8036Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.238093280317519" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 92.8161,95.8047 h 292.7013 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 407.1839,95.8047 l -25.7377,-8.3627 l 4.3965,8.3627 l -4.3965,8.3627 Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 385.8428,95.8047 h -0.3255 v -0.6190 l 0.3255,0.6190 h -0.3255 v 0.6190 Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.238093280317519" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 162.9048,124.8364 l 152.5237,-0.0000 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 337.0952,124.8364 l -25.7377,-8.3627 l 4.3965,8.3627 l -4.3965,8.3627 Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 315.7540,124.8364 l -0.3255,0.0000 l -0.0000,-0.6190 l 0.3255,0.6190 l -0.3255,0.0000 l 0.0000,0.6190 Z"/></g></svg>
diff --git a/diagrams/src_Diagrams_TwoD_Arrowheads_blockEx.svg b/diagrams/src_Diagrams_TwoD_Arrowheads_blockEx.svg
--- a/diagrams/src_Diagrams_TwoD_Arrowheads_blockEx.svg
+++ b/diagrams/src_Diagrams_TwoD_Arrowheads_blockEx.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="100.0" height="100.0" font-size="1" viewBox="0 0 100 100" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="0.5" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><g stroke-width="0.0"><path d="M 100.0,100.0 l -1.1102230246251565e-14,-100.0 h -100.0 l -1.1102230246251565e-14,100.0 Z" /></g><g><g><g stroke-width="0.0"><path d="M 3.500000000000001,50.0 h -3.3000000000000007 " /></g><g stroke-width="0.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 3.500000000000001,48.660607986722184 l -3.8857805861880484e-16,2.6787840265556295 h -3.5000000000000004 l -3.8857805861880484e-16,-2.6787840265556295 Z" /></g></g></g></g><g stroke-width="0.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="" /></g></g></g></g></g></g></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="63.6364" stroke-opacity="1" viewBox="0 0 100 64" font-size="1" width="100.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 54.5455,54.5455 l -0.0000,-45.4545 h -45.4545 l -0.0000,45.4545 Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 54.5455,31.8182 h 45.4545 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 54.5455,49.2129 l -0.0000,-34.7894 h -45.4545 l -0.0000,34.7894 Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"></g></svg>
diff --git a/diagrams/src_Diagrams_TwoD_Arrowheads_dart'Ex.svg b/diagrams/src_Diagrams_TwoD_Arrowheads_dart'Ex.svg
--- a/diagrams/src_Diagrams_TwoD_Arrowheads_dart'Ex.svg
+++ b/diagrams/src_Diagrams_TwoD_Arrowheads_dart'Ex.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="100.0" height="100.0" font-size="1" viewBox="0 0 100 100" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="0.5" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><g stroke-width="0.0"><path d="M 100.0,100.0 l -1.1102230246251565e-14,-100.0 h -100.0 l -1.1102230246251565e-14,100.0 Z" /></g><g><g><g stroke-width="0.0"><path d="M 3.5000000000000013,50.0 h -3.3000000000000087 " /></g><g stroke-width="0.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 3.5000000000000013,50.0 h 0.0 h 0.0 h 0.0 h 0.0 h 0.0 Z" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 4.440892098500626e-16,50.0 l 4.221039653541545,1.371498922015771 l -0.7210396535415439,-1.371498922015771 l 0.7210396535415439,-1.371498922015771 Z" /></g></g></g></g><g stroke-width="0.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="" /></g></g></g></g></g></g></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="63.6364" stroke-opacity="1" viewBox="0 0 100 64" font-size="1" width="100.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 54.5455,54.5455 l -0.0000,-45.4545 h -45.4545 l -0.0000,45.4545 Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 54.5455,31.8182 h 45.4545 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 9.0909,31.8182 l 54.8187,-17.8117 l -9.3642,17.8117 l 9.3642,17.8117 Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 54.5455,31.8182 h 0.0000 h -0.0000 h 0.0000 h 0.0000 h 0.0000 Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"></g></svg>
diff --git a/diagrams/src_Diagrams_TwoD_Arrowheads_dartEx.svg b/diagrams/src_Diagrams_TwoD_Arrowheads_dartEx.svg
--- a/diagrams/src_Diagrams_TwoD_Arrowheads_dartEx.svg
+++ b/diagrams/src_Diagrams_TwoD_Arrowheads_dartEx.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="100.0" height="100.0" font-size="1" viewBox="0 0 100 100" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="0.5" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><g stroke-width="0.0"><path d="M 100.0,100.0 l -1.1102230246251565e-14,-100.0 h -100.0 l -1.1102230246251565e-14,100.0 Z" /></g><g><g><g stroke-width="0.0"><path d="M 0.0,50.0 h -3.3000000000000087 " /></g><g stroke-width="0.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="" /></g></g></g></g><g stroke-width="0.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 0.19999999999999218,50.0 l -4.221039653541545,1.371498922015771 l 0.7210396535415439,-1.371498922015771 l -0.7210396535415439,-1.371498922015771 Z" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M -3.3000000000000087,50.0 h 0.0 h 0.0 h 0.0 h 0.0 h 0.0 Z" /></g></g></g></g></g></g></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="63.6364" stroke-opacity="1" viewBox="0 0 100 64" font-size="1" width="100.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 54.5455,54.5455 l -0.0000,-45.4545 h -45.4545 l -0.0000,45.4545 Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 9.0909,31.8182 h 45.4545 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 100.0000,31.8182 l -54.8187,-17.8117 l 9.3642,17.8117 l -9.3642,17.8117 Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 54.5455,31.8182 h -0.0000 h 0.0000 h 0.0000 h 0.0000 h 0.0000 Z"/></g></svg>
diff --git a/diagrams/src_Diagrams_TwoD_Arrowheads_halfDart'Ex.svg b/diagrams/src_Diagrams_TwoD_Arrowheads_halfDart'Ex.svg
new file mode 100644
--- /dev/null
+++ b/diagrams/src_Diagrams_TwoD_Arrowheads_halfDart'Ex.svg
@@ -0,0 +1,1 @@
+<svg xmlns="http://www.w3.org/2000/svg" height="63.6364" stroke-opacity="1" viewBox="0 0 100 64" font-size="1" width="100.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 54.5455,54.5455 l -0.0000,-45.4545 h -45.4545 l -0.0000,45.4545 Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 54.5455,31.8182 h 45.4545 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 9.0909,31.8182 l 54.8187,-17.8117 l -9.3642,17.8117 Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 54.5455,31.8182 h 0.0000 h -0.0000 Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"></g></svg>
diff --git a/diagrams/src_Diagrams_TwoD_Arrowheads_halfDartEx.svg b/diagrams/src_Diagrams_TwoD_Arrowheads_halfDartEx.svg
new file mode 100644
--- /dev/null
+++ b/diagrams/src_Diagrams_TwoD_Arrowheads_halfDartEx.svg
@@ -0,0 +1,1 @@
+<svg xmlns="http://www.w3.org/2000/svg" height="63.6364" stroke-opacity="1" viewBox="0 0 100 64" font-size="1" width="100.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 54.5455,54.5455 l -0.0000,-45.4545 h -45.4545 l -0.0000,45.4545 Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 9.0909,31.8182 h 45.4545 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 100.0000,31.8182 l -54.8187,-17.8117 l 9.3642,17.8117 Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 54.5455,31.8182 h -0.0000 h 0.0000 Z"/></g></svg>
diff --git a/diagrams/src_Diagrams_TwoD_Arrowheads_quillEx.svg b/diagrams/src_Diagrams_TwoD_Arrowheads_quillEx.svg
--- a/diagrams/src_Diagrams_TwoD_Arrowheads_quillEx.svg
+++ b/diagrams/src_Diagrams_TwoD_Arrowheads_quillEx.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="100.0" height="100.0" font-size="1" viewBox="0 0 100 100" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="0.5" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><g stroke-width="0.0"><path d="M 100.0,100.0 l -1.1102230246251565e-14,-100.0 h -100.0 l -1.1102230246251565e-14,100.0 Z" /></g><g><g><g stroke-width="0.0"><path d="M 3.5000000000000004,50.0 h -3.3000000000000007 " /></g><g stroke-width="0.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 3.5000000000000004,50.0 h 0.0 h 0.0 h 0.0 h 0.0 h 0.0 h 0.0 Z" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 3.5000000000000004,50.0 l -1.6304662335935967,1.7143736525197137 h -3.645833333333334 l 1.7762995669269297,-1.7143736525197137 l -1.7762995669269297,-1.7143736525197137 h 3.645833333333334 l 1.6304662335935967,1.7143736525197137 Z" /></g></g></g></g><g stroke-width="0.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="" /></g></g></g></g></g></g></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="63.6364" stroke-opacity="1" viewBox="0 0 100 64" font-size="1" width="100.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 54.5455,54.5455 l -0.0000,-45.4545 h -45.4545 l -0.0000,45.4545 Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 54.5455,31.8182 h 45.4545 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 54.5455,31.8182 l -21.1749,-22.2646 h -47.3485 l 23.0688,22.2646 l -23.0688,22.2646 h 47.3485 l 21.1749,-22.2646 Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 54.5455,31.8182 h 0.0000 h 0.0000 h 0.0000 h 0.0000 h 0.0000 h 0.0000 Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"></g></svg>
diff --git a/diagrams/src_Diagrams_TwoD_Arrowheads_spike'Ex.svg b/diagrams/src_Diagrams_TwoD_Arrowheads_spike'Ex.svg
--- a/diagrams/src_Diagrams_TwoD_Arrowheads_spike'Ex.svg
+++ b/diagrams/src_Diagrams_TwoD_Arrowheads_spike'Ex.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="100.0" height="100.0" font-size="1" viewBox="0 0 100 100" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="0.5" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><g stroke-width="0.0"><path d="M 100.0,100.0 l -1.1102230246251565e-14,-100.0 h -100.0 l -1.1102230246251565e-14,100.0 Z" /></g><g><g><g stroke-width="0.0"><path d="M 3.500000000000001,50.0 h -3.3000000000000007 " /></g><g stroke-width="0.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 3.500000000000001,50.0 Z" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 4.440892098500626e-16,50.0 l 4.224873734152917,1.7500000000000004 c -0.9664983122038887,-0.9664983122038886 -0.9664983122038892,-2.533501687796112 -5.495323605393214e-16 -3.5000000000000004l -4.224873734152917,1.7500000000000004 Z" /></g></g></g></g><g stroke-width="0.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="" /></g></g></g></g></g></g></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="63.6364" stroke-opacity="1" viewBox="0 0 100 64" font-size="1" width="100.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 54.5455,54.5455 l -0.0000,-45.4545 h -45.4545 l -0.0000,45.4545 Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 54.5455,31.8182 h 45.4545 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 9.0909,31.8182 l 54.8685,-22.7273 c -12.5519,12.5519 -12.5519,32.9026 0.0000 45.4545l -54.8685,-22.7273 Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 54.5455,31.8182 Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"></g></svg>
diff --git a/diagrams/src_Diagrams_TwoD_Arrowheads_spikeEx.svg b/diagrams/src_Diagrams_TwoD_Arrowheads_spikeEx.svg
--- a/diagrams/src_Diagrams_TwoD_Arrowheads_spikeEx.svg
+++ b/diagrams/src_Diagrams_TwoD_Arrowheads_spikeEx.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="100.0" height="100.0" font-size="1" viewBox="0 0 100 100" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="0.5" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><g stroke-width="0.0"><path d="M 100.0,100.0 l -1.1102230246251565e-14,-100.0 h -100.0 l -1.1102230246251565e-14,100.0 Z" /></g><g><g><g stroke-width="0.0"><path d="M 0.0,50.0 h -3.3000000000000007 " /></g><g stroke-width="0.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="" /></g></g></g></g><g stroke-width="0.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 0.19999999999999973,50.0 l -4.224873734152917,1.7500000000000004 c 0.9664983122038887,-0.9664983122038886 0.9664983122038892,-2.533501687796112 5.495323605393214e-16 -3.5000000000000004l 4.224873734152917,1.7500000000000004 Z" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M -3.3000000000000007,50.0 Z" /></g></g></g></g></g></g></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="63.6364" stroke-opacity="1" viewBox="0 0 100 64" font-size="1" width="100.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 54.5455,54.5455 l -0.0000,-45.4545 h -45.4545 l -0.0000,45.4545 Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 9.0909,31.8182 h 45.4545 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 100.0000,31.8182 l -54.8685,-22.7273 c 12.5519,12.5519 12.5519,32.9026 0.0000 45.4545l 54.8685,-22.7273 Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 54.5455,31.8182 Z"/></g></svg>
diff --git a/diagrams/src_Diagrams_TwoD_Arrowheads_thorn'Ex.svg b/diagrams/src_Diagrams_TwoD_Arrowheads_thorn'Ex.svg
--- a/diagrams/src_Diagrams_TwoD_Arrowheads_thorn'Ex.svg
+++ b/diagrams/src_Diagrams_TwoD_Arrowheads_thorn'Ex.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="100.0" height="100.0" font-size="1" viewBox="0 0 100 100" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="0.5" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><g stroke-width="0.0"><path d="M 100.0,100.0 l -1.1102230246251565e-14,-100.0 h -100.0 l -1.1102230246251565e-14,100.0 Z" /></g><g><g><g stroke-width="0.0"><path d="M 3.500000000000001,50.0 h -3.3000000000000007 " /></g><g stroke-width="0.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 3.500000000000001,50.0 h 0.0 h 0.0 h 0.0 h 0.0 h 0.0 Z" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 8.881784197001252e-16,50.0 c 2.3333333333333335,0.0 3.9832491561019445,1.649915822768611 3.9832491561019445 1.649915822768611l -0.48324915610194413,-1.649915822768611 h -3.5 c 2.3333333333333335,0.0 3.9832491561019445,-1.649915822768611 3.9832491561019445 -1.649915822768611l -0.48324915610194413,1.649915822768611 Z" /></g></g></g></g><g stroke-width="0.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="" /></g></g></g></g></g></g></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="63.6364" stroke-opacity="1" viewBox="0 0 100 64" font-size="1" width="100.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 54.5455,54.5455 l -0.0000,-45.4545 h -45.4545 l -0.0000,45.4545 Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 54.5455,31.8182 h 45.4545 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 9.0909,31.8182 c 30.3030,0.0000 51.7305,-21.4275 51.7305 -21.4275l -6.2760,21.4275 h -45.4545 c 30.3030,0.0000 51.7305,21.4275 51.7305 21.4275l -6.2760,-21.4275 Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 54.5455,31.8182 h 0.0000 h -0.0000 h 0.0000 h 0.0000 h 0.0000 Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"></g></svg>
diff --git a/diagrams/src_Diagrams_TwoD_Arrowheads_thornEx.svg b/diagrams/src_Diagrams_TwoD_Arrowheads_thornEx.svg
--- a/diagrams/src_Diagrams_TwoD_Arrowheads_thornEx.svg
+++ b/diagrams/src_Diagrams_TwoD_Arrowheads_thornEx.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="100.0" height="100.0" font-size="1" viewBox="0 0 100 100" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="0.5" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><g stroke-width="0.0"><path d="M 100.0,100.0 l -1.1102230246251565e-14,-100.0 h -100.0 l -1.1102230246251565e-14,100.0 Z" /></g><g><g><g stroke-width="0.0"><path d="M 0.0,50.0 h -3.2999999478459427 " /></g><g stroke-width="0.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="" /></g></g></g></g><g stroke-width="0.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 0.20000005215405725,50.0 c -2.3333333333333335,0.0 -3.9832491561019445,1.649915822768611 -3.9832491561019445 1.649915822768611l 0.48324915610194413,-1.649915822768611 h 3.5 c -2.3333333333333335,0.0 -3.9832491561019445,-1.649915822768611 -3.9832491561019445 -1.649915822768611l 0.48324915610194413,1.649915822768611 Z" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M -3.2999999478459427,50.0 h 0.0 h 0.0 h 0.0 h 0.0 h 0.0 Z" /></g></g></g></g></g></g></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="63.6364" stroke-opacity="1" viewBox="0 0 100 64" font-size="1" width="100.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 54.5455,54.5455 l -0.0000,-45.4545 h -45.4545 l -0.0000,45.4545 Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 9.0909,31.8182 h 45.4545 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 100.0000,31.8182 c -30.3030,0.0000 -51.7305,-21.4275 -51.7305 -21.4275l 6.2760,21.4275 h 45.4545 c -30.3030,0.0000 -51.7305,21.4275 -51.7305 21.4275l 6.2760,-21.4275 Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 54.5455,31.8182 h -0.0000 h 0.0000 h 0.0000 h 0.0000 h 0.0000 Z"/></g></svg>
diff --git a/diagrams/src_Diagrams_TwoD_Arrowheads_tri'Ex.svg b/diagrams/src_Diagrams_TwoD_Arrowheads_tri'Ex.svg
--- a/diagrams/src_Diagrams_TwoD_Arrowheads_tri'Ex.svg
+++ b/diagrams/src_Diagrams_TwoD_Arrowheads_tri'Ex.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="100.0" height="100.0" font-size="1" viewBox="0 0 100 100" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="0.5" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><g stroke-width="0.0"><path d="M 100.0,100.0 l -1.1102230246251565e-14,-100.0 h -100.0 l -1.1102230246251565e-14,100.0 Z" /></g><g><g><g stroke-width="0.0"><path d="M 3.5,50.0 h -3.300000000000003 " /></g><g stroke-width="0.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 0.0,50.0 l 3.5,2.0207259421636903 v -4.041451884327381 Z" /></g></g></g></g><g stroke-width="0.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="" /></g></g></g></g></g></g></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="63.6364" stroke-opacity="1" viewBox="0 0 100 64" font-size="1" width="100.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 54.5455,54.5455 l -0.0000,-45.4545 h -45.4545 l -0.0000,45.4545 Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 54.5455,31.8182 h 45.4545 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 9.0909,31.8182 l 45.4545,-26.2432 v 52.4864 Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"></g></svg>
diff --git a/diagrams/src_Diagrams_TwoD_Arrowheads_tri25Ex.svg b/diagrams/src_Diagrams_TwoD_Arrowheads_tri25Ex.svg
--- a/diagrams/src_Diagrams_TwoD_Arrowheads_tri25Ex.svg
+++ b/diagrams/src_Diagrams_TwoD_Arrowheads_tri25Ex.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="120.0" height="119.99999999999996" font-size="1" viewBox="0 0 120 120" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="0.5" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><g stroke-width="0.0"><path d="M 120.0,119.99999999999996 l -1.3322676295501874e-14,-119.99999999999996 h -119.99999999999996 l -1.3322676295501874e-14,119.99999999999996 Z" /></g><g><g><g stroke-width="0.0"><path d="M 0.0,59.99999999999998 h -3.999999999999999 " /></g><g stroke-width="0.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="" /></g></g></g></g><g stroke-width="0.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 0.20000000000000018,59.99999999999998 l -4.199999999999999,1.3646627241782066 v -2.729325448356413 Z" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="" /></g></g></g></g></g></g></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="120.0000" stroke-opacity="1" viewBox="0 0 120 120" font-size="1" width="120.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 105.0000,105.0000 l -0.0000,-90.0000 h -90.0000 l -0.0000,90.0000 Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 15.0000,60.0000 h -0.0000 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 90.0000,60.0000 l -75.0000,-24.3690 v 48.7380 Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"></g></svg>
diff --git a/diagrams/src_Diagrams_TwoD_Arrowheads_triEx.svg b/diagrams/src_Diagrams_TwoD_Arrowheads_triEx.svg
--- a/diagrams/src_Diagrams_TwoD_Arrowheads_triEx.svg
+++ b/diagrams/src_Diagrams_TwoD_Arrowheads_triEx.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="100.0" height="100.0" font-size="1" viewBox="0 0 100 100" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="0.5" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><g stroke-width="0.0"><path d="M 100.0,100.0 l -1.1102230246251565e-14,-100.0 h -100.0 l -1.1102230246251565e-14,100.0 Z" /></g><g><g><g stroke-width="0.0"><path d="M 0.0,50.0 h -3.300000000000003 " /></g><g stroke-width="0.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="" /></g></g></g></g><g stroke-width="0.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="M 0.19999999999999707,50.0 l -3.5,2.0207259421636903 v -4.041451884327381 Z" /></g></g></g><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><g fill="rgb(0,0,0)" fill-opacity="1.0"><path d="" /></g></g></g></g></g></g></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="63.6364" stroke-opacity="1" viewBox="0 0 100 64" font-size="1" width="100.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 54.5455,54.5455 l -0.0000,-45.4545 h -45.4545 l -0.0000,45.4545 Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 9.0909,31.8182 h 45.4545 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 100.0000,31.8182 l -45.4545,-26.2432 v 52.4864 Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"></g></svg>
diff --git a/diagrams/src_Diagrams_TwoD_Curvature_diagramA.svg b/diagrams/src_Diagrams_TwoD_Curvature_diagramA.svg
--- a/diagrams/src_Diagrams_TwoD_Curvature_diagramA.svg
+++ b/diagrams/src_Diagrams_TwoD_Curvature_diagramA.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="400.0" height="200.0" font-size="1" viewBox="0 0 400 200" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="1.0285189544531599" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><g stroke-width="1.9284730395996748"><path d="M 18.18181818181816,175.13148009015777 c 218.1818181818182,0.0 145.45454545454547,-181.81818181818184 363.6363636363637 -145.45454545454547" /></g></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="200.0000" stroke-opacity="1" viewBox="0 0 400 200" font-size="1" width="400.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.9284730395996748" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 18.1818,175.1315 c 218.1818,-0.0000 145.4545,-181.8182 363.6364 -145.4545"/></g></svg>
diff --git a/diagrams/src_Diagrams_TwoD_Curvature_diagramNeg.svg b/diagrams/src_Diagrams_TwoD_Curvature_diagramNeg.svg
--- a/diagrams/src_Diagrams_TwoD_Curvature_diagramNeg.svg
+++ b/diagrams/src_Diagrams_TwoD_Curvature_diagramNeg.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="400.0" height="200.0" font-size="1" viewBox="0 0 400 200" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="1.0285189544531599" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><g><g stroke="rgb(255,0,0)" stroke-opacity="1.0"><g><path d="M 281.16363636363644,30.840570999248655 l 37.77763883175646,135.36987248046086 " /><g><path d="M 459.483626004958,166.2104434797095 c 0.0,-77.61939705749228 -62.922953752072814,-140.5423508095651 -140.54235080956508 -140.5423508095651c -77.61939705749228,-4.75281730791027e-15 -140.5423508095651,62.92295375207281 -140.5423508095651 140.54235080956505c -9.50563461582054e-15,77.61939705749228 62.9229537520728,140.5423508095651 140.54235080956505 140.5423508095651c 77.61939705749228,1.425845192373081e-14 140.5423508095651,-62.92295375207279 140.54235080956516 -140.54235080956505Z" /></g></g></g><g stroke-width="1.9284730395996748"><path d="M 18.18181818181816,175.13148009015777 c 218.1818181818182,0.0 145.45454545454547,-181.81818181818184 363.6363636363637 -145.45454545454547" /></g></g></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="200.0000" stroke-opacity="1" viewBox="0 0 400 200" font-size="1" width="400.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(255,0,0)" stroke-width="1.0285189544531599" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 281.1636,30.8406 l 37.7776,135.3699 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(255,0,0)" stroke-width="1.0285189544531599" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 459.4836,166.2104 c 0.0000,-77.6194 -62.9230,-140.5424 -140.5424 -140.5424c -77.6194,-0.0000 -140.5424,62.9230 -140.5424 140.5424c -0.0000,77.6194 62.9230,140.5424 140.5424 140.5424c 77.6194,0.0000 140.5424,-62.9230 140.5424 -140.5424Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.9284730395996748" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 18.1818,175.1315 c 218.1818,-0.0000 145.4545,-181.8182 363.6364 -145.4545"/></g></svg>
diff --git a/diagrams/src_Diagrams_TwoD_Curvature_diagramPos.svg b/diagrams/src_Diagrams_TwoD_Curvature_diagramPos.svg
--- a/diagrams/src_Diagrams_TwoD_Curvature_diagramPos.svg
+++ b/diagrams/src_Diagrams_TwoD_Curvature_diagramPos.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="400.0" height="200.0" font-size="1" viewBox="0 0 400 200" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="1.0285189544531599" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><g><g stroke="rgb(255,0,0)" stroke-opacity="1.0"><g><path d="M 118.83636363636364,156.51329827197594 l -70.91174171622768,-156.36948173322 " /><g><path d="M 219.62170963785124,0.14381653875594225 c 0.0,-94.82568313685418 -76.87140458086108,-171.69708771771528 -171.69708771771525 -171.69708771771528c -94.82568313685418,-5.806398466525481e-15 -171.69708771771528,76.87140458086107 -171.69708771771528 171.69708771771522c -1.1612796933050962e-14,94.82568313685418 76.87140458086105,171.69708771771528 171.6970877177152 171.69708771771528c 94.82568313685418,1.741919539957644e-14 171.69708771771528,-76.87140458086105 171.6970877177153 -171.69708771771522Z" /></g></g></g><g stroke-width="1.9284730395996748"><path d="M 18.18181818181816,175.13148009015777 c 218.1818181818182,0.0 145.45454545454547,-181.81818181818184 363.6363636363637 -145.45454545454547" /></g></g></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="200.0000" stroke-opacity="1" viewBox="0 0 400 200" font-size="1" width="400.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(255,0,0)" stroke-width="1.0285189544531599" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 118.8364,156.5133 l -70.9117,-156.3695 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(255,0,0)" stroke-width="1.0285189544531599" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 219.6217,0.1438 c 0.0000,-94.8257 -76.8714,-171.6971 -171.6971 -171.6971c -94.8257,-0.0000 -171.6971,76.8714 -171.6971 171.6971c -0.0000,94.8257 76.8714,171.6971 171.6971 171.6971c 94.8257,0.0000 171.6971,-76.8714 171.6971 -171.6971Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.9284730395996748" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 18.1818,175.1315 c 218.1818,-0.0000 145.4545,-181.8182 363.6364 -145.4545"/></g></svg>
diff --git a/diagrams/src_Diagrams_TwoD_Curvature_diagramZero.svg b/diagrams/src_Diagrams_TwoD_Curvature_diagramZero.svg
--- a/diagrams/src_Diagrams_TwoD_Curvature_diagramZero.svg
+++ b/diagrams/src_Diagrams_TwoD_Curvature_diagramZero.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="400.0" height="200.0" font-size="1" viewBox="0 0 400 200" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="1.0285189544531599" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><g><g stroke="rgb(255,0,0)" stroke-opacity="1.0"><g><path d="M 189.01818181818183,101.12693463561232 l -602.0741002308241,-540.4757599431822 " /><g><path d="M 396.0221181542372,-439.3488253075699 c 0.0,-446.8414610189286 -362.2365755479508,-809.0780365668795 -809.0780365668793 -809.0780365668795c -446.8414610189286,-2.7361148248157886e-14 -809.0780365668795,362.2365755479508 -809.0780365668795 809.0780365668793c -5.472229649631577e-14,446.8414610189286 362.23657554795074,809.0780365668795 809.0780365668792 809.0780365668795c 446.8414610189286,8.208344474447366e-14 809.0780365668795,-362.2365755479507 809.0780365668796 -809.0780365668793Z" /></g></g></g><g stroke-width="1.9284730395996748"><path d="M 18.18181818181816,175.13148009015777 c 218.1818181818182,0.0 145.45454545454547,-181.81818181818184 363.6363636363637 -145.45454545454547" /></g></g></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="200.0000" stroke-opacity="1" viewBox="0 0 400 200" font-size="1" width="400.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(255,0,0)" stroke-width="1.0285189544531599" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 189.0182,101.1269 l -602.0741,-540.4758 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(255,0,0)" stroke-width="1.0285189544531599" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 396.0221,-439.3488 c 0.0000,-446.8415 -362.2366,-809.0780 -809.0780 -809.0780c -446.8415,-0.0000 -809.0780,362.2366 -809.0780 809.0780c -0.0000,446.8415 362.2366,809.0780 809.0780 809.0780c 446.8415,0.0000 809.0780,-362.2366 809.0780 -809.0780Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="1.9284730395996748" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 18.1818,175.1315 c 218.1818,-0.0000 145.4545,-181.8182 363.6364 -145.4545"/></g></svg>
diff --git a/diagrams/src_Diagrams_TwoD_Offset_cubicOffsetExample.svg b/diagrams/src_Diagrams_TwoD_Offset_cubicOffsetExample.svg
--- a/diagrams/src_Diagrams_TwoD_Offset_cubicOffsetExample.svg
+++ b/diagrams/src_Diagrams_TwoD_Offset_cubicOffsetExample.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="600.0" height="302.85875688987323" font-size="1" viewBox="0 0 600 303" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="1.7051228888683605" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><g><g><g><g stroke-width="3.1971054166281756"><g stroke="rgb(0,128,0)" stroke-opacity="1.0"><path d="M 511.9817800443453,129.7570514462028 c 10.606235857710121,25.069284754587564 34.20547084215346,55.8254698109027 80.48722731216127 86.67997412424124" /></g><g stroke="rgb(255,0,0)" stroke-opacity="1.0"><path d="M 504.6599970504862,99.66254214599796 c 0.33466387043136825,8.255042137307122 2.4133795608657396,18.492828458584018 7.321782993859167 30.094509300204834" /></g><g stroke="rgb(0,128,0)" stroke-opacity="1.0"><path d="M 506.49373385140154,85.26625987587948 c -1.4640943353929654,2.9281886707859424 -2.1082544888015438,7.624845968926011 -1.8337368009153654 14.396282270118487" /></g><g stroke="rgb(255,0,0)" stroke-opacity="1.0"><path d="M 506.20843689577913,85.59271401011557 c 6.779273038019215e-2,-7.684807703746527e-2 0.22264374631797684,-0.20114771562720807 0.2852969556224121 -0.3264541342360786" /></g><g stroke="rgb(0,128,0)" stroke-opacity="1.0"><path d="M 502.6579126738121,87.93569090398208 c 1.0996662998461504,-0.4143670115362421 2.4468736239330267,-1.09190726288214 3.550524221967022 -2.3429768938665214" /></g><g stroke="rgb(255,0,0)" stroke-opacity="1.0"><path d="M 494.06231178115127,87.58378657314935 c 2.9457623866121128,1.3739128917795689 5.382041925447614,1.56281060833337 8.595600892660828 0.35190433083272776" /></g><g stroke="rgb(0,128,0)" stroke-opacity="1.0"><path d="M 489.69619466917715,83.76303109322222 c 1.2338357087118965,2.0880296608970546 2.8653457932043813,3.120790991330947 4.3661171119741375 3.820755479927119" /></g><g stroke="rgb(255,0,0)" stroke-opacity="1.0"><path d="M 489.27962586563393,82.94401200781272 c 7.734890935360485e-2,0.32804714747133107 0.30246544790101604,0.6259210989381142 0.4165688035432176 0.8190190854095305" /></g><g stroke="rgb(0,128,0)" stroke-opacity="1.0"><path d="M 489.54489237921933,85.09467757558335 c -5.201273523887837e-2,-0.8562096416246061 -0.12423198149539025,-1.552519112523536 -0.2652665135854216 -2.1506655677706314" /></g><g stroke="rgb(255,0,0)" stroke-opacity="1.0"><path d="M 488.88654448360757,96.10544324136518 c 0.6285951592007363,-4.609697834138748 0.828592417895299,-8.2082789143452 0.6583478956117675 -11.010765665781841" /></g><g stroke="rgb(0,128,0)" stroke-opacity="1.0"><path d="M 441.84915448663645,221.4997735858574 c 31.929731500854007,-63.859463001708015 44.04397766876603,-103.4426399376551 47.0373899969711 -125.39433034449225" /></g></g><g stroke="rgb(0,0,255)" stroke-opacity="1.0" stroke-width="3.1971054166281756"><path d="M 453.61585838946286,227.38312553727062 c 131.55574898915938,-263.11149797831877 -65.77787449457969,-131.55574898915938 131.55574898915938 0.0" /></g></g></g><g><g stroke-width="3.1971054166281756"><g stroke="rgb(0,128,0)" stroke-opacity="1.0"><path d="M 364.7622235703774,85.96753101537462 c 0.0,15.32911917179821 0.6082191299019319,77.38134470418049 61.92469581709475 138.6978213913733" /></g><g stroke="rgb(255,0,0)" stroke-opacity="1.0"><path d="M 364.7418968655278,83.13929813428342 c 1.788756316072539e-2,0.7020868540585622 2.0326704849611067e-2,1.6834288388046041 2.0326704849611067e-2 2.8282328810911928" /></g><g stroke="rgb(0,128,0)" stroke-opacity="1.0"><path d="M 364.66018914900314,81.56310499408985 c 3.509055922831261e-2,0.4103645954199807 6.611191242317345e-2,0.9640578292107734 8.170771652464312e-2 1.5761931401935576" /></g><g stroke="rgb(255,0,0)" stroke-opacity="1.0"><path d="M 364.0519985963925,78.3408445789562 c 0.1986120881746295,0.6454892865675517 0.49647125301243666,1.9157652726099432 0.6081905526106672 3.222260415133674" /></g><g stroke="rgb(0,128,0)" stroke-opacity="1.0"><path d="M 361.61586606058245,73.77595634835652 c 0.7782819994477024,0.9536356598170914 1.821193672048922,2.5663369233759687 2.4361325358100574 4.56488823059968" /></g><g stroke="rgb(255,0,0)" stroke-opacity="1.0"><path d="M 357.18966169675525,70.25802410049732 c 1.5342253961814387,0.7533004195932371 3.0492264459247083,1.8307093052441525 4.4262043638271615 3.5179322478592" /></g><g stroke="rgb(0,128,0)" stroke-opacity="1.0"><path d="M 349.91728913050906,68.98396616497621 c 2.6563706456126566,-0.29220077101738523 4.874998058580779,9.695369318400074e-2 7.272372566246194 1.2740579355211068" /></g><g stroke="rgb(255,0,0)" stroke-opacity="1.0"><path d="M 344.50737812673475,70.81874430723295 c 1.8904834233446657,-1.1435066965469183 3.695186810264414,-1.646158480970656 5.409911003774321 -1.8347781422567455" /></g><g stroke="rgb(0,128,0)" stroke-opacity="1.0"><path d="M 341.90372938933297,72.87554041429576 c 0.8842995586107709,-0.8970890150369701 1.797912982551884,-1.5694264639648254 2.603648737401782 -2.0567961070628042" /></g><g stroke="rgb(255,0,0)" stroke-opacity="1.0"><path d="M 339.9429387947987,75.39357199790629 c 0.6567471005360201,-1.07633552587847 1.4089406003338527,-1.9582002878411218 1.9607905945342574 -2.518031583610547" /></g><g stroke="rgb(0,128,0)" stroke-opacity="1.0"><path d="M 338.2153466102729,79.15920115255244 c 0.597623909908983,-1.6434657522496974 1.3914287352020123,-3.2146946126988167 1.7275921845258109 -3.7656291546461453" /></g><g stroke="rgb(255,0,0)" stroke-opacity="1.0"><path d="M 331.02089158742825,99.97173175435304 c 4.036215742086064,-11.099593290736674 6.185401087323137,-18.037632279116448 7.194455022844654 -20.812530601800606" /></g><g stroke="rgb(0,128,0)" stroke-opacity="1.0"><path d="M 274.0620702740554,228.08439667676572 c 32.5250961454588,-65.0501922909176 48.82754727700816,-105.75166132240976 56.95882131337286 -128.11266492241268" /></g></g><g stroke="rgb(0,0,255)" stroke-opacity="1.0" stroke-width="3.1971054166281756"><path d="M 285.8287741768818,233.96774862817892 c 131.55574898915938,-263.11149797831877 0.0,-131.55574898915938 131.55574898915938 0.0" /></g></g></g><g><g><g stroke-width="3.1971054166281756"><g stroke="rgb(0,128,0)" stroke-opacity="1.0"><path d="M 243.50666848816087,119.71820244879379 c -3.7564422059063327,1.274913718368207 -8.501013484230306,2.111132473581956 -14.329190482484984 2.111132473581956" /></g><g stroke="rgb(255,0,0)" stroke-opacity="1.0"><path d="M 255.13710847034906,112.19787026866632 c -2.6841784256200127,3.067632486422875 -6.357946646148891,5.7308798963808005 -11.630439982188191 7.520332180127452" /></g><g stroke="rgb(0,128,0)" stroke-opacity="1.0"><path d="M 258.96767454384855,87.61006066523365 c 3.4874720283559038,9.299925408949084 2.272509976123352,17.612865546720847 -3.830566073499483 24.58780960343268" /></g><g stroke="rgb(255,0,0)" stroke-opacity="1.0"><path d="M 220.95524369385342,62.629247877254016 c 17.797228450008376,0.0 33.56312373749303,13.115993821307395 38.01243084999512 24.980812787979637" /></g><g stroke="rgb(0,128,0)" stroke-opacity="1.0"><path d="M 193.4370789740102,72.62776873252105 c 9.382487531803335,-7.358813750433995 18.687588219322443,-9.998520855267019 27.518164719843227 -9.998520855267019" /></g><g stroke="rgb(255,0,0)" stroke-opacity="1.0"><path d="M 170.96813963611902,103.1924277725802 c 6.767680004875894,-14.76584728336559 14.6245829686032,-24.412222671990158 22.468939337891168 -30.564659040059155" /></g><g stroke="rgb(0,128,0)" stroke-opacity="1.0"><path d="M 150.24402861218024,240.2295090126192 c 0.0,-68.44669429030839 8.959835442792022,-111.36957088117335 20.724111023938775 -137.037081240039" /></g></g><g stroke="rgb(0,0,255)" stroke-opacity="1.0" stroke-width="3.1971054166281756"><path d="M 163.3996035110962,240.2295090126192 c 0.0,-263.11149797831877 131.55574898915938,-131.55574898915938 65.77787449457969 -131.55574898915938" /></g></g></g><g><g stroke-width="3.1971054166281756"><g stroke="rgb(0,128,0)" stroke-opacity="1.0"><path d="M 107.3603699766031,38.693005210400855 c 6.432503982934959,-12.169602129876955 14.760815226591284,-20.476100728687896 25.887308602478793 -24.92669807904294" /></g><g stroke="rgb(255,0,0)" stroke-opacity="1.0"><path d="M 95.42391061094953,75.63181695246936 c 2.8371303744504006,-14.299137087230031 6.687768172920306,-27.008855431492076 11.936459365653556 -36.938811742068495" /></g><g stroke="rgb(0,128,0)" stroke-opacity="1.0"><path d="M 83.97921363564316,165.6871778325085 c 4.142251616420563,-31.481112284796282 6.26688245478068,-63.95917569658957 11.444696975306384 -90.05536088003915" /></g><g stroke="rgb(255,0,0)" stroke-opacity="1.0"><path d="M 62.05745780862836,244.98865707076718 c 12.61861350979178,-21.354576708878394 18.039105516309633,-49.793336876899446 21.921755827014795 -79.30147923825866" /></g><g stroke="rgb(0,128,0)" stroke-opacity="1.0"><path d="M 6.577787449457958,275.93687485959947 c 26.333097622202164,0.0 44.78184945015078,-12.844213173568285 55.4796703591704 -30.94821778883227" /></g></g><g stroke="rgb(0,0,255)" stroke-opacity="1.0" stroke-width="3.1971054166281756"><path d="M 6.577787449457958,289.0924497585154 c 131.55574898915938,0.0 65.77787449457969,-236.8003481804869 131.55574898915938 -263.11149797831877" /></g></g></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="302.8588" stroke-opacity="1" viewBox="0 0 600 303" font-size="1" width="600.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,128,0)" stroke-width="3.197105416628175" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 511.9818,129.7571 c 10.6062,25.0693 34.2055,55.8255 80.4872 86.6800"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(255,0,0)" stroke-width="3.197105416628175" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 504.6600,99.6625 c 0.3347,8.2550 2.4134,18.4928 7.3218 30.0945"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,128,0)" stroke-width="3.197105416628175" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 506.4937,85.2663 c -1.4641,2.9282 -2.1083,7.6248 -1.8337 14.3963"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(255,0,0)" stroke-width="3.197105416628175" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 506.2084,85.5927 c 0.0678,-0.0768 0.2226,-0.2011 0.2853 -0.3265"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,128,0)" stroke-width="3.197105416628175" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 502.6579,87.9357 c 1.0997,-0.4144 2.4469,-1.0919 3.5505 -2.3430"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(255,0,0)" stroke-width="3.197105416628175" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 494.0623,87.5838 c 2.9458,1.3739 5.3820,1.5628 8.5956 0.3519"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,128,0)" stroke-width="3.197105416628175" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 489.6962,83.7630 c 1.2338,2.0880 2.8653,3.1208 4.3661 3.8208"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(255,0,0)" stroke-width="3.197105416628175" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 489.2796,82.9440 c 0.0773,0.3280 0.3025,0.6259 0.4166 0.8190"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,128,0)" stroke-width="3.197105416628175" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 489.5449,85.0947 c -0.0520,-0.8562 -0.1242,-1.5525 -0.2653 -2.1507"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(255,0,0)" stroke-width="3.197105416628175" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 488.8865,96.1054 c 0.6286,-4.6097 0.8286,-8.2083 0.6583 -11.0108"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,128,0)" stroke-width="3.197105416628175" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 441.8492,221.4998 c 31.9297,-63.8595 44.0440,-103.4426 47.0374 -125.3943"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,255)" stroke-width="3.197105416628175" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 453.6159,227.3831 c 131.5557,-263.1115 -65.7779,-131.5557 131.5557 -0.0000"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,128,0)" stroke-width="3.197105416628175" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 364.7622,85.9675 c 0.0000,15.3291 0.6082,77.3813 61.9247 138.6978"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(255,0,0)" stroke-width="3.197105416628175" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 364.7419,83.1393 c 0.0179,0.7021 0.0203,1.6834 0.0203 2.8282"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,128,0)" stroke-width="3.197105416628175" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 364.6602,81.5631 c 0.0351,0.4104 0.0661,0.9641 0.0817 1.5762"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(255,0,0)" stroke-width="3.197105416628175" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 364.0520,78.3408 c 0.1986,0.6455 0.4965,1.9158 0.6082 3.2223"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,128,0)" stroke-width="3.197105416628175" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 361.6159,73.7760 c 0.7783,0.9536 1.8212,2.5663 2.4361 4.5649"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(255,0,0)" stroke-width="3.197105416628175" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 357.1897,70.2580 c 1.5342,0.7533 3.0492,1.8307 4.4262 3.5179"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,128,0)" stroke-width="3.197105416628175" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 349.9173,68.9840 c 2.6564,-0.2922 4.8750,0.0970 7.2724 1.2741"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(255,0,0)" stroke-width="3.197105416628175" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 344.5074,70.8187 c 1.8905,-1.1435 3.6952,-1.6462 5.4099 -1.8348"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,128,0)" stroke-width="3.197105416628175" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 341.9037,72.8755 c 0.8843,-0.8971 1.7979,-1.5694 2.6036 -2.0568"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(255,0,0)" stroke-width="3.197105416628175" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 339.9429,75.3936 c 0.6567,-1.0763 1.4089,-1.9582 1.9608 -2.5180"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,128,0)" stroke-width="3.197105416628175" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 338.2153,79.1592 c 0.5976,-1.6435 1.3914,-3.2147 1.7276 -3.7656"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(255,0,0)" stroke-width="3.197105416628175" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 331.0209,99.9717 c 4.0362,-11.0996 6.1854,-18.0376 7.1945 -20.8125"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,128,0)" stroke-width="3.197105416628175" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 274.0621,228.0844 c 32.5251,-65.0502 48.8275,-105.7517 56.9588 -128.1127"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,255)" stroke-width="3.197105416628175" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 285.8288,233.9677 c 131.5557,-263.1115 0.0000,-131.5557 131.5557 -0.0000"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,128,0)" stroke-width="3.197105416628175" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 243.5067,119.7182 c -3.7564,1.2749 -8.5010,2.1111 -14.3292 2.1111"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(255,0,0)" stroke-width="3.197105416628175" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 255.1371,112.1979 c -2.6842,3.0676 -6.3579,5.7309 -11.6304 7.5203"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,128,0)" stroke-width="3.197105416628175" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 258.9677,87.6101 c 3.4875,9.2999 2.2725,17.6129 -3.8306 24.5878"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(255,0,0)" stroke-width="3.197105416628175" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 220.9552,62.6292 c 17.7972,-0.0000 33.5631,13.1160 38.0124 24.9808"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,128,0)" stroke-width="3.197105416628175" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 193.4371,72.6278 c 9.3825,-7.3588 18.6876,-9.9985 27.5182 -9.9985"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(255,0,0)" stroke-width="3.197105416628175" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 170.9681,103.1924 c 6.7677,-14.7658 14.6246,-24.4122 22.4689 -30.5647"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,128,0)" stroke-width="3.197105416628175" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 150.2440,240.2295 c 0.0000,-68.4467 8.9598,-111.3696 20.7241 -137.0371"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,255)" stroke-width="3.197105416628175" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 163.3996,240.2295 c 0.0000,-263.1115 131.5557,-131.5557 65.7779 -131.5557"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,128,0)" stroke-width="3.197105416628175" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 107.3604,38.6930 c 6.4325,-12.1696 14.7608,-20.4761 25.8873 -24.9267"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(255,0,0)" stroke-width="3.197105416628175" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 95.4239,75.6318 c 2.8371,-14.2991 6.6878,-27.0089 11.9365 -36.9388"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,128,0)" stroke-width="3.197105416628175" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 83.9792,165.6872 c 4.1423,-31.4811 6.2669,-63.9592 11.4447 -90.0554"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(255,0,0)" stroke-width="3.197105416628175" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 62.0575,244.9887 c 12.6186,-21.3546 18.0391,-49.7933 21.9218 -79.3015"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,128,0)" stroke-width="3.197105416628175" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 6.5778,275.9369 c 26.3331,-0.0000 44.7818,-12.8442 55.4797 -30.9482"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,255)" stroke-width="3.197105416628175" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 6.5778,289.0924 c 131.5557,-0.0000 65.7779,-236.8003 131.5557 -263.1115"/></g></svg>
diff --git a/diagrams/src_Diagrams_TwoD_Offset_expandLoopExample.svg b/diagrams/src_Diagrams_TwoD_Offset_expandLoopExample.svg
--- a/diagrams/src_Diagrams_TwoD_Offset_expandLoopExample.svg
+++ b/diagrams/src_Diagrams_TwoD_Offset_expandLoopExample.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="300.0" height="300.00000000000006" font-size="1" viewBox="0 0 300 300" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="1.2" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><g><g fill="rgb(0,128,0)" fill-opacity="1.0" stroke-width="0.0"><g fill="rgb(0,128,0)" fill-opacity="1.0"><g fill="rgb(0,128,0)" fill-opacity="1.0"><path d="M 36.363636363636374,286.3636363636364 h 113.63636363636363 c 6.027647496353275,-2.892321107515236e-15 11.80841824405711,-2.3944736446685924 16.070608663330628 -6.656664063942104l 113.63636363636363,-113.63636363636363 c 4.262190419273511,-4.262190419273516 6.656664063942097,-10.042961166977355 6.656664063942101 -16.070608663330628v -113.63636363636363 c 0.0,-12.551926132518032 -10.175346594754691,-22.727272727272727 -22.727272727272723 -22.727272727272727c -6.027647496353271,2.1541471862354763e-15 -11.80841824405711,2.394473644668591 -16.070608663330628 6.6566640639421015l -227.27272727272725,227.27272727272725 c -8.875552085256137,8.875552085256135 -8.87555208525614,23.265665241405113 -5.0464682937507114e-15 32.14121732666125c 4.262190419273514,4.262190419273512 10.042961166977355,6.656664063942098 16.07060866333063 6.656664063942117ZM 36.363636363636374,240.9090909090909 c -12.551926132518032,3.7848512203130333e-14 -22.727272727272727,10.17534659475473 -22.727272727272727 22.72727272727276c -2.5232341468753557e-15,12.551926132518032 10.17534659475469,22.727272727272727 22.727272727272716 22.727272727272727c 6.027647496353271,-1.2616170734376779e-15 11.80841824405711,-2.3944736446685897 16.070608663330628 -6.656664063942099l 227.27272727272725,-227.27272727272725 c 8.875552085256135,-8.875552085256134 8.875552085256137,-23.265665241405113 0.0 -32.14121732666125c -8.875552085256134,-8.875552085256135 -23.265665241405113,-8.875552085256137 -32.14121732666125 -2.5232341468753557e-15c -4.262190419273512,4.262190419273517 -6.656664063942098,10.042961166977355 -6.6566640639421015 16.070608663330628v 113.63636363636363 c -2.5232341468753557e-15,12.551926132518032 10.17534659475469,22.727272727272727 22.72727272727272 22.72727272727273c 12.551926132518032,2.5232341468753557e-15 22.727272727272727,-10.17534659475469 22.72727272727273 -22.727272727272716c 2.5232341468753557e-15,-12.551926132518032 -10.175346594754686,-22.727272727272727 -22.727272727272712 -22.72727272727273c -6.027647496353266,1.2616170734376779e-15 -11.808418244057094,2.3944736446685777 -16.07060866333061 6.656664063942079l -113.63636363636363,113.63636363636363 c -8.875552085256132,8.875552085256139 -8.875552085256128,23.265665241405113 1.0092936587501423e-14 32.14121732666125c 8.875552085256139,8.875552085256132 23.265665241405113,8.87555208525613 32.14121732666125 -7.569702440626068e-15c 8.875552085256134,-8.875552085256139 8.87555208525613,-23.265665241405113 -5.0464682937507114e-15 -32.14121732666124c -4.262190419273514,-4.262190419273507 -10.042961166977339,-6.656664063942092 -16.070608663330603 -6.656664063942101Z" /></g></g></g><g stroke="rgb(255,255,255)" stroke-opacity="1.0" stroke-width="3.0"><path d="M 36.363636363636374,263.6363636363636 h 113.63636363636363 l 113.63636363636363,-113.63636363636363 v -113.63636363636363 Z" /></g></g></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="300.0000" stroke-opacity="1" viewBox="0 0 300 300" font-size="1" width="300.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,128,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 36.3636,286.3636 h 113.6364 c 6.0276,-0.0000 11.8084,-2.3945 16.0706 -6.6567l 113.6364,-113.6364 c 4.2622,-4.2622 6.6567,-10.0430 6.6567 -16.0706v -113.6364 c 0.0000,-12.5519 -10.1753,-22.7273 -22.7273 -22.7273c -6.0276,0.0000 -11.8084,2.3945 -16.0706 6.6567l -227.2727,227.2727 c -8.8756,8.8756 -8.8756,23.2657 -0.0000 32.1412c 4.2622,4.2622 10.0430,6.6567 16.0706 6.6567ZM 36.3636,240.9091 c -12.5519,0.0000 -22.7273,10.1753 -22.7273 22.7273c -0.0000,12.5519 10.1753,22.7273 22.7273 22.7273c 6.0276,-0.0000 11.8084,-2.3945 16.0706 -6.6567l 227.2727,-227.2727 c 8.8756,-8.8756 8.8756,-23.2657 0.0000 -32.1412c -8.8756,-8.8756 -23.2657,-8.8756 -32.1412 -0.0000c -4.2622,4.2622 -6.6567,10.0430 -6.6567 16.0706v 113.6364 c -0.0000,12.5519 10.1753,22.7273 22.7273 22.7273c 12.5519,0.0000 22.7273,-10.1753 22.7273 -22.7273c 0.0000,-12.5519 -10.1753,-22.7273 -22.7273 -22.7273c -6.0276,0.0000 -11.8084,2.3945 -16.0706 6.6567l -113.6364,113.6364 c -8.8756,8.8756 -8.8756,23.2657 0.0000 32.1412c 8.8756,8.8756 23.2657,8.8756 32.1412 -0.0000c 8.8756,-8.8756 8.8756,-23.2657 -0.0000 -32.1412c -4.2622,-4.2622 -10.0430,-6.6567 -16.0706 -6.6567Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(255,255,255)" stroke-width="3.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 36.3636,263.6364 h 113.6364 l 113.6364,-113.6364 v -113.6364 Z"/></g></svg>
diff --git a/diagrams/src_Diagrams_TwoD_Offset_expandTrailExample.svg b/diagrams/src_Diagrams_TwoD_Offset_expandTrailExample.svg
--- a/diagrams/src_Diagrams_TwoD_Offset_expandTrailExample.svg
+++ b/diagrams/src_Diagrams_TwoD_Offset_expandTrailExample.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="600.0" height="197.3830287816636" font-size="1" viewBox="0 0 600 197" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="1.376545341172593" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><g><g><g><g fill="rgb(0,0,0)" fill-opacity="1.0" font-weight="bold" font-family="Helvetica"><g fill="rgb(0,0,0)" fill-opacity="1.0"><text transform="matrix(12.98696646675048,0.0,0.0,12.98696646675048,481.81818181818187,168.9306232278259)" dominant-baseline="middle" text-anchor="middle" stroke="none">LineCapSquare</text></g></g></g><g><g fill="rgb(0,128,0)" fill-opacity="1.0" stroke-width="0.0"><g fill="rgb(0,128,0)" fill-opacity="1.0"><g fill="rgb(0,128,0)" fill-opacity="1.0"><path d="M 416.8830238425919,97.50165637702322 h -25.97393293350096 v 51.94786586700192 h 25.97393293350096 h 129.86966466750482 c 14.345007052300385,-8.783783485172937e-16 25.97393293350096,-11.628925881200574 25.973932933500958 -25.973932933500958c 0.0,-6.076251092058475 -2.130283781570332,-11.960201272862653 -6.020204939150425 -16.62810666195877l -64.93483233375241,-77.92179880050288 l -16.628106661958775,-19.953727994350533 l -39.907455988701045,33.25621332391753 l 16.628106661958775,19.953727994350533 l 64.93483233375241,77.92179880050288 c 9.183449727959651,11.020139673551585 25.561694982757718,12.509071060351415 36.5818346563093 3.325621332391765c 11.020139673551585,-9.183449727959651 12.509071060351415,-25.561694982757714 3.3256213323917683 -36.5818346563093c -4.934886876493225,-5.921864251791868 -12.245188268797092,-9.34582627154219 -19.95372799435053 -9.34582627154219Z" /></g></g></g><g stroke="rgb(255,255,255)" stroke-opacity="1.0" stroke-width="3.4413633529314827"><path d="M 416.8830238425919,123.47558931052419 h 129.86966466750482 l -64.93483233375241,-77.92179880050288 " /></g></g></g><g><g><g fill="rgb(0,0,0)" fill-opacity="1.0" font-weight="bold" font-family="Helvetica"><g fill="rgb(0,0,0)" fill-opacity="1.0"><text transform="matrix(12.98696646675048,0.0,0.0,12.98696646675048,287.0130335332496,163.62699800825925)" dominant-baseline="middle" text-anchor="middle" stroke="none">LineCapRound</text></g></g></g><g><g fill="rgb(0,128,0)" fill-opacity="1.0" stroke-width="0.0"><g fill="rgb(0,128,0)" fill-opacity="1.0"><g fill="rgb(0,128,0)" fill-opacity="1.0"><path d="M 222.07787555765964,92.19803115745658 c -14.345007052300385,-8.783783485172937e-16 -25.97393293350096,11.628925881200571 -25.97393293350096 25.973932933500954c -1.7567566970345874e-15,14.345007052300385 11.628925881200571,25.97393293350096 25.97393293350095 25.97393293350096h 129.86966466750482 c 14.345007052300385,-8.783783485172937e-16 25.97393293350096,-11.628925881200574 25.973932933500958 -25.973932933500958c 0.0,-6.076251092058475 -2.130283781570332,-11.960201272862653 -6.020204939150425 -16.62810666195877l -64.93483233375241,-77.92179880050288 c -9.183449727959651,-11.020139673551583 -25.56169498275772,-12.50907106035141 -36.5818346563093 -3.3256213323917594c -11.020139673551583,9.183449727959651 -12.509071060351411,25.56169498275772 -3.3256213323917625 36.5818346563093l 64.93483233375241,77.92179880050288 c 9.183449727959651,11.020139673551585 25.561694982757718,12.509071060351415 36.5818346563093 3.325621332391765c 11.020139673551585,-9.183449727959651 12.509071060351415,-25.561694982757714 3.3256213323917683 -36.5818346563093c -4.934886876493225,-5.921864251791868 -12.245188268797092,-9.34582627154219 -19.95372799435053 -9.34582627154219Z" /></g></g></g><g stroke="rgb(255,255,255)" stroke-opacity="1.0" stroke-width="3.4413633529314827"><path d="M 222.07787555765964,118.17196409095754 h 129.86966466750482 l -64.93483233375241,-77.92179880050288 " /></g></g></g><g><g fill="rgb(0,0,0)" fill-opacity="1.0" font-weight="bold" font-family="Helvetica"><g fill="rgb(0,0,0)" fill-opacity="1.0"><text transform="matrix(12.98696646675048,0.0,0.0,12.98696646675048,105.19485171506778,158.95375923065063)" dominant-baseline="middle" text-anchor="middle" stroke="none">LineCapButt</text></g></g></g><g><g fill="rgb(0,128,0)" fill-opacity="1.0" stroke-width="0.0"><g fill="rgb(0,128,0)" fill-opacity="1.0"><g fill="rgb(0,128,0)" fill-opacity="1.0"><path d="M 27.272727272727366,87.52479237984795 v 51.94786586700192 h 129.86966466750482 c 14.345007052300385,-8.783783485172937e-16 25.97393293350096,-11.628925881200574 25.973932933500958 -25.973932933500958c 0.0,-6.076251092058475 -2.130283781570332,-11.960201272862653 -6.020204939150425 -16.62810666195877l -64.93483233375241,-77.92179880050288 l -39.907455988701045,33.25621332391753 l 64.93483233375241,77.92179880050288 c 9.183449727959651,11.020139673551585 25.561694982757718,12.509071060351415 36.5818346563093 3.325621332391765c 11.020139673551585,-9.183449727959651 12.509071060351415,-25.561694982757714 3.3256213323917683 -36.5818346563093c -4.934886876493225,-5.921864251791868 -12.245188268797092,-9.34582627154219 -19.95372799435053 -9.34582627154219Z" /></g></g></g><g stroke="rgb(255,255,255)" stroke-opacity="1.0" stroke-width="3.4413633529314827"><path d="M 27.272727272727366,113.49872531334891 h 129.86966466750482 l -64.93483233375241,-77.92179880050288 " /></g></g></g></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="197.3830" stroke-opacity="1" viewBox="0 0 600 197" font-size="1" width="600.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" font-size="12.98696646675048px" stroke="rgb(0,0,0)" stroke-width="1.376545341172593" fill="rgb(0,0,0)" stroke-linecap="butt" font-family="Helvetica" stroke-miterlimit="10.0" font-weight="bold"><text dominant-baseline="middle" transform="matrix(1.0000,0.0000,0.0000,1.0000,481.8182,168.9306)" stroke="none" text-anchor="middle">LineCapSquare</text></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,128,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 416.8830,97.5017 h -25.9739 v 51.9479 h 25.9739 h 129.8697 c 14.3450,-0.0000 25.9739,-11.6289 25.9739 -25.9739c 0.0000,-6.0763 -2.1303,-11.9602 -6.0202 -16.6281l -64.9348,-77.9218 l -16.6281,-19.9537 l -39.9075,33.2562 l 16.6281,19.9537 l 64.9348,77.9218 c 9.1834,11.0201 25.5617,12.5091 36.5818 3.3256c 11.0201,-9.1834 12.5091,-25.5617 3.3256 -36.5818c -4.9349,-5.9219 -12.2452,-9.3458 -19.9537 -9.3458Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(255,255,255)" stroke-width="3.4413633529314827" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 416.8830,123.4756 h 129.8697 l -64.9348,-77.9218 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" font-size="12.98696646675048px" stroke="rgb(0,0,0)" stroke-width="1.376545341172593" fill="rgb(0,0,0)" stroke-linecap="butt" font-family="Helvetica" stroke-miterlimit="10.0" font-weight="bold"><text dominant-baseline="middle" transform="matrix(1.0000,0.0000,0.0000,1.0000,287.0130,163.6270)" stroke="none" text-anchor="middle">LineCapRound</text></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,128,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 222.0779,92.1980 c -14.3450,-0.0000 -25.9739,11.6289 -25.9739 25.9739c -0.0000,14.3450 11.6289,25.9739 25.9739 25.9739h 129.8697 c 14.3450,-0.0000 25.9739,-11.6289 25.9739 -25.9739c 0.0000,-6.0763 -2.1303,-11.9602 -6.0202 -16.6281l -64.9348,-77.9218 c -9.1834,-11.0201 -25.5617,-12.5091 -36.5818 -3.3256c -11.0201,9.1834 -12.5091,25.5617 -3.3256 36.5818l 64.9348,77.9218 c 9.1834,11.0201 25.5617,12.5091 36.5818 3.3256c 11.0201,-9.1834 12.5091,-25.5617 3.3256 -36.5818c -4.9349,-5.9219 -12.2452,-9.3458 -19.9537 -9.3458Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(255,255,255)" stroke-width="3.4413633529314827" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 222.0779,118.1720 h 129.8697 l -64.9348,-77.9218 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" font-size="12.98696646675048px" stroke="rgb(0,0,0)" stroke-width="1.376545341172593" fill="rgb(0,0,0)" stroke-linecap="butt" font-family="Helvetica" stroke-miterlimit="10.0" font-weight="bold"><text dominant-baseline="middle" transform="matrix(1.0000,0.0000,0.0000,1.0000,105.1949,158.9538)" stroke="none" text-anchor="middle">LineCapButt</text></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(0,128,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 27.2727,87.5248 v 51.9479 h 129.8697 c 14.3450,-0.0000 25.9739,-11.6289 25.9739 -25.9739c 0.0000,-6.0763 -2.1303,-11.9602 -6.0202 -16.6281l -64.9348,-77.9218 l -39.9075,33.2562 l 64.9348,77.9218 c 9.1834,11.0201 25.5617,12.5091 36.5818 3.3256c 11.0201,-9.1834 12.5091,-25.5617 3.3256 -36.5818c -4.9349,-5.9219 -12.2452,-9.3458 -19.9537 -9.3458Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(255,255,255)" stroke-width="3.4413633529314827" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 27.2727,113.4987 h 129.8697 l -64.9348,-77.9218 "/></g></svg>
diff --git a/diagrams/src_Diagrams_TwoD_Offset_offsetTrailExample.svg b/diagrams/src_Diagrams_TwoD_Offset_offsetTrailExample.svg
--- a/diagrams/src_Diagrams_TwoD_Offset_offsetTrailExample.svg
+++ b/diagrams/src_Diagrams_TwoD_Offset_offsetTrailExample.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="600.0" height="185.1008379753402" font-size="1" viewBox="0 0 600 185" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="1.333029648793779" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><g stroke-width="3.0"><g><g><g fill="rgb(0,0,0)" fill-opacity="1.0" font-weight="bold" font-family="Helvetica"><g fill="rgb(0,0,0)" fill-opacity="1.0"><text transform="matrix(13.702641330909062,0.0,0.0,13.702641330909062,493.6874054156325,156.13320152555207)" dominant-baseline="middle" text-anchor="middle" stroke="none">LineJoinBevel</text></g></g></g><g><g stroke="rgb(0,128,0)" stroke-opacity="1.0"><path d="M 414.64753810399236,135.57923952918844 h 137.02641330909063 l 21.0533213141897,-44.949717090309534 l -68.51320665454531,-82.21584798545437 " /></g><g stroke="rgb(0,0,255)" stroke-opacity="1.0"><path d="M 414.64753810399236,108.17395686737032 h 137.02641330909063 l -68.51320665454531,-82.21584798545437 " /></g></g></g><g><g><g fill="rgb(0,0,0)" fill-opacity="1.0" font-weight="bold" font-family="Helvetica"><g fill="rgb(0,0,0)" fill-opacity="1.0"><text transform="matrix(13.702641330909062,0.0,0.0,13.702641330909062,318.7290487876289,156.13320152555207)" dominant-baseline="middle" text-anchor="middle" stroke="none">LineJoinRound</text></g></g></g><g><g stroke="rgb(0,128,0)" stroke-opacity="1.0"><path d="M 236.51320080217454,135.57923952918844 h 137.02641330909063 c 15.135519678924403,-9.267832864113272e-16 27.405282661818124,-12.269762982893718 27.40528266181812 -27.40528266181812c 0.0,-6.411096044960741 -2.247677674893909,-12.619294021209988 -6.3519613476284205 -17.54443442849141l -68.51320665454531,-82.21584798545437 " /></g><g stroke="rgb(0,0,255)" stroke-opacity="1.0"><path d="M 236.51320080217454,108.17395686737032 h 137.02641330909063 l -68.51320665454531,-82.21584798545437 " /></g></g></g><g><g fill="rgb(0,0,0)" fill-opacity="1.0" font-weight="bold" font-family="Helvetica"><g fill="rgb(0,0,0)" fill-opacity="1.0"><text transform="matrix(13.702641330909062,0.0,0.0,13.702641330909062,125.0416433719964,156.13320152555207)" dominant-baseline="middle" text-anchor="middle" stroke="none">LineJoinMiter</text></g></g></g><g><g stroke="rgb(0,128,0)" stroke-opacity="1.0"><path d="M 27.27272727272728,135.57923952918844 h 137.02641330909063 h 58.51141888944763 l -37.45809757525794,-44.949717090309534 l -68.51320665454531,-82.21584798545437 " /></g><g stroke="rgb(0,0,255)" stroke-opacity="1.0"><path d="M 27.27272727272728,108.17395686737032 h 137.02641330909063 l -68.51320665454531,-82.21584798545437 " /></g></g></g></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="185.1008" stroke-opacity="1" viewBox="0 0 600 185" font-size="1" width="600.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" font-size="13.702641330909062px" stroke="rgb(0,0,0)" stroke-width="3.0" fill="rgb(0,0,0)" stroke-linecap="butt" font-family="Helvetica" stroke-miterlimit="10.0" font-weight="bold"><text dominant-baseline="middle" transform="matrix(1.0000,0.0000,0.0000,1.0000,493.6874,156.1332)" stroke="none" text-anchor="middle">LineJoinBevel</text></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,128,0)" stroke-width="3.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 414.6475,135.5792 h 137.0264 l 21.0533,-44.9497 l -68.5132,-82.2158 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,255)" stroke-width="3.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 414.6475,108.1740 h 137.0264 l -68.5132,-82.2158 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" font-size="13.702641330909062px" stroke="rgb(0,0,0)" stroke-width="3.0" fill="rgb(0,0,0)" stroke-linecap="butt" font-family="Helvetica" stroke-miterlimit="10.0" font-weight="bold"><text dominant-baseline="middle" transform="matrix(1.0000,0.0000,0.0000,1.0000,318.7290,156.1332)" stroke="none" text-anchor="middle">LineJoinRound</text></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,128,0)" stroke-width="3.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 236.5132,135.5792 h 137.0264 c 15.1355,-0.0000 27.4053,-12.2698 27.4053 -27.4053c 0.0000,-6.4111 -2.2477,-12.6193 -6.3520 -17.5444l -68.5132,-82.2158 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,255)" stroke-width="3.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 236.5132,108.1740 h 137.0264 l -68.5132,-82.2158 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" font-size="13.702641330909062px" stroke="rgb(0,0,0)" stroke-width="3.0" fill="rgb(0,0,0)" stroke-linecap="butt" font-family="Helvetica" stroke-miterlimit="10.0" font-weight="bold"><text dominant-baseline="middle" transform="matrix(1.0000,0.0000,0.0000,1.0000,125.0416,156.1332)" stroke="none" text-anchor="middle">LineJoinMiter</text></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,128,0)" stroke-width="3.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 27.2727,135.5792 h 137.0264 h 58.5114 l -37.4581,-44.9497 l -68.5132,-82.2158 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,255)" stroke-width="3.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 27.2727,108.1740 h 137.0264 l -68.5132,-82.2158 "/></g></svg>
diff --git a/diagrams/src_Diagrams_TwoD_Offset_offsetTrailLeftExample.svg b/diagrams/src_Diagrams_TwoD_Offset_offsetTrailLeftExample.svg
--- a/diagrams/src_Diagrams_TwoD_Offset_offsetTrailLeftExample.svg
+++ b/diagrams/src_Diagrams_TwoD_Offset_offsetTrailLeftExample.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="200.0" height="154.67216693398285" font-size="1" viewBox="0 0 200 155" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="0.7035274935556856" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><g stroke-width="3.0"><g stroke="rgb(0,128,0)" stroke-opacity="1.0"><path d="M 9.090909090909093,7.030553042453764 h 151.51451832306768 c 7.088955375224059,5.0464472042177966e-15 13.953559821257857,2.4853295947320184 19.399446190621173 7.023568235868117c 12.856821943491788,10.714018286243158 14.59390752436739,29.82195967587481 3.8798892381242314 42.678781619366596l -75.75725916153384,90.9087109938406 " /></g><g stroke="rgb(0,0,255)" stroke-opacity="1.0"><path d="M 9.090909090909093,37.3334567070673 h 151.51451832306768 l -75.75725916153384,90.9087109938406 " /></g></g></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="154.6722" stroke-opacity="1" viewBox="0 0 200 155" font-size="1" width="200.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,128,0)" stroke-width="3.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 9.0909,7.0306 h 151.5145 c 7.0890,0.0000 13.9536,2.4853 19.3994 7.0236c 12.8568,10.7140 14.5939,29.8220 3.8799 42.6788l -75.7573,90.9087 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,255)" stroke-width="3.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 9.0909,37.3335 h 151.5145 l -75.7573,90.9087 "/></g></svg>
diff --git a/diagrams/src_Diagrams_TwoD_Offset_offsetTrailOuterExample.svg b/diagrams/src_Diagrams_TwoD_Offset_offsetTrailOuterExample.svg
--- a/diagrams/src_Diagrams_TwoD_Offset_offsetTrailOuterExample.svg
+++ b/diagrams/src_Diagrams_TwoD_Offset_offsetTrailOuterExample.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="300.0" height="271.2911579538083" font-size="1" viewBox="0 0 300 271" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="1.141138711190835" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><g stroke-width="3.0"><g stroke="rgb(0,128,0)" stroke-opacity="1.0"><path d="M 232.44254819939368,239.47922220266122 l 48.701298701298725,-84.35312374523753 c 6.959719283925273,-12.05458740617544 6.959719283925287,-26.906451554863526 1.9464949133038462e-14 -38.961038961038966l -48.701298701298676,-84.35312374523755 c -6.959719283925259,-12.054587406175445 -19.82181093024447,-19.480519480519487 -33.741249498095 -19.4805194805195l -97.40259740259742,-4.325544251786325e-14 c -13.919438567850523,-7.0337922695555446e-15 -26.781530214169745,7.42593207434402 -33.741249498095016 19.480519480519458l -48.70129870129873,84.35312374523753 c -6.959719283925277,12.05458740617544 -6.959719283925293,26.906451554863523 -2.811603763661111e-14 38.961038961038966l 48.70129870129864,84.35312374523757 c 6.9597192839252635,12.054587406175456 19.82181093024449,19.480519480519504 33.74124949809503 19.4805194805195h 97.40259740259745 c 13.919438567850523,2.238416443174295e-15 26.78153021416974,-7.42593207434403 33.74124949809499 -19.480519480519447Z" /></g><g stroke="rgb(0,0,255)" stroke-opacity="1.0"><path d="M 198.70129870129864,219.99870272214173 l 48.701298701298725,-84.35312374523753 l -48.701298701298676,-84.35312374523755 l -97.40259740259742,-4.325544251786325e-14 l -48.70129870129873,84.35312374523753 l 48.70129870129864,84.35312374523757 Z" /></g></g></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="271.2912" stroke-opacity="1" viewBox="0 0 300 271" font-size="1" width="300.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,128,0)" stroke-width="3.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 232.4425,239.4792 l 48.7013,-84.3531 c 6.9597,-12.0546 6.9597,-26.9065 -0.0000 -38.9610l -48.7013,-84.3531 c -6.9597,-12.0546 -19.8218,-19.4805 -33.7412 -19.4805h -97.4026 c -13.9194,-0.0000 -26.7815,7.4259 -33.7412 19.4805l -48.7013,84.3531 c -6.9597,12.0546 -6.9597,26.9065 -0.0000 38.9610l 48.7013,84.3531 c 6.9597,12.0546 19.8218,19.4805 33.7412 19.4805l 97.4026,-0.0000 c 13.9194,-0.0000 26.7815,-7.4259 33.7412 -19.4805Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,255)" stroke-width="3.0" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 198.7013,219.9987 l 48.7013,-84.3531 l -48.7013,-84.3531 h -97.4026 l -48.7013,84.3531 l 48.7013,84.3531 Z"/></g></svg>
diff --git a/diagrams/src_Diagrams_TwoD_Shapes_decagonEx.svg b/diagrams/src_Diagrams_TwoD_Shapes_decagonEx.svg
--- a/diagrams/src_Diagrams_TwoD_Shapes_decagonEx.svg
+++ b/diagrams/src_Diagrams_TwoD_Shapes_decagonEx.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="100.0" height="95.10565162951534" font-size="1" viewBox="0 0 100 95" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="0.5" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><path d="M 86.7734997443158,74.27033728259734 l 8.681045710229654,-26.717511467839685 l -8.681045710229668,-26.717511467839678 l -22.727272727272723,-16.512330181940012 l -28.092454034086124,4.678333393029941e-15 l -22.72727272727272,16.51233018194002 l -8.681045710229657,26.717511467839685 l 8.681045710229663,26.71751146783968 l 22.727272727272723,16.512330181940015 l 28.092454034086124,-1.5594444643433139e-15 Z" /></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="95.1057" stroke-opacity="1" viewBox="0 0 100 95" font-size="1" width="100.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.5" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 86.7735,74.2703 l 8.6810,-26.7175 l -8.6810,-26.7175 l -22.7273,-16.5123 l -28.0925,0.0000 l -22.7273,16.5123 l -8.6810,26.7175 l 8.6810,26.7175 l 22.7273,16.5123 l 28.0925,-0.0000 Z"/></g></svg>
diff --git a/diagrams/src_Diagrams_TwoD_Shapes_dodecagonEx.svg b/diagrams/src_Diagrams_TwoD_Shapes_dodecagonEx.svg
--- a/diagrams/src_Diagrams_TwoD_Shapes_dodecagonEx.svg
+++ b/diagrams/src_Diagrams_TwoD_Shapes_dodecagonEx.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="100.0" height="99.99999999999999" font-size="1" viewBox="0 0 100 100" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="0.5" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><path d="M 95.45454545454545,62.179508746869196 l -5.408788415759074e-15,-24.35901749373842 l -12.179508746869214,-21.09552796080702 l -21.095527960807022,-12.179508746869208 l -24.35901749373842,3.917228775555017e-15 l -21.09552796080702,12.179508746869208 l -12.179508746869214,21.09552796080702 l -8.391907696167188e-15,24.35901749373842 l 12.1795087468692,21.095527960807026 l 21.095527960807015,12.179508746869216 l 24.35901749373842,-9.341094951469035e-16 l 21.095527960807015,-12.17950874686922 Z" /></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="100.0000" stroke-opacity="1" viewBox="0 0 100 100" font-size="1" width="100.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.5" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 95.4545,62.1795 l -0.0000,-24.3590 l -12.1795,-21.0955 l -21.0955,-12.1795 l -24.3590,0.0000 l -21.0955,12.1795 l -12.1795,21.0955 l -0.0000,24.3590 l 12.1795,21.0955 l 21.0955,12.1795 l 24.3590,-0.0000 l 21.0955,-12.1795 Z"/></g></svg>
diff --git a/diagrams/src_Diagrams_TwoD_Shapes_hendecagonEx.svg b/diagrams/src_Diagrams_TwoD_Shapes_hendecagonEx.svg
--- a/diagrams/src_Diagrams_TwoD_Shapes_hendecagonEx.svg
+++ b/diagrams/src_Diagrams_TwoD_Shapes_hendecagonEx.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="100.0" height="98.98214418809326" font-size="1" viewBox="0 0 100 99" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="0.5" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><path d="M 95.45454545454545,57.04953832667333 l -3.6824569441366046,-25.612050621948153 l -16.94479989871783,-19.55534153624188 l -24.827288611691024,-7.289949684219485 l -24.827288611691028,7.289949684219488 l -16.944799898717825,19.55534153624188 l -3.6824569441365966,25.612050621948153 l 10.74904007121057,23.537114601287985 l 21.767792813036245,13.989311000023635 l 25.875425140597297,-1.4363746381527874e-15 l 21.767792813036245,-13.989311000023637 Z" /></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="98.9821" stroke-opacity="1" viewBox="0 0 100 99" font-size="1" width="100.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.5" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 95.4545,57.0495 l -3.6825,-25.6121 l -16.9448,-19.5553 l -24.8273,-7.2899 l -24.8273,7.2899 l -16.9448,19.5553 l -3.6825,25.6121 l 10.7490,23.5371 l 21.7678,13.9893 l 25.8754,-0.0000 l 21.7678,-13.9893 Z"/></g></svg>
diff --git a/diagrams/src_Diagrams_TwoD_Shapes_heptagonEx.svg b/diagrams/src_Diagrams_TwoD_Shapes_heptagonEx.svg
--- a/diagrams/src_Diagrams_TwoD_Shapes_heptagonEx.svg
+++ b/diagrams/src_Diagrams_TwoD_Shapes_heptagonEx.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="100.0" height="97.49279121818235" font-size="1" viewBox="0 0 100 97" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="0.5" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><path d="M 95.45454545454544,61.66054654499813 l -9.002830190689187,-39.443976283414365 l -36.45171526385628,-17.554220883072148 l -36.45171526385627,17.554220883072173 l -9.002830190689156,39.443976283414365 l 25.22536964033506,31.631613031861047 l 40.45835162842079,-1.0106503541157029e-14 Z" /></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="97.4928" stroke-opacity="1" viewBox="0 0 100 97" font-size="1" width="100.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.5" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 95.4545,61.6605 l -9.0028,-39.4440 l -36.4517,-17.5542 l -36.4517,17.5542 l -9.0028,39.4440 l 25.2254,31.6316 l 40.4584,-0.0000 Z"/></g></svg>
diff --git a/diagrams/src_Diagrams_TwoD_Shapes_hexagonEx.svg b/diagrams/src_Diagrams_TwoD_Shapes_hexagonEx.svg
--- a/diagrams/src_Diagrams_TwoD_Shapes_hexagonEx.svg
+++ b/diagrams/src_Diagrams_TwoD_Shapes_hexagonEx.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="100.0" height="86.6025403784439" font-size="1" viewBox="0 0 100 87" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="0.5" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><path d="M 72.72727272727272,82.66606127033282 l 22.72727272727274,-39.364791081110845 l -22.727272727272712,-39.36479108111086 l -45.45454545454545,-2.018587317500285e-14 l -22.727272727272744,39.36479108111084 l 22.727272727272698,39.36479108111087 Z" /></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="86.6025" stroke-opacity="1" viewBox="0 0 100 87" font-size="1" width="100.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.5" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 72.7273,82.6661 l 22.7273,-39.3648 l -22.7273,-39.3648 l -45.4545,-0.0000 l -22.7273,39.3648 l 22.7273,39.3648 Z"/></g></svg>
diff --git a/diagrams/src_Diagrams_TwoD_Shapes_hruleEx.svg b/diagrams/src_Diagrams_TwoD_Shapes_hruleEx.svg
--- a/diagrams/src_Diagrams_TwoD_Shapes_hruleEx.svg
+++ b/diagrams/src_Diagrams_TwoD_Shapes_hruleEx.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="300.0" height="48.00000000000001" font-size="1" viewBox="0 0 300 48" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="0.5" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><g><g><path d="M 13.636363636363626,45.81818181818183 h 272.72727272727275 " /></g><g><g><path d="M 40.90909090909091,34.909090909090914 h 218.1818181818182 " /></g><path d="M 68.18181818181819,24.000000000000004 h 163.63636363636363 " /></g><g><path d="M 95.45454545454545,13.090909090909093 h 109.0909090909091 " /></g><path d="M 122.72727272727272,2.1818181818181834 h 54.54545454545455 " /></g></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="48.0000" stroke-opacity="1" viewBox="0 0 300 48" font-size="1" width="300.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.5" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 13.6364,45.8182 h 272.7273 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.5" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 40.9091,34.9091 h 218.1818 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.5" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 68.1818,24.0000 h 163.6364 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.5" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 95.4545,13.0909 h 109.0909 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.5" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 122.7273,2.1818 h 54.5455 "/></g></svg>
diff --git a/diagrams/src_Diagrams_TwoD_Shapes_nonagonEx.svg b/diagrams/src_Diagrams_TwoD_Shapes_nonagonEx.svg
--- a/diagrams/src_Diagrams_TwoD_Shapes_nonagonEx.svg
+++ b/diagrams/src_Diagrams_TwoD_Shapes_nonagonEx.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="100.0" height="98.48077530122083" font-size="1" viewBox="0 0 100 98" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="0.5" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><path d="M 89.97205643508258,73.84920813714508 l 5.482489019462867,-31.09274030233352 l -15.786197969720943,-27.342496941897323 l -29.668347484824512,-10.798395384342669 l -29.668347484824512,10.798395384342673 l -15.786197969720938,27.342496941897327 l 5.4824890194628795,31.09274030233352 l 24.185858465361633,20.294344917990855 l 31.57239593944188,5.257860137182526e-15 Z" /></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="98.4808" stroke-opacity="1" viewBox="0 0 100 98" font-size="1" width="100.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.5" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 89.9721,73.8492 l 5.4825,-31.0927 l -15.7862,-27.3425 l -29.6683,-10.7984 l -29.6683,10.7984 l -15.7862,27.3425 l 5.4825,31.0927 l 24.1859,20.2943 l 31.5724,0.0000 Z"/></g></svg>
diff --git a/diagrams/src_Diagrams_TwoD_Shapes_octagonEx.svg b/diagrams/src_Diagrams_TwoD_Shapes_octagonEx.svg
--- a/diagrams/src_Diagrams_TwoD_Shapes_octagonEx.svg
+++ b/diagrams/src_Diagrams_TwoD_Shapes_octagonEx.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="100.0" height="99.99999999999999" font-size="1" viewBox="0 0 100 100" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="0.5" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><path d="M 95.45454545454544,68.82788919877703 l -8.361262437429426e-15,-37.65577839755409 l -26.626656255768403,-26.6266562557684 l -37.65577839755409,6.0555110132310925e-15 l -26.6266562557684,26.626656255768403 l 3.74975958903276e-15,37.65577839755409 l 26.626656255768403,26.626656255768403 l 37.65577839755409,-1.4440081648344269e-15 Z" /></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="100.0000" stroke-opacity="1" viewBox="0 0 100 100" font-size="1" width="100.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.5" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 95.4545,68.8279 l -0.0000,-37.6558 l -26.6267,-26.6267 l -37.6558,0.0000 l -26.6267,26.6267 l 0.0000,37.6558 l 26.6267,26.6267 l 37.6558,-0.0000 Z"/></g></svg>
diff --git a/diagrams/src_Diagrams_TwoD_Shapes_pentagonEx.svg b/diagrams/src_Diagrams_TwoD_Shapes_pentagonEx.svg
--- a/diagrams/src_Diagrams_TwoD_Shapes_pentagonEx.svg
+++ b/diagrams/src_Diagrams_TwoD_Shapes_pentagonEx.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="100.0" height="95.10565162951536" font-size="1" viewBox="0 0 100 95" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="0.5" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><path d="M 78.09245403408613,91.239057046097 l 17.362091420459326,-53.43502293567938 l -45.45454545454545,-33.024660363880045 l -45.45454545454546,33.02466036388004 l 17.362091420459322,53.435022935679385 Z" /></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="95.1057" stroke-opacity="1" viewBox="0 0 100 95" font-size="1" width="100.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.5" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 78.0925,91.2391 l 17.3621,-53.4350 l -45.4545,-33.0247 l -45.4545,33.0247 l 17.3621,53.4350 Z"/></g></svg>
diff --git a/diagrams/src_Diagrams_TwoD_Shapes_rectEx.svg b/diagrams/src_Diagrams_TwoD_Shapes_rectEx.svg
--- a/diagrams/src_Diagrams_TwoD_Shapes_rectEx.svg
+++ b/diagrams/src_Diagrams_TwoD_Shapes_rectEx.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="150.0" height="104.99999999999999" font-size="1" viewBox="0 0 150 105" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="0.5019960159204453" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><path d="M 143.1818181818182,100.22727272727272 l -1.5139404881252133e-14,-95.45454545454544 h -136.36363636363635 l -1.5139404881252133e-14,95.45454545454544 Z" /></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="105.0000" stroke-opacity="1" viewBox="0 0 150 105" font-size="1" width="150.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.5019960159204453" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 143.1818,100.2273 l -0.0000,-95.4545 h -136.3636 l -0.0000,95.4545 Z"/></g></svg>
diff --git a/diagrams/src_Diagrams_TwoD_Shapes_roundedRectEx.svg b/diagrams/src_Diagrams_TwoD_Shapes_roundedRectEx.svg
--- a/diagrams/src_Diagrams_TwoD_Shapes_roundedRectEx.svg
+++ b/diagrams/src_Diagrams_TwoD_Shapes_roundedRectEx.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="400.0" height="76.19047619047622" font-size="1" viewBox="0 0 400 76" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="0.6982972487551757" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><g><g><path d="M 381.81818181818187,55.41125541125544 v -17.31601731601732 c -19.126744582884623,-7.689856447620133e-15 -34.63203463203463,-15.505290049150023 -34.63203463203463 -34.63203463203465h -51.94805194805195 c -19.126744582884626,-1.1711753265769319e-15 -34.63203463203464,15.505290049150009 -34.63203463203464 34.63203463203463v 34.63203463203464 h 103.89610389610392 c 9.563372291442313,1.7567629898653979e-15 17.31601731601732,-7.752645024575003 17.31601731601728 -17.316017316017295Z" /></g><g><path d="M 225.97402597402595,55.41125541125544 v -34.632034632034646 c -9.563372291442311,-3.844928223810067e-15 -17.316017316017316,-7.752645024575012 -17.316017316017316 -17.316017316017327h -51.94805194805196 c -3.844928223810067e-15,9.56337229144231 -7.752645024575012,17.316017316017316 -17.316017316017327 17.316017316017312v 34.63203463203464 c 9.563372291442311,3.844928223810067e-15 17.316017316017316,7.752645024575012 17.316017316017312 17.316017316017327h 51.94805194805197 c 0.0,-9.563372291442311 7.752645024575012,-17.316017316017316 17.316017316017323 -17.31601731601731Z" /></g><path d="M 104.76190476190474,55.41125541125544 v -34.632034632034646 c 0.0,-9.563372291442313 -7.752645024575005,-17.31601731601732 -17.316017316017316 -17.31601731601732h -51.94805194805196 c -9.563372291442313,-5.855876632884659e-16 -17.31601731601732,7.7526450245750045 -17.31601731601732 17.316017316017316v 34.63203463203464 c -1.1711753265769319e-15,9.563372291442313 7.7526450245750045,17.31601731601732 17.316017316017316 17.316017316017327h 51.94805194805197 c 9.563372291442313,1.7567629898653979e-15 17.31601731601732,-7.752645024575003 17.31601731601731 -17.316017316017316Z" /></g></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="76.1905" stroke-opacity="1" viewBox="0 0 400 76" font-size="1" width="400.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.6982972487551757" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 381.8182,55.4113 v -17.3160 c -19.1267,-0.0000 -34.6320,-15.5053 -34.6320 -34.6320h -51.9481 c -19.1267,-0.0000 -34.6320,15.5053 -34.6320 34.6320v 34.6320 h 103.8961 c 9.5634,0.0000 17.3160,-7.7526 17.3160 -17.3160Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.6982972487551757" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 225.9740,55.4113 v -34.6320 c -9.5634,-0.0000 -17.3160,-7.7526 -17.3160 -17.3160h -51.9481 c -0.0000,9.5634 -7.7526,17.3160 -17.3160 17.3160v 34.6320 c 9.5634,0.0000 17.3160,7.7526 17.3160 17.3160h 51.9481 c 0.0000,-9.5634 7.7526,-17.3160 17.3160 -17.3160Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.6982972487551757" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 104.7619,55.4113 v -34.6320 c 0.0000,-9.5634 -7.7526,-17.3160 -17.3160 -17.3160h -51.9481 c -9.5634,-0.0000 -17.3160,7.7526 -17.3160 17.3160v 34.6320 c -0.0000,9.5634 7.7526,17.3160 17.3160 17.3160h 51.9481 c 9.5634,0.0000 17.3160,-7.7526 17.3160 -17.3160Z"/></g></svg>
diff --git a/diagrams/src_Diagrams_TwoD_Shapes_squareEx.svg b/diagrams/src_Diagrams_TwoD_Shapes_squareEx.svg
--- a/diagrams/src_Diagrams_TwoD_Shapes_squareEx.svg
+++ b/diagrams/src_Diagrams_TwoD_Shapes_squareEx.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="200.0" height="85.71428571428572" font-size="1" viewBox="0 0 200 86" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="0.5237229365663817" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><g><g><path d="M 190.90909090909093,81.81818181818181 l -8.651088503572648e-15,-77.92207792207792 h -77.92207792207792 l -8.651088503572648e-15,77.92207792207792 Z" /></g><g><path d="M 100.0,68.83116883116884 l -5.767392335715099e-15,-51.94805194805195 h -51.94805194805195 l -5.767392335715099e-15,51.94805194805195 Z" /></g><path d="M 35.06493506493507,55.84415584415585 l -2.8836961678575494e-15,-25.974025974025974 h -25.974025974025974 l -2.8836961678575494e-15,25.974025974025974 Z" /></g></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="85.7143" stroke-opacity="1" viewBox="0 0 200 86" font-size="1" width="200.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.5237229365663817" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 190.9091,81.8182 l -0.0000,-77.9221 h -77.9221 l -0.0000,77.9221 Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.5237229365663817" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 100.0000,68.8312 l -0.0000,-51.9481 h -51.9481 l -0.0000,51.9481 Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.5237229365663817" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 35.0649,55.8442 l -0.0000,-25.9740 h -25.9740 l -0.0000,25.9740 Z"/></g></svg>
diff --git a/diagrams/src_Diagrams_TwoD_Shapes_triangleEx.svg b/diagrams/src_Diagrams_TwoD_Shapes_triangleEx.svg
--- a/diagrams/src_Diagrams_TwoD_Shapes_triangleEx.svg
+++ b/diagrams/src_Diagrams_TwoD_Shapes_triangleEx.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="100.0" height="86.60254037844385" font-size="1" viewBox="0 0 100 87" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="0.5" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><path d="M 95.45454545454545,83.97822097303646 l -45.454545454545475,-78.72958216222167 l -45.454545454545446,78.72958216222169 Z" /></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="86.6025" stroke-opacity="1" viewBox="0 0 100 87" font-size="1" width="100.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.5" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 95.4545,83.9782 l -45.4545,-78.7296 l -45.4545,78.7296 Z"/></g></svg>
diff --git a/diagrams/src_Diagrams_TwoD_Shapes_unitSquareEx.svg b/diagrams/src_Diagrams_TwoD_Shapes_unitSquareEx.svg
--- a/diagrams/src_Diagrams_TwoD_Shapes_unitSquareEx.svg
+++ b/diagrams/src_Diagrams_TwoD_Shapes_unitSquareEx.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="100.0" height="100.0" font-size="1" viewBox="0 0 100 100" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="0.5" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><path d="M 95.45454545454545,95.45454545454545 l -1.0092936587501423e-14,-90.9090909090909 h -90.9090909090909 l -1.0092936587501423e-14,90.9090909090909 Z" /><g fill="rgb(255,0,0)" fill-opacity="1.0" stroke-width="0.0"><g fill="rgb(255,0,0)" fill-opacity="1.0"><g fill="rgb(255,0,0)" fill-opacity="1.0"><path d="M 51.99999999999999,50.0 c 0.0,-1.104569499661587 -0.895430500338413,-2.0 -1.9999999999999998 -2.0c -1.104569499661587,-6.76353751098178e-17 -2.0,0.8954305003384128 -2.0 1.9999999999999996c -1.352707502196356e-16,1.104569499661587 0.8954305003384126,2.0 1.9999999999999991 2.0c 1.104569499661587,2.029061253294534e-16 2.0,-0.8954305003384126 2.000000000000001 -1.9999999999999996Z" /></g></g></g></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="100.0000" stroke-opacity="1" viewBox="0 0 100 100" font-size="1" width="100.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.5" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 95.4545,95.4545 l -0.0000,-90.9091 h -90.9091 l -0.0000,90.9091 Z"/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="1.0" stroke="rgb(0,0,0)" stroke-width="0.0" fill="rgb(255,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 52.0000,50.0000 c 0.0000,-1.1046 -0.8954,-2.0000 -2.0000 -2.0000c -1.1046,-0.0000 -2.0000,0.8954 -2.0000 2.0000c -0.0000,1.1046 0.8954,2.0000 2.0000 2.0000c 1.1046,0.0000 2.0000,-0.8954 2.0000 -2.0000Z"/></g></svg>
diff --git a/diagrams/src_Diagrams_TwoD_Shapes_vruleEx.svg b/diagrams/src_Diagrams_TwoD_Shapes_vruleEx.svg
--- a/diagrams/src_Diagrams_TwoD_Shapes_vruleEx.svg
+++ b/diagrams/src_Diagrams_TwoD_Shapes_vruleEx.svg
@@ -1,4 +1,1 @@
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
-    "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="50.00000000000001" height="100.0" font-size="1" viewBox="0 0 50 100" stroke="rgb(0,0,0)" stroke-opacity="1"><g><g fill="rgb(0,0,0)" fill-opacity="0.0"><g stroke="rgb(0,0,0)" stroke-opacity="1.0" stroke-width="0.5" stroke-linecap="butt" stroke-linejoin="miter" font-size="1.0em" stroke-miterlimit="10.0"><g><g><g><path d="M 47.727272727272734,4.545454545454547 v 90.9090909090909 " /></g><path d="M 38.63636363636364,9.090909090909086 v 81.81818181818183 " /></g><g><g><path d="M 29.545454545454547,13.636363636363633 v 72.72727272727273 " /></g><path d="M 20.454545454545457,18.18181818181818 v 63.63636363636364 " /></g><g><path d="M 11.363636363636365,22.727272727272723 v 54.545454545454554 " /></g><path d="M 2.2727272727272734,27.27272727272727 v 45.45454545454546 " /></g></g></g></g></svg>
+<svg xmlns="http://www.w3.org/2000/svg" height="100.0000" stroke-opacity="1" viewBox="0 0 50 100" font-size="1" width="50.0000" xmlns:xlink="http://www.w3.org/1999/xlink" stroke="rgb(0,0,0)" version="1.1"><defs></defs><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.5" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 47.7273,4.5455 v 90.9091 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.5" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 38.6364,9.0909 v 81.8182 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.5" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 29.5455,13.6364 v 72.7273 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.5" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 20.4545,18.1818 v 63.6364 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.5" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 11.3636,22.7273 v 54.5455 "/></g><g stroke-linejoin="miter" stroke-opacity="1.0" fill-opacity="0.0" stroke="rgb(0,0,0)" stroke-width="0.5" fill="rgb(0,0,0)" stroke-linecap="butt" stroke-miterlimit="10.0"><path d="M 2.2727,27.2727 v 45.4545 "/></g></svg>
diff --git a/src/Diagrams.hs b/src/Diagrams.hs
new file mode 100644
--- /dev/null
+++ b/src/Diagrams.hs
@@ -0,0 +1,153 @@
+{-# OPTIONS_GHC -fno-warn-duplicate-exports #-}
+-----------------------------------------------------------------------------
+-- |
+-- Module      :  Diagrams
+-- Copyright   :  (c) 2015 diagrams-lib team (see LICENSE)
+-- License     :  BSD-style (see LICENSE)
+-- Maintainer  :  diagrams-discuss@googlegroups.com
+--
+-- This module only contains exports defined in @diagrams-lib@ or
+-- @diagrams-core@. This module can be used if you want to avoid some
+-- potential conflicts with other modules, but importing
+-- "Diagrams.Prelude" (which includes re-exports from other packages)
+-- is often more convenient.
+--
+-----------------------------------------------------------------------------
+
+module Diagrams
+  (
+    -- * Core library
+    -- | The core definitions of transformations, diagrams,
+    --   backends, and so on.
+    module Diagrams.Core
+
+    -- * Standard library
+
+    -- | Attributes (color, line style, etc.) and styles.
+  , module Diagrams.Attributes
+
+    -- | Alignment of diagrams relative to their envelopes.
+  , module Diagrams.Align
+
+    -- | Creating and using bounding boxes.
+  , module Diagrams.BoundingBox
+
+    -- | Combining multiple diagrams into one.
+  , module Diagrams.Combinators
+
+    -- | Giving concrete locations to translation-invariant things.
+  , module Diagrams.Located
+
+    -- | Linear and cubic bezier segments.
+  , module Diagrams.Segment
+
+    -- | Trails.
+  , module Diagrams.Trail
+
+    -- | Parametrization of segments and trails.
+  , module Diagrams.Parametric
+
+    -- | Adjusting the length of parameterized objects.
+  , module Diagrams.Parametric.Adjust
+
+    -- | Computing tangent and normal vectors of segments and
+    --   trails.
+  , module Diagrams.Tangent
+
+    -- | Trail-like things.
+  , module Diagrams.TrailLike
+
+    -- | Paths.
+  , module Diagrams.Path
+
+    -- | Cubic splines.
+  , module Diagrams.CubicSpline
+
+    -- | Some additional transformation-related functions, like
+    --   conjugation of transformations.
+  , module Diagrams.Transform
+
+    -- | Projective transformations and other deformations
+    -- lacking an inverse.
+  , module Diagrams.Deform
+
+    -- | Giving names to subdiagrams and later retrieving
+    --   subdiagrams by name.
+  , module Diagrams.Names
+
+    -- | Envelopes, aka functional bounding regions.
+  , module Diagrams.Envelope
+
+    -- | Traces, aka embedded raytracers, for finding points on
+    --   the boundary of a diagram.
+  , module Diagrams.Trace
+
+    -- | A query is a function that maps points in a vector space
+    --   to values in some monoid; they can be used to annotate
+    --   the points of a diagram with some values.
+  , module Diagrams.Query
+
+    -- | Utilities for working with points.
+  , module Diagrams.Points
+
+    -- | Utilities for working with size.
+  , module Diagrams.Size
+
+    -- | Angles
+  , module Diagrams.Angle
+
+    -- | Convenience infix operators for working with coordinates.
+  , module Diagrams.Coordinates
+
+    -- | Directions, distinguished from angles or vectors
+  , module Diagrams.Direction
+
+    -- | A wide range of things (shapes, transformations,
+    --   combinators) specific to creating two-dimensional
+    --   diagrams.
+  , module Diagrams.TwoD
+
+    -- | Extra things for three-dimensional diagrams.
+  , module Diagrams.ThreeD
+
+    -- | Tools for making animations.
+  , module Diagrams.Animation
+
+    -- | Various utility definitions.
+  , module Diagrams.Util
+
+  ) where
+
+import           Diagrams.Core
+
+import           Diagrams.Align
+import           Diagrams.Angle
+import           Diagrams.Animation
+import           Diagrams.Attributes
+import           Diagrams.BoundingBox       hiding (contains, inside,
+                                             intersection, outside, union)
+import           Diagrams.Combinators
+import           Diagrams.Coordinates
+import           Diagrams.CubicSpline
+import           Diagrams.Deform
+import           Diagrams.Direction         hiding (dir)
+import           Diagrams.Envelope
+import           Diagrams.Located
+import           Diagrams.Names
+import           Diagrams.Parametric
+import           Diagrams.Parametric.Adjust
+import           Diagrams.Path              hiding (pathPoints)
+import           Diagrams.Points
+import           Diagrams.Query
+import           Diagrams.Segment
+import           Diagrams.Size
+import           Diagrams.Tangent
+import           Diagrams.ThreeD
+import           Diagrams.Trace
+import           Diagrams.Trail             hiding (linePoints, loopPoints,
+                                             trailPoints)
+import           Diagrams.TrailLike
+import           Diagrams.Transform
+import           Diagrams.TwoD
+import           Diagrams.Util
+
diff --git a/src/Diagrams/Align.hs b/src/Diagrams/Align.hs
--- a/src/Diagrams/Align.hs
+++ b/src/Diagrams/Align.hs
@@ -1,6 +1,9 @@
-{-# LANGUAGE FlexibleContexts     #-}
-{-# LANGUAGE TypeFamilies         #-}
-{-# LANGUAGE UndecidableInstances #-}
+{-# LANGUAGE ConstrainedClassMethods #-}
+{-# LANGUAGE ConstraintKinds         #-}
+{-# LANGUAGE FlexibleContexts        #-}
+{-# LANGUAGE TypeFamilies            #-}
+{-# LANGUAGE TypeOperators           #-}
+{-# LANGUAGE UndecidableInstances    #-}
 
 -----------------------------------------------------------------------------
 -- |
@@ -38,15 +41,20 @@
 import           Diagrams.Core
 import           Diagrams.Util    (applyAll)
 
-import           Data.AffineSpace (alerp, (.-.))
-import           Data.VectorSpace
 import           Data.Maybe       (fromMaybe)
 import           Data.Ord         (comparing)
+import           Data.Traversable
+import           Prelude
 
+import qualified Data.Foldable    as F
 import qualified Data.Map         as M
 import qualified Data.Set         as S
-import qualified Data.Foldable    as F
 
+import           Linear.Affine
+import           Linear.Metric
+import           Linear.Vector        (negated)
+import           Linear.Vector.Compat (lerp)
+
 -- | Class of things which can be aligned.
 class Alignable a where
 
@@ -56,61 +64,60 @@
   --   edge of the boundary in the direction of the negation of @v@.
   --   Other values of @d@ interpolate linearly (so for example, @d =
   --   0@ centers the origin along the direction of @v@).
-  alignBy' :: ( HasOrigin a, AdditiveGroup (V a), Num (Scalar (V a))
-              , Fractional (Scalar (V a)))
-            => (V a -> a -> Point (V a)) -> V a -> Scalar (V a) -> a -> a
+  alignBy' :: (InSpace v n a, Fractional n, HasOrigin a)
+           => (v n -> a -> Point v n) -> v n -> n -> a -> a
   alignBy' = alignBy'Default
 
-  defaultBoundary :: V a -> a -> Point (V a)
+  defaultBoundary :: (V a ~ v, N a ~ n) => v n -> a -> Point v n
 
-  alignBy :: (HasOrigin a, Num (Scalar (V a)), Fractional (Scalar (V a)))
-           => V a -> Scalar (V a) -> a -> a
+  alignBy :: (InSpace v n a, Fractional n, HasOrigin a)
+          => v n -> n -> a -> a
   alignBy = alignBy' defaultBoundary
 
 -- | Default implementation of 'alignBy' for types with 'HasOrigin'
 --   and 'AdditiveGroup' instances.
-alignBy'Default :: ( HasOrigin a, AdditiveGroup (V a), Num (Scalar (V a))
-                   , Fractional (Scalar (V a)))
-                 => (V a -> a -> Point (V a)) -> V a -> Scalar (V a) -> a -> a
-alignBy'Default boundary v d a = moveOriginTo (alerp (boundary (negateV v) a)
-                                    (boundary v a)
-                                    ((d + 1) / 2)) a
+alignBy'Default :: (InSpace v n a, Fractional n, HasOrigin a)
+                => (v n -> a -> Point v n) -> v n -> n -> a -> a
+alignBy'Default boundary v d a = moveOriginTo (lerp ((d + 1) / 2)
+                                                    (boundary (negated v) a)
+                                                    (boundary v a)
+                                              ) a
+{-# ANN alignBy'Default ("HLint: ignore Use camelCase" :: String) #-}
 
+
 -- | Some standard functions which can be used as the `boundary` argument to
 --  `alignBy'`.
-envelopeBoundary :: Enveloped a => V a -> a -> Point (V a)
+envelopeBoundary :: (V a ~ v, N a ~ n, Enveloped a) => v n -> a -> Point v n
 envelopeBoundary = envelopeP
 
-traceBoundary :: Traced a => V a -> a -> Point (V a)
+traceBoundary :: (V a ~ v, N a ~ n, Num n, Traced a) => v n -> a -> Point v n
 traceBoundary v a = fromMaybe origin (maxTraceP origin v a)
 
 combineBoundaries
-  :: (F.Foldable f, InnerSpace (V a), Ord (Scalar (V a)))
-  => (V a -> a -> Point (V a)) -> (V a -> f a -> Point (V a))
+  :: (InSpace v n a, Metric v, Ord n, F.Foldable f)
+  => (v n -> a -> Point v n) -> v n -> f a -> Point v n
 combineBoundaries b v fa
-    = b v $ F.maximumBy (comparing (magnitudeSq . (.-. origin) . b v)) fa
+  = b v $ F.maximumBy (comparing (dot v . (.-.origin) . b v)) fa
 
-instance (InnerSpace v, OrderedField (Scalar v)) => Alignable (Envelope v) where
+instance (Metric v, OrderedField n) => Alignable (Envelope v n) where
   defaultBoundary = envelopeBoundary
 
-instance (InnerSpace v, OrderedField (Scalar v)) => Alignable (Trace v) where
+instance (Metric v, OrderedField n) => Alignable (Trace v n) where
   defaultBoundary = traceBoundary
 
-instance (InnerSpace (V b), Ord (Scalar (V b)), Alignable b)
-       => Alignable [b] where
+instance (V b ~ v, N b ~ n, Metric v, OrderedField n, Alignable b) => Alignable [b] where
   defaultBoundary = combineBoundaries defaultBoundary
 
-instance (InnerSpace (V b), Ord (Scalar (V b)), Alignable b)
-       => Alignable (S.Set b) where
+instance (V b ~ v, N b ~ n, Metric v, OrderedField n, Alignable b)
+    => Alignable (S.Set b) where
   defaultBoundary = combineBoundaries defaultBoundary
 
-instance (InnerSpace (V b), Ord (Scalar (V b)), Alignable b)
-       => Alignable (M.Map k b) where
+instance (V b ~ v, N b ~ n, Metric v, OrderedField n, Alignable b)
+    => Alignable (M.Map k b) where
   defaultBoundary = combineBoundaries defaultBoundary
 
-instance ( HasLinearMap v, InnerSpace v, OrderedField (Scalar v)
-         , Monoid' m
-         ) => Alignable (QDiagram b v m) where
+instance (Metric v, OrderedField n, Monoid' m)
+    => Alignable (QDiagram b v n m) where
   defaultBoundary = envelopeBoundary
 
 -- | Although the 'alignBy' method for the @(b -> a)@ instance is
@@ -118,8 +125,8 @@
 --   'defaultBoundary'. Instead, we provide a total method, but one that
 --   is not sensible. This should not present a serious problem as long
 --   as your use of 'Alignable' happens through 'alignBy'.
-instance (HasOrigin a, Alignable a) => Alignable (b -> a) where
-  alignBy v d f b = alignBy v d (f b)
+instance (InSpace v n a, HasOrigin a, Alignable a) => Alignable (b -> a) where
+  alignBy v d f b     = alignBy v d (f b)
   defaultBoundary _ _ = origin
 
 -- | @align v@ aligns an enveloped object along the edge in the
@@ -127,42 +134,41 @@
 --   direction of @v@ until it is on the edge of the envelope.  (Note
 --   that if the local origin is outside the envelope to begin with,
 --   it may have to move \"backwards\".)
-align :: ( Alignable a, HasOrigin a, Num (Scalar (V a))
-         , Fractional (Scalar (V a))) => V a -> a -> a
+align :: (InSpace v n a, Fractional n, Alignable a, HasOrigin a) => v n -> a -> a
 align v = alignBy v 1
 
 -- | Version of @alignBy@ specialized to use @traceBoundary@
-snugBy :: (Alignable a, Traced a, HasOrigin a, Num (Scalar (V a)), Fractional (Scalar (V a)))
-       => V a -> Scalar (V a) -> a -> a
+snugBy :: (InSpace v n a, Fractional n, Alignable a, Traced a, HasOrigin a)
+       => v n -> n -> a -> a
 snugBy = alignBy' traceBoundary
 
 -- | Like align but uses trace.
-snug :: (Fractional (Scalar (V a)), Alignable a, Traced a, HasOrigin a)
-      => V a -> a -> a
-snug v = snugBy  v 1
+snug :: (InSpace v n a, Fractional n, Alignable a, Traced a, HasOrigin a)
+      => v n -> a -> a
+snug v = snugBy v 1
 
 -- | @centerV v@ centers an enveloped object along the direction of
 --   @v@.
-centerV :: ( Alignable a, HasOrigin a, Num (Scalar (V a))
-          , Fractional (Scalar (V a))) => V a -> a -> a
+centerV :: (InSpace v n a, Fractional n, Alignable a, HasOrigin a) => v n -> a -> a
 centerV v = alignBy v 0
 
 -- | @center@ centers an enveloped object along all of its basis vectors.
-center :: ( HasLinearMap (V a), Alignable a, HasOrigin a, Num (Scalar (V a)),
-             Fractional (Scalar (V a))) => a -> a
-center d = applyAll fs d
+center :: (InSpace v n a, Fractional n, Traversable v, Alignable a, HasOrigin a) => a -> a
+center = applyAll fs
   where
     fs = map centerV basis
 
 -- | Like @centerV@ using trace.
 snugCenterV
-  :: (Fractional (Scalar (V a)), Alignable a, Traced a, HasOrigin a)
-   => V a -> a -> a
-snugCenterV v = (alignBy' traceBoundary) v 0
+  :: (InSpace v n a, Fractional n, Alignable a, Traced a, HasOrigin a)
+   => v n -> a -> a
+snugCenterV v = alignBy' traceBoundary v 0
 
 -- | Like @center@ using trace.
-snugCenter :: ( HasLinearMap (V a), Alignable a, HasOrigin a, Num (Scalar (V a)),
-                      Fractional (Scalar (V a)), Traced a) => a -> a
-snugCenter d = applyAll fs d
+snugCenter :: (InSpace v n a, Traversable v, Fractional n, Alignable a, HasOrigin a, Traced a)
+           => a -> a
+snugCenter = applyAll fs
   where
     fs = map snugCenterV basis
+
+{-# ANN module ("HLint: ignore Use camelCase" :: String) #-}
diff --git a/src/Diagrams/Angle.hs b/src/Diagrams/Angle.hs
--- a/src/Diagrams/Angle.hs
+++ b/src/Diagrams/Angle.hs
@@ -1,6 +1,12 @@
+{-# LANGUAGE ConstraintKinds            #-}
+{-# LANGUAGE DeriveFunctor              #-}
+{-# LANGUAGE FlexibleContexts           #-}
+{-# LANGUAGE FlexibleInstances          #-}
 {-# LANGUAGE GeneralizedNewtypeDeriving #-}
+{-# LANGUAGE MultiParamTypeClasses      #-}
 {-# LANGUAGE RankNTypes                 #-}
 {-# LANGUAGE TypeFamilies               #-}
+{-# LANGUAGE TypeOperators              #-}
 -----------------------------------------------------------------------------
 -- |
 -- Module      :  Diagrams.Angle
@@ -8,106 +14,271 @@
 -- License     :  BSD-style (see LICENSE)
 -- Maintainer  :  diagrams-discuss@googlegroups.com
 --
--- Type for representing angles, independent of vector-space
+-- Type for representing angles.
 --
 -----------------------------------------------------------------------------
 
 module Diagrams.Angle
-       (
+       ( -- * Angle type
          Angle
-       , rad, turn, deg
-       , fullTurn, fullCircle, angleRatio
-       , sinA, cosA, tanA, asinA, acosA, atanA
-       , (@@)
-       , angleBetween
+
+         -- ** Using angles
+       , (@@), rad, turn, deg
+
+         -- ** Common angles
+       , fullTurn, halfTurn, quarterTurn
+
+         -- ** Trigonometric functions
+       , sinA, cosA, tanA
+       , asinA, acosA, atanA, atan2A, atan2A'
+
+         -- ** Angle utilities
+       , angleBetween, angleRatio, normalizeAngle
+
+         -- ** Classes
        , HasTheta(..)
+       , HasPhi(..)
+
+         -- * Rotation
+       , rotation, rotate
        ) where
 
-import           Control.Lens            (Iso', Lens', iso, review, (^.))
-                                         -- , review , (^.), _1, _2, Lens', lens)
+import           Control.Applicative
+import           Control.Lens            (AReview, Iso', Lens', iso, over,
+                                          review, (^.))
+import           Data.Fixed
+import           Data.Monoid             hiding ((<>))
+import           Data.Monoid.Action
+import           Data.Semigroup
+import           Prelude
+import           Text.Read
 
-import           Data.VectorSpace
+import           Diagrams.Core           (OrderedField)
+import           Diagrams.Core.Transform
+import           Diagrams.Core.V
+import           Diagrams.Points
+import           Linear.V2               (V2 (..))
 
+import           Linear.Metric
+import           Linear.Vector
+
 -- | Angles can be expressed in a variety of units.  Internally,
--- they are represented in radians.
-newtype Angle = Radians Double
-              deriving (Read, Show, Eq, Ord, Enum, AdditiveGroup)
+--   they are represented in radians.
+newtype Angle n = Radians n
+  deriving (Eq, Ord, Enum, Functor)
 
-instance VectorSpace Angle where
-  type Scalar Angle = Double
-  s *^ Radians t = Radians (s*t)
+instance Show n => Show (Angle n) where
+  showsPrec d (Radians a) = showParen (d > 5) $
+    showsPrec 6 a . showString " @@ rad"
 
--- | The radian measure of an @Angle@ @a@ can be accessed as @a
--- ^. rad@.  A new @Angle@ can be defined in radians as @pi \@\@ rad@.
-rad :: Iso' Angle Double
+instance Read n => Read (Angle n) where
+  readPrec = parens . prec 5 $ do
+    x <- readPrec
+    Symbol "@@" <- lexP
+    Ident "rad" <- lexP
+    pure (Radians x)
+
+type instance N (Angle n) = n
+
+instance Applicative Angle where
+  pure = Radians
+  {-# INLINE pure #-}
+  Radians f <*> Radians x = Radians (f x)
+  {-# INLINE (<*>) #-}
+
+instance Additive Angle where
+  zero = pure 0
+  {-# INLINE zero #-}
+
+instance Num n => Semigroup (Angle n) where
+  (<>) = (^+^)
+  {-# INLINE (<>) #-}
+
+instance Num n => Monoid (Angle n) where
+  mappend = (<>)
+  mempty  = Radians 0
+
+-- | The radian measure of an 'Angle' @a@ can be accessed as @a '^.'
+--   rad@. A new 'Angle' can be defined in radians as @pi \@\@
+--   rad@.
+rad :: Iso' (Angle n) n
 rad = iso (\(Radians r) -> r) Radians
+{-# INLINE rad #-}
 
--- | The measure of an @Angle@ @a@ in full circles can be accessed as
--- @a ^. turn@.  A new @Angle@ of one-half circle can be defined in as
--- @1/2 \@\@ turn@.
-turn :: Iso' Angle Double
-turn = iso (\(Radians r) -> r/2/pi) (Radians . (*(2*pi)))
+-- | The measure of an 'Angle' @a@ in full circles can be accessed as
+--   @a '^.' turn@.  A new 'Angle' of one-half circle can be defined in as
+--   @1/2 \@\@ turn@.
+turn :: Floating n => Iso' (Angle n) n
+turn = iso (\(Radians r) -> r / (2*pi)) (Radians . (*(2*pi)))
+{-# INLINE turn #-}
 
--- | The degree measure of an @Angle@ @a@ can be accessed as @a
--- ^. deg@.  A new @Angle@ can be defined in degrees as @180 \@\@
--- deg@.
-deg :: Iso' Angle Double
-deg = iso (\(Radians r) -> r/2/pi*360) (Radians . (*(2*pi/360)))
+-- | The degree measure of an 'Angle' @a@ can be accessed as @a
+--   '^.' deg@. A new 'Angle' can be defined in degrees as @180 \@\@
+--   deg@.
+deg :: Floating n => Iso' (Angle n) n
+deg = iso (\(Radians r) -> r / (2*pi/360)) (Radians . ( * (2*pi/360)))
+{-# INLINE deg #-}
 
 -- | An angle representing one full turn.
-fullTurn :: Angle
+fullTurn :: Floating v => Angle v
 fullTurn = 1 @@ turn
 
--- | Deprecated synonym for 'fullTurn', retained for backwards compatibility.
-fullCircle :: Angle
-fullCircle = fullTurn
+-- | An angle representing a half turn.
+halfTurn :: Floating v => Angle v
+halfTurn = 0.5 @@ turn
 
+-- | An angle representing a quarter turn.
+quarterTurn :: Floating v => Angle v
+quarterTurn = 0.25 @@ turn
+
 -- | Calculate ratio between two angles.
-angleRatio :: Angle -> Angle -> Double
-angleRatio a b = (a^.rad) / (b^.rad)
+angleRatio :: Floating n => Angle n -> Angle n -> n
+angleRatio a b = (a ^. rad) / (b ^. rad)
 
 -- | The sine of the given @Angle@.
-sinA :: Angle -> Double
+sinA :: Floating n => Angle n -> n
 sinA (Radians r) = sin r
 
 -- | The cosine of the given @Angle@.
-cosA :: Angle -> Double
+cosA :: Floating n => Angle n -> n
 cosA (Radians r) = cos r
 
 -- | The tangent function of the given @Angle@.
-tanA :: Angle -> Double
+tanA :: Floating n => Angle n -> n
 tanA (Radians r) = tan r
 
 -- | The @Angle@ with the given sine.
-asinA :: Double -> Angle
+asinA :: Floating n => n -> Angle n
 asinA = Radians . asin
 
 -- | The @Angle@ with the given cosine.
-acosA :: Double -> Angle
+acosA :: Floating n => n -> Angle n
 acosA = Radians . acos
 
 -- | The @Angle@ with the given tangent.
-atanA :: Double -> Angle
+atanA :: Floating n => n -> Angle n
 atanA = Radians . atan
 
--- | @30 \@\@ deg@ is an @Angle@ of the given measure and units.
+-- | @atan2A y x@ is the angle between the positive x-axis and the vector given
+--   by the coordinates (x, y). The 'Angle' returned is in the [-pi,pi] range.
+atan2A :: RealFloat n => n -> n -> Angle n
+atan2A y x = Radians $ atan2 y x
+
+-- | Similar to 'atan2A' but without the 'RealFloat' constraint. This means it
+--   doesn't handle negative zero cases. However, for most geometric purposes,
+--   the outcome will be the same.
+atan2A' :: OrderedField n => n -> n -> Angle n
+atan2A' y x = atan2' y x @@ rad
+
+-- atan2 without negative zero tests
+atan2' :: OrderedField n => n -> n -> n
+atan2' y x
+  | x > 0            =  atan (y/x)
+  | x == 0 && y > 0  =  pi/2
+  | x <  0 && y > 0  =  pi + atan (y/x)
+  | x <= 0 && y < 0  = -atan2' (-y) x
+  | y == 0 && x < 0  =  pi    -- must be after the previous test on zero y
+  | x==0 && y==0     =  y     -- must be after the other double zero tests
+  | otherwise        =  x + y -- x or y is a NaN, return a NaN (via +)
+
+-- | @30 \@\@ deg@ is an 'Angle' of the given measure and units.
 --
--- More generally, @\@\@@ reverses the @Iso\'@ on its right, and
--- applies the @Iso\'@ to the value on the left.  @Angle@s are the
--- motivating example where this order improves readability.
-(@@) :: b -> Iso' a b -> a
--- The signature above is slightly specialized, in favor of readability
+-- >>> pi @@ rad
+-- 3.141592653589793 @@ rad
+--
+-- >>> 1 @@ turn
+-- 6.283185307179586 @@ rad
+--
+-- >>> 30 @@ deg
+-- 0.5235987755982988 @@ rad
+--
+--   For 'Iso''s, ('@@') reverses the 'Iso'' on its right, and applies
+--   the 'Iso'' to the value on the left. 'Angle's are the motivating
+--   example where this order improves readability.
+--
+--   This is the same as a flipped 'review'.
+--
+-- @
+-- ('@@') :: a -> 'Iso''      s a -> s
+-- ('@@') :: a -> 'Prism''    s a -> s
+-- ('@@') :: a -> 'Review'    s a -> s
+-- ('@@') :: a -> 'Equality'' s a -> s
+-- @
+(@@) :: b -> AReview a b -> a
 a @@ i = review i a
 
 infixl 5 @@
 
--- | compute the positive angle between the two vectors in their common plane
-angleBetween  :: (InnerSpace v, Scalar v ~ Double) => v -> v -> Angle
-angleBetween v1 v2 = acos (normalized v1 <.> normalized v2) @@ rad
+-- | Compute the positive angle between the two vectors in their common
+--   plane in the [0,pi] range. For a signed angle see
+--   'Diagrams.TwoD.Vector.signedAngleBetween'.
+--
+--   Returns NaN if either of the vectors are zero.
+angleBetween  :: (Metric v, Floating n, Ord n) => v n -> v n -> Angle n
+angleBetween v1 v2 = acosA (min 1 . max (-1) $ signorm v1 `dot` signorm v2)
+-- N.B.: Currently discards the common plane information.
 
+-- | Normalize an angle so that it lies in the [0,tau) range.
+normalizeAngle :: (Floating n, Real n) => Angle n -> Angle n
+normalizeAngle = over rad (`mod'` (2 * pi))
+
 ------------------------------------------------------------
+-- Rotation
+
+-- These functions are defined here (instead of in
+-- Diagrams.TwoD.Transform) because the Action instance needs to go
+-- here.
+
+-- | Create a transformation which performs a rotation about the local
+--   origin by the given angle.  See also 'rotate'.
+rotation :: Floating n => Angle n -> Transformation V2 n
+rotation theta = fromLinear r (linv r)
+    where
+    c = cosA theta
+    s = sinA theta
+    r               = rot c s <-> rot c (-s)
+    rot co si (V2 x y) = V2 (co * x - si * y)
+                            (si * x + co * y)
+
+-- | Rotate about the local origin by the given angle. Positive angles
+--   correspond to counterclockwise rotation, negative to
+--   clockwise. The angle can be expressed using any of the 'Iso's on
+--   'Angle'.  For example, @rotate (1\/4 \@\@ 'turn')@, @rotate
+--   (tau\/4 \@\@ rad)@, and @rotate (90 \@\@ deg)@ all
+--   represent the same transformation, namely, a counterclockwise
+--   rotation by a right angle.  To rotate about some point other than
+--   the local origin, see 'rotateAbout'.
+--
+--   Note that writing @rotate (1\/4)@, with no 'Angle' constructor,
+--   will yield an error since GHC cannot figure out which sort of
+--   angle you want to use.  In this common situation you can use
+--   'rotateBy', which interprets its argument as a number of turns.
+
+rotate :: (InSpace V2 n t, Transformable t, Floating n) => Angle n -> t -> t
+rotate = transform . rotation
+
+-- | Angles act on other things by rotation.
+instance (V t ~ V2, N t ~ n, Transformable t, Floating n)
+  => Action (Angle n) t where
+  act = rotate
+
+------------------------------------------------------------
 -- Polar Coordinates
 
--- | The class of types with at least one angle coordinate, called _theta.
+-- | The class of types with at least one angle coordinate, called '_theta'.
 class HasTheta t where
-    _theta :: Lens' t Angle
+  _theta :: RealFloat n => Lens' (t n) (Angle n)
+
+-- | The class of types with at least two angle coordinates, the second called
+--   '_phi'. '_phi' is the positive angle measured from the z axis.
+class HasTheta t => HasPhi t where
+  _phi :: RealFloat n => Lens' (t n) (Angle n)
+
+-- Point instances
+instance HasTheta v => HasTheta (Point v) where
+  _theta = lensP . _theta
+  {-# INLINE _theta #-}
+
+instance HasPhi v => HasPhi (Point v) where
+  _phi = lensP . _phi
+  {-# INLINE _phi #-}
diff --git a/src/Diagrams/Animation.hs b/src/Diagrams/Animation.hs
--- a/src/Diagrams/Animation.hs
+++ b/src/Diagrams/Animation.hs
@@ -1,3 +1,4 @@
+{-# LANGUAGE ConstraintKinds       #-}
 {-# LANGUAGE FlexibleContexts      #-}
 {-# LANGUAGE MultiParamTypeClasses #-}
 {-# LANGUAGE TypeFamilies          #-}
@@ -29,6 +30,9 @@
 
        ) where
 
+import           Data.Active
+import           Data.Semigroup
+
 import           Diagrams.Core
 
 import           Diagrams.Animation.Active ()
@@ -38,18 +42,13 @@
 import           Diagrams.TwoD.Shapes
 import           Diagrams.TwoD.Types
 
-import           Data.Active
-import           Data.Semigroup
-
-import           Control.Applicative       ((<$>))
-import           Data.Foldable             (foldMap)
-import           Data.VectorSpace
+import           Linear.Metric
 
 -- | A value of type @QAnimation b v m@ is an animation (a
 --   time-varying diagram with start and end times) that can be
---   rendered by backspace @b@, with vector space @v@ and monoidal
+--   rendered by backend @b@, with vector space @v@ and monoidal
 --   annotations of type @m@.
-type QAnimation b v m = Active (QDiagram b v m)
+type QAnimation b v n m = Active (QDiagram b v n m)
 
 -- | A value of type @Animation b v@ is an animation (a time-varying
 --   diagram with start and end times) in vector space @v@ that can be
@@ -58,7 +57,7 @@
 --   Note that @Animation@ is actually a synonym for @QAnimation@
 --   where the type of the monoidal annotations has been fixed to
 --   'Any' (the default).
-type Animation b v = QAnimation b v Any
+type Animation b v n = QAnimation b v n Any
 
 -- $animComb
 -- Most combinators for working with animations are to be found in the
@@ -90,16 +89,16 @@
 --
 --   See also 'animRect' for help constructing a background to go
 --   behind an animation.
-animEnvelope :: (Backend b v, OrderedField (Scalar v), InnerSpace v, Monoid' m)
-           => QAnimation b v m -> QAnimation b v m
+animEnvelope :: (OrderedField n, Metric v, Monoid' m)
+           => QAnimation b v n m -> QAnimation b v n m
 animEnvelope = animEnvelope' 30
 
 -- | Like 'animEnvelope', but with an adjustible sample rate.  The first
 --   parameter is the number of samples per time unit to use.  Lower
 --   rates will be faster but less accurate; higher rates are more
 --   accurate but slower.
-animEnvelope' :: (Backend b v, OrderedField (Scalar v), InnerSpace v, Monoid' m)
-            => Rational -> QAnimation b v m -> QAnimation b v m
+animEnvelope' :: (OrderedField n, Metric v, Monoid' m)
+            => Rational -> QAnimation b v n m -> QAnimation b v n m
 animEnvelope' r a = withEnvelope (simulate r a) <$> a
 
 -- | @animRect@ works similarly to 'animEnvelope' for 2D diagrams, but
@@ -109,18 +108,16 @@
 --
 --   Uses 30 samples per time unit by default; to adjust this number
 --   see 'animRect''.
-animRect :: (TrailLike t, Enveloped t, Transformable t, Monoid t, V t ~ R2
-            , Monoid' m)
-         => QAnimation b R2 m -> t
+animRect :: (InSpace V2 n t, Monoid' m, TrailLike t, Enveloped t, Transformable t, Monoid t)
+         => QAnimation b V2 n m -> t
 animRect = animRect' 30
 
 -- | Like 'animRect', but with an adjustible sample rate.  The first
 --   parameter is the number of samples per time unit to use.  Lower
 --   rates will be faster but less accurate; higher rates are more
 --   accurate but slower.
-animRect' :: (TrailLike t, Enveloped t, Transformable t, Monoid t, V t ~ R2
-             , Monoid' m)
-          => Rational -> QAnimation b R2 m -> t
+animRect' :: (InSpace V2 n t, Monoid' m, TrailLike t, Enveloped t, Transformable t, Monoid t)
+          => Rational -> QAnimation b V2 n m -> t
 animRect' r anim
     | null results = rect 1 1
     | otherwise    = boxFit (foldMap boundingBox results) (rect 1 1)
diff --git a/src/Diagrams/Animation/Active.hs b/src/Diagrams/Animation/Active.hs
--- a/src/Diagrams/Animation/Active.hs
+++ b/src/Diagrams/Animation/Active.hs
@@ -37,14 +37,13 @@
 
 module Diagrams.Animation.Active where
 
-import           Control.Applicative (pure, (<$>))
-
 import           Diagrams.Core
 import           Diagrams.TrailLike
 
 import           Data.Active
 
 type instance V (Active a) = V a
+type instance N (Active a) = N a
 
 -- Yes, these are all orphan instances. Get over it.  We don't want to
 -- put them in the 'active' package because 'active' is supposed to be
@@ -95,5 +94,5 @@
       )
       a1
 
---instance Alignable a => Alignable (Active a) where
---  alignBy v d a = alignBy v d <$> a
+-- instance Alignable a => Alignable (Active a) where
+--   alignBy v d a = alignBy v d <$> a
diff --git a/src/Diagrams/Attributes.hs b/src/Diagrams/Attributes.hs
--- a/src/Diagrams/Attributes.hs
+++ b/src/Diagrams/Attributes.hs
@@ -1,12 +1,19 @@
+{-# LANGUAGE ConstraintKinds            #-}
 {-# LANGUAGE DeriveDataTypeable         #-}
+{-# LANGUAGE DeriveFunctor              #-}
 {-# LANGUAGE ExistentialQuantification  #-}
+{-# LANGUAGE FlexibleInstances          #-}
 {-# LANGUAGE GeneralizedNewtypeDeriving #-}
+{-# LANGUAGE LambdaCase                 #-}
+{-# LANGUAGE MultiParamTypeClasses      #-}
 {-# LANGUAGE ScopedTypeVariables        #-}
 {-# LANGUAGE TypeFamilies               #-}
+{-# LANGUAGE TypeOperators              #-}
+{-# LANGUAGE ViewPatterns               #-}
 -----------------------------------------------------------------------------
 -- |
 -- Module      :  Diagrams.Attributes
--- Copyright   :  (c) 2011 diagrams-lib team (see LICENSE)
+-- Copyright   :  (c) 2011-2015 diagrams-lib team (see LICENSE)
 -- License     :  BSD-style (see LICENSE)
 -- Maintainer  :  diagrams-discuss@googlegroups.com
 --
@@ -24,43 +31,220 @@
 -----------------------------------------------------------------------------
 
 module Diagrams.Attributes (
+    -- ** Standard measures
+    ultraThin, veryThin, thin, medium, thick, veryThick, ultraThick, none
+  , tiny, verySmall, small, normal, large, veryLarge, huge
+
+    -- ** Line width
+  , LineWidth, getLineWidth
+  , _LineWidth, _LineWidthM
+  , lineWidth, lineWidthM
+  , _lineWidth, _lw, _lineWidthU
+  , lw, lwN, lwO, lwL, lwG
+
+    -- ** Dashing
+  , Dashing(..), getDashing
+  , dashing, dashingN, dashingO, dashingL, dashingG
+  , _dashing, _dashingU
+
   -- * Color
   -- $color
 
-    Color(..), SomeColor(..), someToAlpha
+  , Color(..), SomeColor(..), _SomeColor, someToAlpha
 
   -- ** Opacity
-  , Opacity, getOpacity, opacity
+  , Opacity, _Opacity
+  , getOpacity, opacity, _opacity
 
+  , FillOpacity, _FillOpacity
+  , getFillOpacity, fillOpacity, _fillOpacity
+
+  , StrokeOpacity, _StrokeOpacity
+  , getStrokeOpacity, strokeOpacity, _strokeOpacity
+
   -- ** Converting colors
   , colorToSRGBA, colorToRGBA
 
   -- * Line stuff
   -- ** Cap style
-  , LineCap(..), LineCapA, getLineCap, lineCap
+  , LineCap(..)
+  , getLineCap, lineCap, _lineCap
 
   -- ** Join style
-  , LineJoin(..), LineJoinA, getLineJoin, lineJoin
+  , LineJoin(..)
+  , getLineJoin, lineJoin, _lineJoin
 
   -- ** Miter limit
-  , LineMiterLimit(..), getLineMiterLimit, lineMiterLimit, lineMiterLimitA
+  , LineMiterLimit(..), _LineMiterLimit
+  , getLineMiterLimit, lineMiterLimit, lineMiterLimitA, _lineMiterLimit
 
+  -- * Recommend optics
+
+  , _Recommend
+  , _Commit
+  , _recommend
+  , isCommitted
+  , committed
+
   ) where
 
+import           Control.Lens          hiding (none, over)
 import           Data.Colour
-import           Data.Colour.RGBSpace        (RGB (..))
-import           Data.Colour.SRGB            (toSRGB)
-import           Data.Default.Class
-
+import           Data.Colour.RGBSpace  (RGB (..))
+import           Data.Colour.SRGB      (toSRGB)
+import           Data.Default
+import           Data.Distributive
+import           Data.Monoid.Recommend
 import           Data.Semigroup
 import           Data.Typeable
 
 import           Diagrams.Core
 
-------------------------------------------------------------
---  Color  -------------------------------------------------
-------------------------------------------------------------
+------------------------------------------------------------------------
+-- Standard measures
+------------------------------------------------------------------------
 
+none, ultraThin, veryThin, thin, medium, thick, veryThick, ultraThick,
+  tiny, verySmall, small, normal, large, veryLarge, huge
+  :: OrderedField n => Measure n
+none       = output 0
+ultraThin  = normalized 0.0005 `atLeast` output 0.5
+veryThin   = normalized 0.001  `atLeast` output 0.5
+thin       = normalized 0.002  `atLeast` output 0.5
+medium     = normalized 0.004  `atLeast` output 0.5
+thick      = normalized 0.0075 `atLeast` output 0.5
+veryThick  = normalized 0.01   `atLeast` output 0.5
+ultraThick = normalized 0.02   `atLeast` output 0.5
+
+tiny      = normalized 0.01
+verySmall = normalized 0.015
+small     = normalized 0.023
+normal    = normalized 0.035
+large     = normalized 0.05
+veryLarge = normalized 0.07
+huge      = normalized 0.10
+
+------------------------------------------------------------------------
+-- Line width
+------------------------------------------------------------------------
+
+-- | Line widths specified on child nodes always override line widths
+--   specified at parent nodes.
+newtype LineWidth n = LineWidth (Last n)
+  deriving (Typeable, Semigroup)
+
+_LineWidth :: Iso' (LineWidth n) n
+_LineWidth = iso getLineWidth (LineWidth . Last)
+
+_LineWidthM :: Iso' (LineWidthM n) (Measure n)
+_LineWidthM = mapping _LineWidth
+
+instance Typeable n => AttributeClass (LineWidth n)
+
+type LineWidthM n = Measured n (LineWidth n)
+
+instance OrderedField n => Default (LineWidthM n) where
+  def = fmap (LineWidth . Last) medium
+
+getLineWidth :: LineWidth n -> n
+getLineWidth (LineWidth (Last w)) = w
+
+-- | Set the line (stroke) width.
+lineWidth :: (N a ~ n, HasStyle a, Typeable n) => Measure n -> a -> a
+lineWidth = applyMAttr . fmap (LineWidth . Last)
+
+-- | Apply a 'LineWidth' attribute.
+lineWidthM :: (N a ~ n, HasStyle a, Typeable n) => LineWidthM n -> a -> a
+lineWidthM = applyMAttr
+
+-- | Default for 'lineWidth'.
+lw :: (N a ~ n, HasStyle a, Typeable n) => Measure n -> a -> a
+lw = lineWidth
+
+-- | A convenient synonym for 'lineWidth (global w)'.
+lwG :: (N a ~ n, HasStyle a, Typeable n, Num n) => n -> a -> a
+lwG = lw . global
+
+-- | A convenient synonym for 'lineWidth (normalized w)'.
+lwN :: (N a ~ n, HasStyle a, Typeable n, Num n) => n -> a -> a
+lwN = lw . normalized
+
+-- | A convenient synonym for 'lineWidth (output w)'.
+lwO :: (N a ~ n, HasStyle a, Typeable n) => n -> a -> a
+lwO = lw . output
+
+-- | A convenient sysnonym for 'lineWidth (local w)'.
+lwL :: (N a ~ n, HasStyle a, Typeable n, Num n) => n -> a -> a
+lwL = lw . local
+
+-- | Lens onto a measured line width in a style.
+_lineWidth, _lw :: (Typeable n, OrderedField n) => Lens' (Style v n) (Measure n)
+_lineWidth = atMAttr . anon def (const False) . _LineWidthM
+_lw = _lineWidth
+
+-- | Lens onto the unmeasured linewith attribute. This is useful for
+--   backends to use on styles once they have been unmeasured. Using on
+--   a diagram style could lead to unexpected results.
+_lineWidthU :: Typeable n => Lens' (Style v n) (Maybe n)
+_lineWidthU = atAttr . mapping _LineWidth
+
+------------------------------------------------------------------------
+-- Dashing
+------------------------------------------------------------------------
+
+-- | Create lines that are dashing... er, dashed.
+data Dashing n = Dashing [n] n
+  deriving (Functor, Typeable, Eq)
+
+instance Semigroup (Dashing n) where
+  _ <> b = b
+
+instance Typeable n => AttributeClass (Dashing n)
+
+getDashing :: Dashing n -> Dashing n
+getDashing = id
+
+-- | Set the line dashing style.
+dashing :: (N a ~ n, HasStyle a, Typeable n)
+        => [Measure n]  -- ^ A list specifying alternate lengths of on
+                        --   and off portions of the stroke.  The empty
+                        --   list indicates no dashing.
+        -> Measure n    -- ^ An offset into the dash pattern at which the
+                        --   stroke should start.
+        -> a -> a
+dashing ds offs = applyMAttr . distribute $ Dashing ds offs
+
+-- | A convenient synonym for 'dashing (global w)'.
+dashingG :: (N a ~ n, HasStyle a, Typeable n, Num n) => [n] -> n -> a -> a
+dashingG w v = dashing (map global w) (global v)
+
+-- | A convenient synonym for 'dashing (normalized w)'.
+dashingN :: (N a ~ n, HasStyle a, Typeable n, Num n) => [n] -> n -> a -> a
+dashingN w v = dashing (map normalized w) (normalized v)
+
+-- | A convenient synonym for 'dashing (output w)'.
+dashingO :: (N a ~ n, HasStyle a, Typeable n) => [n] -> n -> a -> a
+dashingO w v = dashing (map output w) (output v)
+
+-- | A convenient sysnonym for 'dashing (local w)'.
+dashingL :: (N a ~ n, HasStyle a, Typeable n, Num n) => [n] -> n -> a -> a
+dashingL w v = dashing (map local w) (local v)
+
+-- | Lens onto a measured dashing attribute in a style.
+_dashing :: Typeable n
+         => Lens' (Style v n) (Maybe (Measured n (Dashing n)))
+_dashing = atMAttr
+
+-- | Lens onto the unmeasured 'Dashing' attribute. This is useful for
+--   backends to use on styles once they have been unmeasured. Using on
+--   a diagram style could lead to unexpected results.
+_dashingU :: Typeable n => Lens' (Style v n) (Maybe (Dashing n))
+_dashingU = atAttr
+
+------------------------------------------------------------------------
+-- Color
+------------------------------------------------------------------------
+
 -- $color
 -- Diagrams outsources all things color-related to Russell O\'Connor\'s
 -- very nice colour package
@@ -86,20 +270,36 @@
 data SomeColor = forall c. Color c => SomeColor c
   deriving Typeable
 
+instance Show SomeColor where
+  showsPrec d (colorToSRGBA -> (r,g,b,a)) =
+    showParen (d > 10) $ showString "SomeColor " .
+      if a == 0
+        then showString "transparent"
+        else showString "(sRGB " . showsPrec 11 r . showChar ' '
+                                 . showsPrec 11 g . showChar ' '
+                                 . showsPrec 11 b .
+                        (if a /= 1
+                           then showString " `withOpacity` " . showsPrec 11 a
+                           else id) . showChar ')'
+
+-- | Isomorphism between 'SomeColor' and 'AlphaColour' 'Double'.
+_SomeColor :: Iso' SomeColor (AlphaColour Double)
+_SomeColor = iso toAlphaColour fromAlphaColour
+
 someToAlpha :: SomeColor -> AlphaColour Double
 someToAlpha (SomeColor c) = toAlphaColour c
 
-instance (Floating a, Real a) => Color (Colour a) where
-  toAlphaColour   = opaque . colourConvert
-  fromAlphaColour = colourConvert . (`over` black)
+instance a ~ Double => Color (Colour a) where
+  toAlphaColour   = opaque
+  fromAlphaColour = (`over` black)
 
-instance (Floating a, Real a) => Color (AlphaColour a) where
-  toAlphaColour   = alphaColourConvert
-  fromAlphaColour = alphaColourConvert
+instance a ~ Double => Color (AlphaColour a) where
+  toAlphaColour   = id
+  fromAlphaColour = id
 
 instance Color SomeColor where
   toAlphaColour (SomeColor c) = toAlphaColour c
-  fromAlphaColour c = SomeColor c
+  fromAlphaColour             = SomeColor
 
 -- | Convert to sRGBA.
 colorToSRGBA, colorToRGBA :: Color c => c -> (Double, Double, Double, Double)
@@ -113,12 +313,13 @@
 colorToRGBA = colorToSRGBA
 {-# DEPRECATED colorToRGBA "Renamed to colorToSRGBA." #-}
 
-alphaToColour :: (Floating a, Ord a, Fractional a) => AlphaColour a -> Colour a
+alphaToColour :: (Floating a, Ord a) => AlphaColour a -> Colour a
 alphaToColour ac | alphaChannel ac == 0 = ac `over` black
                  | otherwise = darken (recip (alphaChannel ac)) (ac `over` black)
 
-------------------------------------------------------------
+------------------------------------------------------------------------
 -- Opacity
+------------------------------------------------------------------------
 
 -- | Although the individual colors in a diagram can have
 --   transparency, the opacity/transparency of a diagram as a whole
@@ -132,6 +333,9 @@
   deriving (Typeable, Semigroup)
 instance AttributeClass Opacity
 
+_Opacity :: Iso' Opacity Double
+_Opacity = iso getOpacity (Opacity . Product)
+
 getOpacity :: Opacity -> Double
 getOpacity (Opacity (Product d)) = d
 
@@ -141,64 +345,139 @@
 opacity :: HasStyle a => Double -> a -> a
 opacity = applyAttr . Opacity . Product
 
-------------------------------------------------------------
---  Line stuff    -------------------------------------
-------------------------------------------------------------
+-- | Lens onto the opacity in a style.
+_opacity :: Lens' (Style v n) Double
+_opacity = atAttr . mapping _Opacity . non 1
 
+-- fill opacity --------------------------------------------------------
+
+-- | Like 'Opacity', but set the opacity only for fills (as opposed to strokes).
+--   As with 'Opacity', the fill opacity is a value between 1
+--   (completely opaque, the default) and 0 (completely transparent),
+--   and is multiplicative.
+newtype FillOpacity = FillOpacity (Product Double)
+  deriving (Typeable, Semigroup)
+instance AttributeClass FillOpacity
+
+_FillOpacity :: Iso' FillOpacity Double
+_FillOpacity = iso getFillOpacity (FillOpacity . Product)
+
+getFillOpacity :: FillOpacity -> Double
+getFillOpacity (FillOpacity (Product d)) = d
+
+-- | Multiply the fill opacity (see 'FillOpacity') by the given value.  For
+--   example, @fillOpacity 0.8@ means \"decrease this diagram's fill opacity to
+--   80% of its previous value\".
+fillOpacity :: HasStyle a => Double -> a -> a
+fillOpacity = applyAttr . FillOpacity . Product
+
+-- | Lens onto the fill opacity in a style.
+_fillOpacity :: Lens' (Style v n) Double
+_fillOpacity = atAttr . mapping _FillOpacity . non 1
+
+-- stroke opacity --------------------------------------------------------
+
+-- | Like 'Opacity', but set the opacity only for strokes (as opposed to fills).
+--   As with 'Opacity', the fill opacity is a value between 1
+--   (completely opaque, the default) and 0 (completely transparent),
+--   and is multiplicative.
+newtype StrokeOpacity = StrokeOpacity (Product Double)
+  deriving (Typeable, Semigroup)
+instance AttributeClass StrokeOpacity
+
+_StrokeOpacity :: Iso' StrokeOpacity Double
+_StrokeOpacity = iso getStrokeOpacity (StrokeOpacity . Product)
+
+getStrokeOpacity :: StrokeOpacity -> Double
+getStrokeOpacity (StrokeOpacity (Product d)) = d
+
+-- | Multiply the stroke opacity (see 'StrokeOpacity') by the given value.  For
+--   example, @strokeOpacity 0.8@ means \"decrease this diagram's
+--   stroke opacity to 80% of its previous value\".
+strokeOpacity :: HasStyle a => Double -> a -> a
+strokeOpacity = applyAttr . StrokeOpacity . Product
+
+-- | Lens onto the stroke opacity in a style.
+_strokeOpacity :: Lens' (Style v n) Double
+_strokeOpacity = atAttr . mapping _StrokeOpacity . non 1
+
+------------------------------------------------------------------------
+-- Line stuff
+------------------------------------------------------------------------
+
+-- line cap ------------------------------------------------------------
+
 -- | What sort of shape should be placed at the endpoints of lines?
 data LineCap = LineCapButt   -- ^ Lines end precisely at their endpoints.
              | LineCapRound  -- ^ Lines are capped with semicircles
                              --   centered on endpoints.
              | LineCapSquare -- ^ Lines are capped with a squares
                              --   centered on endpoints.
-  deriving (Eq,Show,Typeable)
-
-newtype LineCapA = LineCapA (Last LineCap)
-  deriving (Typeable, Semigroup, Eq)
-instance AttributeClass LineCapA
+  deriving (Eq, Ord, Show, Typeable)
 
 instance Default LineCap where
-    def = LineCapButt
+  def = LineCapButt
 
-getLineCap :: LineCapA -> LineCap
-getLineCap (LineCapA (Last c)) = c
+instance AttributeClass LineCap
 
+-- | Last semigroup structure.
+instance Semigroup LineCap where
+  _ <> b = b
+
+getLineCap :: LineCap -> LineCap
+getLineCap = id
+
 -- | Set the line end cap attribute.
 lineCap :: HasStyle a => LineCap -> a -> a
-lineCap = applyAttr . LineCapA . Last
+lineCap = applyAttr
 
+-- | Lens onto the line cap in a style.
+_lineCap :: Lens' (Style v n) LineCap
+_lineCap = atAttr . non def
 
+-- line join -----------------------------------------------------------
+
 -- | How should the join points between line segments be drawn?
 data LineJoin = LineJoinMiter    -- ^ Use a \"miter\" shape (whatever that is).
               | LineJoinRound    -- ^ Use rounded join points.
               | LineJoinBevel    -- ^ Use a \"bevel\" shape (whatever
                                  --   that is).  Are these...
                                  --   carpentry terms?
-  deriving (Eq,Show,Typeable)
+  deriving (Eq, Ord, Show, Typeable)
 
-newtype LineJoinA = LineJoinA (Last LineJoin)
-  deriving (Typeable, Semigroup, Eq)
-instance AttributeClass LineJoinA
+instance AttributeClass LineJoin
 
+-- | Last semigroup structure.
+instance Semigroup LineJoin where
+  _ <> b = b
+
 instance Default LineJoin where
-    def = LineJoinMiter
+  def = LineJoinMiter
 
-getLineJoin :: LineJoinA -> LineJoin
-getLineJoin (LineJoinA (Last j)) = j
+getLineJoin :: LineJoin -> LineJoin
+getLineJoin = id
 
 -- | Set the segment join style.
 lineJoin :: HasStyle a => LineJoin -> a -> a
-lineJoin = applyAttr . LineJoinA . Last
+lineJoin = applyAttr
 
+-- | Lens onto the line join type in a style.
+_lineJoin :: Lens' (Style v n) LineJoin
+_lineJoin = atAttr . non def
 
+-- miter limit ---------------------------------------------------------
+
 -- | Miter limit attribute affecting the 'LineJoinMiter' joins.
 --   For some backends this value may have additional effects.
 newtype LineMiterLimit = LineMiterLimit (Last Double)
-  deriving (Typeable, Semigroup)
+  deriving (Typeable, Semigroup, Eq, Ord)
 instance AttributeClass LineMiterLimit
 
+_LineMiterLimit :: Iso' LineMiterLimit Double
+_LineMiterLimit = iso getLineMiterLimit (LineMiterLimit . Last)
+
 instance Default LineMiterLimit where
-    def = LineMiterLimit (Last 10)
+  def = LineMiterLimit (Last 10)
 
 getLineMiterLimit :: LineMiterLimit -> Double
 getLineMiterLimit (LineMiterLimit (Last l)) = l
@@ -210,3 +489,40 @@
 -- | Apply a 'LineMiterLimit' attribute.
 lineMiterLimitA :: HasStyle a => LineMiterLimit -> a -> a
 lineMiterLimitA = applyAttr
+
+-- | Lens onto the line miter limit in a style.
+_lineMiterLimit :: Lens' (Style v n) Double
+_lineMiterLimit = atAttr . non def . _LineMiterLimit
+
+------------------------------------------------------------------------
+-- Recommend optics
+------------------------------------------------------------------------
+
+-- | Prism onto a 'Recommend'.
+_Recommend :: Prism' (Recommend a) a
+_Recommend = prism' Recommend $ \case (Recommend a) -> Just a; _ -> Nothing
+
+-- | Prism onto a 'Commit'.
+_Commit :: Prism' (Recommend a) a
+_Commit = prism' Commit $ \case (Commit a) -> Just a; _ -> Nothing
+
+-- | Lens onto the value inside either a 'Recommend' or 'Commit'. Unlike
+--   'committed', this is a valid lens.
+_recommend :: Lens (Recommend a) (Recommend b) a b
+_recommend f (Recommend a) = Recommend <$> f a
+_recommend f (Commit a)    = Commit <$> f a
+
+-- | Lens onto whether something is committed or not.
+isCommitted :: Lens' (Recommend a) Bool
+isCommitted f r@(Recommend a) = f False <&> \b -> if b then Commit a else r
+isCommitted f r@(Commit a)    = f True  <&> \b -> if b then r else Recommend a
+
+-- | 'Commit' a value for any 'Recommend'. This is *not* a valid 'Iso'
+--   because the resulting @Recommend b@ is always a 'Commit'. This is
+--   useful because it means any 'Recommend' styles set with a lens will
+--   not be accidentally overridden. If you want a valid lens onto a
+--   recommend value use '_recommend'.
+--
+--   Other lenses that use this are labeled with a warning.
+committed :: Iso (Recommend a) (Recommend b) a b
+committed = iso getRecommend Commit
diff --git a/src/Diagrams/Attributes/Compile.hs b/src/Diagrams/Attributes/Compile.hs
--- a/src/Diagrams/Attributes/Compile.hs
+++ b/src/Diagrams/Attributes/Compile.hs
@@ -2,6 +2,10 @@
 {-# LANGUAGE GADTs               #-}
 {-# LANGUAGE ScopedTypeVariables #-}
 {-# LANGUAGE TypeFamilies        #-}
+
+{-# OPTIONS_GHC -fno-warn-unused-imports #-}
+  -- for Data.Semigroup
+
 -----------------------------------------------------------------------------
 -- |
 -- Module      :  Diagrams.Attributes.Compile
@@ -21,12 +25,13 @@
 
 import           Control.Arrow       (second)
 import           Control.Lens        ((%~), (&), _Wrapping')
-import qualified Data.Map            as M
-import           Data.Semigroup      ((<>))
+import           Data.Kind           (Type)
+import qualified Data.HashMap.Strict as HM
+import           Data.Semigroup
 import           Data.Tree           (Tree (..))
 
 import           Diagrams.Core
-import           Diagrams.Core.Style (Style (..), attrToStyle)
+import           Diagrams.Core.Style (Style (..), attributeToStyle)
 import           Diagrams.Core.Types (RNode (..), RTree)
 
 ------------------------------------------------------------
@@ -35,8 +40,8 @@
 -- splitFills; it's done this way to facilitate testing.
 
 class (AttributeClass (AttrType code), Typeable (PrimType code)) => SplitAttribute code where
-  type AttrType code :: *
-  type PrimType code :: *
+  type AttrType code :: Type
+  type PrimType code :: Type
 
   primOK :: code -> PrimType code -> Bool
 
@@ -44,7 +49,7 @@
 --   containing only "safe" nodes.  In particular this is used to push
 --   fill attributes down until they are over only loops; see
 --   'splitFills'.
-splitAttr :: forall code b v a. SplitAttribute code => code -> RTree b v a -> RTree b v a
+splitAttr :: forall code b v n a. SplitAttribute code => code -> RTree b v n a -> RTree b v n a
 splitAttr code = fst . splitAttr' Nothing
   where
 
@@ -57,7 +62,7 @@
   -- Output: tree with attributes pushed down appropriately, and
   -- a Bool indicating whether the tree contains only "safe" prims (True) or
   -- contains some unsafe ones (False).
-  splitAttr' :: Maybe (AttrType code) -> RTree b v a -> (RTree b v a, Bool)
+  splitAttr' :: Maybe (AttrType code) -> RTree b v n a -> (RTree b v n a, Bool)
 
   -- RStyle node: Check for the special attribute, and split it out of
   -- the style, combining it with the incoming attribute.  Recurse and
@@ -73,8 +78,8 @@
   splitAttr' mattr (Node (RStyle sty) cs) = (t', ok)
     where
       mattr' = mattr <> getAttr sty
-      sty' = sty & _Wrapping' Style %~ M.delete ty
-      ty   = show . typeOf $ (undefined :: AttrType code)
+      sty' = sty & _Wrapping' Style %~ HM.delete ty
+      ty   = typeOf (undefined :: AttrType code)
       (cs', ok) = splitAttr'Forest mattr' cs
       t' | ok        = rebuildNode Nothing ok (RStyle sty) cs'
          | otherwise = rebuildNode mattr ok (RStyle sty') cs'
@@ -87,9 +92,9 @@
       case cast prm :: Maybe (PrimType code) of
         Nothing  -> (Node rp [], True)
         Just p ->
-          case primOK code p of
-            True  -> (rebuildNode mattr True rp [], True)
-            False -> (Node rp [], False)
+          if primOK code p
+            then (rebuildNode mattr True rp [], True)
+            else (Node rp [], False)
 
   -- RFrozenTr, RAnnot, REmpty cases: just recurse and rebuild.  Note
   -- we assume that transformations do not affect the attributes.
@@ -101,7 +106,7 @@
   -- Recursively call splitAttr' on all subtrees, returning the
   -- logical AND of the Bool results returned (the whole forest is
   -- safe iff all subtrees are).
-  splitAttr'Forest :: Maybe (AttrType code) -> [RTree b v a] -> ([RTree b v a], Bool)
+  splitAttr'Forest :: Maybe (AttrType code) -> [RTree b v n a] -> ([RTree b v n a], Bool)
   splitAttr'Forest mattr cs = (cs', ok)
     where
       (cs', ok) = second and . unzip . map (splitAttr' mattr) $ cs
@@ -110,13 +115,13 @@
   -- subforest contains only loops, a node, and a subforest, rebuild a
   -- tree, applying the fill attribute as appropriate (only if the
   -- Bool is true and the attribute is not Nothing).
-  rebuildNode :: Maybe (AttrType code) -> Bool -> RNode b v a -> [RTree b v a] -> RTree b v a
+  rebuildNode :: Maybe (AttrType code) -> Bool -> RNode b v n a -> [RTree b v n a] -> RTree b v n a
   rebuildNode mattr ok nd cs
     | ok        = applyMattr mattr (Node nd cs)
     | otherwise = Node nd cs
 
   -- Prepend a new fill color node if Just; the identity function if
   -- Nothing.
-  applyMattr :: Maybe (AttrType code) -> RTree b v a -> RTree b v a
+  applyMattr :: Maybe (AttrType code) -> RTree b v n a -> RTree b v n a
   applyMattr Nothing  t = t
-  applyMattr (Just a) t = Node (RStyle $ attrToStyle a) [t]
+  applyMattr (Just a) t = Node (RStyle $ attributeToStyle (Attribute a)) [t]
diff --git a/src/Diagrams/Backend/CmdLine.hs b/src/Diagrams/Backend/CmdLine.hs
--- a/src/Diagrams/Backend/CmdLine.hs
+++ b/src/Diagrams/Backend/CmdLine.hs
@@ -1,3 +1,5 @@
+{-# LANGUAGE CPP                       #-}
+{-# LANGUAGE ConstrainedClassMethods   #-}
 {-# LANGUAGE DeriveDataTypeable        #-}
 {-# LANGUAGE FlexibleContexts          #-}
 {-# LANGUAGE FlexibleInstances         #-}
@@ -13,98 +15,94 @@
 -- License     :  BSD-style (see LICENSE)
 -- Maintainer  :  diagrams-discuss@googlegroups.com
 --
--- Convenient creation of command-line-driven executables for
--- rendering diagrams.  This module provides a general framework
--- and default behaviors for parsing command-line arguments,
--- records for diagram creation options in various forms, and
--- classes and instances for a unified entry point to command-line-driven
--- diagram creation executables.
+-- Convenient creation of command-line-driven executables for rendering
+-- diagrams.  This module provides a general framework and default
+-- behaviors for parsing command-line arguments, records for diagram
+-- creation options in various forms, and classes and instances for a
+-- unified entry point to command-line-driven diagram creation
+-- executables.
 --
 -- For a tutorial on command-line diagram creation see
--- <http://projects.haskell.org/diagrams/doc/cmdline.html>.
+-- <https://diagrams.github.io/doc/cmdline.html>.
 --
 -----------------------------------------------------------------------------
 
 module Diagrams.Backend.CmdLine
-       (
-
-         -- * Options
+  (
 
-         -- ** Standard options
-         DiagramOpts(..)
-       , diagramOpts
-       , width
-       , height
-       , output
+    -- * Options
 
-         -- ** Multi-diagram options
-       , DiagramMultiOpts(..)
-       , diagramMultiOpts
-       , selection
-       , list
+    -- ** Standard options
+    DiagramOpts(..)
+  , diagramOpts
+  , width
+  , height
+  , output
 
-         -- ** Animation options
-       , DiagramAnimOpts(..)
-       , diagramAnimOpts
-       , fpu
+    -- ** Multi-diagram options
+  , DiagramMultiOpts(..)
+  , diagramMultiOpts
+  , selection
+  , list
 
-         -- ** Loop options
-       , DiagramLoopOpts(..)
-       , diagramLoopOpts
-       , loop
-       , src
-       , interval
+    -- ** Animation options
+  , DiagramAnimOpts(..)
+  , diagramAnimOpts
+  , fpu
 
-         -- * Parsing
-       , Parseable(..)
-       , readHexColor
+    -- * Parsing
+  , Parseable(..)
+  , readHexColor
 
-         -- * Command-line programs (@Mainable@)
-         -- ** Arguments, rendering, and entry point
-       , Mainable(..)
+    -- * Command-line programs (@Mainable@)
+    -- ** Arguments, rendering, and entry point
+  , Mainable(..)
 
-         -- ** General currying
-       , ToResult(..)
+    -- ** General currying
+  , ToResult(..)
 
-         -- ** Default @mainRender@ implementations
-       , defaultAnimMainRender
-       , defaultMultiMainRender
-       ) where
+    -- ** helper functions for implementing @mainRender@
+  , defaultAnimMainRender
+  , defaultMultiMainRender
+  ) where
 
-import           Control.Lens        hiding (argument)
+import           Control.Lens              (Lens', makeLenses, (&), (.~), (^.))
 import           Diagrams.Animation
 import           Diagrams.Attributes
-import           Diagrams.Core       hiding (value)
+import           Diagrams.Core             hiding (output)
 
 import           Options.Applicative
 import           Options.Applicative.Types (readerAsk)
 
-import           Prelude
+import           Control.Monad             (forM_)
 
-import           Control.Monad       (forM_)
+-- MonadFail comes from Prelude in base-4.13 and up
+#if !MIN_VERSION_base(4,13,0)
+import           Control.Monad.Fail        (MonadFail)
+#endif
 
-import           Data.Active         hiding (interval)
-import           Data.Char           (isDigit)
+import           Data.Active               hiding (interval)
+import           Data.Char                 (isDigit)
 import           Data.Colour
 import           Data.Colour.Names
 import           Data.Colour.SRGB
 import           Data.Data
-import           Data.List           (intercalate)
+import           Data.Functor.Identity
+import           Data.Kind                 (Type)
 import           Data.Monoid
-
 import           Numeric
 
-import           System.Environment  (getProgName)
-import           System.FilePath     (addExtension, splitExtension)
+import           System.Environment        (getProgName)
+import           System.FilePath           (addExtension, splitExtension)
 
 import           Text.Printf
 
 -- | Standard options most diagrams are likely to have.
 data DiagramOpts = DiagramOpts
-    { _width  :: Maybe Int -- ^ Final output width of diagram.
-    , _height :: Maybe Int -- ^ Final output height of diagram.
-    , _output :: FilePath  -- ^ Output file path, format is typically chosen by extension.
-    }
+  { _width  :: Maybe Int -- ^ Final output width of diagram.
+  , _height :: Maybe Int -- ^ Final output height of diagram.
+  , _output :: FilePath  -- ^ Output file path, format is typically chosen by extension.
+  }
   deriving (Show, Data, Typeable)
 
 makeLenses ''DiagramOpts
@@ -112,110 +110,91 @@
 -- | Extra options for a program that can offer a choice
 --   between multiple diagrams.
 data DiagramMultiOpts = DiagramMultiOpts
-    { _selection :: Maybe String -- ^ Selected diagram to render.
-    , _list      :: Bool         -- ^ Flag to indicate that a list of available diagrams should
-                                 --   be printed to standard out.
-    }
+  { _selection :: Maybe String -- ^ Selected diagram to render.
+  , _list      :: Bool         -- ^ Flag to indicate that a list of available diagrams should
+                               --   be printed to standard out.
+  }
   deriving (Show, Data, Typeable)
 
 makeLenses ''DiagramMultiOpts
 
 -- | Extra options for animations.
 data DiagramAnimOpts = DiagramAnimOpts
-    { _fpu :: Double -- ^ Number of frames per unit time to generate for the animation.
-    }
+  { _fpu :: Double -- ^ Number of frames per unit time to generate for the animation.
+  }
   deriving (Show, Data, Typeable)
 
 makeLenses ''DiagramAnimOpts
 
--- | Extra options for command-line looping.
-data DiagramLoopOpts = DiagramLoopOpts
-    { _loop     :: Bool            -- ^ Flag to indicate that the program should loop creation.
-    , _src      :: Maybe FilePath  -- ^ File path for the source file to recompile.
-    , _interval :: Int             -- ^ Interval in seconds at which to check for recompilation.
-    }
-
-makeLenses ''DiagramLoopOpts
-
 -- | Command line parser for 'DiagramOpts'.
 --   Width is option @--width@ or @-w@.
 --   Height is option @--height@ or @-h@ (note we change help to be @-?@ due to this).
 --   Output is option @--output@ or @-o@.
 diagramOpts :: Parser DiagramOpts
 diagramOpts = DiagramOpts
-    <$> (optional . option auto)
-        ( long "width" <> short 'w'
-       <> metavar "WIDTH"
-       <> help "Desired WIDTH of the output image")
-    <*> (optional . option auto)
-        ( long "height" <> short 'h'
-       <> metavar "HEIGHT"
-       <> help "Desired HEIGHT of the output image")
-    <*> strOption
-        ( long "output" <> short 'o'
-       <> value ""
-       <> metavar "OUTPUT"
-       <> help "OUTPUT file")
+  <$> (optional . option auto)
+      ( long "width" <> short 'w'
+     <> metavar "WIDTH"
+     <> help "Desired WIDTH of the output image")
+  <*> (optional . option auto)
+      ( long "height" <> short 'h'
+     <> metavar "HEIGHT"
+     <> help "Desired HEIGHT of the output image")
+  <*> strOption
+      ( long "output" <> short 'o'
+     <> value ""
+     <> metavar "OUTPUT"
+     <> help "OUTPUT file")
 
 -- | Command line parser for 'DiagramMultiOpts'.
---   Selection is option @--selection@ or @-s@.
---   List is @--list@ or @-l@.
+--   Selection is option @--selection@ or @-S@.
+--   List is @--list@ or @-L@.
 diagramMultiOpts :: Parser DiagramMultiOpts
 diagramMultiOpts = DiagramMultiOpts
-    <$> (optional . strOption)
-        ( long "selection" <> short 's'
-       <> metavar "NAME"
-       <> help "NAME of the diagram to render")
-    <*> switch
-        ( long "list" <> short 'l'
-       <> help "List all available diagrams")
+  <$> (optional . strOption)
+      ( long "selection" <> short 'S'
+     <> metavar "NAME"
+     <> help "NAME of the diagram to render")
+  <*> switch
+      ( long "list" <> short 'L'
+     <> help "List all available diagrams")
 
 -- | Command line parser for 'DiagramAnimOpts'
 --   Frames per unit is @--fpu@ or @-f@.
 diagramAnimOpts :: Parser DiagramAnimOpts
 diagramAnimOpts = DiagramAnimOpts
-    <$> option auto
-        ( long "fpu" <> short 'f'
-       <> value 30.0
-       <> help "Frames per unit time (for animations)")
-
--- | CommandLine parser for 'DiagramLoopOpts'
---   Loop is @--loop@ or @-l@.
---   Source is @--src@ or @-s@.
---   Interval is @-i@ defaulting to one second.
-diagramLoopOpts :: Parser DiagramLoopOpts
-diagramLoopOpts = DiagramLoopOpts
-    <$> switch (long "loop" <> short 'l' <> help "Run in a self-recompiling loop")
-    <*> (optional . strOption)
-        ( long "src" <> short 's'
-       <> help "Source file to watch")
-    <*> option auto
-        ( long "interval" <> short 'i'
-       <> value 1
-       <> metavar "INTERVAL"
-       <> help "When running in a loop, check for changes every INTERVAL seconds.")
+  <$> option auto
+      ( long "fpu" <> short 'f'
+     <> value 30.0
+     <> help "Frames per unit time (for animations)")
 
 -- | A hidden \"helper\" option which always fails.
 --   Taken from Options.Applicative.Extra but without the
 --   short option 'h'.  We want the 'h' for Height.
 helper' :: Parser (a -> a)
-helper' = abortOption ShowHelpText $ mconcat
+helper' = abortOption param $ mconcat
   [ long "help"
   , short '?'
   , help "Show this help text"
   ]
+  where
+#if MIN_VERSION_optparse_applicative(0,16,0)
+    param = ShowHelpText Nothing
+#else
+    param = ShowHelpText 
+#endif
 
 -- | Apply a parser to the command line that includes the standard
 --   program description and help behavior.  Results in parsed commands
 --   or fails with a help message.
 defaultOpts :: Parser a -> IO a
 defaultOpts optsParser = do
-    prog <- getProgName
-    let p = info (helper' <*> optsParser)
-                ( fullDesc
-               <> progDesc "Command-line diagram generation."
-               <> header prog)
-    execParser p
+  prog <- getProgName
+  let p = info (helper' <*> optsParser)
+              ( fullDesc
+             <> progDesc "Command-line diagram generation."
+             <> header prog)
+  execParser p
 
 -- | Parseable instances give a command line parser for a type.  If a custom
 --   parser for a common type is wanted a newtype wrapper could be used to make
@@ -223,7 +202,7 @@
 --   instances as 'Read' because we want to limit ourselves to things that make
 --   sense to parse from the command line.
 class Parseable a where
-    parser :: Parser a
+  parser :: Parser a
 
 -- The following instance would overlap with the product instance for
 -- Parseable.  We can't tell if one wants to parse (a,b) as one argument or a
@@ -235,51 +214,46 @@
 
 -- | Parse 'Int' according to its 'Read' instance.
 instance Parseable Int where
-    parser = argument auto mempty
+  parser = argument auto mempty
 
 -- | Parse 'Double' according to its 'Read' instance.
 instance Parseable Double where
-    parser = argument auto mempty
+  parser = argument auto mempty
 
 -- | Parse a string by just accepting the given string.
 instance Parseable String where
-    parser = argument str mempty
+  parser = argument str mempty
 
 -- | Parse 'DiagramOpts' using the 'diagramOpts' parser.
 instance Parseable DiagramOpts where
-    parser = diagramOpts
+  parser = diagramOpts
 
 -- | Parse 'DiagramMultiOpts' using the 'diagramMultiOpts' parser.
 instance Parseable DiagramMultiOpts where
-    parser = diagramMultiOpts
+  parser = diagramMultiOpts
 
 -- | Parse 'DiagramAnimOpts' using the 'diagramAnimOpts' parser.
 instance Parseable DiagramAnimOpts where
-    parser = diagramAnimOpts
-
--- | Parse 'DiagramLoopOpts' using the 'diagramLoopOpts' parser.
-instance Parseable DiagramLoopOpts where
-    parser = diagramLoopOpts
-
+  parser = diagramAnimOpts
 
 -- | Parse @'Colour' Double@ as either a named color from "Data.Colour.Names"
 --   or a hexadecimal color.
 instance Parseable (Colour Double) where
-    parser = argument (rc <|> rh) mempty
-      where
-        rh, rc :: ReadM (Colour Double)
-        rh = f . colorToSRGBA <$> (readerAsk >>= readHexColor)
-        rc = readerAsk >>= readColourName
-        f (r,g,b,_) = sRGB r g b -- TODO: this seems unfortunate.  Should the alpha
-                                 -- value be applied to the r g b values?
+  parser = argument (rc <|> rh) mempty
+    where
+      rh, rc :: ReadM (Colour Double)
+      rh = f . colorToSRGBA <$> (readerAsk >>= readHexColor)
+      rc = readerAsk >>= readColourName
+      f (r,g,b,_) = sRGB r g b -- TODO: this seems unfortunate.  Should the alpha
+                               -- value be applied to the r g b values?
 
 -- | Parse @'AlphaColour' Double@ as either a named color from "Data.Colour.Names"
 --   or a hexadecimal color.
 instance Parseable (AlphaColour Double) where
-    parser = argument (rc <|> rh) mempty
-      where
-        rh = readerAsk >>= readHexColor
-        rc = opaque <$> (readerAsk >>= readColourName)
+  parser = argument (rc <|> rh) mempty
+    where
+      rh = readerAsk >>= readHexColor
+      rc = opaque <$> (readerAsk >>= readColourName)
 
 -- Addapted from the Clay.Color module of the clay package
 
@@ -289,11 +263,11 @@
 --   example, @\"0xfc4\"@ is the same as @\"0xffcc44\"@.  When eight or six
 --   digits are given each pair of digits is a color or alpha channel with the
 --   order being red, green, blue, alpha.
-readHexColor :: (Applicative m, Monad m) => String -> m (AlphaColour Double)
+readHexColor :: (Applicative m, MonadFail m) => String -> m (AlphaColour Double)
 readHexColor cs = case cs of
-     ('0':'x':hs) -> handle hs
-     ('#':hs)     -> handle hs
-     hs           -> handle hs
+  ('0':'x':hs) -> handle hs
+  ('#':hs)     -> handle hs
+  hs           -> handle hs
   where
     handle hs | length hs <= 8 && all isHexDigit hs
       = case hs of
@@ -304,70 +278,76 @@
         _                 -> fail $ "could not parse as a colour" ++ cs
     handle _ = fail $ "could not parse as a colour: " ++ cs
 
-    isHexDigit c = isDigit c|| c `elem` "abcdef"
+    isHexDigit c = isDigit c || c `elem` "abcdef"
 
     hex a b = (/ 255) <$> case readHex [a,b] of
                 [(h,"")] -> return h
-                _        -> fail $ "could not parse as a hex value" ++ (a:b:[])
+                _        -> fail $ "could not parse as a hex value" ++ [a,b]
 
 
 -- | This instance is needed to signal the end of a chain of
 --   nested tuples, it always just results in the unit value
 --   without consuming anything.
 instance Parseable () where
-    parser = pure ()
+  parser = pure ()
 
 -- | Allow 'Parseable' things to be combined.
 instance (Parseable a, Parseable b) => Parseable (a,b) where
-    parser = (,) <$> parser <*> parser
+  parser = (,) <$> parser <*> parser
 
+-- | Triples of Parsebales should also be Parseable.
+instance (Parseable a, Parseable b, Parseable c) => Parseable (a, b, c) where
+  parser = (,,) <$> parser <*> parser <*> parser
 
+instance (Parseable a, Parseable b, Parseable c, Parseable d) => Parseable (a, b, c, d) where
+  parser = (,,,) <$> parser <*> parser <*> parser <*> parser
+
 -- | This class allows us to abstract over functions that take some arguments
 --   and produce a final value.  When some @d@ is an instance of
 --   'ToResult' we get a type @'Args' d@ that is a type of /all/ the arguments
 --   at once, and a type @'ResultOf' d@ that is the type of the final result from
 --   some base case instance.
 class ToResult d where
-    type Args d :: *
-    type ResultOf d :: *
+  type Args d :: Type
+  type ResultOf d :: Type
 
-    toResult :: d -> Args d -> ResultOf d
+  toResult :: d -> Args d -> ResultOf d
 
 -- | A diagram can always produce a diagram when given @()@ as an argument.
 --   This is our base case.
-instance ToResult (Diagram b v) where
-    type Args (Diagram b v) = ()
-    type ResultOf (Diagram b v) = Diagram b v
+instance ToResult (QDiagram b v n Any) where
+  type Args (QDiagram b v n Any) = ()
+  type ResultOf (QDiagram b v n Any) = QDiagram b v n Any
 
-    toResult d _ = d
+  toResult d _ = d
 
 -- | A list of diagrams can produce pages.
-instance ToResult [Diagram b v] where
-   type Args [Diagram b v] = ()
-   type ResultOf [Diagram b v] = [Diagram b v]
+instance ToResult [QDiagram b v n Any] where
+  type Args [QDiagram b v n Any] = ()
+  type ResultOf [QDiagram b v n Any] = [QDiagram b v n Any]
 
-   toResult ds _ = ds
+  toResult ds _ = ds
 
 -- | A list of named diagrams can give the multi-diagram interface.
-instance ToResult [(String,Diagram b v)] where
-   type Args [(String,Diagram b v)]  = ()
-   type ResultOf [(String,Diagram b v)] = [(String,Diagram b v)]
+instance ToResult [(String, QDiagram b v n Any)] where
+  type Args [(String,QDiagram b v n Any)] = ()
+  type ResultOf [(String,QDiagram b v n Any)] = [(String,QDiagram b v n Any)]
 
-   toResult ds _ = ds
+  toResult ds _ = ds
 
 -- | An animation is another suitable base case.
-instance ToResult (Animation b v) where
-   type Args (Animation b v) = ()
-   type ResultOf (Animation b v) = Animation b v
+instance ToResult (Animation b v n) where
+  type Args (Animation b v n) = ()
+  type ResultOf (Animation b v n) = Animation b v n
 
-   toResult a _ = a
+  toResult a _ = a
 
 -- | Diagrams that require IO to build are a base case.
 instance ToResult d => ToResult (IO d) where
-   type Args (IO d) = Args d
-   type ResultOf (IO d) = IO (ResultOf d)
+  type Args (IO d) = Args d
+  type ResultOf (IO d) = IO (ResultOf d)
 
-   toResult d args = flip toResult args <$> d
+  toResult d args = flip toResult args <$> d
 
 -- | An instance for a function that, given some 'a', can produce a 'd' that is
 --   also an instance of 'ToResult'.  For this to work we need both the
@@ -379,10 +359,10 @@
 --   is clearer and easier to understand then paragraphs in English written by
 --   me.
 instance ToResult d => ToResult (a -> d) where
-    type Args (a -> d) = (a, Args d)
-    type ResultOf (a -> d) = ResultOf d
+  type Args (a -> d) = (a, Args d)
+  type ResultOf (a -> d) = ResultOf d
 
-    toResult f (a,args) = toResult (f a) args
+  toResult f (a,args) = toResult (f a) args
 
 
 -- | This class represents the various ways we want to support diagram creation
@@ -401,62 +381,59 @@
 --   The associated type 'MainOpts' describes the options which need to be parsed
 --   from the command-line and passed to @mainRender@.
 class Mainable d where
-    -- | Associated type that describes the options which need to be parsed
-    -- from the command-line and passed to @mainRender@.
-    type MainOpts d :: *
+  -- | Associated type that describes the options which need to be parsed
+  -- from the command-line and passed to @mainRender@.
+  type MainOpts d :: Type
 
-    -- | This method invokes the command-line parser resulting in an options
-    -- value or ending the program with an error or help message.
-    -- Typically the default instance will work.  If a different help message
-    -- or parsing behavior is desired a new implementation is appropriate.
-    --
-    -- Note the @d@ argument should only be needed to fix the type @d@.  Its
-    -- value should not be relied on as a parameter.
-    mainArgs :: Parseable (MainOpts d) => d -> IO (MainOpts d)
-    mainArgs _ = defaultOpts parser
+  -- | This method invokes the command-line parser resulting in an options
+  -- value or ending the program with an error or help message.
+  -- Typically the default instance will work.  If a different help message
+  -- or parsing behavior is desired a new implementation is appropriate.
+  mainArgs :: Parseable (MainOpts d) => proxy d -> IO (MainOpts d)
+  mainArgs _ = defaultOpts parser
 
-    -- | Backend specific work of rendering with the given options and mainable
-    -- value is done here.  All backend instances should implement this method.
-    mainRender :: MainOpts d -> d -> IO ()
+  -- | Backend specific work of rendering with the given options and mainable
+  -- value is done here.  All backend instances should implement this method.
+  mainRender :: MainOpts d -> d -> IO ()
 
-    -- | Main entry point for command-line diagram creation.  This is the method
-    -- that users will call from their program @main@.  For instance an expected
-    -- user program would take the following form.
-    --
-    -- @
-    -- import Diagrams.Prelude
-    -- import Diagrams.Backend.TheBestBackend.CmdLine
-    --
-    -- d :: Diagram B R2
-    -- d = ...
-    --
-    -- main = mainWith d
-    -- @
-    --
-    -- Most backends should be able to use the default implementation.  A different
-    -- implementation should be used to handle more complex interactions with the user.
-    mainWith :: Parseable (MainOpts d) => d -> IO ()
-    mainWith d = do
-        opts <- mainArgs d
-        mainRender opts d
+  -- | Main entry point for command-line diagram creation.  This is the method
+  -- that users will call from their program @main@.  For instance an expected
+  -- user program would take the following form.
+  --
+  -- @
+  -- import Diagrams.Prelude
+  -- import Diagrams.Backend.TheBestBackend.CmdLine
+  --
+  -- d :: Diagram B R2
+  -- d = ...
+  --
+  -- main = mainWith d
+  -- @
+  --
+  -- Most backends should be able to use the default implementation.  A different
+  -- implementation should be used to handle more complex interactions with the user.
+  mainWith :: Parseable (MainOpts d) => d -> IO ()
+  mainWith d = do
+    opts <- mainArgs (Identity d)
+    mainRender opts d
 
 -- | This instance allows functions resulting in something that is 'Mainable' to
 --   be 'Mainable'.  It takes a parse of collected arguments and applies them to
 --   the given function producing the 'Mainable' result.
-instance (Parseable (Args (a -> d)), ToResult d, Mainable (ResultOf d))
+instance (ToResult d, Mainable (ResultOf d))
         => Mainable (a -> d) where
-    type MainOpts (a -> d) = (MainOpts (ResultOf (a -> d)), Args (a -> d))
+  type MainOpts (a -> d) = (MainOpts (ResultOf (a -> d)), Args (a -> d))
 
-    mainRender (opts, a) f  = mainRender opts (toResult f a)
+  mainRender (opts, a) f  = mainRender opts (toResult f a)
 -- TODO: why can't we get away with: instance (Parseable (Args (a -> d)), Mainable (ResultOf d)) => ...
 --       Doesn't `Args (a -> d)` imply `ToResult (a -> d)` which implies `ToResult d` ?
 
 -- | With this instance we can perform IO to produce something
 --   'Mainable' before rendering.
 instance Mainable d => Mainable (IO d) where
-    type MainOpts (IO d) = MainOpts d
+  type MainOpts (IO d) = MainOpts d
 
-    mainRender opts dio = dio >>= mainRender opts
+  mainRender opts dio = dio >>= mainRender opts
 
 -- | @defaultMultiMainRender@ is an implementation of 'mainRender' where
 --   instead of a single diagram it takes a list of diagrams paired with names
@@ -464,11 +441,11 @@
 --   specifying the name of the diagram that should be rendered.  The list of
 --   available diagrams may also be printed by passing the option @--list@.
 --
---   Typically a backend can write its @[(String,Diagram B V)]@ instance as
+--   Typically a backend can write its @[(String,QDiagram b v n Any)]@ instance as
 --
 --   @
---   instance Mainable [(String,Diagram B V)] where
---       type MainOpts [(String,Diagram B V)] = (DiagramOpts, DiagramMultiOpts)
+--   instance Mainable [(String,QDiagram b v n Any)] where
+--       type MainOpts [(String,QDiagram b v n Any)] = (DiagramOpts, DiagramMultiOpts)
 --       mainRender = defaultMultiMainRender
 --   @
 --
@@ -476,19 +453,19 @@
 --   opt-in to this form or provide a different instance that makes more sense.
 defaultMultiMainRender :: Mainable d => (MainOpts d, DiagramMultiOpts) -> [(String, d)] -> IO ()
 defaultMultiMainRender (opts,multi) ds =
-    if multi^.list
-      then showDiaList (map fst ds)
-      else case multi^.selection of
-             Nothing  -> putStrLn "No diagram selected." >> showDiaList (map fst ds)
-             Just sel -> case lookup sel ds of
-                           Nothing -> putStrLn $ "Unknown diagram: " ++ sel
-                           Just d  -> mainRender opts d
+  if multi^.list
+    then showDiaList (map fst ds)
+    else case multi^.selection of
+           Nothing  -> putStrLn "No diagram selected." >> showDiaList (map fst ds)
+           Just sel -> case lookup sel ds of
+                         Nothing -> putStrLn $ "Unknown diagram: " ++ sel
+                         Just d  -> mainRender opts d
 
 -- | Display the list of diagrams available for rendering.
 showDiaList :: [String] -> IO ()
 showDiaList ds = do
   putStrLn "Available diagrams:"
-  putStrLn $ "  " ++ intercalate " " ds
+  putStrLn $ "  " ++ unwords ds
 
 -- | @defaultAnimMainRender@ is an implementation of 'mainRender' which renders
 --   an animation as numbered frames, named by extending the given output file
@@ -506,9 +483,8 @@
 --   be output for each second (unit time) of animation.
 --
 --   This function requires a lens into the structure that the particular backend
---   uses for it's diagram base case.  If @MainOpts (Diagram b v) ~ DiagramOpts@
---   then this lens will simply be 'output'.  For a backend supporting looping
---   it will most likely be @_1 . output@.  This lens is required because the
+--   uses for its diagram base case.  If @MainOpts (QDiagram b v n Any) ~ DiagramOpts@
+--   then this lens will simply be 'output'.  This lens is required because the
 --   implementation works by modifying the output field and running the base @mainRender@.
 --   Typically a backend can write its @Animation B V@ instance as
 --
@@ -520,21 +496,23 @@
 --
 --   We do not provide this instance in general so that backends can choose to
 --   opt-in to this form or provide a different instance that makes more sense.
-defaultAnimMainRender :: (Mainable (Diagram b v))
-                      => (Lens' (MainOpts (Diagram b v)) FilePath) -- ^ A lens into the output path.
-                      -> (MainOpts (Diagram b v),DiagramAnimOpts)
-                      -> Animation b v
-                      -> IO ()
-defaultAnimMainRender out (opts,animOpts) anim = do
-    let frames  = simulate (toRational $ animOpts^.fpu) anim
-        nDigits = length . show . length $ frames
-    forM_ (zip [1..] frames) $ \(i,d) -> mainRender (indexize out nDigits i opts) d
 
+defaultAnimMainRender ::
+    (opts -> QDiagram b v n Any -> IO ())
+    -> Lens' opts FilePath -- ^ A lens into the output path.
+    -> (opts, DiagramAnimOpts)
+    -> Animation b v n
+    -> IO ()
+defaultAnimMainRender renderF out (opts,animOpts) anim = do
+  let frames  = simulate (toRational $ animOpts^.fpu) anim
+      nDigits = length . show . length $ frames
+  forM_ (zip [1..] frames) $ \(i,d) -> renderF (indexize out nDigits i opts) d
+
 -- | @indexize d n@ adds the integer index @n@ to the end of the
 --   output file name, padding with zeros if necessary so that it uses
 --   at least @d@ digits.
-indexize :: Lens' s FilePath ->  Int -> Integer -> s -> s
+indexize :: Lens' s FilePath -> Int -> Integer -> s -> s
 indexize out nDigits i opts = opts & out .~ output'
   where fmt         = "%0" ++ show nDigits ++ "d"
-        output'     = addExtension (base ++ printf fmt (i::Integer)) ext
+        output'     = addExtension (base ++ printf fmt i) ext
         (base, ext) = splitExtension (opts^.out)
diff --git a/src/Diagrams/BoundingBox.hs b/src/Diagrams/BoundingBox.hs
--- a/src/Diagrams/BoundingBox.hs
+++ b/src/Diagrams/BoundingBox.hs
@@ -1,16 +1,19 @@
-{-# LANGUAGE DeriveDataTypeable         #-}
+{-# LANGUAGE ConstraintKinds #-}
 {-# LANGUAGE DeriveFunctor              #-}
 {-# LANGUAGE FlexibleContexts           #-}
+{-# LANGUAGE FlexibleInstances          #-}
 {-# LANGUAGE GeneralizedNewtypeDeriving #-}
+{-# LANGUAGE MultiParamTypeClasses      #-}
 {-# LANGUAGE NoMonomorphismRestriction  #-}
 {-# LANGUAGE ScopedTypeVariables        #-}
 {-# LANGUAGE StandaloneDeriving         #-}
 {-# LANGUAGE TypeFamilies               #-}
-{-# LANGUAGE UndecidableInstances       #-}
+{-# LANGUAGE ViewPatterns               #-}
+
 -----------------------------------------------------------------------------
 -- |
 -- Module      :  Diagrams.BoundingBox
--- Copyright   :  (c) 2011 diagrams-lib team (see LICENSE)
+-- Copyright   :  (c) 2011-2015 diagrams-lib team (see LICENSE)
 -- License     :  BSD-style (see LICENSE)
 -- Maintainer  :  diagrams-discuss@googlegroups.com
 --
@@ -23,310 +26,309 @@
 -----------------------------------------------------------------------------
 
 module Diagrams.BoundingBox
-       ( -- * Bounding boxes
-         BoundingBox()
+  ( -- * Bounding boxes
+    BoundingBox
 
-         -- * Constructing bounding boxes
-       , emptyBox, fromCorners, fromPoint, fromPoints
-       , boundingBox
+    -- * Constructing bounding boxes
+  , emptyBox, fromCorners, fromPoint, fromPoints
+  , boundingBox
 
-         -- * Queries on bounding boxes
-       , isEmptyBox
-       , getCorners, getAllCorners
-       , boxExtents, boxTransform, boxFit
-       , contains, contains'
-       , inside, inside', outside, outside'
+    -- * Queries on bounding boxes
+  , isEmptyBox
+  , getCorners, getAllCorners
+  , boxExtents, boxCenter
+  , mCenterPoint, centerPoint
+  , boxTransform, boxFit
+  , contains, contains'
+  , inside, inside', outside, outside'
 
-         -- * Operations on bounding boxes
-       , union, intersection
-       ) where
+  , boxGrid
 
-import           Control.Applicative     ((<$>))
-import qualified Data.Foldable           as F
-import           Data.Map                (Map, fromDistinctAscList, fromList,
-                                          toAscList, toList)
+    -- * Operations on bounding boxes
+  , union, intersection
+  ) where
 
+import           Control.Lens            (AsEmpty (..), Each (..), nearly)
+import           Data.Foldable           as F
 import           Data.Maybe              (fromMaybe)
-
-import           Data.VectorSpace
--- (VectorSpace, Scalar, AdditiveGroup, zeroV, negateV, (^+^), (^-^))
-import           Data.Basis              (Basis, HasBasis, basisValue,
-                                          decompose, recompose)
-import           Data.Monoid             (Monoid (..))
-import           Data.Semigroup          (Option (..), Semigroup (..))
+import           Data.Semigroup
+import           Text.Read
 
-import           Data.Data               (Data)
-import           Data.Typeable           (Typeable)
+import           Diagrams.Align
+import           Diagrams.Core
+import           Diagrams.Core.Transform
+import           Diagrams.Path
+import           Diagrams.Query
+import           Diagrams.ThreeD.Shapes  (cube)
+import           Diagrams.ThreeD.Types
+import           Diagrams.TwoD.Path      ()
+import           Diagrams.TwoD.Shapes
+import           Diagrams.TwoD.Types
 
-import           Diagrams.Core.Envelope  (Enveloped (..), appEnvelope)
-import           Diagrams.Core.HasOrigin (HasOrigin (..))
-import           Diagrams.Core.Points    (Point (..))
-import           Diagrams.Core.Transform (HasLinearMap, Transformable (..),
-                                          Transformation (..), (<->))
-import           Diagrams.Core.V         (V)
+import           Control.Applicative
+import           Data.Traversable        as T
+import           Linear.Affine
+import           Linear.Metric
+import           Linear.Vector           hiding (lerp)
+import           Linear.Vector.Compat    (lerp)
 
 -- Unexported utility newtype
 
-newtype NonEmptyBoundingBox v = NonEmptyBoundingBox (Point v, Point v)
-  deriving (Eq, Data, Typeable)
+newtype NonEmptyBoundingBox v n = NonEmptyBoundingBox (Point v n, Point v n)
+  deriving (Eq, Functor)
 
-fromNonEmpty :: NonEmptyBoundingBox v -> BoundingBox v
-fromNonEmpty = BoundingBox . Option . Just
+type instance V (NonEmptyBoundingBox v n) = v
+type instance N (NonEmptyBoundingBox v n) = n
 
-fromMaybeEmpty :: Maybe (NonEmptyBoundingBox v) -> BoundingBox v
+fromNonEmpty :: NonEmptyBoundingBox v n -> BoundingBox v n
+fromNonEmpty = BoundingBox . Just
+
+fromMaybeEmpty :: Maybe (NonEmptyBoundingBox v n) -> BoundingBox v n
 fromMaybeEmpty = maybe emptyBox fromNonEmpty
 
-nonEmptyCorners :: NonEmptyBoundingBox v -> (Point v, Point v)
+nonEmptyCorners :: NonEmptyBoundingBox v n -> (Point v n, Point v n)
 nonEmptyCorners (NonEmptyBoundingBox x) = x
 
-instance (HasBasis v, Ord (Basis v), AdditiveGroup (Scalar v), Ord (Scalar v))
-    => Semigroup (NonEmptyBoundingBox v) where
+instance (Additive v, Ord n) => Semigroup (NonEmptyBoundingBox v n) where
   (NonEmptyBoundingBox (ul, uh)) <> (NonEmptyBoundingBox (vl, vh))
-    = NonEmptyBoundingBox
-    $ mapT toPoint (combineP min ul vl, combineP max uh vh)
-
+    = NonEmptyBoundingBox (liftU2 min ul vl, liftU2 max uh vh)
 
 -- | A bounding box is an axis-aligned region determined by two points
 --   indicating its \"lower\" and \"upper\" corners.  It can also represent
 --   an empty bounding box - the points are wrapped in @Maybe@.
-newtype BoundingBox v = BoundingBox (Option (NonEmptyBoundingBox v))
-  deriving (Eq, Data, Typeable)
+newtype BoundingBox v n = BoundingBox (Maybe (NonEmptyBoundingBox v n))
+  deriving (Eq, Functor)
 
-deriving instance
-  ( HasBasis v, Ord (Basis v), AdditiveGroup (Scalar v), Ord (Scalar v)
-  ) => Semigroup (BoundingBox v)
-deriving instance
-  ( HasBasis v, Ord (Basis v), AdditiveGroup (Scalar v), Ord (Scalar v)
-  ) => Monoid (BoundingBox v)
+deriving instance (Additive v, Ord n) => Semigroup (BoundingBox v n)
+deriving instance (Additive v, Ord n) => Monoid (BoundingBox v n)
 
-type instance V (BoundingBox v) = v
+instance AsEmpty (BoundingBox v n) where
+  _Empty = nearly emptyBox isEmptyBox
 
--- Map a function on a homogenous 2-tuple. (unexported utility)
+-- | Only valid if the second point is not smaller than the first.
+instance (Additive v', Foldable v', Ord n') =>
+    Each (BoundingBox v n) (BoundingBox v' n') (Point v n) (Point v' n') where
+  each f (getCorners -> Just (l, u)) = fromCorners <$> f l <*> f u
+  each _ _                           = pure emptyBox
+
+type instance V (BoundingBox v n) = v
+type instance N (BoundingBox v n) = n
+
+-- Map a function on a homogeneous 2-tuple. (unexported utility)
 mapT :: (a -> b) -> (a, a) -> (b, b)
 mapT f (x, y) = (f x, f y)
 
-instance ( VectorSpace v, HasBasis v, Ord (Basis v)
-         , AdditiveGroup (Scalar v), Ord (Scalar v)
-         )  => HasOrigin (BoundingBox v) where
+instance (Additive v, Num n) => HasOrigin (BoundingBox v n) where
   moveOriginTo p b
     = fromMaybeEmpty
-    ( NonEmptyBoundingBox . mapT (moveOriginTo p) <$> getCorners b )
+    (NonEmptyBoundingBox . mapT (moveOriginTo p) <$> getCorners b)
 
-instance ( InnerSpace v, HasBasis v, Ord (Basis v)
-         , AdditiveGroup (Scalar v), Ord (Scalar v), Floating (Scalar v)
-         ) => Enveloped (BoundingBox v) where
+instance (Additive v, Foldable v, Ord n)
+     => HasQuery (BoundingBox v n) Any where
+  getQuery bb = Query $ Any . contains bb
+
+instance (Metric v, Traversable v, OrderedField n)
+     => Enveloped (BoundingBox v n) where
   getEnvelope = getEnvelope . getAllCorners
 
-instance Show v => Show (BoundingBox v) where
-  show
-    = maybe "emptyBox" (\(l, u) -> "fromCorners " ++ show l ++ " " ++ show u)
-    . getCorners
+-- Feels like cheating.
+-- Should be possible to generalise this.
+instance RealFloat n => Traced (BoundingBox V2 n) where
+  getTrace = getTrace
+           . ((`boxFit` rect 1 1) . boundingBox :: Envelope V2 n -> Path V2 n)
+           . getEnvelope
 
-{- TODO
-instance Read v => Read (BoundingBox v) where
-  read "emptyBox" = emptyBox
--}
+instance TypeableFloat n => Traced (BoundingBox V3 n) where
+  getTrace bb = foldMap (\tr -> getTrace $ transform tr cube) $
+                boxTransform (boundingBox cube) bb
 
+instance (Metric v, Traversable v, OrderedField n) => Alignable (BoundingBox v n) where
+  defaultBoundary = envelopeP
+
+instance Show (v n) => Show (BoundingBox v n) where
+  showsPrec d b = case getCorners b of
+    Just (l, u) -> showParen (d > 10) $
+      showString "fromCorners " . showsPrec 11 l . showChar ' ' . showsPrec 11 u
+    Nothing     -> showString "emptyBox"
+
+instance Read (v n) => Read (BoundingBox v n) where
+  readPrec = parens $
+    (do
+      Ident "emptyBox" <- lexP
+      pure emptyBox
+    ) <|>
+    (prec 10 $ do
+      Ident "fromCorners" <- lexP
+      l <- step readPrec
+      h <- step readPrec
+      pure . fromNonEmpty $ NonEmptyBoundingBox (l, h)
+    )
+
 -- | An empty bounding box.  This is the same thing as @mempty@, but it doesn't
---   require the same type constraints that the @Monoid@
-emptyBox :: BoundingBox v
-emptyBox = BoundingBox $ Option Nothing
+--   require the same type constraints that the @Monoid@ instance does.
+emptyBox :: BoundingBox v n
+emptyBox = BoundingBox Nothing
 
 -- | Create a bounding box from a point that is component-wise @(<=)@ than the
 --   other.  If this is not the case, then @mempty@ is returned.
 fromCorners
-  :: (HasBasis v, Ord (Basis v), AdditiveGroup (Scalar v), Ord (Scalar v))
-  => Point v -> Point v -> BoundingBox v
+  :: (Additive v, Foldable v, Ord n)
+  => Point v n -> Point v n -> BoundingBox v n
 fromCorners l h
-  | F.and (combineP (<=) l h) = fromNonEmpty $ NonEmptyBoundingBox (l, h)
-  | otherwise = mempty
+  | F.and (liftI2 (<=) l h) = fromNonEmpty $ NonEmptyBoundingBox (l, h)
+  | otherwise               = mempty
 
 -- | Create a degenerate bounding \"box\" containing only a single point.
-fromPoint
-  :: (HasBasis v, Ord (Basis v), AdditiveGroup (Scalar v), Ord (Scalar v))
-  => Point v -> BoundingBox v
+fromPoint :: Point v n -> BoundingBox v n
 fromPoint p = fromNonEmpty $ NonEmptyBoundingBox (p, p)
 
 -- | Create the smallest bounding box containing all the given points.
-fromPoints
-  :: (HasBasis v, Ord (Basis v), AdditiveGroup (Scalar v), Ord (Scalar v))
-  => [Point v] -> BoundingBox v
+fromPoints :: (Additive v, Ord n) => [Point v n] -> BoundingBox v n
 fromPoints = mconcat . map fromPoint
 
 -- | Create a bounding box for any enveloped object (such as a diagram or path).
-boundingBox :: forall a. ( Enveloped a, HasBasis (V a), AdditiveGroup (V a)
-                         , Ord (Basis (V a))
-                         ) => a -> BoundingBox (V a)
+boundingBox :: (InSpace v n a, HasBasis v, Enveloped a)
+            => a -> BoundingBox v n
 boundingBox a = fromMaybeEmpty $ do
-    env <- appEnvelope $ getEnvelope a
-    let h = recompose $ map (\v -> (v,          env           $ basisValue v)) us
-        l = recompose $ map (\v -> (v, negate . env . negateV $ basisValue v)) us
-    return $ NonEmptyBoundingBox (P l, P h)
-  where
-    -- The units. Might not work if 0-components aren't reported.
-    --TODO: Depend on Enum Basis?
-    us = map fst $ decompose (zeroV :: V a)
+  env <- (appEnvelope . getEnvelope) a
+  let h = fmap env eye
+      l = negated $ fmap (env . negated) eye
+  return $ NonEmptyBoundingBox (P l, P h)
 
 -- | Queries whether the BoundingBox is empty.
-isEmptyBox :: BoundingBox v -> Bool
-isEmptyBox (BoundingBox (Option Nothing)) = True
-isEmptyBox _ = False
+isEmptyBox :: BoundingBox v n -> Bool
+isEmptyBox (BoundingBox Nothing) = True
+isEmptyBox _                              = False
 
 -- | Gets the lower and upper corners that define the bounding box.
-getCorners :: BoundingBox v -> Maybe (Point v, Point v)
-getCorners (BoundingBox p) = nonEmptyCorners <$> getOption p
+getCorners :: BoundingBox v n -> Maybe (Point v n, Point v n)
+getCorners (BoundingBox p) = nonEmptyCorners <$> p
 
 -- | Computes all of the corners of the bounding box.
-getAllCorners :: (HasBasis v, AdditiveGroup (Scalar v), Ord (Basis v))
-              => BoundingBox v -> [Point v]
-getAllCorners (BoundingBox (Option Nothing)) = []
-getAllCorners (BoundingBox (Option (Just (NonEmptyBoundingBox (l, u)))))
-  = map (P . recompose)
-  -- Enumerate all combinations of selections of lower / higher values.
-  . mapM (\(b, (l', u')) -> [(b, l'), (b, u')])
-  -- List of [(basis, (lower, upper))]
-  . toList
-  $ combineP (,) l u
+getAllCorners :: (Additive v, Traversable v) => BoundingBox v n -> [Point v n]
+getAllCorners (BoundingBox Nothing) = []
+getAllCorners (BoundingBox (Just (NonEmptyBoundingBox (l, u))))
+  = T.sequence (liftI2 (\a b -> [a,b]) l u)
 
 -- | Get the size of the bounding box - the vector from the (component-wise)
 --   lesser point to the greater point.
-boxExtents :: (AdditiveGroup v) => BoundingBox v -> v
-boxExtents = maybe zeroV (\(P l, P h) -> h ^-^ l) . getCorners
+boxExtents :: (Additive v, Num n) => BoundingBox v n -> v n
+boxExtents = maybe zero (\(l,u) -> u .-. l) . getCorners
 
--- | Create a transformation mapping points from one bounding box to the other.
-boxTransform :: (AdditiveGroup v, HasLinearMap v,
-                 Fractional (Scalar v), AdditiveGroup (Scalar v), Ord (Basis v))
-             => BoundingBox v -> BoundingBox v -> Maybe (Transformation v)
+-- | Get the center point in a bounding box.
+boxCenter :: (Additive v, Fractional n) => BoundingBox v n -> Maybe (Point v n)
+boxCenter = fmap (uncurry (lerp 0.5)) . getCorners
+
+-- | Get the center of a the bounding box of an enveloped object, return
+--   'Nothing' for object with empty envelope.
+mCenterPoint :: (InSpace v n a, HasBasis v, Enveloped a)
+            => a -> Maybe (Point v n)
+mCenterPoint = boxCenter . boundingBox
+
+-- | Get the center of a the bounding box of an enveloped object, return
+--   the origin for object with empty envelope.
+centerPoint :: (InSpace v n a, HasBasis v, Enveloped a)
+            => a -> Point v n
+centerPoint = fromMaybe origin . mCenterPoint
+
+-- | Create a transformation mapping points from one bounding box to the
+--   other. Returns 'Nothing' if either of the boxes are empty.
+boxTransform
+  :: (Additive v, Fractional n)
+  => BoundingBox v n -> BoundingBox v n -> Maybe (Transformation v n)
 boxTransform u v = do
-    ((P ul), _) <- getCorners u
-    ((P vl), _) <- getCorners v
-    let lin_map = box_scale (v, u) <-> box_scale (u, v)
-        box_scale = combineV' (*) . uncurry (combineV' (/)) . mapT boxExtents
-        combineV' f x = toVector . combineV f x
-    return $ Transformation lin_map lin_map (vl ^-^ box_scale (v, u) ul)
+  (P ul, _) <- getCorners u
+  (P vl, _) <- getCorners v
+  let i  = s (v, u) <-> s (u, v)
+      s = liftU2 (*) . uncurry (liftU2 (/)) . mapT boxExtents
+  return $ Transformation i i (vl ^-^ s (v, u) ul)
 
--- | Transforms an enveloped thing to fit within a @BoundingBox@.  If it's
---   empty, then the result is also @mempty@.
-boxFit :: (Enveloped a, Transformable a, Monoid a, Ord (Basis (V a)))
-       => BoundingBox (V a) -> a -> a
+-- | Transforms an enveloped thing to fit within a @BoundingBox@.  If the
+--   bounding box is empty, then the result is also @mempty@.
+boxFit
+  :: (InSpace v n a, HasBasis v, Enveloped a, Transformable a, Monoid a)
+  => BoundingBox v n -> a -> a
 boxFit b x = maybe mempty (`transform` x) $ boxTransform (boundingBox x) b
 
 -- | Check whether a point is contained in a bounding box (including its edges).
-contains
-  :: (HasBasis v, Ord (Basis v), AdditiveGroup (Scalar v), Ord (Scalar v))
-  => BoundingBox v -> Point v -> Bool
+contains :: (Additive v, Foldable v, Ord n) => BoundingBox v n -> Point v n -> Bool
 contains b p = maybe False check $ getCorners b
   where
-    check (l, h) = F.and (combineP (<=) l p)
-                && F.and (combineP (<=) p h)
+    check (l, h) = F.and (liftI2 (<=) l p)
+                && F.and (liftI2 (<=) p h)
 
 -- | Check whether a point is /strictly/ contained in a bounding box.
-contains'
-  :: (HasBasis v, Ord (Basis v), AdditiveGroup (Scalar v), Ord (Scalar v))
-  => BoundingBox v -> Point v -> Bool
+contains' :: (Additive v, Foldable v, Ord n) => BoundingBox v n -> Point v n -> Bool
 contains' b p = maybe False check $ getCorners b
   where
-    check (l, h) = F.and (combineP (<) l p)
-                && F.and (combineP (<) p h)
+    check (l, h) = F.and (liftI2 (<) l p)
+                && F.and (liftI2 (<) p h)
 
 -- | Test whether the first bounding box is contained inside
 --   the second.
-inside
-  :: (HasBasis v, Ord (Basis v), AdditiveGroup (Scalar v), Ord (Scalar v))
-  => BoundingBox v -> BoundingBox v -> Bool
+inside :: (Additive v, Foldable v, Ord n) => BoundingBox v n -> BoundingBox v n -> Bool
 inside u v = fromMaybe False $ do
   (ul, uh) <- getCorners u
   (vl, vh) <- getCorners v
-  return $ F.and (combineP (>=) ul vl)
-        && F.and (combineP (<=) uh vh)
+  return $ F.and (liftI2 (>=) ul vl)
+        && F.and (liftI2 (<=) uh vh)
 
 -- | Test whether the first bounding box is /strictly/ contained
 --   inside the second.
-inside'
-  :: (HasBasis v, Ord (Basis v), AdditiveGroup (Scalar v), Ord (Scalar v))
-  => BoundingBox v -> BoundingBox v -> Bool
+inside' :: (Additive v, Foldable v, Ord n) => BoundingBox v n -> BoundingBox v n -> Bool
 inside' u v = fromMaybe False $ do
   (ul, uh) <- getCorners u
   (vl, vh) <- getCorners v
-  return $ F.and (combineP (>) ul vl)
-        && F.and (combineP (<) uh vh)
+  return $ F.and (liftI2 (>) ul vl)
+        && F.and (liftI2 (<) uh vh)
 
 -- | Test whether the first bounding box lies outside the second
 --   (although they may intersect in their boundaries).
-outside
-  :: (HasBasis v, Ord (Basis v), AdditiveGroup (Scalar v), Ord (Scalar v))
-  => BoundingBox v -> BoundingBox v -> Bool
+outside :: (Additive v, Foldable v, Ord n) => BoundingBox v n -> BoundingBox v n -> Bool
 outside u v = fromMaybe True $ do
   (ul, uh) <- getCorners u
   (vl, vh) <- getCorners v
-  return $ F.or (combineP (<=) uh vl)
-        || F.or (combineP (>=) ul vh)
+  return $ F.or (liftI2 (<=) uh vl)
+        || F.or (liftI2 (>=) ul vh)
 
 -- | Test whether the first bounding box lies /strictly/ outside the second
 --   (they do not intersect at all).
-outside'
-  :: (HasBasis v, Ord (Basis v), AdditiveGroup (Scalar v), Ord (Scalar v))
-  => BoundingBox v -> BoundingBox v -> Bool
+outside' :: (Additive v, Foldable v, Ord n) => BoundingBox v n -> BoundingBox v n -> Bool
 outside' u v = fromMaybe True $ do
   (ul, uh) <- getCorners u
   (vl, vh) <- getCorners v
-  return $ F.or (combineP (<) uh vl)
-        || F.or (combineP (>) ul vh)
+  return $ F.or (liftI2 (<) uh vl)
+        || F.or (liftI2 (>) ul vh)
 
 -- | Form the largest bounding box contained within this given two
 --   bounding boxes, or @Nothing@ if the two bounding boxes do not
 --   overlap at all.
 intersection
-  :: (HasBasis v, Ord (Basis v), AdditiveGroup (Scalar v), Ord (Scalar v))
-  => BoundingBox v -> BoundingBox v -> BoundingBox v
+  :: (Additive v, Foldable v, Ord n)
+  => BoundingBox v n -> BoundingBox v n -> BoundingBox v n
 intersection u v = maybe mempty (uncurry fromCorners) $ do
   (ul, uh) <- getCorners u
   (vl, vh) <- getCorners v
-  return $ mapT toPoint (combineP max ul vl, combineP min uh vh)
+  return (liftI2 max ul vl, liftI2 min uh vh)
 
 -- | Form the smallest bounding box containing the given two bound union.  This
 --   function is just an alias for @mappend@.
-union :: (HasBasis v, Ord (Basis v), AdditiveGroup (Scalar v), Ord (Scalar v))
-      => BoundingBox v -> BoundingBox v -> BoundingBox v
+union :: (Additive v, Ord n) => BoundingBox v n -> BoundingBox v n -> BoundingBox v n
 union = mappend
 
--- internals using Map (Basis v) (Scalar v)
--- probably paranoia, but decompose might not always
---   1. contain basis elements whose component is zero
---   2. have basis elements in the same order
-
-fromVector :: (HasBasis v, Ord (Basis v)) => v -> Map (Basis v) (Scalar v)
-fromVector = fromList . decompose
-
-toVector :: HasBasis v => Map (Basis v) (Scalar v) -> v
-toVector = recompose . toList
-
-toPoint :: HasBasis v => Map (Basis v) (Scalar v) -> Point v
-toPoint = P . toVector
-
-combineV :: (HasBasis v, Ord (Basis v), AdditiveGroup (Scalar v))
-         => (Scalar v -> Scalar v -> a) -> v -> v -> Map (Basis v) a
-combineV f u v = combineDefault zeroV zeroV f (fromVector u) (fromVector v)
-
-combineP :: (HasBasis v, Ord (Basis v), AdditiveGroup (Scalar v))
-         => (Scalar v -> Scalar v -> a) -> Point v -> Point v -> Map (Basis v) a
-combineP f (P u) (P v) = combineV f u v
-
-combineDefault :: Ord k => a -> b -> (a -> b -> c) -> Map k a -> Map k b -> Map k c
-combineDefault a b f = combine g
+-- | @boxGrid f box@ returns a grid of regularly spaced points inside
+--   the box, such that there are @(1/f)@ points along each dimension.
+--   For example, for a 3D box with corners at (0,0,0) and (2,2,2),
+--   @boxGrid 0.1@ would yield a grid of approximately 1000 points (it
+--   might actually be @11^3@ instead of @10^3@) spaced @0.2@ units
+--   apart.
+boxGrid
+  :: (Traversable v, Additive v, Num n, Enum n)
+  => n -> BoundingBox v n -> [Point v n]
+boxGrid f = maybe [] (sequenceA . uncurry (liftI2 mkRange)) . getCorners
   where
-    g Nothing  Nothing  = f a b
-    g Nothing  (Just y) = f a y
-    g (Just x) Nothing  = f x b
-    g (Just x) (Just y) = f x y
+    mkRange lo hi = [lo, (1-f)*lo + f*hi .. hi]
 
-combine :: Ord k => (Maybe a -> Maybe b -> c) -> Map k a -> Map k b -> Map k c
-combine f am bm = fromDistinctAscList $ merge (toAscList am) (toAscList bm)
-  where
-    merge [] [] = []
-    merge ((x,a):xs) [] = (x, f (Just a) Nothing) : merge xs []
-    merge [] ((y,b):ys) = (y, f Nothing (Just b)) : merge [] ys
-    merge xs0@((x,a):xs) ys0@((y,b):ys) = case compare x y of
-      LT -> (x, f (Just a) Nothing ) : merge xs ys0
-      EQ -> (x, f (Just a) (Just b)) : merge xs ys
-      GT -> (y, f Nothing  (Just b)) : merge xs0 ys
+    -- liftA2 mkRange on the two corner points creates a (Point V2
+    -- [n]), where each component is the range of values for that
+    -- dimension.  sequenceA then yields a grid of type [Point V2 n].
diff --git a/src/Diagrams/Combinators.hs b/src/Diagrams/Combinators.hs
--- a/src/Diagrams/Combinators.hs
+++ b/src/Diagrams/Combinators.hs
@@ -1,4 +1,4 @@
-{-# LANGUAGE CPP                   #-}
+{-# LANGUAGE ConstraintKinds #-}
 {-# LANGUAGE FlexibleContexts      #-}
 {-# LANGUAGE MultiParamTypeClasses #-}
 {-# LANGUAGE Rank2Types            #-}
@@ -28,41 +28,38 @@
        , atop
        , beneath
        , beside
+       , atDirection
 
          -- * n-ary operations
        , appends
-       , position, decorateTrail, decorateLocatedTrail, decoratePath
+       , position, atPoints
        , cat, cat'
        , CatOpts(_catMethod, _sep), catMethod, sep
        , CatMethod(..)
+       , composeAligned
 
        ) where
 
-import           Data.Typeable
-
-import           Control.Lens          (Lens', generateSignatures,
-                                        lensRules, makeLensesWith, (%~), (&),
-                                        (.~), (^.), _Wrapping)
-import           Data.AdditiveGroup
-import           Data.AffineSpace      ((.+^))
-import           Data.Default.Class
+import           Control.Lens          hiding (beside, ( # ))
+import           Data.Default
+import           Data.Maybe            (fromJust)
 import           Data.Monoid.Deletable (toDeletable)
 import           Data.Monoid.MList     (inj)
-#if __GLASGOW_HASKELL__ < 707
 import           Data.Proxy
-#endif
 import           Data.Semigroup
 import qualified Data.Tree.DUAL        as D
-import           Data.VectorSpace
 
 import           Diagrams.Core
 import           Diagrams.Core.Types   (QDiagram (QD))
-import           Diagrams.Located
-import           Diagrams.Path
+import           Diagrams.Direction
+import           Diagrams.Names        (named)
 import           Diagrams.Segment      (straight)
-import           Diagrams.Trail        (Trail, trailVertices)
 import           Diagrams.Util
 
+import           Linear.Affine
+import           Linear.Metric
+import           Linear.Vector
+
 ------------------------------------------------------------
 -- Working with envelopes
 ------------------------------------------------------------
@@ -76,23 +73,23 @@
 --   >     circle 1 # fc green
 --   >     |||
 --   >     (    c # dashingG [0.1,0.1] 0 # lc white
---   >       <> square 2 # withEnvelope (c :: D R2) # fc blue
+--   >       <> square 2 # withEnvelope (c :: D V2 Double) # fc blue
 --   >     )
 --   > c = circle 0.8
 --   > withEnvelopeEx = sqNewEnv # centerXY # pad 1.5
-withEnvelope :: (HasLinearMap (V a), Enveloped a, Monoid' m)
-           => a -> QDiagram b (V a) m -> QDiagram b (V a) m
+withEnvelope :: (InSpace v n a, Monoid' m, Enveloped a)
+           => a -> QDiagram b v n m -> QDiagram b v n m
 withEnvelope = setEnvelope . getEnvelope
 
 -- | Use the trace from some object as the trace for a diagram, in
 --   place of the diagram's default trace.
-withTrace :: (HasLinearMap (V a), Traced a, OrderedField (Scalar (V a)), InnerSpace (V a), Monoid' m)
-          => a -> QDiagram b (V a) m -> QDiagram b (V a) m
+withTrace :: (InSpace v n a, Metric v, OrderedField n, Monoid' m, Traced a)
+          => a -> QDiagram b v n m -> QDiagram b v n m
 withTrace = setTrace . getTrace
 
 -- | @phantom x@ produces a \"phantom\" diagram, which has the same
 --   envelope and trace as @x@ but produces no output.
-phantom :: (Backend b (V a), Typeable (V a), Enveloped a, Traced a, Monoid' m) => a -> QDiagram b (V a) m
+phantom :: (InSpace v n a, Monoid' m, Enveloped a, Traced a) => a -> QDiagram b v n m
 phantom a = QD $ D.leafU ((inj . toDeletable . getEnvelope $ a) <> (inj . toDeletable . getTrace $ a))
 
 -- | @pad s@ \"pads\" a diagram, expanding its envelope by a factor of
@@ -101,39 +98,31 @@
 --   origin, so if the origin is not centered the padding may appear
 --   \"uneven\".  If this is not desired, the origin can be centered
 --   (using, e.g., 'centerXY' for 2D diagrams) before applying @pad@.
-pad :: ( Backend b v
-       , InnerSpace v, OrderedField (Scalar v)
-       , Monoid' m )
-    => Scalar v -> QDiagram b v m -> QDiagram b v m
+pad :: (Metric v, OrderedField n, Monoid' m)
+    => n -> QDiagram b v n m -> QDiagram b v n m
 pad s d = withEnvelope (d # scale s) d
 
 -- | @frame s@ increases the envelope of a diagram by and absolute amount @s@,
 --   s is in the local units of the diagram. This function is similar to @pad@,
 --   only it takes an absolute quantity and pre-centering should not be
 --   necessary.
-frame :: ( Backend b v, InnerSpace v, OrderedField (Scalar v), Monoid' m)
-        => Scalar v -> QDiagram b v m -> QDiagram b v m
-frame s d = setEnvelope (onEnvelope t (d^.envelope)) d
-  where
-    t f = \x -> f x + s
+frame :: (Metric v, OrderedField n, Monoid' m)
+        => n -> QDiagram b v n m -> QDiagram b v n m
+frame s = over envelope (onEnvelope $ \f x -> f x + s)
 
 -- | @strut v@ is a diagram which produces no output, but with respect
 --   to alignment and envelope acts like a 1-dimensional segment
 --   oriented along the vector @v@, with local origin at its
 --   center. (Note, however, that it has an empty trace; for 2D struts
---   with a nonempty trace see 'strutR2', 'strutX', and 'strutY' from
+--   with a nonempty trace see 'strutR2' from
 --   "Diagrams.TwoD.Combinators".) Useful for manually creating
 --   separation between two diagrams.
 --
 --   <<diagrams/src_Diagrams_Combinators_strutEx.svg#diagram=strutEx&width=300>>
 --
 --   > strutEx = (circle 1 ||| strut unitX ||| circle 1) # centerXY # pad 1.1
-strut :: ( Backend b v, Typeable v
-         , InnerSpace v
-         , OrderedField (Scalar v)
-         , Monoid' m
-         )
-      => v -> QDiagram b v m
+strut :: (Metric v, OrderedField n)
+      => v n -> QDiagram b v n m
 strut v = QD $ D.leafU (inj . toDeletable $ env)
   where env = translate ((-0.5) *^ v) . getEnvelope $ straight v
   -- note we can't use 'phantom' here because it tries to construct a
@@ -154,10 +143,9 @@
 --   the cosine of the difference in angle, and leaving it unchanged
 --   when this factor is negative.
 extrudeEnvelope
-  :: ( Ord (Scalar v), Num (Scalar v), AdditiveGroup (Scalar v)
-     , Floating (Scalar v), HasLinearMap v, InnerSpace v, Monoid' m )
-  => v -> QDiagram b v m -> QDiagram b v m
-extrudeEnvelope = deformEnvelope 0.5
+  :: (Metric v, OrderedField n, Monoid' m)
+  => v n -> QDiagram b v n m -> QDiagram b v n m
+extrudeEnvelope = deformEnvelope 1
 
 -- | @intrudeEnvelope v d@ asymmetrically \"intrudes\" the envelope of
 --   a diagram away from the given direction.  All parts of the envelope
@@ -167,24 +155,22 @@
 --   Note that this could create strange inverted envelopes, where
 --   @ diameter v d < 0 @.
 intrudeEnvelope
-  :: ( Ord (Scalar v), Num (Scalar v), AdditiveGroup (Scalar v)
-     , Floating (Scalar v), HasLinearMap v, InnerSpace v, Monoid' m )
-  => v -> QDiagram b v m -> QDiagram b v m
-intrudeEnvelope = deformEnvelope (-0.5)
+  :: (Metric v, OrderedField n, Monoid' m)
+  => v n -> QDiagram b v n m -> QDiagram b v n m
+intrudeEnvelope = deformEnvelope (-1)
 
 -- Utility for extrudeEnvelope / intrudeEnvelope
 deformEnvelope
-  :: ( Ord (Scalar v), Num (Scalar v), AdditiveGroup (Scalar v)
-     , Floating (Scalar v), HasLinearMap v, InnerSpace v, Monoid' m )
-  => (Scalar v) -> v -> QDiagram b v m -> QDiagram b v m
-deformEnvelope s v d = setEnvelope (getEnvelope d & _Wrapping Envelope %~ deformE) d
+  :: (Metric v, OrderedField n, Monoid' m)
+  => n -> v n -> QDiagram b v n m -> QDiagram b v n m
+deformEnvelope s v = over (envelope . _Wrapping Envelope) deformE
   where
-    deformE = Option . fmap deformE' . getOption
+    deformE = fmap deformE'
     deformE' env v'
-        | dot > 0 = Max $ getMax (env v') + (dot * s) / magnitude v'
+        | dp > 0    = Max $ getMax (env v') + (dp * s) / quadrance v'
         | otherwise = env v'
       where
-        dot = v' <.> v
+        dp = v' `dot` v
 
 ------------------------------------------------------------
 -- Combining two objects
@@ -193,8 +179,8 @@
 -- | @beneath@ is just a convenient synonym for @'flip' 'atop'@; that is,
 --   @d1 \`beneath\` d2@ is the diagram with @d2@ superimposed on top of
 --   @d1@.
-beneath :: (HasLinearMap v, OrderedField (Scalar v), InnerSpace v, Monoid' m)
-     => QDiagram b v m -> QDiagram b v m -> QDiagram b v m
+beneath :: (Metric v, OrderedField n, Monoid' m)
+     => QDiagram b v n m -> QDiagram b v n m -> QDiagram b v n m
 beneath = flip atop
 
 infixl 6 `beneath`
@@ -234,9 +220,18 @@
 --   To get something like @beside v x1 x2@ whose local origin is
 --   identified with that of @x2@ instead of @x1@, use @beside
 --   (negateV v) x2 x1@.
-beside :: (Juxtaposable a, Semigroup a) => V a -> a -> a -> a
+beside :: (Juxtaposable a, Semigroup a) => Vn a -> a -> a -> a
 beside v d1 d2 = d1 <> juxtapose v d1 d2
 
+-- | Place two diagrams (or other juxtaposable objects) adjacent to
+--   one another, with the second diagram placed in the direction 'd'
+--   from the first.  The local origin of the resulting combined
+--   diagram is the same as the local origin of the first.  See the
+--   documentation of 'beside' for more information.
+atDirection :: (InSpace v n a, Metric v, Floating n, Juxtaposable a, Semigroup a)
+            => Direction v n -> a -> a -> a
+atDirection = beside . fromDirection
+
 ------------------------------------------------------------
 -- Combining multiple objects
 ------------------------------------------------------------
@@ -251,7 +246,7 @@
 --   > appendsEx = appends c (zip (iterateN 6 (rotateBy (1/6)) unitX) (repeat c))
 --   >             # centerXY # pad 1.1
 --   >   where c = circle 1
-appends :: (Juxtaposable a, Monoid' a) => a -> [(V a,a)] -> a
+appends :: (Juxtaposable a, Monoid' a) => a -> [(Vn a,a)] -> a
 appends d1 apps = d1 <> mconcat (map (\(v,d) -> juxtapose v d1 d) apps)
 
 -- | Position things absolutely: combine a list of objects
@@ -260,39 +255,17 @@
 --
 --   <<diagrams/src_Diagrams_Combinators_positionEx.svg#diagram=positionEx&height=300>>
 --
---   > positionEx = position (zip (map mkPoint [-3, -2.8 .. 3]) (repeat dot))
---   >   where dot       = circle 0.2 # fc black
---   >         mkPoint x = p2 (x,x^2)
-position :: (HasOrigin a, Monoid' a) => [(Point (V a), a)] -> a
+--   > positionEx = position (zip (map mkPoint [-3, -2.8 .. 3]) (repeat spot))
+--   >   where spot      = circle 0.2 # fc black
+--   >         mkPoint :: Double -> P2 Double
+--   >         mkPoint x = p2 (x,x*x)
+position :: (InSpace v n a, HasOrigin a, Monoid' a) => [(Point v n, a)] -> a
 position = mconcat . map (uncurry moveTo)
 
--- | Combine a list of diagrams (or paths) by using them to
---   \"decorate\" a trail, placing the local origin of one object at
---   each successive vertex of the trail.  The first vertex of the
---   trail is placed at the origin.  If the trail and list of objects
---   have different lengths, the extra tail of the longer one is
---   ignored.
-decorateTrail :: (InnerSpace (V a), OrderedField (Scalar (V a)), HasOrigin a, Monoid' a)
-              => Trail (V a) -> [a] -> a
-decorateTrail = decorateLocatedTrail . (`at` origin)
-
--- | Combine a list of diagrams (or paths) by using them to
---   \"decorate\" a concretely located trail, placing the local origin
---   of one object at each successive vertex of the trail. If the
---   trail and list of objects have different lengths, the extra tail
---   of the longer one is ignored.
-decorateLocatedTrail :: (InnerSpace (V a), OrderedField (Scalar (V a)), HasOrigin a, Monoid' a)
-              => Located (Trail (V a)) -> [a] -> a
-decorateLocatedTrail t = position . zip (trailVertices t)
-
--- | Combine a list of diagrams (or paths) by using them to
---   \"decorate\" a path, placing the local origin of one object at
---   each successive vertex of the path.  If the path and list of objects
---   have different lengths, the extra tail of the longer one is
---   ignored.
-decoratePath :: (InnerSpace (V a), OrderedField (Scalar (V a)), HasOrigin a, Monoid' a)
-             => Path (V a) -> [a] -> a
-decoratePath p = position . zip (concat $ pathVertices p)
+-- | Curried version of @position@, takes a list of points and a list of
+--   objects.
+atPoints :: (InSpace v n a, HasOrigin a, Monoid' a) => [Point v n] -> [a] -> a
+atPoints ps as = position $ zip ps as
 
 -- | Methods for concatenating diagrams.
 data CatMethod = Cat     -- ^ Normal catenation: simply put diagrams
@@ -311,9 +284,9 @@
                          --   of separation, diagrams may overlap.
 
 -- | Options for 'cat''.
-data CatOpts v = CatOpts { _catMethod       :: CatMethod
-                         , _sep             :: Scalar v
-                         , catOptsvProxy__ :: Proxy v
+data CatOpts n = CatOpts { _catMethod    :: CatMethod
+                         , _sep          :: n
+                         , catOptsvProxy :: Proxy n
                          }
 
 -- The reason the proxy field is necessary is that without it,
@@ -327,24 +300,22 @@
 -- this is not a problem when using the 'sep' lens, as its type is
 -- more restricted.
 
-makeLensesWith
-  ( lensRules & generateSignatures .~ False)
-  ''CatOpts
+makeLensesWith (lensRules & generateSignatures .~ False) ''CatOpts
 
 -- | Which 'CatMethod' should be used:
 --   normal catenation (default), or distribution?
-catMethod :: forall v. Lens' (CatOpts v) CatMethod
+catMethod :: Lens' (CatOpts n) CatMethod
 
 -- | How much separation should be used between successive diagrams
 --   (default: 0)?  When @catMethod = Cat@, this is the distance between
 --   /envelopes/; when @catMethod = Distrib@, this is the distance
 --   between /origins/.
-sep :: forall v. Lens' (CatOpts v) (Scalar v)
+sep :: Lens' (CatOpts n) n
 
-instance Num (Scalar v) => Default (CatOpts v) where
-  def = CatOpts { _catMethod       = Cat
-                , _sep             = 0
-                , catOptsvProxy__ = Proxy
+instance Num n => Default (CatOpts n) where
+  def = CatOpts { _catMethod    = Cat
+                , _sep          = 0
+                , catOptsvProxy = Proxy
                 }
 
 -- | @cat v@ positions a list of objects so that their local origins
@@ -355,10 +326,8 @@
 --
 --   See also 'cat'', which takes an extra options record allowing
 --   certain aspects of the operation to be tweaked.
-cat :: ( Juxtaposable a, Monoid' a, HasOrigin a
-       , InnerSpace (V a), OrderedField (Scalar (V a))
-       )
-       => V a -> [a] -> a
+cat :: (InSpace v n a, Metric v, Floating n, Juxtaposable a, Monoid' a, HasOrigin a)
+       => v n -> [a] -> a
 cat v = cat' v def
 
 -- | Like 'cat', but taking an extra 'CatOpts' arguments allowing the
@@ -378,13 +347,53 @@
 --   Note that @cat' v (with & catMethod .~ Distrib) === mconcat@
 --   (distributing with a separation of 0 is the same as
 --   superimposing).
-cat' :: ( Juxtaposable a, Monoid' a, HasOrigin a
-        , InnerSpace (V a), OrderedField (Scalar (V a))
-        )
-     => V a -> CatOpts (V a) -> [a] -> a
+cat' :: (InSpace v n a, Metric v, Floating n, Juxtaposable a, Monoid' a, HasOrigin a)
+     => v n -> CatOpts n -> [a] -> a
 cat' v (CatOpts { _catMethod = Cat, _sep = s }) = foldB comb mempty
   where comb d1 d2 = d1 <> (juxtapose v d1 d2 # moveOriginBy vs)
-        vs = s *^ normalized (negateV v)
+        vs = s *^ signorm (negated v)
 
 cat' v (CatOpts { _catMethod = Distrib, _sep = s }) =
-  position . zip (iterate (.+^ (s *^ normalized v)) origin)
+  position . zip (iterate (.+^ (s *^ signorm v)) origin)
+
+-- | Compose a list of diagrams using the given composition function,
+--   first aligning them all according to the given alignment, /but/
+--   retain the local origin of the first diagram, as it would be if
+--   the composition function were applied directly.  That is,
+--   @composeAligned algn comp@ is equivalent to @translate v . comp
+--   . map algn@ for some appropriate translation vector @v@.
+--
+--   Unfortunately, this only works for diagrams (and not, say, paths)
+--   because there is no most general type for alignment functions,
+--   and no generic way to find out what an alignment function does to
+--   the origin of things.  (However, it should be possible to make a
+--   version of this function that works /specifically/ on paths, if
+--   such a thing were deemed useful.)
+--
+--   <<diagrams/src_Diagrams_Combinators_alignedEx1.svg#diagram=alignedEx1&width=400>>
+--
+--   > alignedEx1 = (hsep 2 # composeAligned alignT) (map circle [1,3,5,2])
+--   >            # showOrigin
+--   >            # frame 0.5
+--
+--   <<diagrams/src_Diagrams_Combinators_alignedEx2.svg#diagram=alignedEx2&width=400>>
+--
+--   > alignedEx2 = (mconcat # composeAligned alignTL) [circle 1, square 1, triangle 1, pentagon 1]
+--   >            # showOrigin
+--   >            # frame 0.1
+composeAligned
+  :: (Monoid' m, Floating n, Ord n, Metric v)
+  => (QDiagram b v n m -> QDiagram b v n m)    -- ^ Alignment function
+  -> ([QDiagram b v n m] -> QDiagram b v n m)  -- ^ Composition function
+  -> ([QDiagram b v n m] -> QDiagram b v n m)
+composeAligned _ combine [] = combine []
+composeAligned algn comb (d:ds) = (comb $ map algn (d:ds)) # moveOriginTo l
+  where
+    mss = ( (() .>> d)   -- qualify first to avoid stomping on an existing () name
+          # named ()     -- Mark the origin
+          # algn         -- Apply the alignment function
+          )
+          -- then find out what happened to the origin
+        ^. subMap . _Wrapped . Control.Lens.at (toName ())
+    l   = location . head . fromJust $ mss
+          -- the fromJust is Justified since we put the () name in
diff --git a/src/Diagrams/Coordinates.hs b/src/Diagrams/Coordinates.hs
--- a/src/Diagrams/Coordinates.hs
+++ b/src/Diagrams/Coordinates.hs
@@ -1,5 +1,7 @@
-{-# LANGUAGE TypeFamilies  #-}
-{-# LANGUAGE TypeOperators #-}
+{-# LANGUAGE FlexibleContexts     #-}
+{-# LANGUAGE TypeFamilies         #-}
+{-# LANGUAGE TypeOperators        #-}
+{-# LANGUAGE UndecidableInstances #-}
 -----------------------------------------------------------------------------
 -- |
 -- Module      :  Diagrams.Coordinates
@@ -14,23 +16,12 @@
 
 module Diagrams.Coordinates
     ( (:&)(..), Coordinates(..)
-
-    -- * Lenses for particular axes
-    , HasX(..), HasY(..), HasZ(..), HasR(..)
     )
     where
 
-import           Control.Lens          (Lens')
-
-import           Diagrams.Core.Points
-
--- | A pair of values, with a convenient infix (left-associative)
---   data constructor.
-data a :& b = a :& b
-  deriving (Eq, Ord, Show)
-
-infixl 7 :&
-
+import           Data.Kind       (Type)
+import           Diagrams.Points
+import           Linear          (V2 (..), V3 (..), V4 (..))
 
 -- | Types which are instances of the @Coordinates@ class can be
 --   constructed using '^&' (for example, a three-dimensional vector
@@ -45,13 +36,13 @@
 class Coordinates c where
 
   -- | The type of the final coordinate.
-  type FinalCoord c    :: *
+  type FinalCoord c    :: Type
 
   -- | The type of everything other than the final coordinate.
-  type PrevDim c       :: *
+  type PrevDim c       :: Type
 
   -- | Decomposition of @c@ into applications of ':&'.
-  type Decomposition c :: *
+  type Decomposition c :: Type
     -- Decomposition c = Decomposition (PrevDim c) :& FinalCoord c  (essentially)
 
   -- | Construct a value of type @c@ by providing something of one
@@ -60,7 +51,7 @@
   --
   -- @
   -- 2 ^& 3 :: P2
-  -- 3 ^& 5 ^& 6 :: R3
+  -- 3 ^& 5 ^& 6 :: V3
   -- @
   --
   --   Note that @^&@ is left-associative.
@@ -76,6 +67,22 @@
 
 infixl 7 ^&
 
+-- | A pair of values, with a convenient infix (left-associative)
+--   data constructor.
+data a :& b = a :& b
+  deriving (Eq, Ord, Show)
+
+infixl 7 :&
+
+-- Instance for :& (the buck stops here)
+instance Coordinates (a :& b) where
+  type FinalCoord (a :& b) = b
+  type PrevDim (a :& b) = a
+  type Decomposition (a :& b) = a :& b
+  x ^& y                    = x :& y
+  coords (x :& y)           = x :& y
+
+
 -- Some standard instances for plain old tuples
 
 instance Coordinates (a,b) where
@@ -83,7 +90,7 @@
   type PrevDim (a,b)       = a
   type Decomposition (a,b) = a :& b
 
-  x ^& y                    = (x,y)
+  x ^& y                   = (x,y)
   coords (x,y)             = x :& y
 
 instance Coordinates (a,b,c) where
@@ -99,30 +106,40 @@
   type PrevDim (a,b,c,d)       = (a,b,c)
   type Decomposition (a,b,c,d) = Decomposition (a,b,c) :& d
 
-  (w,x,y)  ^& z                  = (w,x,y,z)
+  (w,x,y)  ^& z                = (w,x,y,z)
   coords (w,x,y,z)             = coords (w,x,y) :& z
 
-instance Coordinates v => Coordinates (Point v) where
-  type FinalCoord (Point v)    = FinalCoord v
-  type PrevDim (Point v)       = PrevDim v
-  type Decomposition (Point v) = Decomposition v
+instance Coordinates (v n) => Coordinates (Point v n) where
+  type FinalCoord (Point v n)    = FinalCoord (v n)
+  type PrevDim (Point v n)       = PrevDim (v n)
+  type Decomposition (Point v n) = Decomposition (v n)
 
-  x ^& y        = P (x ^& y)
+  x ^& y       = P (x ^& y)
   coords (P v) = coords v
 
--- | The class of types with at least one coordinate, called _x.
-class HasX t where
-    _x :: Lens' t Double
+-- instances for linear
 
--- | The class of types with at least two coordinates, the second called _y.
-class HasY t where
-    _y :: Lens' t Double
+instance Coordinates (V2 n) where
+  type FinalCoord (V2 n)    = n
+  type PrevDim (V2 n)       = n
+  type Decomposition (V2 n) = n :& n
 
--- | The class of types with at least three coordinates, the third called _z.
-class HasZ t where
-    _z :: Lens' t Double
+  x ^& y          = V2 x y
+  coords (V2 x y) = x :& y
 
--- | The class of types with a single length coordinate _r.  _r is
--- magnitude of a vector, or the distance from the origin of a point.
-class HasR t where
-    _r :: Lens' t Double
+instance Coordinates (V3 n) where
+  type FinalCoord (V3 n)    = n
+  type PrevDim (V3 n)       = V2 n
+  type Decomposition (V3 n) = n :& n :& n
+
+  V2 x y ^& z       = V3 x y z
+  coords (V3 x y z) = x :& y :& z
+
+instance Coordinates (V4 n) where
+  type FinalCoord (V4 n)    = n
+  type PrevDim (V4 n)       = V3 n
+  type Decomposition (V4 n) = n :& n :& n :& n
+
+  V3 x y z ^& w       = V4 x y z w
+  coords (V4 x y z w) = x :& y :& z :& w
+
diff --git a/src/Diagrams/CubicSpline.hs b/src/Diagrams/CubicSpline.hs
--- a/src/Diagrams/CubicSpline.hs
+++ b/src/Diagrams/CubicSpline.hs
@@ -1,6 +1,10 @@
+{-# LANGUAGE ConstraintKinds  #-}
 {-# LANGUAGE FlexibleContexts #-}
 {-# LANGUAGE TypeFamilies     #-}
+{-# LANGUAGE TypeOperators    #-}
+
 {-# OPTIONS_GHC -fno-warn-incomplete-patterns #-}
+
 -----------------------------------------------------------------------------
 -- |
 -- Module      :  Diagrams.CubicSpline
@@ -8,31 +12,43 @@
 -- License     :  BSD-style (see LICENSE)
 -- Maintainer  :  diagrams-discuss@googlegroups.com
 --
--- A /cubic spline/ is a smooth, connected sequence of cubic curves
--- passing through a given sequence of points.  This module provides
--- the 'cubicSpline' method, which can be used to create closed or
--- open cubic splines from a list of points.  For access to the
--- internals of the spline generation algorithm (including in
--- particular a solver for cyclic tridiagonal systems of linear
--- equations), see "Diagrams.CubicSpline.Internal".
+-- A /cubic spline/ is a smooth, connected sequence of cubic curves.
+-- This module provides two methods for constructing splines.
 --
+-- The 'cubicSpline' method can be used to create closed or open cubic
+-- splines from a list of points. The resulting splines /pass through/
+-- all the control points, but depend on the control points in a
+-- "global" way (that is, changing one control point may alter the
+-- entire curve).  For access to the internals of the spline
+-- generation algorithm, see "Diagrams.CubicSpline.Internal".
+--
+-- 'bspline' creates a cubic B-spline, which starts and ends at the
+-- first and last control points, but does not necessarily pass
+-- through any of the other control points.  It depends on the control
+-- points in a "local" way, that is, changing one control point will
+-- only affect a local portion of the curve near that control point.
+--
 -----------------------------------------------------------------------------
 module Diagrams.CubicSpline
        (
          -- * Constructing paths from cubic splines
          cubicSpline
+       , BSpline
+       , bspline
        ) where
 
+import           Control.Lens                  (view)
+
 import           Diagrams.Core
-import           Diagrams.Core.Points
+import           Diagrams.CubicSpline.Boehm
 import           Diagrams.CubicSpline.Internal
 import           Diagrams.Located              (Located, at, mapLoc)
 import           Diagrams.Segment
 import           Diagrams.Trail
 import           Diagrams.TrailLike            (TrailLike (..))
 
-import           Data.AffineSpace.Point
-import           Data.VectorSpace
+import           Linear.Affine
+import           Linear.Metric
 
 -- | Construct a spline path-like thing of cubic segments from a list of
 --   vertices, with the first vertex as the starting point.  The first
@@ -41,22 +57,23 @@
 --   <<diagrams/src_Diagrams_CubicSpline_cubicSplineEx.svg#diagram=cubicSplineEx&width=600>>
 --
 --   > pts = map p2 [(0,0), (2,3), (5,-2), (-4,1), (0,3)]
---   > dot = circle 0.2 # fc blue # lw none
---   > mkPath closed = position (zip pts (repeat dot))
+--   > spot = circle 0.2 # fc blue # lw none
+--   > mkPath closed = position (zip pts (repeat spot))
 --   >              <> cubicSpline closed pts
 --   > cubicSplineEx = (mkPath False ||| strutX 2 ||| mkPath True)
 --   >               # centerXY # pad 1.1
 --
 --   For more information, see <http://mathworld.wolfram.com/CubicSpline.html>.
-cubicSpline :: (TrailLike t, Fractional (V t)) => Bool -> [Point (V t)] -> t
-cubicSpline closed [] = trailLike . closeIf closed $ emptyLine `at` origin
-cubicSpline closed ps = flattenBeziers . map f . solveCubicSplineCoefficients closed . map unPoint $ ps
+cubicSpline :: (V t ~ v, N t ~ n, TrailLike t, Fractional (v n)) => Bool -> [Point v n] -> t
+cubicSpline closed []  = trailLike . closeIf closed $ emptyLine `at` origin
+cubicSpline closed [p] = trailLike . closeIf closed $ emptyLine `at` p
+cubicSpline closed ps  = flattenBeziers . map f . solveCubicSplineCoefficients closed . map (view lensP) $ ps
   where
     f [a,b,c,d] = [a, (3*a+b)/3, (3*a+2*b+c)/3, a+b+c+d]
     flattenBeziers bs@((b:_):_)
       = trailLike . closeIf closed $ lineFromSegments (map bez bs) `at` P b
     bez [a,b,c,d] = bezier3 (b - a) (c - a) (d - a)
 
-closeIf :: (InnerSpace v, OrderedField (Scalar v))
-        => Bool -> Located (Trail' Line v) -> Located (Trail v)
+closeIf :: (Metric v, OrderedField n)
+        => Bool -> Located (Trail' Line v n) -> Located (Trail v n)
 closeIf c = mapLoc (if c then wrapLoop . glueLine else wrapLine)
diff --git a/src/Diagrams/CubicSpline/Boehm.hs b/src/Diagrams/CubicSpline/Boehm.hs
new file mode 100644
--- /dev/null
+++ b/src/Diagrams/CubicSpline/Boehm.hs
@@ -0,0 +1,149 @@
+{-# LANGUAGE FlexibleContexts #-}
+{-# LANGUAGE TypeFamilies     #-}
+{-# LANGUAGE TypeOperators    #-}
+
+-----------------------------------------------------------------------------
+-- |
+-- Module      :  Diagrams.CubicSpline.Boehm
+-- Copyright   :  (c) 2015 diagrams-lib team (see LICENSE)
+-- License     :  BSD-style (see LICENSE)
+-- Maintainer  :  diagrams-discuss@googlegroups.com
+--
+-- Boehm's algorithm for converting a cubic B-spline into a sequence
+-- of cubic Bezier curves.
+--
+-- See
+--
+--   * Thomas W. Sederberg, /An Introduction to B-Spline Curves/,
+--     <http://web.archive.org/web/20120227050519/http://tom.cs.byu.edu/~455/bs.pdf>
+--
+--   * Lyle Ramshaw, /Blossoming: A Connect-the-Dots Approach to Splines/,
+--     <http://www.hpl.hp.com/techreports/Compaq-DEC/SRC-RR-19.pdf>
+--
+-----------------------------------------------------------------------------
+module Diagrams.CubicSpline.Boehm
+       ( BSpline
+       , bsplineToBeziers
+       , bspline
+       ) where
+
+import           Data.List          (sort, tails)
+import           Diagrams.Core      (N, Point, V, origin)
+import           Diagrams.Located   (at, loc, unLoc)
+import           Diagrams.Segment   (FixedSegment (..), fromFixedSeg)
+import           Diagrams.TrailLike (TrailLike, fromLocSegments)
+import           Diagrams.Util      (iterateN)
+import           Linear.Vector      (Additive)
+import           Linear.Vector.Compat (lerp)
+
+type BSpline v n = [Point v n]
+
+-- | @affineCombo a b t x y@ computes an affine combination of x and y
+--   which lies at parameter t, if x has parameter a and y has parameter b.
+--   The usual @lerp@ arises by giving x parameter 0 and y parameter 1.
+affineCombo :: (Additive f, Fractional a) => a -> a -> a -> f a -> f a -> f a
+affineCombo a b t = lerp ((t-a)/(b-a))
+
+-- | @windows k xs@ yields all the length-@k@ windows from @xs@, e.g.
+--   @windows 3 [a,b,c,d,e] == [[a,b,c], [b,c,d], [c,d,e]]@.
+windows :: Int -> [a] -> [[a]]
+windows k = takeWhile ((==k) . length) . map (take k) . tails
+
+-- | @extend k xs@ extends @xs@ on both ends by prepending @k@ copies
+-- of its head and appending @k@ copies of its last element.  For example,
+-- @extend 2 [1..5] == [1,1,1,2,3,4,5,5,5]@.
+extend :: Int -> [a] -> [a]
+extend k xs = replicate k (head xs) ++ xs ++ replicate k (last xs)
+
+-- | A "polar point" is a point along with three knot values.
+--   We consider the "blossom" of a cubic spline, a 3-ary symmetric
+--   polynomial; a polar point consists of 3 values paired with the
+--   output of the blossom at those input values.  Blossoms have nice
+--   affine properties so this makes it easy to keep track of how
+--   points may be combined to yield other points of interest.
+--
+--   Invariant: knot values are in nondecreasing order.
+data PolarPt v n = PP { unPP :: Point v n, _knots :: [n] }
+
+mkPolarPt :: Ord n => Point v n -> [n] -> PolarPt v n
+mkPolarPt pt kts = PP pt (sort kts)
+
+-- | Precondition: the knots of the two polar points overlap, like abc
+--   and bcd.  The @Int@ should be 0 or 1, indicating which knot to
+--   replicate (0 means to replicate b, yielding bbc, 1 means to
+--   replicate c, yielding bcc).
+combine
+  :: (Additive v, Fractional n, Ord n)
+  => Int -> PolarPt v n -> PolarPt v n -> PolarPt v n
+combine k (PP pt1 kts1) (PP pt2 kts2)
+  = mkPolarPt
+      (affineCombo (head kts1) (last kts2) newKt pt1 pt2)
+      (newKt : drop 1 kts1)
+  where
+    newKt = kts2 !! k
+
+-- | Convert a uniform cubic B-spline to a sequence of cubic beziers.
+--   (/Uniform/ refers to the fact that the knots are assumed to be
+--   evenly spaced, with no duplicates.)  The knots at the end are
+--   replicated so the cubic spline begins and ends at the first and
+--   last control points, tangent to the line from the end control
+--   point to the next.
+bsplineToBeziers
+  :: (Additive v, Fractional n, Num n, Ord n)
+  => BSpline v n
+  -> [FixedSegment v n]
+bsplineToBeziers controls = beziers
+  where
+    n                            = length controls
+    numKnots                     = n + 2
+    knots                        = iterateN numKnots (+1/(fromIntegral numKnots - 1)) 0
+
+    -- The control points are P(a,b,c), P(b,c,d), P(c,d,e), and so on.
+    controls' = zipWith mkPolarPt (extend 2 controls) (windows 3 $ extend 2 knots)
+
+    -- The bezier internal control points are affine combinations of
+    -- the spline control points.
+    bezierControls        = map combineC (windows 2 controls')
+    combineC [pabc, pbcd] = (combine 0 pabc pbcd, combine 1 pabc pbcd)
+    combineC _ = error "combineC must be called on a list of length 2"
+
+    -- The bezier end points are affine combinations of the bezier
+    -- control points.
+    bezierEnds                   = map combineE (windows 2 bezierControls)
+    combineE [(_,pabb),(pbbc,_)] = combine 0 pabb pbbc
+    combineE _ = error "combineE must be called on a list of length 2"
+
+    -- Finally, we actually put together the generated bezier segments.
+    beziers                      = zipWith mkBezier (drop 1 bezierControls) (windows 2 bezierEnds)
+      where
+        mkBezier (paab,pabb) [paaa,pbbb]
+          = FCubic (unPP paaa) (unPP paab) (unPP pabb) (unPP pbbb)
+        mkBezier _ _ = error "mkBezier must be called on a list of length 2"
+
+    -- Note that the above algorithm works in any dimension but is
+    -- very specific to *cubic* splines.  This can of course be
+    -- generalized to higher degree splines but keeping track of
+    -- everything gets a bit more complicated; to be honest I am not
+    -- quite sure how to do it.
+
+-- | Generate a uniform cubic B-spline from the given control points.
+--   The spline starts and ends at the first and last control points,
+--   and is tangent to the line to the second(-to-last) control point.
+--   It does not necessarily pass through any of the other control
+--   points.
+--
+--   <<diagrams/src_Diagrams_CubicSpline_Boehm_bsplineEx.svg#diagram=bsplineEx&width=300>>
+--
+--   > pts = map p2 [(0,0), (2,3), (5,-2), (-4,1), (0,3)]
+--   > spot = circle 0.2 # fc blue # lw none
+--   > bsplineEx = mconcat
+--   >   [ position (zip pts (repeat spot))
+--   >   , bspline pts
+--   >   ]
+--   >   # frame 0.5
+
+bspline :: (TrailLike t, V t ~ v, N t ~ n) => BSpline v n -> t
+bspline = fromLocSegments . fixup . map fromFixedSeg . bsplineToBeziers
+  where
+    fixup []        = [] `at` origin
+    fixup (b1:rest) = (unLoc b1 : map unLoc rest) `at` loc b1
diff --git a/src/Diagrams/CubicSpline/Internal.hs b/src/Diagrams/CubicSpline/Internal.hs
--- a/src/Diagrams/CubicSpline/Internal.hs
+++ b/src/Diagrams/CubicSpline/Internal.hs
@@ -1,7 +1,3 @@
-{-# LANGUAGE TypeFamilies
-           , FlexibleContexts
-  #-}
-{-# OPTIONS_GHC -fno-warn-name-shadowing #-}
 -----------------------------------------------------------------------------
 -- |
 -- Module      :  Diagrams.CubicSpline
@@ -18,76 +14,19 @@
 module Diagrams.CubicSpline.Internal
        (
          -- * Solving for spline coefficents
-         solveTriDiagonal
-       , solveCyclicTriDiagonal
-       , solveCubicSplineDerivatives
+         solveCubicSplineDerivatives
        , solveCubicSplineDerivativesClosed
        , solveCubicSplineCoefficients
        ) where
 
-import Data.List
-
--- | Solves a system of the form 'A*X=D' for 'x' where 'A' is an 
---   'n' by 'n' matrix with 'bs' as the main diagonal and 
---   'as' the diagonal below and 'cs' the diagonal above.
---   See: <http://en.wikipedia.org/wiki/Tridiagonal_matrix_algorithm>
-solveTriDiagonal :: Fractional a => [a] -> [a] -> [a] -> [a] -> [a]
-solveTriDiagonal as (b0:bs) (c0:cs) (d0:ds) = h cs' ds'
-  where
-    cs' = c0 / b0 : f cs' as bs cs
-    f _ [_] _ _ = []
-    f (c':cs') (a:as) (b:bs) (c:cs) = c / (b - c' * a) : f cs' as bs cs
-    f _ _ _ _ = error "solveTriDiagonal.f: impossible!"
-
-    ds' = d0 / b0 : g ds' as bs cs' ds 
-    g _ [] _ _ _ = []
-    g (d':ds') (a:as) (b:bs) (c':cs') (d:ds) = (d - d' * a)/(b - c' * a) : g ds' as bs cs' ds
-    g _ _ _ _ _ = error "solveTriDiagonal.g: impossible!"
-    
-    h _ [d] = [d]
-    h (c:cs) (d:ds) = let xs@(x:_) = h cs ds in d - c * x : xs
-    h _ _ = error "solveTriDiagonal.h: impossible!"
-
-solveTriDiagonal _ _ _ _ = error "arguments 2,3,4 to solveTriDiagonal must be nonempty"
-
--- Helper that applies the passed function only to the last element of a list
-modifyLast :: (a -> a) -> [a] -> [a]
-modifyLast _ []     = []
-modifyLast f [a]    = [f a]
-modifyLast f (a:as) = a : modifyLast f as
-
--- Helper that builds a list of length n of the form: '[s,m,m,...,m,m,e]'
-sparseVector :: Int -> a -> a -> a -> [a]
-sparseVector n s m e 
-    | n < 1     = []
-    | otherwise = s : h (n - 1)
-  where 
-    h 1 = [e]
-    h n = m : h (n - 1)
-    
--- | Solves a system similar to the tri-diagonal system using a special case
---   of the Sherman-Morrison formula <http://en.wikipedia.org/wiki/Sherman-Morrison_formula>.
---   This code is based on /Numerical Recpies in C/'s @cyclic@ function in section 2.7.
-solveCyclicTriDiagonal :: Fractional a => [a] -> [a] -> [a] -> [a] -> a -> a -> [a]
-solveCyclicTriDiagonal as (b0:bs) cs ds alpha beta = zipWith ((+) . (fact *)) zs xs
-  where
-    l = length ds
-    gamma = -b0
-    us = sparseVector l gamma 0 alpha
-    
-    bs' = (b0 - gamma) : modifyLast (subtract (alpha*beta/gamma)) bs
-    
-    xs@(x:_) = solveTriDiagonal as bs' cs ds
-    zs@(z:_) = solveTriDiagonal as bs' cs us
-    
-    fact = -(x + beta * last xs / gamma) / (1.0 + z + beta * last zs / gamma)
+import           Diagrams.Solve.Tridiagonal
 
-solveCyclicTriDiagonal _ _ _ _ _ _ = error "second argument to solveCyclicTriDiagonal must be nonempty"
+import           Data.List
 
 -- | Use the tri-diagonal solver with the appropriate parameters for an open cubic spline.
 solveCubicSplineDerivatives :: Fractional a => [a] -> [a]
 solveCubicSplineDerivatives (x:xs) = solveTriDiagonal as bs as ds
-  where 
+  where
     as = replicate (l - 1) 1
     bs = 2 : replicate (l - 2) 4 ++ [2]
     l  = length ds
@@ -99,7 +38,7 @@
 -- | Use the cyclic-tri-diagonal solver with the appropriate parameters for a closed cubic spline.
 solveCubicSplineDerivativesClosed :: Fractional a => [a] -> [a]
 solveCubicSplineDerivativesClosed xs = solveCyclicTriDiagonal as bs as ds 1 1
-  where 
+  where
     as = replicate (l - 1) 1
     bs = replicate l 4
     l  = length xs
@@ -109,11 +48,11 @@
 
 -- | Use the cyclic-tri-diagonal solver with the appropriate parameters for a closed cubic spline.
 solveCubicSplineCoefficients :: Fractional a => Bool -> [a] -> [[a]]
-solveCubicSplineCoefficients closed xs = 
+solveCubicSplineCoefficients closed xs =
     [ [x,d,3*(x1-x)-2*d-d1,2*(x-x1)+d+d1]
     | (x,x1,d,d1) <- zip4 xs' (tail xs') ds' (tail ds')
     ]
-  where 
+  where
     ds | closed    = solveCubicSplineDerivativesClosed xs
        | otherwise = solveCubicSplineDerivatives xs
     close as | closed    = as ++ [head as]
diff --git a/src/Diagrams/Deform.hs b/src/Diagrams/Deform.hs
--- a/src/Diagrams/Deform.hs
+++ b/src/Diagrams/Deform.hs
@@ -1,19 +1,22 @@
-{-# LANGUAGE FlexibleContexts     #-}
-{-# LANGUAGE FlexibleInstances    #-}
-{-# LANGUAGE GADTs                #-}
-{-# LANGUAGE ScopedTypeVariables  #-}
-{-# LANGUAGE TypeFamilies         #-}
-{-# LANGUAGE UndecidableInstances #-}
+{-# LANGUAGE ConstraintKinds       #-}
+{-# LANGUAGE FlexibleContexts      #-}
+{-# LANGUAGE FlexibleInstances     #-}
+{-# LANGUAGE MultiParamTypeClasses #-}
+{-# LANGUAGE ScopedTypeVariables   #-}
+{-# LANGUAGE TypeFamilies          #-}
+{-# LANGUAGE TypeOperators         #-}
+{-# LANGUAGE UndecidableInstances  #-}
 
-module Diagrams.Deform (Deformation(..), Deformable(..), asDeformation) where
+module Diagrams.Deform
+       ( Deformation(..)
+       , Deformable(..)
+       , asDeformation
+       ) where
 
-import           Control.Lens        (under, _Unwrapped)
-import           Data.AffineSpace
-import           Data.Basis
-import           Data.MemoTrie
+import           Control.Lens        (mapped, over, _Wrapped)
 import           Data.Monoid         hiding ((<>))
 import           Data.Semigroup
-import           Data.VectorSpace
+import           Prelude
 
 import           Diagrams.Core
 import           Diagrams.Located
@@ -22,97 +25,105 @@
 import           Diagrams.Segment
 import           Diagrams.Trail
 
+import           Linear.Affine
+import           Linear.Metric
+import           Linear.Vector
+
 ------------------------------------------------------------
 -- Deformations
 
 -- | @Deformations@ are a superset of the affine transformations
--- represented by the 'Transformation' type.  In general they are not
--- invertable.  @Deformation@s include projective transformations.
--- @Deformation@ can represent other functions from points to points
--- which are "well-behaved", in that they do not introduce small wiggles.
-data Deformation v = Deformation (Point v -> Point v)
+--   represented by the 'Transformation' type.  In general they are not
+--   invertible.  @Deformation@s include projective transformations.
+--   @Deformation@ can represent other functions from points to points
+--   which are "well-behaved", in that they do not introduce small wiggles.
+newtype Deformation v u n = Deformation (Point v n -> Point u n)
 
-instance Semigroup (Deformation v) where
-    (Deformation p1) <> (Deformation p2) = Deformation (p1 . p2)
+instance Semigroup (Deformation v v n) where
+  (Deformation p1) <> (Deformation p2) = Deformation (p1 . p2)
 
-instance Monoid (Deformation v) where
-    mappend = (<>)
-    mempty = Deformation id
+instance Monoid (Deformation v v n) where
+  mappend = (<>)
+  mempty = Deformation id
 
-class Deformable a where
-    -- | @deform' epsilon d a@ transforms @a@ by the deformation @d@.
-    -- If the type of @a@ is not closed under projection, approximate
-    -- to accuracy @epsilon@.
-    deform' :: Scalar (V a) -> Deformation (V a) -> a -> a
+class Deformable a b where
+  -- | @deform' epsilon d a@ transforms @a@ by the deformation @d@.
+  -- If the type of @a@ is not closed under projection, approximate
+  -- to accuracy @epsilon@.
+  deform' :: N a -> Deformation (V a) (V b) (N a) -> a -> b
 
-    -- | @deform d a@ transforms @a@ by the deformation @d@.
-    -- If the type of @a@ is not closed under projection, @deform@
-    -- should call @deform'@ with some reasonable default value of
-    -- @epsilon@.
-    deform  :: Deformation (V a) -> a -> a
+  -- | @deform d a@ transforms @a@ by the deformation @d@.
+  -- If the type of @a@ is not closed under projection, @deform@
+  -- should call @deform'@ with some reasonable default value of
+  -- @epsilon@.
+  deform :: Deformation (V a) (V b) (N a) -> a -> b
 
 -- | @asDeformation@ converts a 'Transformation' to a 'Deformation' by
 -- discarding the inverse transform.  This allows reusing
 -- @Transformation@s in the construction of @Deformation@s.
-asDeformation
-  ::  ( HasTrie (Basis v), HasBasis v) => Transformation v -> Deformation v
-asDeformation t = Deformation f' where
-      f' = papply t
+asDeformation :: (Additive v, Num n) => Transformation v n -> Deformation v v n
+asDeformation t = Deformation (papply t)
 
 ------------------------------------------------------------
 -- Instances
 
-instance Deformable (Point v) where
-    deform' = const deform
-    deform (Deformation l) = l
+instance r ~ Point u n => Deformable (Point v n) r where
+  deform' = const deform
 
+  deform (Deformation l) = l
+
 -- | Cubic curves are not closed under perspective projections.
 -- Therefore @Segment@s are not an instance of Deformable.  However,
 -- the deformation of a @Segment@ can be approximated to arbitrary
 -- precision by a series of @Segment@s.  @deformSegment@ does this,
 -- which allows types built from lists of @Segment@s to themselves be
 -- @Deformable@.
-deformSegment :: (VectorSpace v, InnerSpace v, s ~ Scalar v, Ord s, Fractional s, Floating s) =>
-                  s -> Deformation v -> FixedSegment v -> [FixedSegment v]
-deformSegment epsilon t s
-    | goodEnough epsilon t s = [approx t s]
-    | otherwise  = concatMap (deformSegment epsilon t) [s1, s2]
+deformSegment :: (Metric v, Metric u, OrderedField n)
+   => n -> Deformation v u n -> FixedSegment v n -> [FixedSegment u n]
+deformSegment epsilon t = go (0::Int)
   where
-    (s1, s2) = splitAtParam s 0.5
+    go n s
+      | n == 100               = [approx t s]
+      | goodEnough epsilon t s = [approx t s]
+      | otherwise              = concatMap (go (n+1)) [s1, s2]
+      where
+        (s1, s2) = splitAtParam s 0.5
+-- deformSegment epsilon t s
+--     | goodEnough epsilon t s = [approx t s]
+--     | otherwise              = concatMap (deformSegment epsilon t) [s1, s2]
+--   where
+--     (s1, s2) = splitAtParam s 0.5
 
-approx :: (VectorSpace v, InnerSpace v, s ~ Scalar v, Ord s, Fractional s, Floating s) =>
-          Deformation v -> FixedSegment v -> FixedSegment v
-approx t (FLinear p0 p1) = FLinear (deform t p0) (deform t p1)
-approx t (FCubic p0 c1 c2 p1) = FCubic (f p0) (f c1) (f c2) (f p1) where
-      f = deform t
+approx :: Deformation v u n -> FixedSegment v n -> FixedSegment u n
+approx t (FLinear p0 p1)      = FLinear (deform t p0) (deform t p1)
+approx t (FCubic p0 c1 c2 p1) = FCubic (f p0) (f c1) (f c2) (f p1)
+  where f = deform t
 
-goodEnough :: (VectorSpace v, InnerSpace v, s ~ Scalar v, Ord s, Fractional s, Floating s) =>
-              s -> Deformation v -> FixedSegment v -> Bool
+goodEnough :: (Metric v, Metric u, OrderedField n) => n -> Deformation v u n -> FixedSegment v n -> Bool
 goodEnough e t s =
-    all (< e) [magnitude $ deform t (s `atParam` u) .-. approx t s `atParam` u
+    all (< e) [norm $ deform t (s `atParam` u) .-. approx t s `atParam` u
               | u <- [0.25, 0.5, 0.75]]
 
-instance (VectorSpace v, InnerSpace v,
-          s ~ Scalar v, Ord s, Fractional s, Floating s, Show s, Show v) =>
-         Deformable (Located (Trail v)) where
-             deform' eps p t
-                 | isLine $ unLoc t  = line `at` p0
-                 | otherwise = glueTrail line `at` p0
-               where
-                 segs = concatMap (deformSegment eps p) $ fixTrail t
-                 p0 = case segs of
-                     (FLinear start _:_) -> start
-                     (FCubic start _ _ _:_) -> start
-                     _      -> loc t  -- default in case of empty trail
-                 line = trailFromSegments $ map (unLoc . fromFixedSeg) segs
-             deform p t = deform' (0.01 * extent) p t where
-                           -- estimate the "size" of the Trail' as
-                           -- the maximum distance to any vertex
-                extent = maximum . map dist . trailVertices $ t
-                dist pt = magnitude $ pt .-. loc t
+instance (Metric v, Metric u, OrderedField n, r ~ Located (Trail u n))
+    => Deformable (Located (Trail v n)) r where
+  deform' eps p t
+    | isLine $ unLoc t  = line `at` p0
+    | otherwise = glueTrail line `at` p0
+    where
+      segs = concatMap (deformSegment eps p) $ fixTrail t
+      p0 = case segs of
+             (FLinear start _:_)    -> start
+             (FCubic start _ _ _:_) -> start
+             _                      -> deform p (loc t)
+      line = trailFromSegments $ map (unLoc . fromFixedSeg) segs
 
-instance (VectorSpace v, InnerSpace v,
-          s ~ Scalar v, Ord s, Fractional s, Floating s, Show s, Show v) =>
-         Deformable (Path v) where
-             deform' eps p = under _Unwrapped $ map (deform' eps p)
-             deform p = under _Unwrapped $ map (deform p)
+  deform p t = deform' (0.01 * extent) p t
+    where
+      -- estimate the "size" of the Trail' as
+      -- the maximum distance to any vertex
+      extent = maximum . map dist . trailVertices $ t
+      dist pt = norm $ pt .-. loc t
+
+instance (Metric v, Metric u, OrderedField n, r ~ Path u n) => Deformable (Path v n) r where
+  deform' eps p = over (_Wrapped . mapped) (deform' eps p)
+  deform p      = over (_Wrapped . mapped) (deform p)
diff --git a/src/Diagrams/Direction.hs b/src/Diagrams/Direction.hs
new file mode 100644
--- /dev/null
+++ b/src/Diagrams/Direction.hs
@@ -0,0 +1,86 @@
+{-# LANGUAGE DeriveFunctor        #-}
+{-# LANGUAGE FlexibleContexts     #-}
+{-# LANGUAGE TypeFamilies         #-}
+{-# LANGUAGE TypeOperators        #-}
+{-# LANGUAGE UndecidableInstances #-}
+-----------------------------------------------------------------------------
+-- |
+-- Module      :  Diagrams.Direction
+-- Copyright   :  (c) 2014 diagrams-lib team (see LICENSE)
+-- License     :  BSD-style (see LICENSE)
+-- Maintainer  :  diagrams-discuss@googlegroups.com
+--
+-- Type for representing directions, polymorphic in vector space
+--
+-----------------------------------------------------------------------------
+
+module Diagrams.Direction
+       ( Direction
+       , _Dir
+       , direction, dir, fromDirection, fromDir
+       , angleBetweenDirs
+       , dirBetween
+       ) where
+
+import           Control.Lens   (Iso', iso)
+
+import           Diagrams.Angle
+import           Diagrams.Core
+
+import           Linear.Affine
+import           Linear.Metric
+import           Linear.Vector
+
+--------------------------------------------------------------------------------
+-- Direction
+
+-- | A vector is described by a @Direction@ and a magnitude.  So we
+-- can think of a @Direction@ as a vector that has forgotten its
+-- magnitude.  @Direction@s can be used with 'fromDirection' and the
+-- lenses provided by its instances.
+newtype Direction v n = Dir (v n)
+  deriving (Read, Show, Eq, Ord, Functor) -- todo: special instances
+
+type instance V (Direction v n) = v
+type instance N (Direction v n) = n
+
+instance (V (v n) ~ v, N (v n) ~ n, Transformable (v n)) => Transformable (Direction v n) where
+  transform t (Dir v) = Dir (transform t v)
+
+instance HasTheta v => HasTheta (Direction v) where
+  _theta = _Dir . _theta
+
+instance HasPhi v => HasPhi (Direction v) where
+  _phi = _Dir . _phi
+
+-- | _Dir is provided to allow efficient implementations of functions
+--   in particular vector-spaces, but should be used with care as it
+--   exposes too much information.
+_Dir :: Iso' (Direction v n) (v n)
+_Dir = iso (\(Dir v) -> v) Dir
+
+-- | @direction v@ is the direction in which @v@ points.  Returns an
+--   unspecified value when given the zero vector as input.
+direction :: v n -> Direction v n
+direction = Dir
+
+-- | Synonym for 'direction'.
+dir :: v n -> Direction v n
+dir = Dir
+
+-- | @fromDirection d@ is the unit vector in the direction @d@.
+fromDirection :: (Metric v, Floating n) => Direction v n -> v n
+fromDirection (Dir v) = signorm v
+
+-- | Synonym for 'fromDirection'.
+fromDir :: (Metric v, Floating n) => Direction v n -> v n
+fromDir (Dir v) = signorm v
+
+-- | compute the positive angle between the two directions in their common plane
+angleBetweenDirs :: (Metric v, Floating n, Ord n)
+  => Direction v n -> Direction v n -> Angle n
+angleBetweenDirs d1 d2 = angleBetween (fromDirection d1) (fromDirection d2)
+
+-- | @dirBetween p q@ returns the direction from @p@ to @q@.
+dirBetween :: (Additive v, Num n) => Point v n -> Point v n -> Direction v n
+dirBetween p q = dir $ q .-. p
diff --git a/src/Diagrams/LinearMap.hs b/src/Diagrams/LinearMap.hs
new file mode 100644
--- /dev/null
+++ b/src/Diagrams/LinearMap.hs
@@ -0,0 +1,175 @@
+{-# LANGUAGE ConstraintKinds       #-}
+{-# LANGUAGE FlexibleContexts      #-}
+{-# LANGUAGE FlexibleInstances     #-}
+{-# LANGUAGE GADTs                 #-}
+{-# LANGUAGE ImpredicativeTypes    #-}
+{-# LANGUAGE MultiParamTypeClasses #-}
+{-# LANGUAGE RankNTypes            #-}
+{-# LANGUAGE TypeFamilies          #-}
+{-# LANGUAGE TypeOperators         #-}
+{-# LANGUAGE UndecidableInstances  #-}
+
+-----------------------------------------------------------------------------
+-- |
+-- Module      :  Diagrams.LinearMap
+-- Copyright   :  (c) 2014-2015 diagrams team (see LICENSE)
+-- License     :  BSD-style (see LICENSE)
+-- Maintainer  :  diagrams-discuss@googlegroups.com
+--
+-- Linear maps. Unlike 'Transformation's these are not restricted to the
+-- same space. In practice these are used for projections in
+-- "Diagrams.ThreeD.Projection". Unless you want to work with
+-- projections you're probably better off using 'Diagrams.Transform'.
+--
+-- Currently only path-like things can be projected. In the future we
+-- hope to support projecting diagrams.
+--
+-----------------------------------------------------------------------------
+
+module Diagrams.LinearMap
+  ( -- * Linear maps
+    LinearMap (..)
+  , LinearMappable (..)
+    -- ** Applying linear maps
+  , linmap
+
+    -- * Affine maps
+  , AffineMap (..)
+  , AffineMappable (..)
+
+    -- ** Constructing affine maps
+  , mkAffineMap
+  , toAffineMap
+  ) where
+
+import           Control.Lens
+import           Data.FingerTree         as FT
+import qualified Data.Foldable           as F
+
+import           Diagrams.Core
+import           Diagrams.Core.Transform
+import           Diagrams.Located
+import           Diagrams.Path
+import           Diagrams.Segment
+import           Diagrams.Trail          hiding (offset)
+
+import           Linear.Affine
+import           Linear.Metric
+import           Linear.Vector
+
+
+-- | Type for holding linear maps. Note that these are not affine transforms so
+--   attemping apply a translation with 'LinearMap' will likely produce incorrect
+--   results.
+newtype LinearMap v u n = LinearMap { lapply :: v n -> u n }
+
+toLinearMap :: Transformation v n -> LinearMap v v n
+toLinearMap (Transformation (m :-: _) _ _) = LinearMap m
+
+-- | Class of things that have vectors that can be mapped over.
+class LinearMappable a b where
+  -- | Apply a linear map to an object. If the map is not linear,
+  --   behaviour will likely be wrong.
+  vmap :: (Vn a -> Vn b) -> a -> b
+  -- this uses a function instead of LinearMap so we can also use this
+  -- class to change number types
+
+-- Note: instances need to be of the form
+--
+-- r ~ A u m => LinearMappable (A v n) r
+--
+-- so ghc knows there's only one possible result from calling vmap.
+
+-- | Apply a linear map.
+linmap :: (InSpace v n a, LinearMappable a b, N b ~ n)
+     => LinearMap v (V b) n -> a -> b
+linmap = vmap . lapply
+
+instance r ~ Offset c u m => LinearMappable (Offset c v n) r where
+  vmap f (OffsetClosed v) = OffsetClosed (f v)
+  vmap _ OffsetOpen       = OffsetOpen
+  {-# INLINE vmap #-}
+
+instance r ~ Segment c u m => LinearMappable (Segment c v n) r where
+  vmap f (Linear offset)      = Linear (vmap f offset)
+  vmap f (Cubic v1 v2 offset) = Cubic (f v1) (f v2) (vmap f offset)
+  {-# INLINE vmap #-}
+
+instance (Metric v, Metric u, OrderedField n, OrderedField m, r ~ SegTree u m)
+    => LinearMappable (SegTree v n) r where
+  vmap f = over _Wrapped (fmap' (vmap f))
+  {-# INLINE vmap #-}
+
+instance (Metric v, Metric u, OrderedField n, OrderedField m, r ~ Trail' l u m)
+    => LinearMappable (Trail' l v n) r where
+  vmap f (Line st)        = Line (vmap f st)
+  vmap f (Loop st offset) = Loop (vmap f st) (vmap f offset)
+  {-# INLINE vmap #-}
+
+instance (Metric v, Metric u, OrderedField n, OrderedField m, r ~ Trail u m)
+    => LinearMappable (Trail v n) r where
+  vmap f (Trail (Line st))        = Trail $ Line (vmap f st)
+  vmap f (Trail (Loop st offset)) = Trail $ Loop (vmap f st) (vmap f offset)
+  {-# INLINE vmap #-}
+
+instance LinearMappable (Point v n) (Point u m) where
+  vmap f (P v) = P (f v)
+  {-# INLINE vmap #-}
+
+instance r ~ FixedSegment u m => LinearMappable (FixedSegment v n) r where
+  vmap f (FLinear p0 p1)      = FLinear (vmap f p0) (vmap f p1)
+  vmap f (FCubic p0 p1 p2 p3) = FCubic (vmap f p0) (vmap f p1)
+                                       (vmap f p2) (vmap f p3)
+  {-# INLINE vmap #-}
+
+instance (LinearMappable a b, r ~ Located b) => LinearMappable (Located a) r where
+  vmap f (Loc p a) = Loc (vmap f p) (vmap f a)
+  {-# INLINE vmap #-}
+
+instance (Metric v, Metric u, OrderedField n, OrderedField m, r ~ Path u m)
+    => LinearMappable (Path v n) r where
+  vmap f = _Wrapped . mapped %~ vmap f
+  {-# INLINE vmap #-}
+
+-- | Affine linear maps. Unlike 'Transformation' these do not have to be
+--   invertible so we can map between spaces.
+data AffineMap v u n = AffineMap (LinearMap v u n) (u n)
+
+-- | Make an affine map from a linear function and a translation.
+mkAffineMap :: (v n -> u n) -> u n -> AffineMap v u n
+mkAffineMap f = AffineMap (LinearMap f)
+
+toAffineMap :: Transformation v n -> AffineMap v v n
+toAffineMap t = AffineMap (toLinearMap t) (transl t)
+
+class (LinearMappable a b, N a ~ N b) => AffineMappable a b where
+  -- | Affine map over an object. Has a default implimentation of only
+  --   applying the linear map
+  amap :: (Additive (V a), F.Foldable (V a), Additive (V b), Num (N b))
+       => AffineMap (V a) (V b) (N b) -> a -> b
+  amap (AffineMap f _) = linmap f
+  {-# INLINE amap #-}
+
+instance r ~ Offset c u n => AffineMappable (Offset c v n) r
+instance r ~ Segment c u n => AffineMappable (Segment c v n) r
+instance (Metric v, Metric u, OrderedField n, r ~ SegTree u n) => AffineMappable (SegTree v n) r
+instance (Metric v, Metric u, OrderedField n, r ~ Trail' l u n) => AffineMappable (Trail' l v n) r
+instance (Metric v, Metric u, OrderedField n, r ~ Trail u n) => AffineMappable (Trail v n) r
+
+instance (Additive v, Num n, r ~ Point u n) => AffineMappable (Point v n) r where
+  amap (AffineMap f v) p = linmap f p .+^ v
+  {-# INLINE amap #-}
+
+instance r ~ FixedSegment u n => AffineMappable (FixedSegment v n) r where
+  amap m (FLinear p0 p1)      = FLinear (amap m p0) (amap m p1)
+  amap m (FCubic p0 p1 p2 p3) = FCubic (amap m p0) (amap m p1) (amap m p2) (amap m p3)
+  {-# INLINE amap #-}
+
+instance (LinearMappable a b, N a ~ N b, r ~ Located b) => AffineMappable (Located a) r where
+  amap m@(AffineMap l _) (Loc p x) = Loc (amap m p) (linmap l x)
+  {-# INLINE amap #-}
+
+instance (Metric v, Metric u, OrderedField n, r ~ Path u n)
+    => AffineMappable (Path v n) r where
+  amap m = _Wrapped . mapped %~ amap m
+  {-# INLINE amap #-}
diff --git a/src/Diagrams/Located.hs b/src/Diagrams/Located.hs
--- a/src/Diagrams/Located.hs
+++ b/src/Diagrams/Located.hs
@@ -1,11 +1,15 @@
-{-# LANGUAGE FlexibleContexts     #-}
-{-# LANGUAGE StandaloneDeriving   #-}
-{-# LANGUAGE TypeFamilies         #-}
-{-# LANGUAGE UndecidableInstances #-}
+{-# LANGUAGE ConstraintKinds       #-}
+{-# LANGUAGE DeriveGeneric         #-}
+{-# LANGUAGE FlexibleContexts      #-}
+{-# LANGUAGE MultiParamTypeClasses #-}
+{-# LANGUAGE StandaloneDeriving    #-}
+{-# LANGUAGE TypeFamilies          #-}
+{-# LANGUAGE TypeOperators         #-}
+{-# LANGUAGE UndecidableInstances  #-}
 -----------------------------------------------------------------------------
 -- |
 -- Module      :  Diagrams.Located
--- Copyright   :  (c) 2013 diagrams-lib team (see LICENSE)
+-- Copyright   :  (c) 2013-2015 diagrams-lib team (see LICENSE)
 -- License     :  BSD-style (see LICENSE)
 -- Maintainer  :  diagrams-discuss@googlegroups.com
 --
@@ -18,22 +22,25 @@
 -----------------------------------------------------------------------------
 
 module Diagrams.Located
-    ( Located
-    , at, viewLoc, unLoc, loc, mapLoc, located
+    ( Located (..)
+    , at, viewLoc, mapLoc, located, _loc
     )
     where
 
-import           Control.Lens            (Lens)
-import           Data.AffineSpace
-import           Data.Functor            ((<$>))
-import           Data.VectorSpace
+import           Control.Lens            (Lens, Lens')
+import           Text.Read
 
+import           Linear.Affine
+import           Linear.Vector
+
+import           Diagrams.Align
 import           Diagrams.Core
-import           Diagrams.Core.Points    ()
 import           Diagrams.Core.Transform
 import           Diagrams.Parametric
-  -- for GHC 7.4 type family bug
 
+import           Data.Serialize          (Serialize)
+import           GHC.Generics            (Generic)
+
 -- | \"Located\" things, /i.e./ things with a concrete location:
 --   intuitively, @Located a ~ (Point, a)@.  Wrapping a translationally
 --   invariant thing (/e.g./ a 'Segment' or 'Trail') in 'Located' pins
@@ -49,27 +56,30 @@
 --   'HasOrigin', 'Transformable', 'Enveloped', 'Traced', and
 --   'TrailLike' instances are particularly useful; see the documented
 --   instances below for more information.
-data Located a = Loc { loc   :: Point (V a)   -- ^ Project out the
-                                              --   location of a @Located@
-                                              --   value.
-                     , unLoc :: a             -- ^ Project the value
-                                              --   of type @a@ out of
-                                              --   a @Located a@,
-                                              --   discarding the
-                                              --   location.
-                     }
+data Located a =
+  Loc { loc   :: Point (V a) (N a)  -- ^ Project out the
+                                --   location of a @Located@
+                                --   value.
+      , unLoc :: a              -- ^ Project the value
+                                --   of type @a@ out of
+                                --   a @Located a@,
+                                --   discarding the
+                                --   location.
+      } deriving (Generic)
 
+instance (Serialize a, Serialize (V a (N a))) => Serialize (Located a)
+
 infix 5 `at`
 
 -- | Construct a @Located a@ from a value of type @a@ and a location.
 --   @at@ is intended to be used infix, like @x \`at\` origin@.
-at :: a -> Point (V a) -> Located a
+at :: a -> Point (V a) (N a) -> Located a
 at a p = Loc p a
 
 -- | Deconstruct a @Located a@ into a location and a value of type
 --   @a@.  @viewLoc@ can be especially useful in conjunction with the
 --   @ViewPatterns@ extension.
-viewLoc :: Located a -> (Point (V a), a)
+viewLoc :: Located a -> (Point (V a) (N a), a)
 viewLoc (Loc p a) = (p,a)
 
 -- | 'Located' is not a @Functor@, since changing the type could
@@ -82,32 +92,49 @@
 --   @Located@ is a little-f (endo)functor on the category of types
 --   with associated vector space @v@; but that is not covered by the
 --   standard @Functor@ class.)
-mapLoc :: (V a ~ V b) => (a -> b) -> Located a -> Located b
+mapLoc :: SameSpace a b => (a -> b) -> Located a -> Located b
 mapLoc f (Loc p a) = Loc p (f a)
 
 -- | A lens giving access to the object within a 'Located' wrapper.
-located :: (V a ~ V a') => Lens (Located a) (Located a') a a'
+located :: SameSpace a b => Lens (Located a) (Located b) a b
 located f (Loc p a) = Loc p <$> f a
 
-deriving instance (Eq   (V a), Eq a  ) => Eq   (Located a)
-deriving instance (Ord  (V a), Ord a ) => Ord  (Located a)
-deriving instance (Show (V a), Show a) => Show (Located a)
+-- | Lens onto the location of something 'Located'.
+_loc :: Lens' (Located a) (Point (V a) (N a))
+_loc f (Loc p a) = flip Loc a <$> f p
 
+deriving instance (Eq   (V a (N a)), Eq a  ) => Eq   (Located a)
+deriving instance (Ord  (V a (N a)), Ord a ) => Ord  (Located a)
+
+instance (Show (V a (N a)), Show a) => Show (Located a) where
+  showsPrec d (Loc p a) = showParen (d > 5) $
+    showsPrec 6 a . showString " `at` " . showsPrec 6 p
+
+instance (Read (V a (N a)), Read a) => Read (Located a) where
+  readPrec = parens . prec 5 $ do
+    a <- readPrec
+    Punc "`"   <- lexP
+    Ident "at" <- lexP
+    Punc "`"   <- lexP
+    p <- readPrec
+    return (Loc p a)
+
 type instance V (Located a) = V a
+type instance N (Located a) = N a
 
 -- | @Located a@ is an instance of @HasOrigin@ whether @a@ is or not.
 --   In particular, translating a @Located a@ simply translates the
 --   associated point (and does /not/ affect the value of type @a@).
-instance VectorSpace (V a) => HasOrigin (Located a) where
+instance (Num (N a), Additive (V a)) => HasOrigin (Located a) where
   moveOriginTo o (Loc p a) = Loc (moveOriginTo o p) a
 
 -- | Applying a transformation @t@ to a @Located a@ results in the
 --   transformation being applied to the location, and the /linear/
 --   /portion/ of @t@ being applied to the value of type @a@ (/i.e./
 --   it is not translated).
-instance Transformable a => Transformable (Located a) where
+instance (Additive (V a), Num (N a), Transformable a) => Transformable (Located a) where
   transform t@(Transformation t1 t2 _) (Loc p a)
-    = Loc (transform t p) (transform (Transformation t1 t2 zeroV) a)
+    = Loc (transform t p) (transform (Transformation t1 t2 zero) a)
 
 -- | The envelope of a @Located a@ is the envelope of the @a@,
 --   translated to the location.
@@ -119,38 +146,38 @@
 
 -- | The trace of a @Located a@ is the trace of the @a@,
 --   translated to the location.
-instance Traced a => Traced (Located a) where
+instance (Traced a, Num (N a)) => Traced (Located a) where
   getTrace (Loc p a) = moveTo p (getTrace a)
 
+instance Alignable a => Alignable (Located a) where
+  defaultBoundary v = defaultBoundary v . unLoc
+
 instance Qualifiable a => Qualifiable (Located a) where
-  n |> (Loc p a) = Loc p (n |> a)
+  n .>> Loc p a = Loc p (n .>> a)
 
 type instance Codomain (Located a) = Point (Codomain a)
 
-instance (Codomain a ~ V a, AdditiveGroup (V a), Parametric a)
+instance (InSpace v n a, Parametric a, Codomain a ~ v)
     => Parametric (Located a) where
-  (Loc x a) `atParam` p = x .+^ (a `atParam` p)
+  Loc x a `atParam` p = x .+^ (a `atParam` p)
 
 instance DomainBounds a => DomainBounds (Located a) where
   domainLower (Loc _ a) = domainLower a
   domainUpper (Loc _ a) = domainUpper a
 
-instance (Codomain a ~ V a, AdditiveGroup (V a), EndValues a)
-    => EndValues (Located a)
+instance (InSpace v n a, EndValues a, Codomain a ~ v) => EndValues (Located a)
 
-instance ( Codomain a ~ V a, Fractional (Scalar (V a)), AdditiveGroup (V a)
-         , Sectionable a, Parametric a
-         )
+instance (InSpace v n a, Fractional n, Parametric a, Sectionable a, Codomain a ~ v)
     => Sectionable (Located a) where
   splitAtParam (Loc x a) p = (Loc x a1, Loc (x .+^ (a `atParam` p)) a2)
     where (a1,a2) = splitAtParam a p
 
+  section (Loc x a) p1 p2 = Loc (x .+^ (a `atParam` p1)) (section a p1 p2)
+
   reverseDomain (Loc x a) = Loc (x .+^ y) (reverseDomain a)
-    where y = a `atParam` (domainUpper a)
+    where y = a `atParam` domainUpper a
 
-instance ( Codomain a ~ V a, AdditiveGroup (V a), Fractional (Scalar (V a))
-         , HasArcLength a
-         )
+instance (InSpace v n a, Fractional n, HasArcLength a, Codomain a ~ v)
     => HasArcLength (Located a) where
-  arcLengthBounded eps (Loc _ a)   = arcLengthBounded eps a
-  arcLengthToParam eps (Loc _ a) l = arcLengthToParam eps a l
+  arcLengthBounded eps (Loc _ a) = arcLengthBounded eps a
+  arcLengthToParam eps (Loc _ a) = arcLengthToParam eps a
diff --git a/src/Diagrams/Names.hs b/src/Diagrams/Names.hs
--- a/src/Diagrams/Names.hs
+++ b/src/Diagrams/Names.hs
@@ -1,4 +1,10 @@
+{-# LANGUAGE ConstraintKinds #-}
 {-# LANGUAGE FlexibleContexts #-}
+{-# LANGUAGE MonoLocalBinds   #-}
+
+{-# OPTIONS_GHC -fno-warn-unused-imports #-}
+  -- for Data.Semigroup
+
 -----------------------------------------------------------------------------
 -- |
 -- Module      :  Diagrams.Names
@@ -39,23 +45,22 @@
     ) where
 
 import           Data.Semigroup
-import           Data.VectorSpace
 
-import           Diagrams.Core       (HasLinearMap, OrderedField, Point)
+import           Diagrams.Core       (OrderedField, Point)
 import           Diagrams.Core.Names
 import           Diagrams.Core.Types
 
+import           Linear.Metric
+
 -- | Attach an atomic name to a diagram.
-named :: ( IsName n
-         , HasLinearMap v, InnerSpace v, OrderedField (Scalar v), Semigroup m)
-      => n -> QDiagram b v m -> QDiagram b v m
+named :: (IsName nm, Metric v, OrderedField n, Semigroup m)
+      => nm -> QDiagram b v n m -> QDiagram b v n m
 named = nameSub mkSubdiagram
 
 -- | Attach an atomic name to a certain point (which may be computed
 --   from the given diagram), treated as a subdiagram with no content
 --   and a point envelope.
-namePoint :: ( IsName n
-             , HasLinearMap v, InnerSpace v, OrderedField (Scalar v), Semigroup m)
-          => (QDiagram b v m -> Point v) -> n -> QDiagram b v m -> QDiagram b v m
+namePoint :: (IsName nm , Metric v, OrderedField n, Semigroup m)
+          => (QDiagram b v n m -> Point v n) -> nm -> QDiagram b v n m -> QDiagram b v n m
 namePoint p = nameSub (subPoint . p)
 
diff --git a/src/Diagrams/Parametric.hs b/src/Diagrams/Parametric.hs
--- a/src/Diagrams/Parametric.hs
+++ b/src/Diagrams/Parametric.hs
@@ -22,14 +22,13 @@
 
   ) where
 
-import           Diagrams.Core
-
-import           Data.VectorSpace
-import qualified Numeric.Interval.Kaucher   as I
+import           Data.Kind (Type)
+import           Diagrams.Core.V
+import qualified Numeric.Interval.Kaucher as I
 
 -- | Codomain of parametric classes.  This is usually either @(V p)@, for relative
 --   vector results, or @(Point (V p))@, for functions with absolute coordinates.
-type family Codomain p :: *
+type family Codomain p :: Type -> Type
 
 -- | Type class for parametric functions.
 class Parametric p where
@@ -37,7 +36,7 @@
   -- | 'atParam' yields a parameterized view of an object as a
   --   continuous function. It is designed to be used infix, like @path
   --   ``atParam`` 0.5@.
-  atParam :: p -> Scalar (V p) -> Codomain p
+  atParam :: p -> N p -> Codomain p (N p)
 
 -- | Type class for parametric functions with a bounded domain.  The
 --   default bounds are @[0,1]@.
@@ -48,16 +47,16 @@
 class DomainBounds p where
   -- | 'domainLower' defaults to being constantly 0 (for vector spaces with
   --   numeric scalars).
-  domainLower :: p -> Scalar (V p)
+  domainLower :: p -> N p
 
-  default domainLower :: Num (Scalar (V p)) => p -> Scalar (V p)
+  default domainLower :: Num (N p) => p -> N p
   domainLower = const 0
 
   -- | 'domainUpper' defaults to being constantly 1 (for vector spaces
   --   with numeric scalars).
-  domainUpper :: p -> Scalar (V p)
+  domainUpper :: p -> N p
 
-  default domainUpper :: Num (Scalar (V p)) => p -> Scalar (V p)
+  default domainUpper :: Num (N p) => p -> N p
   domainUpper = const 1
 
 -- | Type class for querying the values of a parametric object at the
@@ -69,7 +68,7 @@
   --
   --   This is the default implementation, but some representations will
   --   have a more efficient and/or precise implementation.
-  atStart :: p -> Codomain p
+  atStart :: p -> Codomain p (N p)
   atStart x = x `atParam` domainLower x
 
   -- | 'atEnd' is the value at the end of the domain. That is,
@@ -78,12 +77,12 @@
   --
   --   This is the default implementation, but some representations will
   --   have a more efficient and/or precise implementation.
-  atEnd :: p -> Codomain p
+  atEnd :: p -> Codomain p (N p)
   atEnd x = x `atParam` domainUpper x
 
 -- | Return the lower and upper bounds of a parametric domain together
 --   as a pair.
-domainBounds :: DomainBounds p => p -> (Scalar (V p), Scalar (V p))
+domainBounds :: DomainBounds p => p -> (N p, N p)
 domainBounds x = (domainLower x, domainUpper x)
 
 -- | Type class for parametric objects which can be split into
@@ -97,10 +96,12 @@
   --   portion of @p@ for parameter values from @0@ to @t@ and @r@ for
   --   to that from @t@ to @1@.  The following property should hold:
   --
-  -- > prop_splitAtParam f t u =
-  -- >   | u < t     = atParam f u == atParam l (u / t)
-  -- >   | otherwise = atParam f u == atParam f t ??? atParam l ((u - t) / (domainUpper f - t))
-  -- >   where (l,r) = splitAtParam f t
+  -- @
+  --   prop_splitAtParam f t u =
+  --     | u < t     = atParam f u == atParam l (u / t)
+  --     | otherwise = atParam f u == atParam f t ??? atParam l ((u - t) / (domainUpper f - t))
+  --     where (l,r) = splitAtParam f t
+  -- @
   --
   --   where @(???) = (^+^)@ if the codomain is a vector type, or
   --   @const flip@ if the codomain is a point type.  Stated more
@@ -113,7 +114,7 @@
   --   result paths where the first is the original path extended to
   --   the parameter 2, and the second result path travels /backwards/
   --   from the end of the first to the end of the original path.
-  splitAtParam :: p -> Scalar (V p) -> (p, p)
+  splitAtParam :: p -> N p -> (p, p)
   splitAtParam x t
     = ( section x (domainLower x) t
       , section x t (domainUpper x))
@@ -129,8 +130,8 @@
   --
   --   That is, the section should have the same domain as the
   --   original, and the reparameterization should be linear.
-  section :: p -> Scalar (V p) -> Scalar (V p) -> p
-  default section :: Fractional (Scalar (V p)) => p -> Scalar (V p) -> Scalar (V p) -> p
+  section :: p -> N p -> N p -> p
+  default section :: Fractional (N p) => p -> N p -> N p -> p
   section x t1 t2 = snd (splitAtParam (fst (splitAtParam x t2)) (t1/t2))
 
   -- | Flip the parameterization on the domain.
@@ -148,18 +149,18 @@
   -- | @arcLengthBounded eps x@ approximates the arc length of @x@.
   --   The true arc length is guaranteed to lie within the interval
   --   returned, which will have a size of at most @eps@.
-  arcLengthBounded :: Scalar (V p) -> p -> I.Interval (Scalar (V p))
+  arcLengthBounded :: N p -> p -> I.Interval (N p)
 
   -- | @arcLength eps s@ approximates the arc length of @x@ up to the
   --   accuracy @eps@ (plus or minus).
-  arcLength :: Scalar (V p) -> p -> Scalar (V p)
-  default arcLength :: Fractional (Scalar (V p)) => Scalar (V p ) -> p -> Scalar (V p)
+  arcLength :: N p -> p -> N p
+  default arcLength :: Fractional (N p) => N p -> p -> N p
   arcLength eps = I.midpoint . arcLengthBounded eps
 
   -- | Approximate the arc length up to a standard accuracy of
   --   'stdTolerance' (@1e-6@).
-  stdArcLength :: p -> Scalar (V p)
-  default stdArcLength :: Fractional (Scalar (V p)) => p -> Scalar (V p)
+  stdArcLength :: p -> N p
+  default stdArcLength :: Fractional (N p) => p -> N p
   stdArcLength = arcLength stdTolerance
 
   -- | @'arcLengthToParam' eps s l@ converts the absolute arc length
@@ -169,11 +170,11 @@
   --
   --   This should work for /any/ arc length, and may return any
   --   parameter value (not just parameters in the domain).
-  arcLengthToParam :: Scalar (V p) -> p -> Scalar (V p) -> Scalar (V p)
+  arcLengthToParam :: N p -> p -> N p -> N p
 
   -- | A simple interface to convert arc length to a parameter,
   --   guaranteed to be accurate within 'stdTolerance', or @1e-6@.
-  stdArcLengthToParam :: p -> Scalar (V p) -> Scalar (V p)
-  default stdArcLengthToParam :: Fractional (Scalar (V p))
-                              => p -> Scalar (V p) -> Scalar (V p)
+  stdArcLengthToParam :: p -> N p -> N p
+  default stdArcLengthToParam :: Fractional (N p) => p -> N p -> N p
   stdArcLengthToParam = arcLengthToParam stdTolerance
+
diff --git a/src/Diagrams/Parametric/Adjust.hs b/src/Diagrams/Parametric/Adjust.hs
--- a/src/Diagrams/Parametric/Adjust.hs
+++ b/src/Diagrams/Parametric/Adjust.hs
@@ -1,5 +1,7 @@
 {-# LANGUAGE FlexibleContexts     #-}
 {-# LANGUAGE TemplateHaskell      #-}
+{-# LANGUAGE TypeFamilies         #-}
+{-# LANGUAGE TypeOperators        #-}
 {-# LANGUAGE UndecidableInstances #-}
 -----------------------------------------------------------------------------
 -- |
@@ -20,23 +22,23 @@
 
     ) where
 
-import           Control.Lens (makeLensesWith, lensRules, generateSignatures, (^.), (&), (.~), Lens')
+import           Control.Lens        (Lens', generateSignatures, lensRules, makeLensesWith, (&),
+                                      (.~), (^.))
 import           Data.Proxy
 
-import           Data.Default.Class
-import           Data.VectorSpace
+import           Data.Default
 
 import           Diagrams.Core.V
 import           Diagrams.Parametric
 
 -- | What method should be used for adjusting a segment, trail, or
 --   path?
-data AdjustMethod v = ByParam (Scalar v)     -- ^ Extend by the given parameter value
-                                             --   (use a negative parameter to shrink)
-                    | ByAbsolute (Scalar v)  -- ^ Extend by the given arc length
-                                             --   (use a negative length to shrink)
-                    | ToAbsolute (Scalar v)  -- ^ Extend or shrink to the given
-                                             --   arc length
+data AdjustMethod n = ByParam n     -- ^ Extend by the given parameter value
+                                    --   (use a negative parameter to shrink)
+                    | ByAbsolute n  -- ^ Extend by the given arc length
+                                    --   (use a negative length to shrink)
+                    | ToAbsolute n  -- ^ Extend or shrink to the given
+                                    --   arc length
 
 -- | Which side of a segment, trail, or path should be adjusted?
 data AdjustSide = Start  -- ^ Adjust only the beginning
@@ -45,43 +47,43 @@
   deriving (Show, Read, Eq, Ord, Bounded, Enum)
 
 -- | How should a segment, trail, or path be adjusted?
-data AdjustOpts v = AO { _adjMethod       :: AdjustMethod v
-                       , _adjSide         :: AdjustSide
-                       , _adjEps          :: Scalar v
-                       , adjOptsvProxy__ :: Proxy v
+data AdjustOpts n = AO { _adjMethod    :: AdjustMethod n
+                       , _adjSide      :: AdjustSide
+                       , _adjEps       :: n
+                       , adjOptsvProxy :: Proxy n
                        }
 
-makeLensesWith
-  ( lensRules & generateSignatures .~ False)
-  ''AdjustOpts
+-- See Diagrams.Combinators for reasoning behind 'Proxy'.
 
+makeLensesWith (lensRules & generateSignatures .~ False) ''AdjustOpts
+
 -- | Which method should be used for adjusting?
-adjMethod :: Lens' (AdjustOpts v) (AdjustMethod v)
+adjMethod :: Lens' (AdjustOpts n) (AdjustMethod n)
 
 -- | Which end(s) of the object should be adjusted?
-adjSide :: Lens' (AdjustOpts v) AdjustSide
+adjSide :: Lens' (AdjustOpts n) AdjustSide
 
 -- | Tolerance to use when doing adjustment.
-adjEps :: Lens' (AdjustOpts v) (Scalar v)
+adjEps :: Lens' (AdjustOpts n) n
 
-instance Fractional (Scalar v) => Default (AdjustMethod v) where
+instance Fractional n => Default (AdjustMethod n) where
   def = ByParam 0.2
 
 instance Default AdjustSide where
   def = Both
 
-instance Fractional (Scalar v) => Default (AdjustOpts v) where
-  def = AO { _adjMethod = def
-           , _adjSide = def
-           , _adjEps = stdTolerance
-           , adjOptsvProxy__ = Proxy
+instance Fractional n => Default (AdjustOpts n) where
+  def = AO { _adjMethod    = def
+           , _adjSide      = def
+           , _adjEps       = stdTolerance
+           , adjOptsvProxy = Proxy
            }
 
 -- | Adjust the length of a parametric object such as a segment or
 --   trail.  The second parameter is an option record which controls how
 --   the adjustment should be performed; see 'AdjustOpts'.
-adjust :: (DomainBounds a, Sectionable a, HasArcLength a, Fractional (Scalar (V a)))
-       => a -> AdjustOpts (V a) -> a
+adjust :: (N t ~ n, Sectionable t, HasArcLength t, Fractional n)
+       => t -> AdjustOpts n -> t
 adjust s opts = section s
   (if opts^.adjSide == End   then domainLower s else getParam s)
   (if opts^.adjSide == Start then domainUpper s else domainUpper s - getParam (reverseDomain s))
diff --git a/src/Diagrams/Path.hs b/src/Diagrams/Path.hs
--- a/src/Diagrams/Path.hs
+++ b/src/Diagrams/Path.hs
@@ -1,15 +1,20 @@
+{-# LANGUAGE ConstraintKinds            #-}
 {-# LANGUAGE DeriveDataTypeable         #-}
-{-# LANGUAGE DeriveFunctor              #-}
+{-# LANGUAGE DeriveGeneric              #-}
 {-# LANGUAGE FlexibleContexts           #-}
 {-# LANGUAGE FlexibleInstances          #-}
 {-# LANGUAGE GeneralizedNewtypeDeriving #-}
 {-# LANGUAGE MultiParamTypeClasses      #-}
 {-# LANGUAGE ScopedTypeVariables        #-}
 {-# LANGUAGE StandaloneDeriving         #-}
-{-# LANGUAGE TemplateHaskell            #-}
 {-# LANGUAGE TypeFamilies               #-}
+{-# LANGUAGE TypeOperators              #-}
 {-# LANGUAGE UndecidableInstances       #-}
 {-# LANGUAGE ViewPatterns               #-}
+
+{-# OPTIONS_GHC -fno-warn-unused-imports #-}
+  -- for Data.Semigroup
+
 -----------------------------------------------------------------------------
 -- |
 -- Module      :  Diagrams.Path
@@ -35,12 +40,15 @@
          -- * Constructing paths
          -- $construct
 
+       , ToPath (..)
        , pathFromTrail
        , pathFromTrailAt
        , pathFromLocTrail
 
          -- * Eliminating paths
 
+       , pathPoints
+       , pathVertices'
        , pathVertices
        , pathOffsets
        , pathCentroid
@@ -58,11 +66,15 @@
 
        ) where
 
+import           Control.Arrow      ((***))
+import           Control.Lens       hiding (at, transform, ( # ))
+import qualified Data.Foldable      as F
+import           Data.List          (partition)
+import           Data.Semigroup
 import           Data.Typeable
 
 import           Diagrams.Align
 import           Diagrams.Core
-import           Diagrams.Core.Points ()
 import           Diagrams.Located
 import           Diagrams.Points
 import           Diagrams.Segment
@@ -70,15 +82,12 @@
 import           Diagrams.TrailLike
 import           Diagrams.Transform
 
-import           Control.Arrow        ((***))
-import           Control.Lens         (Rewrapped, Wrapped (..), iso, mapped, op,
-                                       over, view, (%~), _Unwrapped', _Wrapped)
-import           Data.AffineSpace
-import qualified Data.Foldable        as F
-import           Data.List            (partition)
-import           Data.Semigroup
-import           Data.VectorSpace
+import           Linear.Metric
+import           Linear.Vector
 
+import           Data.Serialize     (Serialize)
+import           GHC.Generics       (Generic)
+
 ------------------------------------------------------------
 --  Paths  -------------------------------------------------
 ------------------------------------------------------------
@@ -87,86 +96,136 @@
 --   Hence, unlike trails, paths are not translationally invariant,
 --   and they form a monoid under /superposition/ (placing one path on
 --   top of another) rather than concatenation.
-newtype Path v = Path [Located (Trail v)]
-  deriving (Semigroup, Monoid, Typeable)
+newtype Path v n = Path [Located (Trail v n)]
+  deriving (Semigroup, Monoid, Generic
+  , Typeable
+  )
 
-instance Wrapped (Path v) where
-    type Unwrapped (Path v) = [Located (Trail v)]
-    _Wrapped' = iso (\(Path x) -> x) Path
+-- instance (OrderedField n, Metric v, Serialize (v n), Serialize (V n (N n))) =>
+instance (OrderedField n, Metric v, Serialize (v n), Serialize (V (v n) (N (v n)))) =>
+  Serialize (Path v n)
 
-instance Rewrapped (Path v) (Path v')
+instance Wrapped (Path v n) where
+  type Unwrapped (Path v n) = [Located (Trail v n)]
+  _Wrapped' = iso (\(Path x) -> x) Path
 
+instance Rewrapped (Path v n) (Path v' n')
+
+instance Each (Path v n) (Path v' n') (Located (Trail v n)) (Located (Trail v' n')) where
+  each = _Wrapped . traverse
+
+instance AsEmpty (Path v n) where
+  _Empty = _Wrapped' . _Empty
+
+instance Cons (Path v n) (Path v' n') (Located (Trail v n)) (Located (Trail v' n')) where
+  _Cons = _Wrapped . _Cons . bimapping id _Unwrapped
+  {-# INLINE _Cons #-}
+
+instance Snoc (Path v n) (Path v' n') (Located (Trail v n)) (Located (Trail v' n')) where
+  _Snoc = _Wrapped . _Snoc . bimapping _Unwrapped id
+  {-# INLINE _Snoc #-}
+
 -- | Extract the located trails making up a 'Path'.
-pathTrails :: Path v -> [Located (Trail v)]
+pathTrails :: Path v n -> [Located (Trail v n)]
 pathTrails = op Path
 
-deriving instance Show v => Show (Path v)
-deriving instance Eq   v => Eq   (Path v)
-deriving instance Ord  v => Ord  (Path v)
+deriving instance Show (v n) => Show (Path v n)
+deriving instance Eq   (v n) => Eq   (Path v n)
+deriving instance Ord  (v n) => Ord  (Path v n)
 
-type instance V (Path v) = v
+type instance V (Path v n) = v
+type instance N (Path v n) = n
 
-instance VectorSpace v => HasOrigin (Path v) where
+instance (Additive v, Num n) => HasOrigin (Path v n) where
   moveOriginTo = over _Wrapped' . map . moveOriginTo
-  --moveOriginTo = over pathTrails . map . moveOriginTo
 
 -- | Paths are trail-like; a trail can be used to construct a
 --   singleton path.
-instance (InnerSpace v, OrderedField (Scalar v)) => TrailLike (Path v) where
+instance (Metric v, OrderedField n) => TrailLike (Path v n) where
   trailLike = Path . (:[])
 
 -- See Note [Transforming paths]
-instance (HasLinearMap v, InnerSpace v, OrderedField (Scalar v))
-    => Transformable (Path v) where
+instance (HasLinearMap v, Metric v, OrderedField n)
+    => Transformable (Path v n) where
   transform = over _Wrapped . map . transform
 
-{- ~~~~ Note [Transforming paths]
-
-Careful!  It's tempting to just define
-
-> transform = fmap . transform
-
-but that doesn't take into account the fact that some
-of the v's are inside Points and hence ought to be translated.
--}
-
-instance (InnerSpace v, OrderedField (Scalar v)) => Enveloped (Path v) where
-  getEnvelope = F.foldMap trailEnvelope . op Path --view pathTrails
+instance (Metric v, OrderedField n) => Enveloped (Path v n) where
+  getEnvelope = F.foldMap trailEnvelope . op Path
           -- this type signature is necessary to work around an apparent bug in ghc 6.12.1
-    where trailEnvelope :: Located (Trail v) -> Envelope v
+    where trailEnvelope :: Located (Trail v n) -> Envelope v n
           trailEnvelope (viewLoc -> (p, t)) = moveOriginTo ((-1) *. p) (getEnvelope t)
 
-instance (InnerSpace v, OrderedField (Scalar v)) => Juxtaposable (Path v) where
+instance (Metric v, OrderedField n) => Juxtaposable (Path v n) where
   juxtapose = juxtaposeDefault
 
-instance (InnerSpace v, OrderedField (Scalar v)) => Alignable (Path v) where
+instance (Metric v, OrderedField n) => Alignable (Path v n) where
   defaultBoundary = envelopeBoundary
 
-instance (HasLinearMap v, InnerSpace v, OrderedField (Scalar v))
-    => Renderable (Path v) NullBackend where
+instance (HasLinearMap v, Metric v, OrderedField n)
+    => Renderable (Path v n) NullBackend where
   render _ _ = mempty
 
 ------------------------------------------------------------
 --  Constructing paths  ------------------------------------
 ------------------------------------------------------------
 
+-- | Type class for things that can be converted to a 'Path'.
+--
+--   Note that this class is very different from 'TrailLike'. 'TrailLike' is
+--   usually the result of a library function to give you a convenient,
+--   polymorphic result ('Path', 'Diagram' etc.).
+--
+class ToPath t where
+  -- | 'toPath' takes something that can be converted to 'Path' and returns
+  --    the 'Path'.
+  toPath :: (Metric (V t), OrderedField (N t)) => t -> Path (V t) (N t)
+
+instance ToPath (Path v n) where
+  toPath = id
+
+instance ToPath (Trail v n) where
+  toPath = pathFromTrail
+
+instance ToPath (Trail' l v n) where
+  toPath t = Path [Trail t `at` origin]
+
+instance ToPath (Located (Trail v n)) where
+  toPath = pathFromLocTrail
+
+instance ToPath (Located (Trail' l v n)) where
+  toPath = pathFromLocTrail . mapLoc Trail
+
+instance ToPath (Located (Segment Closed v n)) where
+  toPath (viewLoc -> (p,seg))
+    = Path [trailFromSegments [seg] `at` p]
+
+instance ToPath (Located [Segment Closed v n]) where
+  toPath (viewLoc -> (p,segs))
+    = Path [trailFromSegments segs `at` p]
+
+instance ToPath (FixedSegment v n) where
+  toPath = toPath . fromFixedSeg
+
+instance ToPath a => ToPath [a] where
+  toPath = F.foldMap toPath
+
 -- $construct
 -- Since paths are 'TrailLike', any function producing a 'TrailLike'
 -- can be used to construct a (singleton) path.  The functions in this
 -- section are provided for convenience.
 
 -- | Convert a trail to a path beginning at the origin.
-pathFromTrail :: (InnerSpace v, OrderedField (Scalar v)) => Trail v -> Path v
+pathFromTrail :: (Metric v, OrderedField n) => Trail v n -> Path v n
 pathFromTrail = trailLike . (`at` origin)
 
 -- | Convert a trail to a path with a particular starting point.
-pathFromTrailAt :: (InnerSpace v, OrderedField (Scalar v)) => Trail v -> Point v -> Path v
+pathFromTrailAt :: (Metric v, OrderedField n) => Trail v n -> Point v n -> Path v n
 pathFromTrailAt t p = trailLike (t `at` p)
 
 -- | Convert a located trail to a singleton path.  This is equivalent
 --   to 'trailLike', but provided with a more specific name and type
 --   for convenience.
-pathFromLocTrail :: (InnerSpace v, OrderedField (Scalar v)) => Located (Trail v) -> Path v
+pathFromLocTrail :: (Metric v, OrderedField n) => Located (Trail v n) -> Path v n
 pathFromLocTrail = trailLike
 
 ------------------------------------------------------------
@@ -174,37 +233,64 @@
 ------------------------------------------------------------
 
 -- | Extract the vertices of a path, resulting in a separate list of
---   vertices for each component trail (see 'trailVertices').
-pathVertices :: (InnerSpace v, OrderedField (Scalar v)) => Path v -> [[Point v]]
+--   vertices for each component trail.  Here a /vertex/ is defined as
+--   a non-differentiable point on the trail, /i.e./ a sharp corner.
+--   (Vertices are thus a subset of the places where segments join; if
+--   you want all joins between segments, see 'pathPoints'.)  The
+--   tolerance determines how close the tangents of two segments must be
+--   at their endpoints to consider the transition point to be
+--   differentiable.  See 'trailVertices' for more information.
+pathVertices' :: (Metric v, OrderedField n) => n -> Path v n -> [[Point v n]]
+pathVertices' toler = map (trailVertices' toler) . op Path
+
+-- | Like 'pathVertices'', with a default tolerance.
+pathVertices :: (Metric v, OrderedField n) => Path v n -> [[Point v n]]
 pathVertices = map trailVertices . op Path
 
+-- | Extract the points of a path, resulting in a separate list of
+--   points for each component trail.  Here a /point/ is any place
+--   where two segments join; see also 'pathVertices' and 'trailPoints'.
+--
+--   This function allows you "observe" the fact that trails are
+--   implemented as lists of segments, which may be problematic if we
+--   want to think of trails as parametric vector functions. This also
+--   means that the behavior of this function may not be stable under
+--   future changes to the implementation of trails and paths.  For an
+--   unproblematic version which only yields vertices at which there
+--   is a sharp corner, excluding points differentiable points, see
+--   'pathVertices'.
+--
+--   This function is not re-exported from "Diagrams.Prelude"; to use
+--   it, import "Diagrams.Path".
+pathPoints :: (Metric v, OrderedField n) => Path v n -> [[Point v n]]
+pathPoints = map trailPoints . op Path
+
 -- | Compute the total offset of each trail comprising a path (see 'trailOffset').
-pathOffsets :: (InnerSpace v, OrderedField (Scalar v)) => Path v -> [v]
+pathOffsets :: (Metric v, OrderedField n) => Path v n -> [v n]
 pathOffsets = map (trailOffset . unLoc) . op Path
 
 -- | Compute the /centroid/ of a path (/i.e./ the average location of
---   its vertices).
-pathCentroid :: (InnerSpace v, OrderedField (Scalar v)) => Path v -> Point v
+--   its /vertices/; see 'pathVertices').
+pathCentroid :: (Metric v, OrderedField n) => Path v n -> Point v n
 pathCentroid = centroid . concat . pathVertices
 
 -- | Convert a path into a list of lists of located segments.
-pathLocSegments :: (InnerSpace v, OrderedField (Scalar v))
-                 => Path v -> [[Located (Segment Closed v)]]
+pathLocSegments :: (Metric v, OrderedField n) => Path v n -> [[Located (Segment Closed v n)]]
 pathLocSegments = map trailLocSegments . op Path
 
 -- | Convert a path into a list of lists of 'FixedSegment's.
-fixPath :: (InnerSpace v, OrderedField (Scalar v)) => Path v -> [[FixedSegment v]]
+fixPath :: (Metric v, OrderedField n) => Path v n -> [[FixedSegment v n]]
 fixPath = map fixTrail . op Path
 
 -- | \"Explode\" a path by exploding every component trail (see
 --   'explodeTrail').
-explodePath :: (VectorSpace (V t), TrailLike t) => Path (V t) -> [[t]]
+explodePath :: (V t ~ v, N t ~ n, TrailLike t) => Path v n -> [[t]]
 explodePath = map explodeTrail . op Path
 
 -- | Partition a path into two paths based on a predicate on trails:
 --   the first containing all the trails for which the predicate returns
 --   @True@, and the second containing the remaining trails.
-partitionPath :: (Located (Trail v) -> Bool) -> Path v -> (Path v, Path v)
+partitionPath :: (Located (Trail v n) -> Bool) -> Path v n -> (Path v n, Path v n)
 partitionPath p = (view _Unwrapped' *** view _Unwrapped') . partition p . op Path
 
 ------------------------------------------------------------
@@ -213,10 +299,13 @@
 
 -- | Scale a path using its centroid (see 'pathCentroid') as the base
 --   point for the scale.
-scalePath :: (HasLinearMap v, InnerSpace v, OrderedField (Scalar v))
-          => Scalar v -> Path v -> Path v
-scalePath d p = (scale d `under` translation (origin .-. pathCentroid p)) p
+scalePath :: (HasLinearMap v, Metric v, OrderedField n) => n -> Path v n -> Path v n
+scalePath d p = under (movedFrom (pathCentroid p)) (scale d) p
 
 -- | Reverse all the component trails of a path.
-reversePath :: (InnerSpace v, OrderedField (Scalar v)) => Path v -> Path v
+reversePath :: (Metric v, OrderedField n) => Path v n -> Path v n
 reversePath = _Wrapped . mapped %~ reverseLocTrail
+
+-- | Same as 'reversePath'.
+instance (Metric v, OrderedField n) => Reversing (Path v n) where
+  reversing = _Wrapped' . mapped %~ reversing
diff --git a/src/Diagrams/Points.hs b/src/Diagrams/Points.hs
--- a/src/Diagrams/Points.hs
+++ b/src/Diagrams/Points.hs
@@ -1,6 +1,3 @@
-{-# LANGUAGE FlexibleContexts #-}
-{-# LANGUAGE TypeFamilies     #-}
-
 -----------------------------------------------------------------------------
 -- |
 -- Module      :  Diagrams.Points
@@ -9,28 +6,36 @@
 -- Maintainer  :  diagrams-discuss@googlegroups.com
 --
 -- Points in space.  For more tools for working with points and
--- vectors, see "Data.AffineSpace" and "Diagrams.Coordinates".
+-- vectors, see "Linear.Affine".
 --
 -----------------------------------------------------------------------------
 
 module Diagrams.Points
        ( -- * Points
-         Point, origin, (*.)
+         Point (..), origin, (*.)
 
          -- * Point-related utilities
        , centroid
        , pointDiagram
-
+       , _Point, lensP
        ) where
 
-import           Diagrams.Core          (pointDiagram)
+import           Diagrams.Core        (pointDiagram)
 import           Diagrams.Core.Points
 
-import           Control.Arrow          ((&&&))
+import           Data.Foldable        as F
 
-import           Data.AffineSpace.Point
-import           Data.VectorSpace
+import           Linear.Affine
+import           Linear.Vector
 
 -- | The centroid of a set of /n/ points is their sum divided by /n/.
-centroid :: (VectorSpace v, Fractional (Scalar v)) => [Point v] -> Point v
-centroid = P . uncurry (^/) . (sumV &&& (fromIntegral . length)) . map unPoint
+--   Returns the origin for an empty list of points.
+centroid :: (Additive v, Fractional n) => [Point v n] -> Point v n
+centroid [] = origin
+centroid ps = meanV ps
+{-# INLINE centroid #-}
+
+meanV :: (Foldable f, Additive v, Fractional a) => f (v a) -> v a
+meanV = uncurry (^/) . F.foldl' (\(s,c) e -> (e ^+^ s,c+1)) (zero,0)
+{-# INLINE meanV #-}
+
diff --git a/src/Diagrams/Prelude.hs b/src/Diagrams/Prelude.hs
--- a/src/Diagrams/Prelude.hs
+++ b/src/Diagrams/Prelude.hs
@@ -1,8 +1,9 @@
 {-# OPTIONS_GHC -fno-warn-duplicate-exports #-}
+{-# LANGUAGE CPP #-}
 -----------------------------------------------------------------------------
 -- |
 -- Module      :  Diagrams.Prelude
--- Copyright   :  (c) 2011 diagrams-lib team (see LICENSE)
+-- Copyright   :  (c) 2011-2015 diagrams-lib team (see LICENSE)
 -- License     :  BSD-style (see LICENSE)
 -- Maintainer  :  diagrams-discuss@googlegroups.com
 --
@@ -12,148 +13,93 @@
 -----------------------------------------------------------------------------
 
 module Diagrams.Prelude
-       (
-         -- * Core library
-         -- | The core definitions of transformations, diagrams,
-         --   backends, and so on.
-         module Diagrams.Core
-
-         -- * Standard library
-
-         -- | Attributes (color, line style, etc.) and styles.
-       , module Diagrams.Attributes
-
-         -- | Alignment of diagrams relative to their envelopes.
-       , module Diagrams.Align
-
-         -- | Combining multiple diagrams into one.
-       , module Diagrams.Combinators
-
-         -- | Giving concrete locations to translation-invariant things.
-       , module Diagrams.Located
-
-         -- | Linear and cubic bezier segments.
-       , module Diagrams.Segment
-
-         -- | Trails.
-       , module Diagrams.Trail
-
-         -- | Parametrization of segments and trails.
-       , module Diagrams.Parametric
-
-         -- | Adjusting the length of parameterized objects.
-       , module Diagrams.Parametric.Adjust
-
-         -- | Computing tangent and normal vectors of segments and
-         --   trails.
-       , module Diagrams.Tangent
-
-         -- | Trail-like things.
-       , module Diagrams.TrailLike
-
-         -- | Paths.
-       , module Diagrams.Path
-
-         -- | Cubic splines.
-       , module Diagrams.CubicSpline
-
-         -- | Some additional transformation-related functions, like
-         --   conjugation of transformations.
-       , module Diagrams.Transform
-
-         -- | Projective transformations and other deformations
-         -- lacking an inverse.
-       , module Diagrams.Deform
+  (
+    -- * Diagrams library
+    -- | Exports from this library for working with diagrams.
+    module Diagrams
 
-         -- | Giving names to subdiagrams and later retrieving
-         --   subdiagrams by name.
-       , module Diagrams.Names
+    -- * Convenience re-exports from other packages
 
-         -- | Envelopes, aka functional bounding regions.
-       , module Diagrams.Envelope
+    -- | For working with default values. Diagrams also exports 'with',
+    --   an alias for 'def'.
+  , module Data.Default
 
-         -- | Traces, aka embedded raytracers, for finding points on
-         --   the boundary of a diagram.
-       , module Diagrams.Trace
+    -- | For representing and operating on colors.
+  , module Data.Colour
 
-         -- | A query is a function that maps points in a vector space
-         --   to values in some monoid; they can be used to annotate
-         --   the points of a diagram with some values.
-       , module Diagrams.Query
+    -- | A large list of color names.
+  , module Data.Colour.Names
 
-         -- | Utilities for working with points.
-       , module Diagrams.Points
+    -- | Specify your own colours.
+  , module Data.Colour.SRGB
 
-         -- | Angles
-       , module Diagrams.Angle
-         -- | Convenience infix operators for working with coordinates.
-       , module Diagrams.Coordinates
+    -- | Semigroups and monoids show up all over the place, so things from
+    --   Data.Semigroup and Data.Monoid often come in handy.
+  , module Data.Semigroup
 
-         -- | A wide range of things (shapes, transformations,
-         --   combinators) specific to creating two-dimensional
-         --   diagrams.
-       , module Diagrams.TwoD
+    -- | For computing with vectors.
+  , module Linear.Vector
 
-         -- | Tools for making animations.
-       , module Diagrams.Animation
+    -- | For computing with points and vectors.
+  , module Linear.Affine
 
-         -- | Various utility definitions.
-       , module Diagrams.Util
+    -- | For computing with dot products and norm.
+  , module Linear.Metric
 
-         -- * Convenience re-exports
-         -- | For representing and operating on colors.
-       , module Data.Colour
-         -- | A large list of color names.
-       , module Data.Colour.Names
-         -- | Semigroups and monoids show up all over the place, so things from
-         --   Data.Semigroup and Data.Monoid often come in handy.
-       , module Data.Semigroup
-         -- | For computing with vectors.
-       , module Data.VectorSpace
-         -- | For computing with points and vectors.
-       , module Data.AffineSpace
+    -- | For working with 'Active' (i.e. animated) things.
+  , module Data.Active
 
-         -- | For working with 'Active' (i.e. animated) things.
-       , module Data.Active
+    -- | Most of the lens package. The following functions are not
+    --   exported from lens because they either conflict with
+    --   diagrams or may conflict with other libraries:
+    --
+    --   * 'Control.Lens.At.at'
+    --   * 'Control.Lens.At.contains'
+    --   * 'Control.Lens.Indexed..>'
+    --   * 'Control.Lens.Indexed.<.>'
+    --   * 'Control.Lens.Indexed.index'
+    --   * 'Control.Lens.Indexed.indices'
+    --   * 'Control.Lens.Indexed.none'
+    --   * 'Control.Lens.Internal.Getter.coerce'
+    --   * 'Control.Lens.Internal.Indexed.indexed'
+    --   * 'Control.Lens.Lens.inside'
+    --   * 'Control.Lens.Level.levels'
+    --   * 'Control.Lens.Plated....'
+    --   * 'Control.Lens.Plated.children'
+    --   * 'Control.Lens.Plated.transform'
+    --   * 'Control.Lens.Prism.outside'
+    --   * 'Control.Lens.Setter.argument'
+    --   * 'Control.Lens.Traversal.beside'
+    --   * 'Control.Lens.Traversal.singular'
+  , module Control.Lens
 
-         -- | Essential Lens Combinators
-       , (&), (.~), (%~)
+  , Applicative(..), (*>), (<*), (<$>), (<$), liftA, liftA2, liftA3
+  ) where
 
-       , Applicative(..), (*>), (<*), (<$>), (<$), liftA, liftA2, liftA3
-       ) where
+import           Diagrams
 
-import           Diagrams.Core
+import           Control.Applicative
 
-import           Diagrams.Align
-import           Diagrams.Angle
-import           Diagrams.Animation
-import           Diagrams.Attributes
-import           Diagrams.Combinators
-import           Diagrams.Coordinates
-import           Diagrams.CubicSpline
-import           Diagrams.Deform
-import           Diagrams.Envelope
-import           Diagrams.Located
-import           Diagrams.Names
-import           Diagrams.Parametric
-import           Diagrams.Parametric.Adjust
-import           Diagrams.Path
-import           Diagrams.Points
-import           Diagrams.Query
-import           Diagrams.Segment
-import           Diagrams.Tangent
-import           Diagrams.Trace
-import           Diagrams.Trail
-import           Diagrams.TrailLike
-import           Diagrams.Transform
-import           Diagrams.TwoD
-import           Diagrams.Util
+#if MIN_VERSION_lens(4,13,0)
+import           Control.Lens        hiding (argument, at, backwards, beside,
+                                      children, contains, indexed, indices,
+                                      inside, levels, none, outside, singular,
+                                      transform, ( # ), (...), (.>), (<.>))
+#else
+import           Control.Lens        hiding (argument, at, backwards, beside,
+                                      children, coerce, contains, indexed,
+                                      indices, inside, levels, none, outside,
+                                      singular, transform, ( # ), (...), (.>),
+                                      (<.>))
+#endif
 
-import           Control.Applicative
 import           Data.Active
-import           Data.AffineSpace
-import           Data.Colour                hiding (AffineSpace (..), atop, over)
-import           Data.Colour.Names          hiding (tan)
+import           Data.Colour         hiding (AffineSpace (..), atop, over)
+import           Data.Colour.Names   hiding (tan)
+import           Data.Colour.SRGB
+import           Data.Default
 import           Data.Semigroup
-import           Data.VectorSpace           hiding (Sum (..))
-import           Control.Lens               ((&), (.~), (%~))
+
+import           Linear.Affine
+import           Linear.Metric
+import           Linear.Vector
diff --git a/src/Diagrams/Prelude/ThreeD.hs b/src/Diagrams/Prelude/ThreeD.hs
deleted file mode 100644
--- a/src/Diagrams/Prelude/ThreeD.hs
+++ /dev/null
@@ -1,154 +0,0 @@
-{-# OPTIONS_GHC -fno-warn-duplicate-exports #-}
------------------------------------------------------------------------------
--- |
--- Module      :  Diagrams.Prelude.ThreeD
--- Copyright   :  (c) 2014 diagrams-lib team (see LICENSE)
--- License     :  BSD-style (see LICENSE)
--- Maintainer  :  diagrams-discuss@googlegroups.com
---
--- A module to re-export most of the functionality of the diagrams
--- core and standard library, including 3D types and functions.
---
------------------------------------------------------------------------------
-
-module Diagrams.Prelude.ThreeD
-       (
-         -- * Core library
-         -- | The core definitions of transformations, diagrams,
-         --   backends, and so on.
-         module Diagrams.Core
-
-         -- * Standard library
-
-         -- | Attributes (color, line style, etc.) and styles.
-       , module Diagrams.Attributes
-
-         -- | Alignment of diagrams relative to their envelopes.
-       , module Diagrams.Align
-
-         -- | Combining multiple diagrams into one.
-       , module Diagrams.Combinators
-
-         -- | Giving concrete locations to translation-invariant things.
-       , module Diagrams.Located
-
-         -- | Linear and cubic bezier segments.
-       , module Diagrams.Segment
-
-         -- | Trails.
-       , module Diagrams.Trail
-
-         -- | Parametrization of segments and trails.
-       , module Diagrams.Parametric
-
-         -- | Adjusting the length of parameterized objects.
-       , module Diagrams.Parametric.Adjust
-
-         -- | Computing tangent and normal vectors of segments and
-         --   trails.
-       , module Diagrams.Tangent
-
-         -- | Trail-like things.
-       , module Diagrams.TrailLike
-
-         -- | Paths.
-       , module Diagrams.Path
-
-         -- | Cubic splines.
-       , module Diagrams.CubicSpline
-
-         -- | Some additional transformation-related functions, like
-         --   conjugation of transformations.
-       , module Diagrams.Transform
-
-         -- | Giving names to subdiagrams and later retrieving
-         --   subdiagrams by name.
-       , module Diagrams.Names
-
-         -- | Envelopes, aka functional bounding regions.
-       , module Diagrams.Envelope
-
-         -- | Traces, aka embedded raytracers, for finding points on
-         --   the boundary of a diagram.
-       , module Diagrams.Trace
-
-         -- | A query is a function that maps points in a vector space
-         --   to values in some monoid; they can be used to annotate
-         --   the points of a diagram with some values.
-       , module Diagrams.Query
-
-         -- | Utilities for working with points.
-       , module Diagrams.Points
-
-         -- | Angles
-       , module Diagrams.Angle
-
-         -- | Convenience infix operators for working with coordinates.
-       , module Diagrams.Coordinates
-
-         -- | things (shapes, transformations, combinators) specific
-         -- to creating three-dimensional diagrams.
-       , module Diagrams.ThreeD
-
-         -- | Tools for making animations.
-       , module Diagrams.Animation
-
-         -- | Various utility definitions.
-       , module Diagrams.Util
-
-         -- * Convenience re-exports
-         -- | For representing and operating on colors.
-       , module Data.Colour
-         -- | A large list of color names.
-       , module Data.Colour.Names
-         -- | Semigroups and monoids show up all over the place, so things from
-         --   Data.Semigroup and Data.Monoid often come in handy.
-       , module Data.Semigroup
-         -- | For computing with vectors.
-       , module Data.VectorSpace
-         -- | For computing with points and vectors.
-       , module Data.AffineSpace
-
-         -- | For working with 'Active' (i.e. animated) things.
-       , module Data.Active
-
-         -- | Essential Lens Combinators
-       , (&), (.~), (%~)
-
-       , Applicative(..), (*>), (<*), (<$>), (<$), liftA, liftA2, liftA3
-       ) where
-
-import           Diagrams.Core
-
-import           Diagrams.Align
-import           Diagrams.Angle
-import           Diagrams.Animation
-import           Diagrams.Attributes
-import           Diagrams.Combinators
-import           Diagrams.Coordinates
-import           Diagrams.CubicSpline
-import           Diagrams.Envelope
-import           Diagrams.Located
-import           Diagrams.Names
-import           Diagrams.Parametric
-import           Diagrams.Parametric.Adjust
-import           Diagrams.Path
-import           Diagrams.Points
-import           Diagrams.Query
-import           Diagrams.Segment
-import           Diagrams.Tangent
-import           Diagrams.Trace
-import           Diagrams.Trail
-import           Diagrams.TrailLike
-import           Diagrams.Transform
-import           Diagrams.ThreeD
-import           Diagrams.Util
-
-import           Control.Applicative
-import           Data.Active
-import           Data.AffineSpace
-import           Data.Colour                hiding (AffineSpace (..), atop, over)
-import           Data.Colour.Names          hiding (tan)
-import           Data.Semigroup
-import           Data.VectorSpace           hiding (Sum (..))
-import           Control.Lens               ((&), (.~), (%~))
diff --git a/src/Diagrams/Query.hs b/src/Diagrams/Query.hs
--- a/src/Diagrams/Query.hs
+++ b/src/Diagrams/Query.hs
@@ -1,3 +1,7 @@
+{-# LANGUAGE FlexibleContexts       #-}
+{-# LANGUAGE FlexibleInstances      #-}
+{-# LANGUAGE FunctionalDependencies #-}
+{-# LANGUAGE MultiParamTypeClasses  #-}
 -----------------------------------------------------------------------------
 -- |
 -- Module      :  Diagrams.Query
@@ -12,8 +16,78 @@
 -----------------------------------------------------------------------------
 
 module Diagrams.Query
-    ( Query(..), query, sample, value, resetValue, clearValue
+  ( -- * Queries
+    Query(..)
+  , HasQuery (..)
+  , sample
+  , inquire
 
-    ) where
+    -- ** Queries on diagrams
+  , query
+  , value
+  , resetValue
+  , clearValue
+  ) where
 
+import           Data.Monoid
+
 import           Diagrams.Core
+
+-- | Types which can answer a 'Query' about points inside the geometric
+--   object.
+--
+--   If @t@ and @m@ are both a 'Semigroup's, 'getQuery' should satisfy
+--
+-- @
+-- 'getQuery' (t1 <> t2) = 'getQuery' t1 <> 'getQuery' t2
+-- @
+class HasQuery t m | t -> m where
+  -- | Extract the query of an object.
+  getQuery :: t -> Query (V t) (N t) m
+
+instance HasQuery (Query v n m) m where
+  getQuery = id
+
+instance Monoid m => HasQuery (QDiagram b v n m) m where
+  getQuery = query
+
+-- | Test if a point is not equal to 'mempty'.
+--
+-- @
+-- 'inquire' :: 'QDiagram' b v n 'Any' -> 'Point' v n -> 'Bool'
+-- 'inquire' :: 'Query' v n 'Any'      -> 'Point' v n -> 'Bool'
+-- 'inquire' :: 'Diagrams.BoundingBox.BoundingBox' v n  -> 'Point' v n -> 'Bool'
+-- @
+inquire :: HasQuery t Any => t -> Point (V t) (N t) -> Bool
+inquire t = getAny . sample t
+
+-- | Sample a diagram's query function at a given point.
+--
+-- @
+-- 'sample' :: 'QDiagram' b v n m -> 'Point' v n -> m
+-- 'sample' :: 'Query' v n m      -> 'Point' v n -> m
+-- 'sample' :: 'Diagrams.BoundingBox.BoundingBox' v n  -> 'Point' v n -> 'Any'
+-- 'sample' :: 'Diagrams.Path.Path' 'V2' 'Double'   -> 'Point' v n -> 'Diagrams.TwoD.Path.Crossings'
+-- @
+sample :: HasQuery t m => t -> Point (V t) (N t) -> m
+sample = runQuery . getQuery
+
+-- | Set the query value for 'True' points in a diagram (/i.e./ points
+--   \"inquire\" the diagram); 'False' points will be set to 'mempty'.
+value :: Monoid m => m -> QDiagram b v n Any -> QDiagram b v n m
+value m = fmap fromAny
+  where fromAny (Any True)  = m
+        fromAny (Any False) = mempty
+
+-- | Reset the query values of a diagram to @True@/@False@: any values
+--   equal to 'mempty' are set to 'False'; any other values are set to
+--   'True'.
+resetValue :: (Eq m, Monoid m) => QDiagram b v n m -> QDiagram b v n Any
+resetValue = fmap toAny
+  where toAny m | m == mempty = Any False
+                | otherwise   = Any True
+
+-- | Set all the query values of a diagram to 'False'.
+clearValue :: QDiagram b v n m -> QDiagram b v n Any
+clearValue = fmap (const (Any False))
+
diff --git a/src/Diagrams/Segment.hs b/src/Diagrams/Segment.hs
--- a/src/Diagrams/Segment.hs
+++ b/src/Diagrams/Segment.hs
@@ -1,3 +1,4 @@
+{-# LANGUAGE ConstraintKinds #-}
 {-# LANGUAGE BangPatterns               #-}
 {-# LANGUAGE DeriveFunctor              #-}
 {-# LANGUAGE EmptyDataDecls             #-}
@@ -11,7 +12,6 @@
 {-# LANGUAGE TypeFamilies               #-}
 {-# LANGUAGE TypeOperators              #-}
 {-# LANGUAGE UndecidableInstances       #-}
-{-# LANGUAGE ViewPatterns               #-}
 
 -----------------------------------------------------------------------------
 -- |
@@ -42,15 +42,17 @@
 
          -- * Segment offsets
 
-       , Offset(..), segOffset
+       , Offset(..) , segOffset
 
          -- * Constructing and modifying segments
 
-       , Segment(..), straight, bezier3, bézier3, reverseSegment
+       , Segment(..), straight, bezier3, bézier3, reverseSegment, mapSegmentVectors
+       , openLinear, openCubic
 
          -- * Fixed (absolutely located) segments
        , FixedSegment(..)
        , mkFixedSeg, fromFixedSeg
+       , fixedSegIso
 
          -- * Segment measures
          -- $segmeas
@@ -64,21 +66,26 @@
 
        ) where
 
-import           Control.Lens (makeLenses, Wrapped(..), Rewrapped, iso, op)
-import           Control.Applicative (liftA2)
-import           Data.AffineSpace
+import           Control.Lens              hiding (at, transform)
 import           Data.FingerTree
 import           Data.Monoid.MList
 import           Data.Semigroup
-import           Data.VectorSpace    hiding (Sum (..))
-import           Numeric.Interval.Kaucher    (Interval (..))
-import qualified Numeric.Interval.Kaucher    as I
+import           Numeric.Interval.Kaucher  (Interval (..))
+import qualified Numeric.Interval.Kaucher  as I
 
-import           Diagrams.Core
+import           Linear.Affine
+import           Linear.Metric
+import           Linear.Vector             hiding (lerp)
+import           Linear.Vector.Compat      (lerp)
+
+import           Control.Applicative
+import           Diagrams.Core             hiding (Measured)
 import           Diagrams.Located
 import           Diagrams.Parametric
-import           Diagrams.Solve
+import           Diagrams.Solve.Polynomial
 
+import           Data.Serialize            (Serialize)
+import qualified Data.Serialize            as Serialize
 
 ------------------------------------------------------------
 --  Open/closed type tags  ---------------------------------
@@ -102,23 +109,35 @@
 --   the context, /i.e./ its endpoint is not fixed.  The offset for a
 --   /closed/ segment is stored explicitly, /i.e./ its endpoint is at
 --   a fixed offset from its start.
-data Offset c v where
-  OffsetOpen   :: Offset Open v
-  OffsetClosed :: !v -> Offset Closed v
+data Offset c v n where
+  OffsetOpen   :: Offset Open v n
+  OffsetClosed :: v n -> Offset Closed v n
 
-deriving instance Show v => Show (Offset c v)
-deriving instance Eq   v => Eq   (Offset c v)
-deriving instance Ord  v => Ord  (Offset c v)
+deriving instance Show (v n) => Show (Offset c v n)
+deriving instance Eq   (v n) => Eq   (Offset c v n)
+deriving instance Ord  (v n) => Ord  (Offset c v n)
 
-instance Functor (Offset c) where
+instance Functor v => Functor (Offset c v) where
   fmap _ OffsetOpen       = OffsetOpen
-  fmap f (OffsetClosed v) = OffsetClosed (f v)
+  fmap f (OffsetClosed v) = OffsetClosed (fmap f v)
 
-type instance V (Offset c v) = v
+instance Each (Offset c v n) (Offset c v' n') (v n) (v' n') where
+  each f (OffsetClosed v) = OffsetClosed <$> f v
+  each _ OffsetOpen       = pure OffsetOpen
+  {-# INLINE each #-}
 
-instance HasLinearMap v => Transformable (Offset c v) where
-  transform = fmap . apply
+-- | Reverses the direction of closed offsets.
+instance (Additive v, Num n) => Reversing (Offset c v n) where
+  reversing (OffsetClosed off) = OffsetClosed $ negated off
+  reversing a@OffsetOpen       = a
 
+type instance V (Offset c v n) = v
+type instance N (Offset c v n) = n
+
+instance Transformable (Offset c v n) where
+  transform _ OffsetOpen       = OffsetOpen
+  transform t (OffsetClosed v) = OffsetClosed (apply t v)
+
 ------------------------------------------------------------
 --  Constructing segments  ---------------------------------
 ------------------------------------------------------------
@@ -130,34 +149,62 @@
 --   \"location\" and are unaffected by translations.  They are,
 --   however, affected by other transformations such as rotations and
 --   scales.
-data Segment c v
-    = Linear !(Offset c v)
+data Segment c v n
+    = Linear !(Offset c v n)
       -- ^ A linear segment with given offset.
 
-    | Cubic !v !v !(Offset c v)
+    | Cubic !(v n) !(v n) !(Offset c v n)
       -- ^ A cubic Bézier segment specified by
       --   three offsets from the starting
       --   point to the first control point,
       --   second control point, and ending
       --   point, respectively.
 
-  deriving (Show, Functor, Eq, Ord)
+  deriving (Functor, Eq, Ord)
 
+instance Show (v n) => Show (Segment c v n) where
+  showsPrec d seg = case seg of
+    Linear (OffsetClosed v)       -> showParen (d > 10) $
+      showString "straight " . showsPrec 11 v
+    Cubic v1 v2 (OffsetClosed v3) -> showParen (d > 10) $
+      showString "bézier3  " . showsPrec 11 v1 . showChar ' '
+                             . showsPrec 11 v2 . showChar ' '
+                             . showsPrec 11 v3
+    Linear OffsetOpen             -> showString "openLinear"
+    Cubic v1 v2 OffsetOpen        -> showParen (d > 10) $
+      showString "openCubic " . showsPrec 11 v1 . showChar ' '
+                              . showsPrec 11 v2
+
+
+instance Each (Segment c v n) (Segment c v' n') (v n) (v' n') where
+  each f (Linear offset)      = Linear <$> each f offset
+  each f (Cubic v1 v2 offset) = Cubic  <$> f v1 <*> f v2 <*> each f offset
+  {-# INLINE each #-}
+
+-- | Reverse the direction of a segment.
+instance (Additive v, Num n) => Reversing (Segment Closed v n) where
+  reversing = reverseSegment
+
+-- | Map over the vectors of each segment.
+mapSegmentVectors :: (v n -> v' n') -> Segment c v n -> Segment c v' n'
+mapSegmentVectors = over each
+
 -- Note, can't yet have Haddock comments on GADT constructors; see
 -- http://trac.haskell.org/haddock/ticket/43. For now we don't need
 -- Segment to be a GADT but we might in the future. (?)
 
-type instance V (Segment c v) = v
+type instance V (Segment c v n) = v
+type instance N (Segment c v n) = n
 
-instance HasLinearMap v => Transformable (Segment c v) where
-  transform = fmap . apply
+instance Transformable (Segment c v n) where
+  transform = mapSegmentVectors . apply
 
-instance HasLinearMap v => Renderable (Segment c v) NullBackend where
+instance Renderable (Segment c v n) NullBackend where
   render _ _ = mempty
 
 -- | @'straight' v@ constructs a translationally invariant linear
 --   segment with direction and length given by the vector @v@.
-straight :: v -> Segment Closed v
+straight :: v n -> Segment Closed v n
 straight = Linear . OffsetClosed
 
 -- Note, if we didn't have a Linear constructor we could also create
@@ -169,40 +216,50 @@
 --   Bézier curve where the offsets from the first endpoint to the
 --   first and second control point and endpoint are respectively
 --   given by @c1@, @c2@, and @x@.
-bezier3 :: v -> v -> v -> Segment Closed v
+bezier3 :: v n -> v n -> v n -> Segment Closed v n
 bezier3 c1 c2 x = Cubic c1 c2 (OffsetClosed x)
 
 -- | @bézier3@ is the same as @bezier3@, but with more snobbery.
-bézier3 :: v -> v -> v -> Segment Closed v
+bézier3 :: v n -> v n -> v n -> Segment Closed v n
 bézier3 = bezier3
 
-type instance Codomain (Segment Closed v) = v
+type instance Codomain (Segment Closed v n) = v
 
 -- | 'atParam' yields a parametrized view of segments as continuous
 --   functions @[0,1] -> v@, which give the offset from the start of
 --   the segment for each value of the parameter between @0@ and @1@.
 --   It is designed to be used infix, like @seg ``atParam`` 0.5@.
-instance (VectorSpace v, Num (Scalar v)) => Parametric (Segment Closed v) where
+instance (Additive v, Num n) => Parametric (Segment Closed v n) where
   atParam (Linear (OffsetClosed x)) t       = t *^ x
   atParam (Cubic c1 c2 (OffsetClosed x2)) t =     (3 * t'*t'*t ) *^ c1
                                               ^+^ (3 * t'*t *t ) *^ c2
                                               ^+^ (    t *t *t ) *^ x2
     where t' = 1-t
 
-instance Num (Scalar v) => DomainBounds (Segment Closed v)
+instance Num n => DomainBounds (Segment Closed v n)
 
-instance (VectorSpace v, Num (Scalar v)) => EndValues (Segment Closed v) where
-  atStart                            = const zeroV
+instance (Additive v, Num n) => EndValues (Segment Closed v n) where
+  atStart                            = const zero
   atEnd (Linear (OffsetClosed v))    = v
   atEnd (Cubic _ _ (OffsetClosed v)) = v
 
 -- | Compute the offset from the start of a segment to the
 --   end.  Note that in the case of a Bézier segment this is /not/ the
 --   same as the length of the curve itself; for that, see 'arcLength'.
-segOffset :: Segment Closed v -> v
+segOffset :: Segment Closed v n -> v n
 segOffset (Linear (OffsetClosed v))    = v
 segOffset (Cubic _ _ (OffsetClosed v)) = v
 
+-- | An open linear segment. This means the trail makes a straight line
+-- from the last segment the beginning to form a loop.
+openLinear :: Segment Open v n
+openLinear = Linear OffsetOpen
+
+-- | An open cubic segment. This means the trail makes a cubic bézier
+-- with control vectors @v1@ and @v2@ to form a loop.
+openCubic :: v n -> v n -> Segment Open v n
+openCubic v1 v2 = Cubic v1 v2 OffsetOpen
+
 ------------------------------------------------------------
 --  Computing segment envelope  ------------------------------
 ------------------------------------------------------------
@@ -230,63 +287,68 @@
 -}
 
 -- | The envelope for a segment is based at the segment's start.
-instance (InnerSpace v, OrderedField (Scalar v)) => Enveloped (Segment Closed v) where
+instance (Metric v, OrderedField n) => Enveloped (Segment Closed v n) where
 
   getEnvelope (s@(Linear {})) = mkEnvelope $ \v ->
-    maximum (map (\t -> ((s `atParam` t) <.> v)) [0,1]) / magnitudeSq v
+    maximum (map (\t -> (s `atParam` t) `dot` v) [0,1]) / quadrance v
 
   getEnvelope (s@(Cubic c1 c2 (OffsetClosed x2))) = mkEnvelope $ \v ->
     maximum .
-    map (\t -> ((s `atParam` t) <.> v) / magnitudeSq v) $
+    map (\t -> ((s `atParam` t) `dot` v) / quadrance v) $
     [0,1] ++
     filter (liftA2 (&&) (>0) (<1))
-      (quadForm (3 * ((3 *^ c1 ^-^ 3 *^ c2 ^+^ x2) <.> v))
-                (6 * (((-2) *^ c1 ^+^ c2) <.> v))
-                ((3 *^ c1) <.> v))
+      (quadForm (3 * ((3 *^ c1 ^-^ 3 *^ c2 ^+^ x2) `dot` v))
+                (6 * (((-2) *^ c1 ^+^ c2) `dot` v))
+                ((3 *^ c1) `dot` v))
 
 ------------------------------------------------------------
 --  Manipulating segments
 ------------------------------------------------------------
 
-instance (VectorSpace v, Fractional (Scalar v)) => Sectionable (Segment Closed v) where
+instance (Additive v, Fractional n) => Sectionable (Segment Closed v n) where
   splitAtParam (Linear (OffsetClosed x1)) t = (left, right)
     where left  = straight p
           right = straight (x1 ^-^ p)
-          p = lerp zeroV x1 t
+          p = lerp t zero x1
   splitAtParam (Cubic c1 c2 (OffsetClosed x2)) t = (left, right)
     where left  = bezier3 a b e
           right = bezier3 (c ^-^ e) (d ^-^ e) (x2 ^-^ e)
-          p = lerp c1    c2 t
-          a = lerp zeroV c1 t
-          b = lerp a     p  t
-          d = lerp c2    x2 t
-          c = lerp p     d  t
-          e = lerp b     c  t
+          p = lerp t c1 c2
+          a = lerp t zero c1
+          b = lerp t a p
+          d = lerp t c2 x2
+          c = lerp t p d
+          e = lerp t b c
 
   reverseDomain = reverseSegment
 
 -- | Reverse the direction of a segment.
-reverseSegment :: AdditiveGroup v => Segment Closed v -> Segment Closed v
-reverseSegment (Linear (OffsetClosed v))       = straight (negateV v)
-reverseSegment (Cubic c1 c2 (OffsetClosed x2)) = bezier3 (c2 ^-^ x2) (c1 ^-^ x2) (negateV x2)
+reverseSegment :: (Num n, Additive v) => Segment Closed v n -> Segment Closed v n
+reverseSegment (Linear (OffsetClosed v))       = straight (negated v)
+reverseSegment (Cubic c1 c2 (OffsetClosed x2)) = bezier3 (c2 ^-^ x2) (c1 ^-^ x2) (negated x2)
 
-instance (InnerSpace v, Floating (Scalar v), Ord (Scalar v), AdditiveGroup v)
-      => HasArcLength (Segment Closed v) where
+-- Imitates I.elem for intervals<0.8 and I.member for intervals>=0.8
+member :: Ord a => a -> I.Interval a -> Bool
+member x (I.I a b) = x >= a && x <= b
+{-# INLINE member #-}
 
-  arcLengthBounded _ (Linear (OffsetClosed x1)) = I.singleton $ magnitude x1
+instance (Metric v, OrderedField n)
+      => HasArcLength (Segment Closed v n) where
+
+  arcLengthBounded _ (Linear (OffsetClosed x1)) = I.singleton $ norm x1
   arcLengthBounded m s@(Cubic c1 c2 (OffsetClosed x2))
     | ub - lb < m = I lb ub
     | otherwise   = arcLengthBounded (m/2) l + arcLengthBounded (m/2) r
    where (l,r) = s `splitAtParam` 0.5
-         ub    = sum (map magnitude [c1, c2 ^-^ c1, x2 ^-^ c2])
-         lb    = magnitude x2
+         ub    = sum (map norm [c1, c2 ^-^ c1, x2 ^-^ c2])
+         lb    = norm x2
 
   arcLengthToParam m s _ | arcLength m s == 0 = 0.5
   arcLengthToParam m s@(Linear {}) len = len / arcLength m s
   arcLengthToParam m s@(Cubic {})  len
-    | len `I.elem` (I (-m/2) (m/2)) = 0
+    | len `member` I (-m/2) (m/2) = 0
     | len < 0              = - arcLengthToParam m (fst (splitAtParam s (-1))) (-len)
-    | len `I.elem` slen    = 1
+    | len `member` slen    = 1
     | len > I.sup slen     = 2 * arcLengthToParam m (fst (splitAtParam s 2)) len
     | len < I.sup llen     = (*0.5) $ arcLengthToParam m l len
     | otherwise            = (+0.5) . (*0.5)
@@ -308,39 +370,30 @@
 --   (Segment Closed v)@, as witnessed by 'mkFixedSeg' and
 --   'fromFixedSeg', but @FixedSegment@ is convenient when one needs
 --   the absolute locations of the vertices and control points.
-data FixedSegment v = FLinear (Point v) (Point v)
-                    | FCubic (Point v) (Point v) (Point v) (Point v)
-  deriving Show
+data FixedSegment v n = FLinear (Point v n) (Point v n)
+                      | FCubic (Point v n) (Point v n) (Point v n) (Point v n)
+  deriving (Eq, Ord, Show)
 
-type instance V (FixedSegment v) = v
+type instance V (FixedSegment v n) = v
+type instance N (FixedSegment v n) = n
 
-instance HasLinearMap v => Transformable (FixedSegment v) where
-  transform t (FLinear p1 p2)
-    = FLinear
-      (transform t p1)
-      (transform t p2)
+instance Each (FixedSegment v n) (FixedSegment v' n') (Point v n) (Point v' n') where
+  each f (FLinear p0 p1)      = FLinear <$> f p0 <*> f p1
+  each f (FCubic p0 p1 p2 p3) = FCubic  <$> f p0 <*> f p1 <*> f p2 <*> f p3
+  {-# INLINE each #-}
 
-  transform t (FCubic p1 c1 c2 p2)
-    = FCubic
-      (transform t p1)
-      (transform t c1)
-      (transform t c2)
-      (transform t p2)
+-- | Reverses the control points.
+instance Reversing (FixedSegment v n) where
+  reversing (FLinear p0 p1)      = FLinear p1 p0
+  reversing (FCubic p0 p1 p2 p3) = FCubic p3 p2 p1 p0
 
-instance VectorSpace v => HasOrigin (FixedSegment v) where
-  moveOriginTo o (FLinear p1 p2)
-    = FLinear
-      (moveOriginTo o p1)
-      (moveOriginTo o p2)
+instance (Additive v, Num n) => Transformable (FixedSegment v n) where
+  transform t = over each (papply t)
 
-  moveOriginTo o (FCubic p1 c1 c2 p2)
-    = FCubic
-      (moveOriginTo o p1)
-      (moveOriginTo o c1)
-      (moveOriginTo o c2)
-      (moveOriginTo o p2)
+instance (Additive v, Num n) => HasOrigin (FixedSegment v n) where
+  moveOriginTo o = over each (moveOriginTo o)
 
-instance (InnerSpace v, OrderedField (Scalar v)) => Enveloped (FixedSegment v) where
+instance (Metric v, OrderedField n) => Enveloped (FixedSegment v n) where
   getEnvelope f = moveTo p (getEnvelope s)
     where (p, s) = viewLoc $ fromFixedSeg f
 
@@ -349,57 +402,67 @@
     -- Envelope, and implement the Segment instance in terms of it,
     -- instead of the other way around
 
+instance (Metric v, OrderedField n)
+      => HasArcLength (FixedSegment v n) where
+  arcLengthBounded m s = arcLengthBounded m (fromFixedSeg s)
+  arcLengthToParam m s = arcLengthToParam m (fromFixedSeg s)
+
 -- | Create a 'FixedSegment' from a located 'Segment'.
-mkFixedSeg :: AdditiveGroup v => Located (Segment Closed v) -> FixedSegment v
+mkFixedSeg :: (Num n, Additive v) => Located (Segment Closed v n) -> FixedSegment v n
 mkFixedSeg ls =
   case viewLoc ls of
     (p, Linear (OffsetClosed v))       -> FLinear p (p .+^ v)
     (p, Cubic c1 c2 (OffsetClosed x2)) -> FCubic  p (p .+^ c1) (p .+^ c2) (p .+^ x2)
 
 -- | Convert a 'FixedSegment' back into a located 'Segment'.
-fromFixedSeg :: AdditiveGroup v => FixedSegment v -> Located (Segment Closed v)
+fromFixedSeg :: (Num n, Additive v) => FixedSegment v n -> Located (Segment Closed v n)
 fromFixedSeg (FLinear p1 p2)      = straight (p2 .-. p1) `at` p1
 fromFixedSeg (FCubic x1 c1 c2 x2) = bezier3 (c1 .-. x1) (c2 .-. x1) (x2 .-. x1) `at` x1
 
-type instance Codomain (FixedSegment v) = Point v
+-- | Use a 'FixedSegment' to make an 'Iso' between an
+-- a fixed segment and a located segment.
+fixedSegIso :: (Num n, Additive v) => Iso' (FixedSegment v n) (Located (Segment Closed v n))
+fixedSegIso = iso fromFixedSeg mkFixedSeg
 
-instance VectorSpace v => Parametric (FixedSegment v) where
-  atParam (FLinear p1 p2) t = alerp p1 p2 t
+type instance Codomain (FixedSegment v n) = Point v
+
+instance (Additive v, Num n) => Parametric (FixedSegment v n) where
+  atParam (FLinear p1 p2) t = lerp t p1 p2
   atParam (FCubic x1 c1 c2 x2) t = p3
-    where p11 = alerp x1 c1 t
-          p12 = alerp c1 c2 t
-          p13 = alerp c2 x2 t
+    where p11 = lerp t x1 c1
+          p12 = lerp t c1 c2
+          p13 = lerp t c2 x2
 
-          p21 = alerp p11 p12 t
-          p22 = alerp p12 p13 t
+          p21 = lerp t p11 p12
+          p22 = lerp t p12 p13
 
-          p3  = alerp p21 p22 t
+          p3  = lerp t p21 p22
 
-instance Num (Scalar v) => DomainBounds (FixedSegment v)
+instance Num n => DomainBounds (FixedSegment v n)
 
-instance (VectorSpace v, Num (Scalar v)) => EndValues (FixedSegment v) where
+instance (Additive v, Num n) => EndValues (FixedSegment v n) where
   atStart (FLinear p0 _)     = p0
   atStart (FCubic  p0 _ _ _) = p0
   atEnd   (FLinear _ p1)     = p1
   atEnd   (FCubic _ _ _ p1 ) = p1
 
-instance (VectorSpace v, Fractional (Scalar v)) => Sectionable (FixedSegment v) where
+instance (Additive v, Fractional n) => Sectionable (FixedSegment v n) where
   splitAtParam (FLinear p0 p1) t = (left, right)
     where left  = FLinear p0 p
           right = FLinear p  p1
-          p = alerp p0 p1 t
+          p = lerp t p0 p1
   splitAtParam (FCubic p0 c1 c2 p1) t = (left, right)
     where left  = FCubic p0 a b cut
           right = FCubic cut c d p1
           -- first round
-          a   = alerp p0 c1 t
-          p   = alerp c1 c2 t
-          d   = alerp c2 p1 t
+          a   = lerp t p0 c1
+          p   = lerp t c1 c2
+          d   = lerp t c2 p1
           -- second round
-          b   = alerp a  p  t
-          c   = alerp p  d  t
+          b   = lerp t a p
+          c   = lerp t p d
           -- final round
-          cut = alerp b  c  t
+          cut = lerp t b c
 
   reverseDomain (FLinear p0 p1) = FLinear p1 p0
   reverseDomain (FCubic p0 c1 c2 p1) = FCubic p1 c2 c1 p0
@@ -417,8 +480,8 @@
   deriving (Semigroup, Monoid)
 
 instance Wrapped SegCount where
-    type Unwrapped SegCount = Sum Int
-    _Wrapped' = iso (\(SegCount x) -> x) SegCount
+  type Unwrapped SegCount = Sum Int
+  _Wrapped' = iso (\(SegCount x) -> x) SegCount
 
 instance Rewrapped SegCount SegCount
 
@@ -428,70 +491,69 @@
 --   a generic arc length function taking the tolerance as an
 --   argument.
 
-newtype ArcLength v
-  = ArcLength (Sum (Interval (Scalar v)), Scalar v -> Sum (Interval (Scalar v)))
+newtype ArcLength n
+  = ArcLength (Sum (Interval n), n -> Sum (Interval n))
 
-instance Wrapped (ArcLength v) where
-    type Unwrapped (ArcLength v) =
-        (Sum (Interval (Scalar v)), Scalar v -> Sum (Interval (Scalar v)))
-    _Wrapped' = iso (\(ArcLength x) -> x) ArcLength
+instance Wrapped (ArcLength n) where
+  type Unwrapped (ArcLength n) = (Sum (Interval n), n -> Sum (Interval n))
+  _Wrapped' = iso (\(ArcLength x) -> x) ArcLength
 
-instance Rewrapped (ArcLength v) (ArcLength v')
+instance Rewrapped (ArcLength n) (ArcLength n')
 
 -- | Project out the cached arc length, stored together with error
 --   bounds.
-getArcLengthCached :: ArcLength v -> Interval (Scalar v)
+getArcLengthCached :: ArcLength n -> Interval n
 getArcLengthCached = getSum . fst . op ArcLength
 
 -- | Project out the generic arc length function taking the tolerance as
 --   an argument.
-getArcLengthFun :: ArcLength v -> Scalar v -> Interval (Scalar v)
+getArcLengthFun :: ArcLength n -> n -> Interval n
 getArcLengthFun = fmap getSum . snd . op ArcLength
 
 -- | Given a specified tolerance, project out the cached arc length if
 --   it is accurate enough; otherwise call the generic arc length
 --   function with the given tolerance.
-getArcLengthBounded :: (Num (Scalar v), Ord (Scalar v))
-                    => Scalar v -> ArcLength v -> Interval (Scalar v)
+getArcLengthBounded :: (Num n, Ord n)
+                    => n -> ArcLength n -> Interval n
 getArcLengthBounded eps al
   | I.width cached <= eps = cached
   | otherwise             = getArcLengthFun al eps
   where
     cached = getArcLengthCached al
-deriving instance (Num (Scalar v), Ord (Scalar v)) => Semigroup (ArcLength v)
-deriving instance (Num (Scalar v), Ord (Scalar v)) => Monoid    (ArcLength v)
+deriving instance (Num n, Ord n) => Semigroup (ArcLength n)
+deriving instance (Num n, Ord n) => Monoid    (ArcLength n)
 
 -- | A type to represent the total cumulative offset of a chain of
 --   segments.
-newtype TotalOffset v = TotalOffset v
+newtype TotalOffset v n = TotalOffset (v n)
 
-instance Wrapped (TotalOffset v) where
-    type Unwrapped (TotalOffset v) = v
-    _Wrapped' = iso (\(TotalOffset x) -> x) TotalOffset
+instance Wrapped (TotalOffset v n) where
+  type Unwrapped (TotalOffset v n) = v n
+  _Wrapped' = iso (\(TotalOffset x) -> x) TotalOffset
 
-instance Rewrapped (TotalOffset v) (TotalOffset v')
+instance Rewrapped (TotalOffset v n) (TotalOffset v' n')
 
-instance AdditiveGroup v => Semigroup (TotalOffset v) where
+instance (Num n, Additive v) => Semigroup (TotalOffset v n) where
   TotalOffset v1 <> TotalOffset v2 = TotalOffset (v1 ^+^ v2)
 
-instance AdditiveGroup v => Monoid (TotalOffset v) where
-  mempty  = TotalOffset zeroV
+instance (Num n, Additive v) => Monoid (TotalOffset v n) where
+  mempty  = TotalOffset zero
   mappend = (<>)
 
 -- | A type to represent the offset and envelope of a chain of
 --   segments.  They have to be paired into one data structure, since
 --   combining the envelopes of two consecutive chains needs to take
---   the offset of the the offset of the first into account.
-data OffsetEnvelope v = OffsetEnvelope
-  { _oeOffset   :: !(TotalOffset v)
-  , _oeEnvelope :: Envelope v
+--   the offset of the first into account.
+data OffsetEnvelope v n = OffsetEnvelope
+  { _oeOffset   :: !(TotalOffset v n)
+  , _oeEnvelope :: Envelope v n
   }
 
 makeLenses ''OffsetEnvelope
 
-instance (InnerSpace v, OrderedField (Scalar v)) => Semigroup (OffsetEnvelope v) where
+instance (Metric v, OrderedField n) => Semigroup (OffsetEnvelope v n) where
   (OffsetEnvelope o1 e1) <> (OffsetEnvelope o2 e2)
-    = let !negOff = negateV . op TotalOffset $ o1
+    = let !negOff = negated . op TotalOffset $ o1
           e2Off = moveOriginBy negOff e2
           !_unused = maybe () (\f -> f `seq` ()) $ appEnvelope e2Off
       in OffsetEnvelope
@@ -500,32 +562,75 @@
 
 -- | @SegMeasure@ collects up all the measurements over a chain of
 --   segments.
-type SegMeasure v = SegCount
-                ::: ArcLength v
-                ::: OffsetEnvelope v
-                ::: ()
+type SegMeasure v n = SegCount
+                  ::: ArcLength n
+                  ::: OffsetEnvelope v n
+                  ::: ()
   -- unfortunately we can't cache Trace, since there is not a generic
   -- instance Traced (Segment Closed v), only Traced (Segment Closed R2).
 
-instance (InnerSpace v, OrderedField (Scalar v))
-    => Measured (SegMeasure v) (SegMeasure v) where
+instance (Metric v, OrderedField n)
+    => Measured (SegMeasure v n) (SegMeasure v n) where
   measure = id
 
-instance (OrderedField (Scalar v), InnerSpace v)
-    => Measured (SegMeasure v) (Segment Closed v) where
-  measure s = (SegCount . Sum $ 1)
+instance (OrderedField n, Metric v)
+    => Measured (SegMeasure v n) (Segment Closed v n) where
+  measure s = (SegCount . Sum) 1
 
             -- cache arc length with two orders of magnitude more
             -- accuracy than standard, so we have a hope of coming out
             -- with an accurate enough total arc length for
             -- reasonable-length trails
-           *: (ArcLength $ ( Sum $ arcLengthBounded (stdTolerance/100) s
-                           , Sum . flip arcLengthBounded s
-                           )
-              )
+            *: ArcLength ( Sum $ arcLengthBounded (stdTolerance/100) s
+                         , Sum . flip arcLengthBounded s               )
 
-           *: (OffsetEnvelope
-                (TotalOffset . segOffset $ s)
-                (getEnvelope s)
-              )
-           *: ()
+            *: OffsetEnvelope (TotalOffset . segOffset $ s)
+                              (getEnvelope s)
+
+            *: ()
+
+------------------------------------------------------------
+--  Serialize instances
+------------------------------------------------------------
+
+instance (Serialize (v n)) => Serialize (Segment Open v n) where
+  {-# INLINE put #-}
+  put segment = case segment of
+    Linear OffsetOpen    -> Serialize.put True
+    Cubic v w OffsetOpen -> do
+      Serialize.put False
+      Serialize.put v
+      Serialize.put w
+
+  {-# INLINE get #-}
+  get = do
+    isLinear <- Serialize.get
+    case isLinear of
+      True  -> return (Linear OffsetOpen)
+      False -> do
+        v <- Serialize.get
+        w <- Serialize.get
+        return (Cubic v w OffsetOpen)
+
+instance (Serialize (v n)) => Serialize (Segment Closed v n) where
+  {-# INLINE put #-}
+  put segment = case segment of
+    Linear (OffsetClosed z)    -> do
+      Serialize.put z
+      Serialize.put True
+    Cubic v w (OffsetClosed z) -> do
+      Serialize.put z
+      Serialize.put False
+      Serialize.put v
+      Serialize.put w
+
+  {-# INLINE get #-}
+  get = do
+    z <- Serialize.get
+    isLinear <- Serialize.get
+    case isLinear of
+      True  -> return (Linear (OffsetClosed z))
+      False -> do
+        v <- Serialize.get
+        w <- Serialize.get
+        return (Cubic v w (OffsetClosed z))
diff --git a/src/Diagrams/Size.hs b/src/Diagrams/Size.hs
new file mode 100644
--- /dev/null
+++ b/src/Diagrams/Size.hs
@@ -0,0 +1,157 @@
+{-# LANGUAGE ConstraintKinds            #-}
+{-# LANGUAGE DeriveDataTypeable         #-}
+{-# LANGUAGE DeriveFunctor              #-}
+{-# LANGUAGE DeriveGeneric              #-}
+{-# LANGUAGE FlexibleContexts           #-}
+{-# LANGUAGE FlexibleInstances          #-}
+{-# LANGUAGE GeneralizedNewtypeDeriving #-}
+{-# LANGUAGE RankNTypes                 #-}
+{-# LANGUAGE ScopedTypeVariables        #-}
+{-# LANGUAGE TypeFamilies               #-}
+{-# LANGUAGE UndecidableInstances       #-}
+{-# LANGUAGE ViewPatterns               #-}
+
+-----------------------------------------------------------------------------
+-- |
+-- Module      :  Diagrams.Size
+-- Copyright   :  (c) 2014 diagrams-lib team (see LICENSE)
+-- License     :  BSD-style (see LICENSE)
+-- Maintainer  :  diagrams-discuss@googlegroups.com
+--
+-- Utilities for working with sizes of objects.
+--
+-----------------------------------------------------------------------------
+module Diagrams.Size
+  ( -- * Size spec
+    SizeSpec
+
+    -- ** Making size spec
+  , mkSizeSpec
+  , dims
+  , absolute
+
+    -- ** Extracting size specs
+  , getSpec
+  , specToSize
+
+    -- ** Functions on size specs
+  , requiredScale
+  , requiredScaling
+  , sized
+  , sizedAs
+  , sizeAdjustment
+  ) where
+
+import           Control.Applicative
+import           Control.Lens         hiding (transform)
+import           Control.Monad
+import           Data.Foldable        as F
+import           Data.Hashable
+import           Data.Maybe
+import           Data.Semigroup
+import           Data.Typeable
+import           GHC.Generics         (Generic)
+import           Prelude
+
+import           Diagrams.BoundingBox
+import           Diagrams.Core
+
+import           Linear.Affine
+import           Linear.Vector
+
+------------------------------------------------------------
+-- Computing diagram sizes
+------------------------------------------------------------
+
+-- | A 'SizeSpec' is a way of specifying a size without needed lengths for all
+--   the dimensions.
+newtype SizeSpec v n = SizeSpec (v n)
+  deriving (
+  Eq,
+  Typeable,
+  Functor,
+  Generic,
+  Hashable,
+  Show)
+
+type instance V (SizeSpec v n) = v
+type instance N (SizeSpec v n) = n
+
+-- | Retrieve a size spec as a vector of maybe values. Only positive sizes are
+--   returned.
+getSpec :: (Functor v, Num n, Ord n) => SizeSpec v n -> v (Maybe n)
+getSpec (SizeSpec sp) = mfilter (>0) . Just <$> sp
+
+-- | Make a 'SizeSpec' from a vector of maybe values. Any negative values will
+--   be ignored. For 2D 'SizeSpec's see 'mkWidth' and 'mkHeight' from
+--   "Diagrams.TwoD.Size".
+mkSizeSpec :: (Functor v, Num n) => v (Maybe n) -> SizeSpec v n
+mkSizeSpec = dims . fmap (fromMaybe 0)
+
+-- | Make a 'SizeSpec' from a vector. Any negative values will be ignored.
+dims :: v n -> SizeSpec v n
+dims = SizeSpec
+
+-- | A size spec with no hints to the size.
+absolute :: (Additive v, Num n) => SizeSpec v n
+absolute = SizeSpec zero
+
+-- | @specToSize n spec@ extracts a size from a 'SizeSpec' @sz@. Any values not
+--   specified in the spec are replaced by the smallest of the values that are
+--   specified. If there are no specified values (i.e. 'absolute') then @n@ is
+--   used.
+specToSize :: (Foldable v, Functor v, Num n, Ord n) => n -> SizeSpec v n -> v n
+specToSize n (getSpec -> spec) = fmap (fromMaybe smallest) spec
+  where
+    smallest = fromMaybe n $ minimumOf (folded . _Just) spec
+
+-- | @requiredScale spec sz@ returns the largest scaling factor to make
+--   something of size @sz@ fit the requested size @spec@ without changing the
+--   aspect ratio. @sz@ should be non-zero (otherwise a scale of 1 is
+--   returned). For non-uniform scaling see 'boxFit'.
+requiredScale :: (Additive v, Foldable v, Fractional n, Ord n)
+              => SizeSpec v n -> v n -> n
+requiredScale (getSpec -> spec) sz
+  | allOf (folded . _Just) (<= 0) usedSz = 1
+  | otherwise                            = fromMaybe 1 mScale
+  where
+    usedSz = liftI2 (<$) sz spec
+    scales = liftI2 (^/) spec sz
+    mScale = minimumOf (folded . _Just) scales
+
+-- | Return the 'Transformation' calcuated from 'requiredScale'.
+requiredScaling :: (Additive v, Foldable v, Fractional n, Ord n)
+  => SizeSpec v n -> v n -> Transformation v n
+requiredScaling spec = scaling . requiredScale spec
+
+-- | Uniformly scale any enveloped object so that it fits within the
+--   given size. For non-uniform scaling see 'boxFit'.
+sized :: (InSpace v n a, HasLinearMap v, Transformable a, Enveloped a)
+      => SizeSpec v n -> a -> a
+sized spec a = transform (requiredScaling spec (size a)) a
+
+-- | Uniformly scale an enveloped object so that it \"has the same
+--   size as\" (fits within the width and height of) some other
+--   object.
+sizedAs :: (InSpace v n a, SameSpace a b, HasLinearMap v, Transformable a,
+            Enveloped a, Enveloped b)
+        => b -> a -> a
+sizedAs other = sized (dims $ size other)
+
+-- | Get the adjustment to fit a 'BoundingBox' in the given 'SizeSpec'. The
+--   vector is the new size and the transformation to position the lower
+--   corner at the origin and scale to the size spec.
+sizeAdjustment :: (Additive v, Foldable v, OrderedField n)
+  => SizeSpec v n -> BoundingBox v n -> (v n, Transformation v n)
+sizeAdjustment spec bb = (sz', t)
+  where
+    v = (0.5 *^ P sz') .-. (s *^ fromMaybe origin (boxCenter bb))
+
+    sz  = boxExtents bb
+    sz' = if allOf folded isJust (getSpec spec)
+            then specToSize 0 spec
+            else s *^ sz
+
+    s = requiredScale spec sz
+
+    t = translation v <> scaling s
diff --git a/src/Diagrams/Solve.hs b/src/Diagrams/Solve.hs
deleted file mode 100644
--- a/src/Diagrams/Solve.hs
+++ /dev/null
@@ -1,187 +0,0 @@
------------------------------------------------------------------------------
--- |
--- Module      :  Diagrams.Solve
--- Copyright   :  (c) 2011 diagrams-lib team (see LICENSE)
--- License     :  BSD-style (see LICENSE)
--- Maintainer  :  diagrams-discuss@googlegroups.com
---
--- Exact solving of low-degree (n <= 4) polynomials.
---
------------------------------------------------------------------------------
-module Diagrams.Solve
-       ( quadForm
-       , cubForm
-       , quartForm
-       , cubForm'
-       , quartForm'
-       ) where
-
-import           Data.List     (maximumBy)
-import           Data.Ord      (comparing)
-
-import           Diagrams.Util (tau)
-
-import           Prelude hiding ((^))
-import qualified Prelude as P ((^))
-
--- | A specialization of (^) to Integer
---   c.f. http://comments.gmane.org/gmane.comp.lang.haskell.libraries/21164
---   for discussion. "The choice in (^) and (^^) to overload on the
---   power's Integral type... was a genuinely bad idea." - Edward Kmett
-(^) :: (Num a) => a -> Integer -> a
-(^) = (P.^)
-
--- | Utility function used to avoid singularities
-aboutZero' :: (Ord a, Num a) => a -> a -> Bool
-aboutZero' toler x = abs x < toler
-
-------------------------------------------------------------
--- Quadratic formula
-------------------------------------------------------------
-
--- | The quadratic formula.
-quadForm :: (Floating d, Ord d) => d -> d -> d -> [d]
-quadForm a b c
-
-    -- There are infinitely many solutions in this case,
-    -- so arbitrarily return 0
-  | a == 0 && b == 0 && c == 0 = [0]
-
-    -- c /= 0
-  | a == 0 && b == 0 = []
-
-    -- linear
-  | a == 0    = [-c/b]
-
-    -- no real solutions
-  | d < 0     = []
-
-    -- ax^2 + c = 0
-  | b == 0    = [sqrt (-c/a), -sqrt (-c/a)]
-
-    -- multiplicity 2 solution
-  | d == 0    = [-b/(2*a)]
-
-    -- see http://www.mpi-hd.mpg.de/astrophysik/HEA/internal/Numerical_Recipes/f5-6.pdf
-  | otherwise = [q/a, c/q]
- where d = b^2 - 4*a*c
-       q = -1/2*(b + signum b * sqrt d)
-
-_quadForm_prop :: Double -> Double -> Double -> Bool
-_quadForm_prop a b c = all (aboutZero' 1e-10 . eval) (quadForm a b c)
-  where eval x = a*x^2 + b*x + c
-
-------------------------------------------------------------
--- Cubic formula
-------------------------------------------------------------
-
--- See http://en.wikipedia.org/wiki/Cubic_formula#General_formula_of_roots
-
--- | Solve the cubic equation ax^3 + bx^2 + cx + d = 0, returning a
---   list of all real roots. First argument is tolerance.
-cubForm' :: (Floating d, Ord d) => d -> d -> d -> d -> d -> [d]
-cubForm' toler a b c d
-  | aboutZero' toler a      = quadForm b c d
-
-    -- three real roots, use trig method to avoid complex numbers
-  | delta >  0              = map trig [0,1,2]
-
-    -- one real root of multiplicity 3
-  | delta == 0 && disc == 0 = [ -b/(3*a) ]
-
-    -- two real roots, one of multiplicity 2
-  | delta == 0 && disc /= 0 = [ (b*c - 9*a*d)/(2*disc)
-                              , (9*a^2*d - 4*a*b*c + b^3)/(a * disc)
-                              ]
-
-    -- one real root (and two complex)
-  | otherwise               = [-b/(3*a) - cc/(3*a) + disc/(3*a*cc)]
-
- where delta  = 18*a*b*c*d - 4*b^3*d + b^2*c^2 - 4*a*c^3 - 27*a^2*d^2
-       disc   = 3*a*c - b^2
-       qq     = sqrt(-27*(a^2)*delta)
-       qq'    | aboutZero' toler disc = maximumBy (comparing (abs . (+xx))) [qq, -qq]
-              | otherwise = qq
-       cc     = cubert (1/2*(qq' + xx))
-       xx     = 2*b^3 - 9*a*b*c + 27*a^2*d
-       p      = disc/(3*a^2)
-       q      = xx/(27*a^3)
-       phi = 1/3*acos(3*q/(2*p)*sqrt(-3/p))
-       trig k = 2 * sqrt(-p/3) * cos(phi - k*tau/3) - b/(3*a)
-       cubert x | x < 0     = -((-x)**(1/3))
-                | otherwise = x**(1/3)
-
--- | Solve the cubic equation ax^3 + bx^2 + cx + d = 0, returning a
---   list of all real roots within 1e-10 tolerance
---   (although currently it's closer to 1e-5)
-cubForm :: (Floating d, Ord d) => d -> d -> d -> d -> [d]
-cubForm = cubForm' 1e-10
-
-_cubForm_prop :: Double -> Double -> Double -> Double -> Bool
-_cubForm_prop a b c d = all (aboutZero' 1e-5 . eval) (cubForm a b c d)
-  where eval x = a*x^3 + b*x^2 + c*x + d
-           -- Basically, however large you set the tolerance it seems
-           -- that quickcheck can always come up with examples where
-           -- the returned solutions evaluate to something near zero
-           -- but larger than the tolerance (but it takes it more
-           -- tries the larger you set the tolerance). Wonder if this
-           -- is an inherent limitation or (more likely) a problem
-           -- with numerical stability.  If this turns out to be an
-           -- issue in practice we could, say, use the solutions
-           -- generated here as very good guesses to a numerical
-           -- solver which can give us a more precise answer?
-           
-------------------------------------------------------------
--- Quartic formula
-------------------------------------------------------------
-
--- Based on http://tog.acm.org/resources/GraphicsGems/gems/Roots3b/and4.c
--- as of 5/12/14, with help from http://en.wikipedia.org/wiki/Quartic_function
-
--- | Solve the quartic equation c4 x^4 + c3 x^3 + c2 x^2 + c1 x + c0 = 0, returning a
---   list of all real roots. First argument is tolerance.
-quartForm' :: (Floating d, Ord d) => d -> d -> d -> d -> d -> d -> [d]
-quartForm' toler c4 c3 c2 c1 c0
-  -- obvious cubic
-  | aboutZero' toler c4 = cubForm c3 c2 c1 c0
-  -- x(ax^3+bx^2+cx+d)
-  | aboutZero' toler c0 = 0 : cubForm c4 c3 c2 c1
-  -- substitute solutions of y back to x
-  | otherwise = map (\x->x-(a/4)) roots
-    where
-      -- eliminate c4: x^4+ax^3+bx^2+cx+d
-      [a,b,c,d] = map (/c4) [c3,c2,c1,c0]
-      -- eliminate cubic term via x = y - a/4
-      -- reduced quartic: y^4 + py^2 + qy + r = 0
-      p = b - 3/8*a^2
-      q = 1/8*a^3-a*b/2+c
-      r = (-3/256)*a^4+a^2*b/16-a*c/4+d
-
-      -- | roots of the reduced quartic
-      roots | aboutZero' toler r =
-                0 : cubForm 1 0 p q   -- no constant term: y(y^3 + py + q) = 0
-            | u < 0 || v < 0 = []     -- no real solutions due to square root
-            | otherwise      = s1++s2 -- solutions of the quadratics
-
-      -- solve the resolvent cubic - only one solution is needed
-      z:_ = cubForm 1 (-p/2) (-r) (p*r/2 - q^2/8)
-      
-      -- solve the two quadratic equations
-      -- y^2 ± v*y-(±u-z)
-      u = z^2 - r
-      v = 2*z - p
-      u' = if aboutZero' toler u then 0 else sqrt u
-      v' = if aboutZero' toler v then 0 else sqrt v
-      s1 = quadForm 1 (if q<0 then -v' else v') (z-u')
-      s2 = quadForm 1 (if q<0 then v' else -v') (z+u')
-
--- | Solve the quartic equation c4 x^4 + c3 x^3 + c2 x^2 + c1 x + c0 = 0, returning a
---   list of all real roots within 1e-10 tolerance
---   (although currently it's closer to 1e-5)
-quartForm :: (Floating d, Ord d) => d -> d -> d -> d -> d -> [d]
-quartForm = quartForm' 1e-10
-
-_quartForm_prop :: Double -> Double -> Double -> Double -> Double -> Bool
-_quartForm_prop a b c d e = all (aboutZero' 1e-5 . eval) (quartForm a b c d e)
-  where eval x = a*x^4 + b*x^3 + c*x^2 + d*x + e
-           -- Same note about tolerance as for cubic
diff --git a/src/Diagrams/Tangent.hs b/src/Diagrams/Tangent.hs
--- a/src/Diagrams/Tangent.hs
+++ b/src/Diagrams/Tangent.hs
@@ -1,6 +1,7 @@
+{-# LANGUAGE ConstraintKinds #-}
+{-# LANGUAGE GADTs                #-} -- for ghc < 7.8, TypeFamilies covers GADT patten mathcing in > 7.8
 {-# LANGUAGE FlexibleContexts     #-}
 {-# LANGUAGE FlexibleInstances    #-}
-{-# LANGUAGE GADTs                #-}
 {-# LANGUAGE TypeFamilies         #-}
 {-# LANGUAGE UndecidableInstances #-}
 
@@ -15,27 +16,30 @@
 --
 -----------------------------------------------------------------------------
 module Diagrams.Tangent
-    ( tangentAtParam
+    ( -- ** Tangents
+      tangentAtParam
     , tangentAtStart
     , tangentAtEnd
+
+      -- ** Normals
     , normalAtParam
     , normalAtStart
     , normalAtEnd
+
+      -- ** Tangent newtype
     , Tangent(..)
     )
     where
 
-import           Control.Lens         (cloneIso, (^.))
-
-import           Data.VectorSpace
 import           Diagrams.Core
 import           Diagrams.Located
 import           Diagrams.Parametric
 import           Diagrams.Segment
-import           Diagrams.Trail
-import           Diagrams.TwoD.Types  (R2)
-import           Diagrams.TwoD.Vector (perp)
 
+import           Linear.Vector
+import           Linear.Metric
+import           Linear.V2
+
 ------------------------------------------------------------
 -- Tangent
 ------------------------------------------------------------
@@ -45,13 +49,13 @@
 newtype Tangent t = Tangent t
 
 type instance V (Tangent t) = V t
+type instance N (Tangent t) = N t
+type instance Codomain (Tangent t) = V t
 
 instance DomainBounds t => DomainBounds (Tangent t) where
   domainLower (Tangent t) = domainLower t
   domainUpper (Tangent t) = domainUpper t
 
-type instance Codomain (Tangent (Located t)) = Codomain (Tangent t)
-
 instance Parametric (Tangent t) => Parametric (Tangent (Located t)) where
   Tangent l `atParam` p = Tangent (unLoc l) `atParam` p
 
@@ -65,92 +69,48 @@
 --
 --   Examples of more specific types this function can have include
 --
---   * @Segment Closed R2 -> Double -> R2@
+--   * @Segment Closed V2 -> Double -> V2 Double@
 --
---   * @Trail' Line R2 -> Double -> R2@
+--   * @Trail' Line V2 -> Double -> V2 Double@
 --
---   * @Located (Trail R2) -> Double -> R2@
+--   * @Located (Trail V2) -> Double -> V2 Double@
 --
 --   See the instances listed for the 'Tangent' newtype for more.
-tangentAtParam :: Parametric (Tangent t) => t -> Scalar (V t) -> Codomain (Tangent t)
+tangentAtParam :: Parametric (Tangent t) => t -> N t -> Vn t
 tangentAtParam t p = Tangent t `atParam` p
 
 -- | Compute the tangent vector at the start of a segment or trail.
-tangentAtStart :: EndValues (Tangent t) => t -> Codomain (Tangent t)
+tangentAtStart :: EndValues (Tangent t) => t -> Vn t
 tangentAtStart = atStart . Tangent
 
 -- | Compute the tangent vector at the end of a segment or trail.
-tangentAtEnd :: EndValues (Tangent t) => t -> Codomain (Tangent t)
+tangentAtEnd :: EndValues (Tangent t) => t -> Vn t
 tangentAtEnd = atEnd . Tangent
 
 --------------------------------------------------
 -- Segment
 
-type instance Codomain (Tangent (Segment Closed v)) = Codomain (Segment Closed v)
-
-instance (VectorSpace v, Num (Scalar v))
-    => Parametric (Tangent (Segment Closed v)) where
+instance (Additive v, Num n)
+    => Parametric (Tangent (Segment Closed v n)) where
   Tangent (Linear (OffsetClosed v)) `atParam` _ = v
   Tangent (Cubic c1 c2 (OffsetClosed x2)) `atParam` p
     = (3*(3*p*p-4*p+1))*^c1 ^+^ (3*(2-3*p)*p)*^c2 ^+^ (3*p*p)*^x2
 
-instance (VectorSpace v, Num (Scalar v))
-    => EndValues (Tangent (Segment Closed v)) where
+instance (Additive v, Num n)
+    => EndValues (Tangent (Segment Closed v n)) where
   atStart (Tangent (Linear (OffsetClosed v)))      = v
   atStart (Tangent (Cubic c1 _ _))                 = c1
   atEnd   (Tangent (Linear (OffsetClosed v)))      = v
   atEnd   (Tangent (Cubic _ c2 (OffsetClosed x2))) = x2 ^-^ c2
 
---------------------------------------------------
--- Trail' and Trail
-
-type instance Codomain (Tangent (Trail' c v)) = Codomain (Trail' c v)
-
-instance ( Parametric (GetSegment (Trail' c v))
-         , VectorSpace v
-         , Num (Scalar v)
-         )
-    => Parametric (Tangent (Trail' c v)) where
-  Tangent tr `atParam` p =
-    case GetSegment tr `atParam` p of
-      Nothing                -> zeroV
-      Just (_, seg, reparam) -> Tangent seg `atParam` (p ^. cloneIso reparam)
-
-instance ( Parametric (GetSegment (Trail' c v))
-         , EndValues (GetSegment (Trail' c v))
-         , VectorSpace v
-         , Num (Scalar v)
-         )
-    => EndValues (Tangent (Trail' c v)) where
-  atStart (Tangent tr) =
-    case atStart (GetSegment tr) of
-      Nothing          -> zeroV
-      Just (_, seg, _) -> atStart (Tangent seg)
-  atEnd (Tangent tr) =
-    case atEnd (GetSegment tr) of
-      Nothing          -> zeroV
-      Just (_, seg, _) -> atEnd (Tangent seg)
-
-type instance Codomain (Tangent (Trail v)) = Codomain (Trail v)
-
-instance ( InnerSpace v
-         , OrderedField (Scalar v)
-         , RealFrac (Scalar v)
-         )
-    => Parametric (Tangent (Trail v)) where
-  Tangent tr `atParam` p
-    = withTrail
-        ((`atParam` p) . Tangent)
-        ((`atParam` p) . Tangent)
-        tr
+instance (Additive v, Num n)
+    => Parametric (Tangent (FixedSegment v n)) where
+  atParam (Tangent fSeg) = atParam $ Tangent (fromFixedSeg fSeg)
 
-instance ( InnerSpace v
-         , OrderedField (Scalar v)
-         , RealFrac (Scalar v)
-         )
-    => EndValues (Tangent (Trail v)) where
-  atStart (Tangent tr) = withTrail (atStart . Tangent) (atStart . Tangent) tr
-  atEnd   (Tangent tr) = withTrail (atEnd   . Tangent) (atEnd   . Tangent) tr
+instance (Additive v, Num n)
+    => EndValues (Tangent (FixedSegment v n)) where
+  atStart (Tangent fSeg) = atStart $ Tangent (fromFixedSeg fSeg)
+  atEnd (Tangent fSeg)   = atEnd $ Tangent (fromFixedSeg fSeg)
 
 ------------------------------------------------------------
 -- Normal
@@ -161,30 +121,30 @@
 --
 --   Examples of more specific types this function can have include
 --
---   * @Segment Closed R2 -> Double -> R2@
+--   * @Segment Closed V2 Double -> Double -> V2 Double@
 --
---   * @Trail' Line R2 -> Double -> R2@
+--   * @Trail' Line V2 Double -> Double -> V2 Double@
 --
---   * @Located (Trail R2) -> Double -> P2@
+--   * @Located (Trail V2 Double) -> Double -> V2 Double@
 --
 --   See the instances listed for the 'Tangent' newtype for more.
 normalAtParam
-  :: (Codomain (Tangent t) ~ R2, Parametric (Tangent t))
-  => t -> Scalar (V t) -> R2
+  :: (InSpace V2 n t, Parametric (Tangent t), Floating n)
+  => t -> n -> V2 n
 normalAtParam t p = normize (t `tangentAtParam` p)
 
 -- | Compute the normal vector at the start of a segment or trail.
 normalAtStart
-  :: (Codomain (Tangent t) ~ R2, EndValues (Tangent t))
-  => t -> R2
+  :: (InSpace V2 n t, EndValues (Tangent t), Floating n)
+  => t -> V2 n
 normalAtStart = normize . tangentAtStart
 
 -- | Compute the normal vector at the end of a segment or trail.
 normalAtEnd
-  :: (Codomain (Tangent t) ~ R2, EndValues (Tangent t))
-  => t -> R2
+  :: (InSpace V2 n t, EndValues (Tangent t), Floating n)
+  => t -> V2 n
 normalAtEnd = normize . tangentAtEnd
 
 -- | Construct a normal vector from a tangent.
-normize :: R2 -> R2
-normize = negateV . perp . normalized
+normize :: Floating n => V2 n -> V2 n
+normize = negated . perp . signorm
diff --git a/src/Diagrams/ThreeD.hs b/src/Diagrams/ThreeD.hs
--- a/src/Diagrams/ThreeD.hs
+++ b/src/Diagrams/ThreeD.hs
@@ -4,7 +4,7 @@
 -----------------------------------------------------------------------------
 -- |
 -- Module      :  Diagrams.ThreeD
--- Copyright   :  (c) 2013 diagrams-lib team (see LICENSE)
+-- Copyright   :  (c) 2013-2015 diagrams-lib team (see LICENSE)
 -- License     :  BSD-style (see LICENSE)
 -- Maintainer  :  diagrams-discuss@googlegroups.com
 --
@@ -17,9 +17,11 @@
 --     diagrams, including types representing the 3D Euclidean vector
 --     space and various systems of representing directions.
 --
---   * "Diagrams.ThreeD.Transform" defines R^3-specific transformations
---     such as rotation by an angle, and scaling, translation, and
---     reflection in the X, Y, and Z directions.
+--   * "Diagrams.ThreeD.Transform" defines R^3-specific
+--     transformations such as rotation by an angle, and scaling,
+--     translation, and reflection in the X, Y, and Z directions.
+--     "Diagrams.ThreeD.Deform" defines several R^3-specific
+--     non-affine transformations, such as projections.
 --
 --   * "Diagrams.ThreeD.Shapes" defines three-dimensional solids,
 --     e.g. spheres and cubes.
@@ -29,24 +31,32 @@
 --
 --   * "Diagrams.ThreeD.Light" and "Diagrams.ThreeD.Camera" define types needed
 --     for rendering 3D geometry to (2D) images.
+--
+--   * "Diagrams.ThreeD.Align" defines many alignment combinators
+--     specialized to three dimensions.
+--
+--   * "Diagrams.ThreeD.Attributes" defines 3D-specific attributes
+--     such as surface color, diffuse reflectance, and specular
+--     highlights.
 -----------------------------------------------------------------------------
 module Diagrams.ThreeD
-       (
-         module Diagrams.ThreeD.Align
-       , module Diagrams.ThreeD.Attributes
-       , module Diagrams.ThreeD.Camera
-       , module Diagrams.ThreeD.Light
-       , module Diagrams.ThreeD.Shapes
-       , module Diagrams.ThreeD.Transform
-       , module Diagrams.ThreeD.Types
-       , module Diagrams.ThreeD.Vector
-       ) where
+  ( module Diagrams.ThreeD.Align
+  , module Diagrams.ThreeD.Attributes
+  , module Diagrams.ThreeD.Camera
+  , module Diagrams.ThreeD.Deform
+  , module Diagrams.ThreeD.Light
+  , module Diagrams.ThreeD.Shapes
+  , module Diagrams.ThreeD.Transform
+  , module Diagrams.ThreeD.Types
+  , module Diagrams.ThreeD.Vector
+  ) where
 
-import Diagrams.ThreeD.Align
-import Diagrams.ThreeD.Attributes
-import Diagrams.ThreeD.Camera
-import Diagrams.ThreeD.Light
-import Diagrams.ThreeD.Shapes
-import Diagrams.ThreeD.Transform
-import Diagrams.ThreeD.Types
-import Diagrams.ThreeD.Vector
+import           Diagrams.ThreeD.Align
+import           Diagrams.ThreeD.Attributes
+import           Diagrams.ThreeD.Camera
+import           Diagrams.ThreeD.Deform
+import           Diagrams.ThreeD.Light
+import           Diagrams.ThreeD.Shapes
+import           Diagrams.ThreeD.Transform
+import           Diagrams.ThreeD.Types
+import           Diagrams.ThreeD.Vector
diff --git a/src/Diagrams/ThreeD/Align.hs b/src/Diagrams/ThreeD/Align.hs
--- a/src/Diagrams/ThreeD/Align.hs
+++ b/src/Diagrams/ThreeD/Align.hs
@@ -1,5 +1,7 @@
-{-# LANGUAGE FlexibleContexts #-}
-{-# LANGUAGE TypeFamilies     #-}
+{-# LANGUAGE ConstraintKinds #-}
+{-# LANGUAGE TypeFamilies    #-}
+{-# LANGUAGE TypeOperators   #-}
+
 -----------------------------------------------------------------------------
 -- |
 -- Module      :  Diagrams.ThreeD.Align
@@ -44,166 +46,95 @@
 import           Diagrams.Align
 import           Diagrams.ThreeD.Types
 import           Diagrams.ThreeD.Vector
-
-import           Data.VectorSpace
+import           Diagrams.TwoD.Align
 
 -- | Translate the diagram along unitX so that all points have
--- positive x-values.
-alignXMin :: (Alignable a, HasOrigin a, V a ~ R3) => a -> a
-alignXMin = align (negateV unitX)
+--   positive x-values.
+alignXMin :: (InSpace v n a, R1 v, Fractional n, Alignable a, HasOrigin a) => a -> a
+alignXMin = align unit_X
 
-snugXMin :: (Fractional (Scalar (V a)), Alignable a, Traced a,
-      HasOrigin a, V a ~ R3) => a -> a
-snugXMin = snug (negateV unitX)
+snugXMin :: (InSpace v n a, R1 v, Fractional n, Alignable a, HasOrigin a, Traced a) => a -> a
+snugXMin = snug unit_X
 
 -- | Translate the diagram along unitX so that all points have
 -- negative x-values.
-alignXMax :: (Alignable a, HasOrigin a, V a ~ R3) => a -> a
+alignXMax :: (InSpace v n a, R1 v, Fractional n, Alignable a, HasOrigin a) => a -> a
 alignXMax = align unitX
 
-snugXMax :: (Fractional (Scalar (V a)), Alignable a, Traced a,
-      HasOrigin a, V a ~ R3) => a -> a
+snugXMax :: (InSpace v n a, R1 v, Fractional n, Alignable a, HasOrigin a, Traced a) => a -> a
 snugXMax = snug unitX
 
 
 -- | Translate the diagram along unitY so that all points have
+--   positive y-values.
+alignYMin :: (InSpace v n a, R2 v, Fractional n, Alignable a, HasOrigin a) => a -> a
+alignYMin = align unit_Y
+
+snugYMin :: (InSpace v n a, R2 v, Fractional n, Alignable a, HasOrigin a, Traced a) => a -> a
+snugYMin = snug unit_Y
+
+-- | Translate the diagram along unitY so that all points have
 -- negative y-values.
-alignYMax :: (Alignable a, HasOrigin a, V a ~ R3) => a -> a
+alignYMax :: (InSpace v n a, R2 v, Fractional n, Alignable a, HasOrigin a) => a -> a
 alignYMax = align unitY
 
--- | Move the origin along unitY until it touches the edge of the
--- diagram.
-snugYMax:: (Fractional (Scalar (V a)), Alignable a, Traced a,
-      HasOrigin a, V a ~ R3) => a -> a
+snugYMax :: (InSpace v n a, R2 v, Fractional n, Alignable a, HasOrigin a, Traced a) => a -> a
 snugYMax = snug unitY
 
--- | Translate the diagram along unitY so that all points have
--- positive y-values.
-alignYMin :: (Alignable a, HasOrigin a, V a ~ R3) => a -> a
-alignYMin = align (negateV unitY)
 
-snugYMin :: (Fractional (Scalar (V a)), Alignable a, Traced a,
-      HasOrigin a, V a ~ R3) => a -> a
-snugYMin = snug (negateV unitY)
+-- | Translate the diagram along unitZ so that all points have
+--   positive z-values.
+alignZMin :: (InSpace v n a, R3 v, Fractional n, Alignable a, HasOrigin a) => a -> a
+alignZMin = align unit_Z
 
+snugZMin :: (InSpace v n a, R3 v, Fractional n, Alignable a, HasOrigin a, Traced a) => a -> a
+snugZMin = snug unit_Z
+
 -- | Translate the diagram along unitZ so that all points have
 -- negative z-values.
-alignZMax :: (Alignable a, HasOrigin a, V a ~ R3) => a -> a
+alignZMax :: (InSpace v n a, R3 v, Fractional n, Alignable a, HasOrigin a) => a -> a
 alignZMax = align unitZ
 
--- | Move the origin along unitZ until it touches the edge of the
--- diagram.
-snugZMax:: (Fractional (Scalar (V a)), Alignable a, Traced a,
-      HasOrigin a, V a ~ R3) => a -> a
+snugZMax :: (InSpace v n a, R3 v, Fractional n, Alignable a, HasOrigin a, Traced a) => a -> a
 snugZMax = snug unitZ
 
--- | Translate the diagram along unitZ so that all points have
--- positive z-values.
-alignZMin :: (Alignable a, HasOrigin a, V a ~ R3) => a -> a
-alignZMin = align (negateV unitZ)
-
--- | Move the origin along unit_Z until it touches the edge of the
--- diagram.
-snugZMin :: (Fractional (Scalar (V a)), Alignable a, Traced a,
-      HasOrigin a, V a ~ R3) => a -> a
-snugZMin = snug (negateV unitZ)
-
--- | @alignX@ and @snugX@ move the local origin along unitX as follows:
---
---   * @alignX (-1)@ moves the local origin to the low-x of the boundary;
---
---   * @align 1@ moves the local origin to the high-x edge;
---
---   * any other argument interpolates linearly between these.  For
---     example, @alignX 0@ centers, @alignX 2@ moves the origin one
---     \"radius\" to the right of the right edge, and so on.
---
---   * @snugX@ works the same way.
-
-alignX :: (Alignable a, HasOrigin a, V a ~ R3) => Double -> a -> a
-alignX = alignBy unitX
-
--- | See the documentation for 'alignX'.
-snugX :: (Fractional (Scalar (V a)), Alignable a, Traced a,
-      HasOrigin a, V a ~ R3) => Double -> a -> a
-snugX = snugBy unitX
-
--- | Like 'alignX', but moving the local origin vertically, with an
---   argument of @1@ corresponding to the top edge and @(-1)@ corresponding
---   to the bottom edge.
-alignY :: (Alignable a, HasOrigin a, V a ~ R3) => Double -> a -> a
-alignY = alignBy unitY
-
-snugY :: (Fractional (Scalar (V a)), Alignable a, Traced a,
-      HasOrigin a, V a ~ R3) => Double -> a -> a
-snugY = snugBy unitY
-
-
 -- | Like 'alignX', but moving the local origin in the Z direction, with an
 --   argument of @1@ corresponding to the top edge and @(-1)@ corresponding
 --   to the bottom edge.
-alignZ :: (Alignable a, HasOrigin a, V a ~ R3) => Double -> a -> a
+alignZ :: (InSpace v n a, R3 v, Fractional n, Alignable a, HasOrigin a) => n -> a -> a
 alignZ = alignBy unitZ
 
-snugZ :: (Fractional (Scalar (V a)), Alignable a, Traced a,
-      HasOrigin a, V a ~ R3) => Double -> a -> a
+-- | See the documentation for 'alignZ'.
+snugZ :: (V a ~ v, N a ~ n, Alignable a, Traced a, HasOrigin a,
+          R3 v, Fractional n) => n -> a -> a
 snugZ = snugBy unitZ
 
--- | Center the local origin along the X-axis.
-centerX  :: (Alignable a, HasOrigin a, V a ~ R3) => a -> a
-centerX  = alignBy unitX 0
 
-snugCenterX :: (Fractional (Scalar (V a)), Alignable a, Traced a,
-      HasOrigin a, V a ~ R3) => a -> a
-snugCenterX = snugBy unitX 0
-
--- | Center the local origin along the Y-axis.
-centerY  :: (Alignable a, HasOrigin a, V a ~ R3) => a -> a
-centerY  = alignBy unitY 0
-
-snugCenterY :: (Fractional (Scalar (V a)), Alignable a, Traced a,
-      HasOrigin a, V a ~ R3) => a -> a
-snugCenterY = snugBy unitY 0
-
 -- | Center the local origin along the Z-axis.
-centerZ  :: (Alignable a, HasOrigin a, V a ~ R3) => a -> a
-centerZ  = alignBy unitZ 0
+centerZ :: (InSpace v n a, R3 v, Fractional n, Alignable a, HasOrigin a) => a -> a
+centerZ = alignBy unitZ 0
 
-snugCenterZ :: (Fractional (Scalar (V a)), Alignable a, Traced a,
-      HasOrigin a, V a ~ R3) => a -> a
+snugCenterZ :: (InSpace v n a, R3 v, Fractional n, Alignable a, HasOrigin a, Traced a) => a -> a
 snugCenterZ = snugBy unitZ 0
 
--- | Center along both the X- and Y-axes.
-centerXY :: (Alignable a, HasOrigin a, V a ~ R3) => a -> a
-centerXY = centerX . centerY
-
-snugCenterXY :: (Fractional (Scalar (V a)), Alignable a, Traced a,
-      HasOrigin a, V a ~ R3) => a -> a
-snugCenterXY = snugCenterX . snugCenterY
-
-
 -- | Center along both the X- and Z-axes.
-centerXZ :: (Alignable a, HasOrigin a, V a ~ R3) => a -> a
+centerXZ :: (InSpace v n a, R3 v, Fractional n, Alignable a, HasOrigin a) => a -> a
 centerXZ = centerX . centerZ
 
-snugCenterXZ :: (Fractional (Scalar (V a)), Alignable a, Traced a,
-      HasOrigin a, V a ~ R3) => a -> a
+snugCenterXZ :: (InSpace v n a, R3 v, Fractional n, Alignable a, HasOrigin a, Traced a) => a -> a
 snugCenterXZ = snugCenterX . snugCenterZ
 
 
 -- | Center along both the Y- and Z-axes.
-centerYZ :: (Alignable a, HasOrigin a, V a ~ R3) => a -> a
+centerYZ :: (InSpace v n a, R3 v, Fractional n, Alignable a, HasOrigin a) => a -> a
 centerYZ = centerZ . centerY
 
-snugCenterYZ :: (Fractional (Scalar (V a)), Alignable a, Traced a,
-      HasOrigin a, V a ~ R3) => a -> a
+snugCenterYZ :: (InSpace v n a, R3 v, Fractional n, Alignable a, HasOrigin a, Traced a) => a -> a
 snugCenterYZ = snugCenterZ . snugCenterY
 
 -- | Center an object in three dimensions.
-centerXYZ :: (Fractional (Scalar (V a)), Alignable a, Traced a,
-      HasOrigin a, V a ~ R3) => a -> a
+centerXYZ :: (InSpace v n a, R3 v, Fractional n, Alignable a, HasOrigin a) => a -> a
 centerXYZ = centerX . centerY . centerZ
 
-snugCenterXYZ :: (Fractional (Scalar (V a)), Alignable a, Traced a,
-      HasOrigin a, V a ~ R3) => a -> a
+snugCenterXYZ :: (InSpace v n a, R3 v, Fractional n, Alignable a, HasOrigin a, Traced a) => a -> a
 snugCenterXYZ = snugCenterX . snugCenterY . snugCenterZ
diff --git a/src/Diagrams/ThreeD/Attributes.hs b/src/Diagrams/ThreeD/Attributes.hs
--- a/src/Diagrams/ThreeD/Attributes.hs
+++ b/src/Diagrams/ThreeD/Attributes.hs
@@ -1,7 +1,9 @@
 {-# LANGUAGE DeriveDataTypeable         #-}
-{-# LANGUAGE ExistentialQuantification  #-}
+{-# LANGUAGE FlexibleContexts           #-}
 {-# LANGUAGE GeneralizedNewtypeDeriving #-}
+{-# LANGUAGE MultiParamTypeClasses      #-}
 {-# LANGUAGE TemplateHaskell            #-}
+{-# LANGUAGE TypeFamilies               #-}
 -----------------------------------------------------------------------------
 -- |
 -- Module      :  Diagrams.ThreeD.Attributes
@@ -25,36 +27,43 @@
 
 module Diagrams.ThreeD.Attributes where
 
-import Control.Lens
-import Data.Semigroup
-import Data.Typeable
+import           Control.Lens
+import           Data.Semigroup
+import           Data.Typeable
 
-import Data.Colour
+import           Data.Colour
 
-import Diagrams.Core
+import           Diagrams.Core
 
 -- | @SurfaceColor@ is the inherent pigment of an object, assumed to
 -- be opaque.
 newtype SurfaceColor = SurfaceColor (Last (Colour Double))
-                     deriving (Typeable, Semigroup)
+  deriving (Typeable, Semigroup, Show)
+
 instance AttributeClass SurfaceColor
 
-surfaceColor :: Iso' SurfaceColor (Colour Double)
-surfaceColor = iso (\(SurfaceColor (Last c)) -> c) (SurfaceColor . Last)
+_SurfaceColor :: Iso' SurfaceColor (Colour Double)
+_SurfaceColor = iso (\(SurfaceColor (Last c)) -> c) (SurfaceColor . Last)
 
 -- | Set the surface color.
 sc :: HasStyle d => Colour Double -> d -> d
-sc = applyAttr . review surfaceColor
+sc = applyAttr . review _SurfaceColor
 
+-- | Lens onto the surface colour of a style.
+_sc :: Lens' (Style v n) (Maybe (Colour Double))
+_sc = atAttr . mapping _SurfaceColor
+
 -- | @Diffuse@ is the fraction of incident light reflected diffusely,
 -- that is, in all directions.  The actual light reflected is the
 -- product of this value, the incident light, and the @SurfaceColor@
 -- Attribute.  For physical reasonableness, @Diffuse@ should have a
 -- value between 0 and 1; this is not checked.
 newtype Diffuse = Diffuse (Last Double)
-                deriving (Typeable, Semigroup)
+  deriving (Typeable, Semigroup, Show)
+
 instance AttributeClass Diffuse
 
+-- | Isomorphism between 'Diffuse' and 'Double'
 _Diffuse :: Iso' Diffuse Double
 _Diffuse = iso (\(Diffuse (Last d)) -> d) (Diffuse . Last)
 
@@ -62,6 +71,10 @@
 diffuse :: HasStyle d => Double -> d -> d
 diffuse = applyAttr . review _Diffuse
 
+-- | Lens onto the possible diffuse reflectance in a style.
+_diffuse :: Lens' (Style v n) (Maybe Double)
+_diffuse = atAttr . mapping _Diffuse
+
 -- | @Ambient@ is an ad-hoc representation of indirect lighting.  The
 -- product of @Ambient@ and @SurfaceColor@ is added to the light
 -- leaving an object due to diffuse and specular terms.  @Ambient@ can
@@ -69,7 +82,8 @@
 -- indirect lighting incident on that object and the diffuse
 -- reflectance.
 newtype Ambient = Ambient (Last Double)
-                deriving (Typeable, Semigroup)
+  deriving (Typeable, Semigroup, Show)
+
 instance AttributeClass Ambient
 
 _Ambient :: Iso' Ambient Double
@@ -79,6 +93,10 @@
 ambient :: HasStyle d => Double -> d -> d
 ambient = applyAttr . review _Ambient
 
+-- | Lens onto the possible ambience in a style.
+_ambient :: Lens' (Style v n) (Maybe Double)
+_ambient = atAttr . mapping _Ambient
+
 -- | A specular highlight has two terms, the intensity, between 0 and
 -- 1, and the size.  The highlight size is assumed to be the exponent
 -- in a Phong shading model (though Backends are free to use a
@@ -86,14 +104,16 @@
 -- between 1 and 50 or so, with higher values for shinier objects.
 -- Physically, the intensity and the value of @Diffuse@ must add up to
 -- less than 1; this is not enforced.
-data Specular = Specular { _specularIntensity :: Double
-                         , _specularSize :: Double
-                         }
+data Specular = Specular
+  { _specularIntensity :: Double
+  , _specularSize      :: Double
+  } deriving Show
 
 makeLenses ''Specular
 
 newtype Highlight = Highlight (Last Specular)
-                    deriving (Typeable, Semigroup)
+  deriving (Typeable, Semigroup, Show)
+
 instance AttributeClass Highlight
 
 _Highlight :: Iso' Highlight Specular
@@ -102,3 +122,17 @@
 -- | Set the specular highlight.
 highlight :: HasStyle d => Specular -> d -> d
 highlight = applyAttr . review _Highlight
+
+-- | Lens onto the possible specular highlight in a style
+_highlight :: Lens' (Style v n) (Maybe Specular)
+_highlight = atAttr . mapping _Highlight
+
+-- | Traversal over the highlight intensity of a style. If the style has
+--   no 'Specular', setting this will do nothing.
+highlightIntensity :: Traversal' (Style v n) Double
+highlightIntensity = _highlight . _Just . specularSize
+
+-- | Traversal over the highlight size in a style. If the style has no
+--   'Specular', setting this will do nothing.
+highlightSize :: Traversal' (Style v n) Double
+highlightSize = _highlight . _Just . specularSize
diff --git a/src/Diagrams/ThreeD/Camera.hs b/src/Diagrams/ThreeD/Camera.hs
--- a/src/Diagrams/ThreeD/Camera.hs
+++ b/src/Diagrams/ThreeD/Camera.hs
@@ -1,9 +1,10 @@
 {-# LANGUAGE DeriveDataTypeable    #-}
 {-# LANGUAGE FlexibleContexts      #-}
-{-# LANGUAGE GADTs                 #-}
 {-# LANGUAGE MultiParamTypeClasses #-}
+{-# LANGUAGE ScopedTypeVariables   #-}
 {-# LANGUAGE TemplateHaskell       #-}
 {-# LANGUAGE TypeFamilies          #-}
+{-# LANGUAGE UndecidableInstances  #-}
 
 -----------------------------------------------------------------------------
 -- |
@@ -30,81 +31,91 @@
        where
 
 import           Control.Lens           (makeLenses)
-import           Data.Cross
 import           Data.Monoid
 import           Data.Typeable
 
 import           Diagrams.Angle
 import           Diagrams.Core
-import           Diagrams.ThreeD.Types
+import           Diagrams.Direction
 import           Diagrams.ThreeD.Vector
 
+import           Linear.V3
+
 -- Parameterize Camera on the lens type, so that Backends can express which
 -- lenses they handle.
-data Camera l = Camera
-    { camLoc  :: P3
-    , forward :: R3
-    , up      :: R3
-    , lens    :: l
+data Camera l n = Camera
+    { camLoc  :: Point V3 n
+    , forward :: V3 n
+    , up      :: V3 n
+    , lens    :: l n
     }
   deriving Typeable
 
+type instance V (Camera l n) = V3
+type instance N (Camera l n) = n
+
 class Typeable l => CameraLens l where
-    -- | The natural aspect ratio of the projection.
-    aspect :: l -> Double
+  -- | The natural aspect ratio of the projection.
+  aspect :: Floating n => l n -> n
 
 -- | A perspective projection
-data PerspectiveLens = PerspectiveLens
-                     { _horizontalFieldOfView :: Angle -- ^ Horizontal field of view.
-                     , _verticalFieldOfView   :: Angle -- ^ Vertical field of view.
-                     }
+data PerspectiveLens n = PerspectiveLens
+  { _horizontalFieldOfView :: Angle n -- ^ Horizontal field of view.
+  , _verticalFieldOfView   :: Angle n -- ^ Vertical field of view.
+  }
   deriving Typeable
 
 makeLenses ''PerspectiveLens
 
+type instance V (PerspectiveLens n) = V3
+type instance N (PerspectiveLens n) = n
+
 instance CameraLens PerspectiveLens where
-    aspect (PerspectiveLens h v) = angleRatio h v
+  aspect (PerspectiveLens h v) = angleRatio h v
 
 -- | An orthographic projection
-data OrthoLens = OrthoLens
-               { _orthoWidth  :: Double -- ^ Width
-               , _orthoHeight :: Double -- ^ Height
+data OrthoLens n = OrthoLens
+               { _orthoWidth  :: n -- ^ Width
+               , _orthoHeight :: n -- ^ Height
                }
   deriving Typeable
 
 makeLenses ''OrthoLens
 
-instance CameraLens OrthoLens where
-    aspect (OrthoLens h v) = h / v
+type instance V (OrthoLens n) = V3
+type instance N (OrthoLens n) = n
 
-type instance V (Camera l) = R3
+instance CameraLens OrthoLens where
+  aspect (OrthoLens h v) = h / v
 
-instance Transformable (Camera l) where
+instance Num n => Transformable (Camera l n) where
   transform t (Camera p f u l) =
       Camera (transform t p)
              (transform t f)
              (transform t u)
              l
 
-instance Renderable (Camera l) NullBackend where
-    render _ _ = mempty
+instance Num n => Renderable (Camera l n) NullBackend where
+  render _ _ = mempty
 
 -- | A camera at the origin facing along the negative Z axis, with its
 -- up-axis coincident with the positive Y axis.  The field of view is
 -- chosen to match a 50mm camera on 35mm film. Note that Cameras take
 -- up no space in the Diagram.
-mm50Camera :: (Backend b R3, Renderable (Camera PerspectiveLens) b) => Diagram b R3
+mm50Camera :: (Typeable n, Floating n, Ord n, Renderable (Camera PerspectiveLens n) b)
+           => QDiagram b V3 n Any
 mm50Camera = facing_ZCamera mm50
 
 -- | 'facing_ZCamera l' is a camera at the origin facing along the
 -- negative Z axis, with its up-axis coincident with the positive Y
 -- axis, with the projection defined by l.
-facing_ZCamera :: (CameraLens l, Backend b R3, Renderable (Camera l) b) =>
-                  l -> Diagram b R3
+facing_ZCamera :: (Floating n, Ord n, Typeable n, CameraLens l, Renderable (Camera l n) b) =>
+                  l n -> QDiagram b V3 n Any
 facing_ZCamera l = mkQD (Prim $ Camera origin unit_Z unitY l)
         mempty mempty mempty (Query . const . Any $ False)
+{-# ANN facing_ZCamera ("HLint: ignore Use camelCase" :: String) #-}
 
-mm50, mm50Wide, mm50Narrow :: PerspectiveLens
+mm50, mm50Wide, mm50Narrow :: Floating n => PerspectiveLens n
 
 -- | mm50 has the field of view of a 50mm lens on standard 35mm film,
 -- hence an aspect ratio of 3:2.
@@ -115,21 +126,21 @@
 mm50Wide = PerspectiveLens (43.2 @@ deg)  (27 @@ deg)
 
 -- | mm50Narrow has the same vertical field of view as mm50, but an
--- aspect ratio of 4:3, for VGA and similar computer resulotions.
+-- aspect ratio of 4:3, for VGA and similar computer resolutions.
 mm50Narrow = PerspectiveLens (36 @@ deg) (27 @@ deg)
 
-camForward :: Camera l -> Direction
+camForward :: Camera l n -> Direction V3 n
 camForward = direction . forward
 
-camUp :: Camera l -> Direction
+camUp :: Camera l n -> Direction V3 n
 camUp = direction . up
 
-camRight :: Camera l -> Direction
+camRight :: Fractional n => Camera l n -> Direction V3 n
 camRight c = direction right where
-  right = cross3 (forward c) (up c)
+  right = cross (forward c) (up c)
 
-camLens :: Camera l -> l
+camLens :: Camera l n -> l n
 camLens = lens
 
-camAspect :: CameraLens l => Camera l -> Double
+camAspect :: (Floating n, CameraLens l) => Camera l n -> n
 camAspect = aspect . camLens
diff --git a/src/Diagrams/ThreeD/Deform.hs b/src/Diagrams/ThreeD/Deform.hs
--- a/src/Diagrams/ThreeD/Deform.hs
+++ b/src/Diagrams/ThreeD/Deform.hs
@@ -1,51 +1,28 @@
-module Diagrams.ThreeD.Deform where
-
-import Control.Lens
-
-import Diagrams.Deform
-
-import Diagrams.Coordinates
-import Diagrams.ThreeD.Types
-
--- | The parallel projection onto the plane x=0
-parallelX0 :: Deformation R3
-parallelX0 = Deformation (& _x .~ 0)
+module Diagrams.ThreeD.Deform
+  ( parallelX0, perspectiveX1, facingX
+  , parallelY0, perspectiveY1, facingY
+  , parallelZ0, perspectiveZ1, facingZ
+  ) where
 
--- | The perspective division onto the plane x=1 along lines going
--- through the origin.
-perspectiveX1 :: Deformation R3
-perspectiveX1 = Deformation (\p -> let x = p^._x in
-                             p & _x .~ 1 & _y //~ x & _z //~ x )
+import           Control.Lens
 
--- | The parallel projection onto the plane y=0
-parallelY0 :: Deformation R3
-parallelY0 = Deformation (& _y .~ 0)
+import           Diagrams.Deform
+import           Diagrams.TwoD.Deform
 
--- | The perspective division onto the plane y=1 along lines going
--- through the origin.
-perspectiveY1 :: Deformation R3
-perspectiveY1 = Deformation (\p -> let y = p^._y in
-                             p & _x //~ y & _y .~ 1 & _z //~ y )
+import           Linear.V3
+import           Linear.Vector
 
 -- | The parallel projection onto the plane z=0
-parallelZ0 :: Deformation R3
-parallelZ0 = Deformation (& _z .~ 0)
+parallelZ0 :: (R3 v, Num n) => Deformation v v n
+parallelZ0 = Deformation (_z .~ 0)
 
 -- | The perspective division onto the plane z=1 along lines going
--- through the origin.
-perspectiveZ1 :: Deformation R3
-perspectiveZ1 = Deformation (\p -> let z = p^._z in
-                             p & _x //~ z & _y //~ z & _z .~ 1 )
-
--- | The viewing transform for a viewer facing along the positive X
--- axis.  X coördinates stay fixed, while Y coördinates are compressed
--- with increasing distance.  @asDeformation (translation unitX) <>
--- parallelX0 <> frustrumX = perspectiveX1@
-facingX :: Deformation R3
-facingX = Deformation (\v -> v & _y //~ (v^._x) & _z //~ (v^._x))
+--   through the origin.
+perspectiveZ1 :: (R3 v, Functor v, Fractional n) => Deformation v v n
+perspectiveZ1 = Deformation $ \p -> p ^/ (p ^. _z)
 
-facingY :: Deformation R3
-facingY = Deformation (\v -> v & _x //~ (v^._y) & _z //~ (v^._y))
+facingZ :: (R3 v, Functor v, Fractional n) => Deformation v v n
+facingZ = Deformation $
+  \p -> let z = p ^. _z
+        in  p ^/ z & _z .~ z
 
-facingZ :: Deformation R3
-facingZ = Deformation (\v -> v & _x //~ (v^._z) & _y //~ (v^._z))
diff --git a/src/Diagrams/ThreeD/Light.hs b/src/Diagrams/ThreeD/Light.hs
--- a/src/Diagrams/ThreeD/Light.hs
+++ b/src/Diagrams/ThreeD/Light.hs
@@ -1,7 +1,9 @@
+{-# LANGUAGE ConstraintKinds #-}
 {-# LANGUAGE DeriveDataTypeable    #-}
 {-# LANGUAGE FlexibleContexts      #-}
 {-# LANGUAGE MultiParamTypeClasses #-}
 {-# LANGUAGE TypeFamilies          #-}
+{-# LANGUAGE UndecidableInstances  #-}
 
 -----------------------------------------------------------------------------
 -- |
@@ -21,35 +23,43 @@
 import           Data.Typeable
 
 import           Diagrams.Core
+import           Diagrams.Direction
 import           Diagrams.ThreeD.Types
 
-data PointLight = PointLight P3 (Colour Double)
+-- | A @PointLight@ radiates uniformly in all directions from a given
+-- point.
+data PointLight n = PointLight (Point V3 n) (Colour Double)
   deriving Typeable
 
-data ParallelLight = ParallelLight R3 (Colour Double)
+type instance V (PointLight n) = V3
+type instance N (PointLight n) = n
+
+-- | A @ParallelLight@ casts parallel rays in the specified direction,
+-- from some distant location outside the scene.
+data ParallelLight n = ParallelLight (V3 n) (Colour Double)
   deriving Typeable
 
-type instance V PointLight = R3
-type instance V ParallelLight = R3
+type instance V (ParallelLight n) = V3
+type instance N (ParallelLight n) = n
 
-instance Transformable PointLight where
-    transform t (PointLight p c) = PointLight (transform t p) c
+instance Fractional n => Transformable (PointLight n) where
+  transform t (PointLight p c) = PointLight (transform t p) c
 
-instance Transformable ParallelLight where
-    transform t (ParallelLight v c) = ParallelLight (transform t v) c
+instance Transformable (ParallelLight n) where
+  transform t (ParallelLight v c) = ParallelLight (transform t v) c
 
 -- | Construct a Diagram with a single PointLight at the origin, which
 -- takes up no space.
-pointLight :: (Backend b R3, Renderable PointLight b)
+pointLight :: (Typeable n, Num n, Ord n, Renderable (PointLight n) b)
               => Colour Double -- ^ The color of the light
-              -> Diagram b R3
+              -> QDiagram b V3 n Any
 pointLight c = mkQD (Prim $ PointLight origin c) mempty mempty mempty
                (Query . const . Any $ False)
 
 -- | Construct a Diagram with a single ParallelLight, which takes up no space.
-parallelLight :: (Backend b R3, Renderable ParallelLight b)
-                 => Direction -- ^ The direction in which the light travels.
-                 -> Colour Double -- ^ The color of the light.
-                 -> Diagram b R3
+parallelLight :: (Typeable n, OrderedField n, Renderable (ParallelLight n) b)
+                 => Direction V3 n -- ^ The direction in which the light travels.
+                 -> Colour Double  -- ^ The color of the light.
+                 -> QDiagram b V3 n Any
 parallelLight d c = mkQD (Prim $ ParallelLight (fromDirection d) c)
                     mempty mempty mempty (Query . const . Any $ False)
diff --git a/src/Diagrams/ThreeD/Projection.hs b/src/Diagrams/ThreeD/Projection.hs
new file mode 100644
--- /dev/null
+++ b/src/Diagrams/ThreeD/Projection.hs
@@ -0,0 +1,168 @@
+{-# LANGUAGE ConstraintKinds       #-}
+{-# LANGUAGE FlexibleContexts      #-}
+{-# LANGUAGE FlexibleInstances     #-}
+{-# LANGUAGE MultiParamTypeClasses #-}
+{-# LANGUAGE RankNTypes            #-}
+{-# LANGUAGE TypeFamilies          #-}
+
+-----------------------------------------------------------------------------
+-- |
+-- Module      :  Diagrams.ThreeD.Projection
+-- Copyright   :  (c) 2014 diagrams team (see LICENSE)
+-- License     :  BSD-style (see LICENSE)
+-- Maintainer  :  diagrams-discuss@googlegroups.com
+--
+-- 3D projections are a way of viewing a three-dimensional objects on a
+-- two-dimensional plane.
+--
+-- This module can be used with the functions in "Linear.Projection".
+--
+-- Disclaimer: This module should be considered experimental and is
+-- likely to change.
+--
+-----------------------------------------------------------------------------
+
+module Diagrams.ThreeD.Projection
+  ( -- * Orthographic projections
+
+    -- $orthographic
+    -- ** Parallel projections
+    facingXY
+  , facingXZ
+  , facingYZ
+
+    -- ** axonometric
+    -- $axonometric
+
+    -- *** Isometric projections
+    -- $isometric
+  , isometricApply
+  , isometric
+
+  , lookingAt
+
+    -- ** Affine maps
+  , m44AffineApply
+  , m44AffineMap
+  , m33AffineApply
+  , m33AffineMap
+
+    -- * Perspective projections
+    -- $perspective
+    -- ** Perspective deformations
+  , m44Deformation
+  , module Linear.Projection
+  ) where
+
+import           Control.Lens           hiding (transform)
+import           Data.Functor.Rep
+
+import           Diagrams.Core
+import           Diagrams.Deform
+import           Diagrams.Direction
+import           Diagrams.LinearMap
+import           Diagrams.ThreeD.Types  (P3)
+import           Diagrams.ThreeD.Vector
+
+import           Linear                 as L
+import           Linear.Affine
+import           Linear.Projection
+
+------------------------------------------------------------------------
+-- Orthographic projections
+------------------------------------------------------------------------
+
+-- $orthographic
+-- Orthographic projections are a form of parallel projections where are
+-- projection lines are orthogonal to the projection plane.
+
+-- Parallel projections
+
+-- | Look at the xy-plane with y as the up direction.
+facingXY :: (Epsilon n, Floating n) => AffineMap V3 V2 n
+facingXY = lookingAt unitZ origin yDir
+
+-- | Look at the xz-plane with z as the up direction.
+facingXZ :: (Epsilon n, Floating n) => AffineMap V3 V2 n
+facingXZ = lookingAt unitY origin zDir
+
+-- | Look at the yz-plane with z as the up direction.
+facingYZ :: (Epsilon n, Floating n) => AffineMap V3 V2 n
+facingYZ = lookingAt unitX origin zDir
+
+-- $axonometric
+-- Axonometric projections are a type of orthographic projection where
+-- the object is rotated along one or more of its axes relative to the
+-- plane of projection.
+
+-- $isometric
+-- Isometric projections are when the scale along each axis of the
+-- projection is the same and the angle between any axis is 120
+-- degrees.
+
+-- | Apply an isometric projection given the up direction
+isometricApply :: (InSpace V3 n a, InSpace V2 n b, AffineMappable a b, Floating n, Epsilon n)
+               => Direction V3 n -> a -> b
+isometricApply up = amap (isometric up)
+
+-- | Make an isometric affine map with the given up direction.
+isometric :: (Floating n, Epsilon n) => Direction V3 n -> AffineMap V3 V2 n
+isometric up = m44AffineMap m
+  where
+    m = lookAt (V3 1 1 1) zero (fromDirection up)
+
+lookingAt :: (Epsilon n, Floating n)
+          => P3 n -- ^ Eye
+          -> P3 n -- ^ Center
+          -> Direction V3 n -- ^ Up
+          -> AffineMap V3 V2 n
+lookingAt (P cam) (P center) d = m44AffineMap m
+  where
+    m = lookAt cam center (d^._Dir)
+
+-- | Apply the affine part of a homogeneous matrix.
+m44AffineApply :: (InSpace V3 n a, InSpace V2 n b, AffineMappable a b)
+               => M44 n -> a -> b
+m44AffineApply = amap . m44AffineMap
+
+-- | Create an 'AffineMap' from a 4x4 homogeneous matrix, ignoring any
+--   perspective transforms.
+m44AffineMap :: Num n => M44 n -> AffineMap V3 V2 n
+m44AffineMap m = AffineMap (LinearMap f) (f v)
+  where
+    f  = view _xy . (m' !*)
+    m' = m ^. linearTransform
+    v  = m ^. L.translation
+
+-- | Apply a transformation matrix and translation.
+m33AffineApply :: (InSpace V3 n a, InSpace V2 n b, AffineMappable a b)
+               => M33 n -> V2 n -> a -> b
+m33AffineApply m = amap . m33AffineMap m
+
+-- | Create an 'AffineMap' from a 3x3 transformation matrix and a
+--   translation vector.
+m33AffineMap :: Num n => M33 n -> V2 n -> AffineMap V3 V2 n
+m33AffineMap m = AffineMap (LinearMap f)
+  where
+    f = view _xy . (m !*)
+
+-- | Extract the linear transform part of a homogeneous matrix.
+linearTransform :: (Representable u, R3 v, R3 u) => Lens' (u (v n)) (M33 n)
+linearTransform = column _xyz . _xyz
+
+------------------------------------------------------------------------
+-- Perspective transforms
+------------------------------------------------------------------------
+
+-- For the time being projective transforms use the deformable class.
+-- Eventually we would like to replace this with a more specialised
+-- method.
+
+-- $perspective
+-- Perspective projections are when closer objects appear bigger.
+
+-- | Make a deformation from a 4x4 homogeneous matrix.
+m44Deformation :: Fractional n => M44 n -> Deformation V3 V2 n
+m44Deformation m =
+  Deformation (P . view _xy . normalizePoint . (m !*) . point . view _Point)
+
diff --git a/src/Diagrams/ThreeD/Shapes.hs b/src/Diagrams/ThreeD/Shapes.hs
--- a/src/Diagrams/ThreeD/Shapes.hs
+++ b/src/Diagrams/ThreeD/Shapes.hs
@@ -1,7 +1,11 @@
+{-# LANGUAGE ConstraintKinds       #-}
 {-# LANGUAGE DeriveDataTypeable    #-}
 {-# LANGUAGE FlexibleContexts      #-}
 {-# LANGUAGE MultiParamTypeClasses #-}
+{-# LANGUAGE RankNTypes            #-}
 {-# LANGUAGE TypeFamilies          #-}
+{-# LANGUAGE TypeOperators         #-}
+{-# LANGUAGE UndecidableInstances  #-}
 -----------------------------------------------------------------------------
 -- |
 -- Module      :  Diagrams.ThreeD.Shapes
@@ -14,149 +18,307 @@
 -----------------------------------------------------------------------------
 
 module Diagrams.ThreeD.Shapes
-       (
-         Ellipsoid(..), sphere
-       , Box(..), cube
-       , Frustum(..) , frustum, cone, cylinder
-       ) where
+  (
+    -- * Skinned class
+    Skinned(..)
 
-import           Control.Applicative
-import           Control.Lens           (review, (^.), _1)
+    -- * Basic 3D shapes
+  , Ellipsoid(..)
+  , sphere
+
+  , Box(..)
+  , cube
+
+  , Frustum(..)
+  , frustum
+  , cone
+  , cylinder
+
+    -- * Constructive solid geometry
+  , CSG(..)
+  , union
+  , intersection
+  , difference
+  ) where
+
+import           Control.Lens              (review, (^.), _1)
 import           Data.Typeable
 
-import           Data.AffineSpace
 import           Data.Semigroup
-import           Data.VectorSpace
 import           Diagrams.Angle
-import           Diagrams.Coordinates
 import           Diagrams.Core
-import           Diagrams.Solve
+import           Diagrams.Core.Trace
+import           Diagrams.Points
+import           Diagrams.Query
+import           Diagrams.Solve.Polynomial
 import           Diagrams.ThreeD.Types
 import           Diagrams.ThreeD.Vector
 
-data Ellipsoid = Ellipsoid T3
+import           Linear.Affine
+import           Linear.Metric
+import           Linear.Vector
+
+data Ellipsoid n = Ellipsoid (Transformation V3 n)
   deriving Typeable
 
-type instance V Ellipsoid = R3
+type instance V (Ellipsoid n) = V3
+type instance N (Ellipsoid n) = n
 
-instance Transformable Ellipsoid where
+instance Fractional n => Transformable (Ellipsoid n) where
   transform t1 (Ellipsoid t2) = Ellipsoid (t1 <> t2)
 
-instance Renderable Ellipsoid NullBackend where
+instance Fractional n => Renderable (Ellipsoid n) NullBackend where
   render _ _ = mempty
 
+instance OrderedField n => Enveloped (Ellipsoid n) where
+  getEnvelope (Ellipsoid tr) = transform tr . mkEnvelope $ \v -> 1 / norm v
+
+instance OrderedField n => Traced (Ellipsoid n) where
+  getTrace (Ellipsoid tr) = transform tr . mkTrace $ \(P p) v -> let
+    a  =    v `dot` v
+    b  = 2 * (p `dot` v)
+    c  =    (p `dot` p) - 1
+    in
+     mkSortedList $ quadForm a b c
+
 -- | A sphere of radius 1 with its center at the origin.
-sphere :: (Backend b R3, Renderable Ellipsoid b) => Diagram b R3
-sphere = mkQD (Prim $ Ellipsoid mempty)
-              (mkEnvelope sphereEnv)
-              (mkTrace sphereTrace)
-              mempty
-              (Query sphereQuery)
-  where sphereEnv v = 1 / magnitude v
-        sphereTrace p v = mkSortedList $ quadForm a b c
-          where a = v <.> v
-                b = 2 *^ p' <.> v
-                c = p' <.> p' - 1
-                p' = p .-. origin
-        sphereQuery v = Any $ magnitudeSq (v .-. origin) <= 1
+sphere :: Num n => Ellipsoid n
+sphere = Ellipsoid mempty
 
-data Box = Box T3
-         deriving (Typeable)
+data Box n = Box (Transformation V3 n)
+  deriving Typeable
 
-type instance V Box = R3
+type instance V (Box n) = V3
+type instance N (Box n) = n
 
-instance Transformable Box where
-    transform t1 (Box t2) = Box (t1 <> t2)
+instance Fractional n => Transformable (Box n) where
+  transform t1 (Box t2) = Box (t1 <> t2)
 
-instance Renderable Box NullBackend where
-    render _ _ = mempty
+instance Fractional n => Renderable (Box n) NullBackend where
+  render _ _ = mempty
 
--- | A cube with side length 1, in the positive octant, with one
--- vertex at the origin.
-cube :: (Backend b R3, Renderable Box b) => Diagram b R3
-cube = mkQD (Prim $ Box mempty)
-            (mkEnvelope boxEnv)
-            (mkTrace boxTrace)
-            mempty
-            (Query boxQuery)
-  where
-    corners = mkR3 <$> [0,1] <*> [0,1] <*> [0,1]
-    boxEnv v = maximum (map (v <.>) corners) / magnitudeSq v
-    -- ts gives all intersections with the planes forming the box
-    -- filter keeps only those actually on the box surface
-    boxTrace p v = mkSortedList . filter (range . atT) $ ts where
-      (x0, y0, z0) = unp3 p
-      (vx, vy, vz) = unr3 v
-      intersections f d = case d of
-          0 -> []
-          _ -> [-f/d, (1-f)/d]
-      ts = concat $ zipWith intersections [x0,y0,z0] [vx,vy,vz]
-      atT t = p .+^ (t*^v)
+instance OrderedField n => Enveloped (Box n) where
+  getEnvelope (Box tr) = transform tr . mkEnvelope $ \v ->
+    maximum (map (v `dot`) corners) / quadrance v where
+      corners = mkR3 <$> [0,1] <*> [0,1] <*> [0,1]
+
+instance (Fractional n, Ord n) => Traced (Box n) where
+  getTrace (Box tr) = transform tr . mkTrace $ \p v -> let
+    (x0, y0, z0) = unp3 p
+    (vx, vy, vz) = unr3 v
+    intersections f d = case d of
+      0 -> []
+      _ -> [-f/d, (1-f)/d]
+    ts = concat $ zipWith intersections [x0,y0,z0] [vx,vy,vz]
+    atT t = p .+^ (t*^v)
     range u = and [x >= 0, x <= 1, y >= 0, y <= 1, z >= 0, z <= 1] where
       (x, y, z) = unp3 u
-    boxQuery = Any . range
+    in
+     -- ts gives all intersections with the planes forming the box
+     -- filter keeps only those actually on the box surface
+     mkSortedList . filter (range . atT) $ ts where
 
-data Frustum = Frustum Double Double T3
-         deriving (Typeable)
+-- | A cube with side length 1, in the positive octant, with one
+-- vertex at the origin.
+cube :: Num n => Box n
+cube = Box mempty
 
-type instance V Frustum = R3
+data Frustum n = Frustum n n (Transformation V3 n)
+  deriving Typeable
 
-instance Transformable Frustum where
-    transform t1 (Frustum r0 r1 t2) = Frustum r0 r1 (t1 <> t2)
+type instance V (Frustum n) = V3
+type instance N (Frustum n) = n
 
-instance Renderable Frustum NullBackend where
-    render _ _ = mempty
+instance Fractional n => Transformable (Frustum n) where
+  transform t1 (Frustum r0 r1 t2) = Frustum r0 r1 (t1 <> t2)
 
+instance Fractional n => Renderable (Frustum n) NullBackend where
+  render _ _ = mempty
+
+instance (OrderedField n, RealFloat n) => Enveloped (Frustum n) where
+  -- The plane containing v and the z axis intersects the frustum in a trapezoid
+  -- Test the four corners of this trapezoid; one must determine the Envelope
+  getEnvelope (Frustum r0 r1 tr) = transform tr . mkEnvelope $ \v ->let
+    θ = v ^. _theta
+    corners = [(r1,θ,1), (-r1,θ,1), (r0,θ,0), (-r0,θ,0)]
+    in
+     maximum . map (norm . project v . review r3CylindricalIso) $ corners
+
+instance (RealFloat n, Ord n) => Traced (Frustum n) where
+  -- The trace can intersect the sides of the cone or one of the end
+  -- caps The sides are described by a quadric equation; substitute
+  -- in the parametric form of the ray but disregard any
+  -- intersections outside z = [0,1] Similarly, find intersections
+  -- with the planes z=0, z=1, but disregard any r>r0, r>r1
+  getTrace (Frustum r0 r1 tr) = transform tr . mkTrace $ \p v -> let
+    (px, py, pz) = unp3 p
+    (vx, vy, vz) = unr3 v
+    ray t = p .+^ t *^ v
+    dr = r1 - r0
+    a = vx**2 + vy**2 - vz**2 * dr**2
+    b = 2 * (px * vx + py * vy - (r0+pz*dr) * dr  * vz)
+    c = px**2 + py**2 - (r0 + dr*pz)**2
+    zbounds t = ray t ^. _z >= 0
+         && ray t ^. _z <= 1
+    ends = concatMap cap [0,1]
+    cap z = [ t | ray t ^. lensP . r3CylindricalIso . _1 < r0 + z * dr ]
+      where
+      t = (z - pz) / vz
+    in
+     mkSortedList $ filter zbounds (quadForm a b c) ++ ends
+
 -- | A frustum of a right circular cone.  It has height 1 oriented
 -- along the positive z axis, and radii r0 and r1 at Z=0 and Z=1.
 -- 'cone' and 'cylinder' are special cases.
-frustum :: (Backend b R3, Renderable Frustum b) => Double -> Double -> Diagram b R3
-frustum r0 r1 = mkQD (Prim $ Frustum r0 r1 mempty)
-                 (mkEnvelope frEnv)
-                 (mkTrace frTrace)
-                 mempty
-                 (Query frQuery)
-  where
-    projectXY u = u ^-^ project unitZ u
-    frQuery p = Any $ x >= 0 && x <= 1 && a <= r where
-      (x, _, z) = unp3 p
-      r = r0 + (r1-r0)*z
-      v = p .-. origin
-      a = magnitude $ projectXY v
-    -- The plane containing v and the z axis intersects the frustum in a trapezoid
-    -- Test the four corners of this trapezoid; one must determine the Envelope
-    frEnv v = maximum . map (magnitude . project v . review cylindrical) $ corners
-      where
-        θ = v^._theta
-        corners = [(r1,θ,1), (-r1,θ,1), (r0,θ,0), (-r0,θ,0)]
-    -- The trace can intersect the sides of the cone or one of the end
-    -- caps The sides are described by a quadric equation; substitute
-    -- in the parametric form of the ray but disregard any
-    -- intersections outside z = [0,1] Similarly, find intersections
-    -- with the planes z=0, z=1, but disregard any r>r0, r>r1
-    frTrace p v = mkSortedList $ filter zbounds (quadForm a b c) ++ ends
-      where
-        (px, py, pz) = unp3 p
-        (vx, vy, vz) = unr3 v
-        ray t = p .+^ t*^v
-        dr = r1-r0
-        a = vx**2 + vy**2 - vz**2 * dr**2
-        b = 2 * (px * vx + py * vy - (r0+pz*dr) * dr  * vz)
-        c = px**2 + py**2 - (r0 + dr*pz)**2
-        zbounds t = (ray t)^._z >= 0 && (ray t)^._z <= 1
-        ends = concatMap cap [0,1]
-        cap z = if (ray t)^.cylindrical._1 < r0 + z*dr
-                then [t]
-                else []
-          where
-            t = (z - pz) / vz
+frustum :: Num n => n -> n -> Frustum n
+frustum r0 r1 = Frustum r0 r1 mempty
 
 -- | A cone with its base centered on the origin, with radius 1 at the
 -- base, height 1, and it's apex on the positive Z axis.
-cone :: (Backend b R3, Renderable Frustum b) => Diagram b R3
+cone :: Num n => Frustum n
 cone = frustum 1 0
 
 -- | A circular cylinder of radius 1 with one end cap centered on the
 -- origin, and extending to Z=1.
-cylinder :: (Backend b R3, Renderable Frustum b) => Diagram b R3
+cylinder :: Num n => Frustum n
 cylinder = frustum 1 1
+
+-- | Types which can be rendered as 3D Diagrams.
+class Skinned t where
+  skin :: (Renderable t b, N t ~ n, TypeableFloat n) => t -> QDiagram b V3 n Any
+
+instance (Num n, Ord n) => HasQuery (Ellipsoid n) Any where
+  getQuery (Ellipsoid tr) = transform tr $
+    Query $ \v -> Any $ quadrance (v .-. origin) <= 1
+
+instance OrderedField n => Skinned (Ellipsoid n) where
+  skin s = mkQD (Prim s) (getEnvelope s) (getTrace s) mempty (getQuery s)
+
+instance (Num n, Ord n) => HasQuery (Box n) Any where
+  getQuery (Box tr) = transform tr . Query $ Any . range where
+    range u = and [x >= 0, x <= 1, y >= 0, y <= 1, z >= 0, z <= 1] where
+      (x, y, z) = unp3 u
+
+instance OrderedField n => Skinned (Box n) where
+  skin s = mkQD (Prim s) (getEnvelope s) (getTrace s) mempty (getQuery s)
+
+instance (OrderedField n) => HasQuery (Frustum n) Any where
+  getQuery (Frustum r0 r1 tr)= transform tr $
+    Query $ \p -> let
+      z = p^._z
+      r = r0 + (r1 - r0)*z
+      v = p .-. origin
+      a = norm $ projectXY v
+      projectXY u = u ^-^ project unitZ u
+      in
+       Any $ z >= 0 && z <= 1 && a <= r
+
+instance Skinned (Frustum n) where
+  skin s = mkQD (Prim s) (getEnvelope s) (getTrace s) mempty (getQuery s)
+
+-- The CSG type needs to form a tree to be useful.  This
+-- implementation requires Backends to support all the included
+-- primitives.  If that turns out to be a problem, we have several
+-- options:
+-- a) accept runtime errors for unsupported primitives
+-- b) carry the set of primitives in a row type in the CSG type
+-- c) implement CSG in Haskell, so Backends supporting triangle meshes
+--    can fall back to those.
+-- (c) is worth doing anyway; I'm ambivalent about the others.  -DMB
+
+-- | A tree of Constructive Solid Geometry operations and the primitives that
+-- can be used in them.
+data CSG n
+  = CsgEllipsoid (Ellipsoid n)
+  | CsgBox (Box n)
+  | CsgFrustum (Frustum n)
+  | CsgUnion [CSG n]
+  | CsgIntersection [CSG n]
+  | CsgDifference (CSG n) (CSG n)
+  deriving Typeable
+
+type instance V (CSG n) = V3
+type instance N (CSG n) = n
+
+instance Fractional n => Transformable (CSG n) where
+  transform t (CsgEllipsoid p) = CsgEllipsoid $ transform t p
+  transform t (CsgBox p) = CsgBox $ transform t p
+  transform t (CsgFrustum p) = CsgFrustum $ transform t p
+  transform t (CsgUnion ps) = CsgUnion $ map (transform t) ps
+  transform t (CsgIntersection ps) = CsgIntersection $ map (transform t) ps
+  transform t (CsgDifference p1 p2) = CsgDifference (transform t p1) (transform t p2)
+
+-- | The Envelope for an Intersection or Difference is simply the
+-- Envelope of the Union.  This is wrong but easy to implement.
+instance RealFloat n => Enveloped (CSG n) where
+  getEnvelope (CsgEllipsoid p)      = getEnvelope p
+  getEnvelope (CsgBox p)            = getEnvelope p
+  getEnvelope (CsgFrustum p)        = getEnvelope p
+  getEnvelope (CsgUnion ps)         = foldMap getEnvelope ps
+  getEnvelope (CsgIntersection ps)  = foldMap getEnvelope ps
+  getEnvelope (CsgDifference p1 p2) = getEnvelope p1 <> getEnvelope p2
+-- TODO after implementing some approximation scheme, calculate
+-- correct (approximate) envelopes for intersections and difference.
+
+instance (Floating n, Ord n) => HasQuery (CSG n) Any where
+  getQuery (CsgEllipsoid prim) = getQuery prim
+  getQuery (CsgBox prim) = getQuery prim
+  getQuery (CsgFrustum prim) = getQuery prim
+  getQuery (CsgUnion ps) = foldMap getQuery ps
+  getQuery (CsgIntersection ps) =
+    Any . getAll <$> foldMap (fmap (All . getAny) . getQuery) ps
+  getQuery (CsgDifference p1 p2) = inOut <$> getQuery p1 <*> getQuery p2 where
+    inOut (Any a) (Any b) = Any $ a && not b
+
+instance (RealFloat n, Ord n) => Traced (CSG n) where
+  getTrace (CsgEllipsoid p) = getTrace p
+  getTrace (CsgBox p) = getTrace p
+  getTrace (CsgFrustum p) = getTrace p
+  -- on surface of some p, and not inside any of the others
+  getTrace (CsgUnion []) = mempty
+  getTrace (CsgUnion (s:ss)) = mkTrace t where
+    t pt v = onSortedList (filter $ without s) (appTrace (getTrace (CsgUnion ss)) pt v)
+         <> onSortedList (filter $ without (CsgUnion ss)) (appTrace (getTrace s) pt v) where
+      newPt dist = pt .+^ v ^* dist
+      without prim = not . inquire prim . newPt
+  -- on surface of some p, and inside all the others
+  getTrace (CsgIntersection []) = mempty
+  getTrace (CsgIntersection (s:ss)) = mkTrace t where
+    t pt v = onSortedList (filter $ within s) (appTrace (getTrace (CsgIntersection ss)) pt v)
+         <> onSortedList (filter $ within (CsgIntersection ss)) (appTrace (getTrace s) pt v) where
+      newPt dist = pt .+^ v ^* dist
+      within prim = inquire prim . newPt
+  -- on surface of p1, outside p2, or on surface of p2, inside p1
+  getTrace (CsgDifference s1 s2) = mkTrace t where
+    t pt v = onSortedList (filter $ not . within s2) (appTrace (getTrace s1) pt v)
+         <> onSortedList (filter $ within s1) (appTrace (getTrace s2) pt v) where
+      newPt dist = pt .+^ v ^* dist
+      within prim = inquire prim . newPt
+
+instance (RealFloat n, Ord n) => Skinned (CSG n) where
+  skin s = mkQD (Prim s) (getEnvelope s) (getTrace s) mempty (getQuery s)
+
+-- | Types which can be included in CSG trees.
+class CsgPrim a where
+  toCsg :: a n -> CSG n
+
+instance CsgPrim Ellipsoid where
+  toCsg = CsgEllipsoid
+
+instance CsgPrim Box where
+  toCsg = CsgBox
+
+instance CsgPrim Frustum where
+  toCsg = CsgFrustum
+
+instance CsgPrim CSG where
+  toCsg = id
+
+union :: (CsgPrim a, CsgPrim b) => a n -> b n -> CSG n
+union a b = CsgUnion [toCsg a, toCsg b]
+
+intersection :: (CsgPrim a, CsgPrim b) => a n -> b n -> CSG n
+intersection a b = CsgIntersection [toCsg a, toCsg b]
+
+difference :: (CsgPrim a, CsgPrim b) => a n -> b n -> CSG n
+difference a b = CsgDifference (toCsg a) (toCsg b)
diff --git a/src/Diagrams/ThreeD/Size.hs b/src/Diagrams/ThreeD/Size.hs
new file mode 100644
--- /dev/null
+++ b/src/Diagrams/ThreeD/Size.hs
@@ -0,0 +1,50 @@
+{-# LANGUAGE ConstraintKinds #-}
+{-# LANGUAGE FlexibleContexts #-}
+{-# LANGUAGE TypeFamilies     #-}
+
+-----------------------------------------------------------------------------
+-- |
+-- Module      :  Diagrams.ThreeD.Size
+-- Copyright   :  (c) 2014 diagrams-lib team (see LICENSE)
+-- License     :  BSD-style (see LICENSE)
+-- Maintainer  :  diagrams-discuss@googlegroups.com
+--
+-- Utilities for working with sizes of three-dimensional objects.
+--
+-----------------------------------------------------------------------------
+module Diagrams.ThreeD.Size
+       (
+         -- ** Computing sizes
+         extentX, extentY, extentZ
+
+         -- ** Specifying sizes
+       , mkSizeSpec3D
+       , dims3D
+
+       ) where
+
+import           Diagrams.Core
+import           Diagrams.Core.Envelope
+import           Diagrams.Size
+import           Diagrams.TwoD.Size
+import           Diagrams.ThreeD.Types
+import           Diagrams.ThreeD.Vector
+
+------------------------------------------------------------
+-- Computing diagram sizes
+------------------------------------------------------------
+
+-- | Compute the absolute z-coordinate range of an enveloped object in
+--   the form @(lo,hi)@. Return @Nothing@ for objects with an empty
+--   envelope.
+extentZ :: (InSpace v n a, R3 v, Enveloped a) => a -> Maybe (n, n)
+extentZ = extent unitZ
+
+-- | Make a 'SizeSpec' from possibly-specified width and height.
+mkSizeSpec3D :: Num n => Maybe n -> Maybe n -> Maybe n -> SizeSpec V3 n
+mkSizeSpec3D x y z = mkSizeSpec (V3 x y z)
+
+-- | Make a 'SizeSpec' from a width and height.
+dims3D :: n -> n -> n -> SizeSpec V3 n
+dims3D x y z = dims (V3 x y z)
+
diff --git a/src/Diagrams/ThreeD/Transform.hs b/src/Diagrams/ThreeD/Transform.hs
--- a/src/Diagrams/ThreeD/Transform.hs
+++ b/src/Diagrams/ThreeD/Transform.hs
@@ -1,8 +1,15 @@
+{-# LANGUAGE ConstraintKinds #-}
 {-# LANGUAGE FlexibleContexts      #-}
 {-# LANGUAGE FlexibleInstances     #-}
 {-# LANGUAGE MultiParamTypeClasses #-}
+{-# LANGUAGE ScopedTypeVariables   #-}
 {-# LANGUAGE TypeFamilies          #-}
+{-# LANGUAGE TypeOperators         #-}
 {-# LANGUAGE ViewPatterns          #-}
+
+{-# OPTIONS_GHC -fno-warn-unused-imports #-}
+  -- for Data.Semigroup
+
 -----------------------------------------------------------------------------
 -- |
 -- Module      :  Diagrams.ThreeD.Transform
@@ -17,10 +24,12 @@
 -----------------------------------------------------------------------------
 
 module Diagrams.ThreeD.Transform
-       (
+       ( T3
+
          -- * Rotation
-         aboutX, aboutY, aboutZ
-       , rotationAbout, pointAt, pointAt'
+       , aboutX, aboutY, aboutZ
+       , rotationAbout, rotateAbout
+       , pointAt, pointAt'
 
        -- * Scaling
        , scalingX, scalingY, scalingZ
@@ -37,26 +46,27 @@
        , reflectionX, reflectX
        , reflectionY, reflectY
        , reflectionZ, reflectZ
-       , reflectionAbout, reflectAbout
+       , reflectionAcross, reflectAcross
 
-       -- * Utilities for Backends
-       , onBasis
        ) where
 
 import           Diagrams.Core
-import qualified Diagrams.Core.Transform as T
+import           Diagrams.Core.Transform
 
 import           Diagrams.Angle
-import           Diagrams.Transform
+import           Diagrams.Direction
+import           Diagrams.Points
 import           Diagrams.ThreeD.Types
-import           Diagrams.Coordinates
+import           Diagrams.Transform
 
-import           Control.Lens                   (view, (*~), (//~))
+import           Control.Lens            (view, (&), (*~), (.~), (//~))
 import           Data.Semigroup
+import           Diagrams.TwoD.Transform
 
-import           Data.AffineSpace
-import           Data.Cross
-import           Data.VectorSpace
+import           Linear.Affine
+import           Linear.Metric
+import           Linear.V3               (cross)
+import           Linear.Vector
 
 -- | Create a transformation which rotates by the given angle about
 --   a line parallel the Z axis passing through the local origin.
@@ -72,192 +82,142 @@
 --   Note that writing @aboutZ (1\/4)@, with no type annotation, will
 --   yield an error since GHC cannot figure out which sort of angle
 --   you want to use.
-aboutZ :: Angle -> T3
-aboutZ ang = fromLinear r (linv r) where
-  r = rot theta <-> rot (-theta)
-  theta = view rad ang
-  rot th (coords -> x :& y :& z) = (cos th * x - sin th * y) ^&
-                                   (sin th * x + cos th * y) ^&
-                                   z
+aboutZ :: Floating n => Angle n -> Transformation V3 n
+aboutZ (view rad -> a) = fromOrthogonal r where
+  r = rot a <-> rot (-a)
+  rot θ (V3 x y z) = V3 (cos θ * x - sin θ * y)
+                        (sin θ * x + cos θ * y)
+                        z
 
 -- | Like 'aboutZ', but rotates about the X axis, bringing positive y-values
 -- towards the positive z-axis.
-aboutX :: Angle -> T3
-aboutX ang = fromLinear r (linv r) where
-  r = rot theta <-> rot (-theta)
-  theta = view rad ang
-  rot th (coords -> x :& y :& z) = (x) ^&
-                                   (cos th * y - sin th * z) ^&
-                                   (sin th * y + cos th * z)
+aboutX :: Floating n => Angle n -> Transformation V3 n
+aboutX (view rad -> a) = fromOrthogonal r where
+  r = rot a <-> rot (-a)
+  rot θ (V3 x y z) = V3 x
+                        (cos θ * y - sin θ * z)
+                        (sin θ * y + cos θ * z)
 
 -- | Like 'aboutZ', but rotates about the Y axis, bringing postive
 -- x-values towards the negative z-axis.
-aboutY :: Angle -> T3
-aboutY ang = fromLinear r (linv r) where
-  r = rot theta <-> rot (-theta)
-  theta = view rad ang
-  rot th (coords -> x :& y :& z) = (cos th * x + sin th * z) ^&
-                                    y ^&
-                                    (-sin th * x + cos th * z)
+aboutY :: Floating n => Angle n -> Transformation V3 n
+aboutY (view rad -> a) = fromOrthogonal r where
+  r = rot a <-> rot (-a)
+  rot θ (V3 x y z) = V3 (cos θ * x + sin θ * z)
+                        y
+                        (-sin θ * x + cos θ * z)
 
 -- | @rotationAbout p d a@ is a rotation about a line parallel to @d@
 --   passing through @p@.
-rotationAbout ::
-     P3        -- ^ origin of rotation
-  -> Direction -- ^ direction of rotation axis
-  -> Angle     -- ^ angle of rotation
-  -> T3
-rotationAbout p d a
-  = mconcat [translation (negateV t),
-             fromLinear r (linv r),
+rotationAbout
+  :: Floating n
+  => Point V3 n         -- ^ origin of rotation
+  -> Direction V3 n     -- ^ direction of rotation axis
+  -> Angle n            -- ^ angle of rotation
+  -> Transformation V3 n
+rotationAbout (P t) d (view rad -> a)
+  = mconcat [translation (negated t),
+             fromOrthogonal r,
              translation t] where
-    r = rot theta <-> rot (-theta)
-    theta = view rad a
+    r = rot a <-> rot (-a)
     w = fromDirection d
-    rot :: Double -> R3 -> R3
-    rot th v = v ^* cos th ^+^
-               cross3 w v ^* sin th ^+^
-               w ^* ((w <.> v) * (1 - cos th))
-    t = p .-. origin
 
+    rot θ v =          v ^* cos θ
+           ^+^ cross w v ^* sin θ
+           ^+^         w ^* ((w `dot` v) * (1 - cos θ))
+
+-- | @rotationAbout p d a@ is a rotation about a line parallel to @d@
+--   passing through @p@.
+rotateAbout
+  :: (InSpace V3 n t, Floating n, Transformable t)
+  => Point V3 n         -- ^ origin of rotation
+  -> Direction V3 n     -- ^ direction of rotation axis
+  -> Angle n            -- ^ angle of rotation
+  -> t -> t
+rotateAbout p d theta = transform (rotationAbout p d theta)
+
 -- | @pointAt about initial final@ produces a rotation which brings
 -- the direction @initial@ to point in the direction @final@ by first
 -- panning around @about@, then tilting about the axis perpendicular
--- to initial and final.  In particular, if this can be accomplished
+-- to @about@ and @final@.  In particular, if this can be accomplished
 -- without tilting, it will be, otherwise if only tilting is
 -- necessary, no panning will occur.  The tilt will always be between
 -- ± 1/4 turn.
-pointAt :: Direction -> Direction -> Direction -> T3
+pointAt :: (Floating n, Ord n)
+        => Direction V3 n -> Direction V3 n -> Direction V3 n
+        -> Transformation V3 n
 pointAt a i f = pointAt' (fromDirection a) (fromDirection i) (fromDirection f)
 
 -- | pointAt' has the same behavior as 'pointAt', but takes vectors
 -- instead of directions.
-pointAt' :: R3 -> R3 -> R3 -> T3
-pointAt' about initial final = tilt <> pan where
-  inPanPlane    = final ^-^ project final initial
-  panAngle      = angleBetween initial inPanPlane
-  pan           = rotationAbout origin (direction about) panAngle
-  tiltAngle     = angleBetween initial inPanPlane
-  tiltDir       = direction $ cross3 inPanPlane about
-  tilt          = rotationAbout origin tiltDir tiltAngle
-
--- Scaling -------------------------------------------------
-
--- | Construct a transformation which scales by the given factor in
---   the x direction.
-scalingX :: Double -> T3
-scalingX c = fromLinear s s
-  where s = (_x *~ c) <-> (_x //~ c)
-
--- | Scale a diagram by the given factor in the x (horizontal)
---   direction.  To scale uniformly, use 'scale'.
-scaleX :: (Transformable t, V t ~ R3) => Double -> t -> t
-scaleX = transform . scalingX
+pointAt' :: (Floating n, Ord n) => V3 n -> V3 n -> V3 n -> Transformation V3 n
+pointAt' about initial final = pointAtUnit (signorm about) (signorm initial) (signorm final)
 
--- | Construct a transformation which scales by the given factor in
---   the y direction.
-scalingY :: Double -> T3
-scalingY c = fromLinear s s
-  where s = (_y *~ c) <-> (_y //~ c)
+-- | pointAtUnit has the same behavior as @pointAt@, but takes unit vectors.
+pointAtUnit :: (Floating n, Ord n) => V3 n -> V3 n -> V3 n -> Transformation V3 n
+pointAtUnit about initial final = tilt <> pan where
+  -- rotating u by (signedAngle rel u v) about rel gives a vector in the direction of v
+  signedAngle rel u v = signum (cross u v `dot` rel) *^ angleBetween u v
+  inPanPlaneF = final ^-^ project about final
+  inPanPlaneI = initial ^-^ project about initial
+  panAngle    = signedAngle about inPanPlaneI inPanPlaneF
+  pan         = rotationAbout origin (direction about) panAngle
+  tiltAngle   = signedAngle tiltAxis (transform pan initial) final
+  tiltAxis    = cross final about
+  tilt        = rotationAbout origin (direction tiltAxis) tiltAngle
 
--- | Scale a diagram by the given factor in the y (vertical)
---   direction.  To scale uniformly, use 'scale'.
-scaleY :: (Transformable t, V t ~ R3) => Double -> t -> t
-scaleY = transform . scalingY
+-- Scaling -------------------------------------------------
 
 -- | Construct a transformation which scales by the given factor in
 --   the z direction.
-scalingZ :: Double -> T3
-scalingZ c = fromLinear s s
-  where s = (_z *~ c) <-> (_z //~ c)
+scalingZ :: (Additive v, R3 v, Fractional n) => n -> Transformation v n
+scalingZ c = fromSymmetric $ (_z *~ c) <-> (_z //~ c)
 
 -- | Scale a diagram by the given factor in the z direction.  To scale
 -- uniformly, use 'scale'.
-scaleZ :: (Transformable t, V t ~ R3) => Double -> t -> t
+scaleZ :: (InSpace v n t, R3 v, Fractional n, Transformable t) => n -> t -> t
 scaleZ = transform . scalingZ
 
 -- Translation ----------------------------------------
 
 -- | Construct a transformation which translates by the given distance
---   in the x direction.
-translationX :: Double -> T3
-translationX x = translation (x ^& 0 ^& 0)
-
--- | Translate a diagram by the given distance in the x
---   direction.
-translateX :: (Transformable t, V t ~ R3) => Double -> t -> t
-translateX = transform . translationX
-
--- | Construct a transformation which translates by the given distance
---   in the y direction.
-translationY :: Double -> T3
-translationY y = translation (0 ^& y ^& 0)
-
--- | Translate a diagram by the given distance in the y
---   direction.
-translateY :: (Transformable t, V t ~ R3) => Double -> t -> t
-translateY = transform . translationY
-
--- | Construct a transformation which translates by the given distance
 --   in the z direction.
-translationZ :: Double -> T3
-translationZ z = translation (0 ^& 0 ^& z)
+translationZ :: (Additive v, R3 v, Num n) => n -> Transformation v n
+translationZ z = translation (zero & _z .~ z)
 
 -- | Translate a diagram by the given distance in the y
 --   direction.
-translateZ :: (Transformable t, V t ~ R3) => Double -> t -> t
+translateZ :: (InSpace v n t, R3 v, Transformable t) => n -> t -> t
 translateZ = transform . translationZ
 
 -- Reflection ----------------------------------------------
 
--- | Construct a transformation which flips a diagram across x=0,
--- i.e. sends the point (x,y,z) to (-x,y,z).
-reflectionX :: T3
-reflectionX = scalingX (-1)
-
--- | Flip a diagram across x=0, i.e. send the point (x,y,z) to (-x,y,z).
-reflectX :: (Transformable t, V t ~ R3) => t -> t
-reflectX = transform reflectionX
-
--- | Construct a transformation which flips a diagram across y=0,
--- i.e. sends the point (x,y,z) to (x,-y,z).
-reflectionY :: T3
-reflectionY = scalingY (-1)
-
--- | Flip a diagram across y=0, i.e. send the point (x,y,z) to
--- (x,-y,z).
-reflectY :: (Transformable t, V t ~ R3) => t -> t
-reflectY = transform reflectionY
-
 -- | Construct a transformation which flips a diagram across z=0,
 -- i.e. sends the point (x,y,z) to (x,y,-z).
-reflectionZ :: T3
-reflectionZ = scalingZ (-1)
+reflectionZ :: (Additive v, R3 v, Num n) => Transformation v n
+reflectionZ = fromSymmetric $ (_z *~ (-1)) <-> (_z *~ (-1))
 
 -- | Flip a diagram across z=0, i.e. send the point (x,y,z) to
 -- (x,y,-z).
-reflectZ :: (Transformable t, V t ~ R3) => t -> t
+reflectZ :: (InSpace v n t, R3 v, Transformable t) => t -> t
 reflectZ = transform reflectionZ
 
--- | @reflectionAbout p v@ is a reflection across the plane through
---   the point @p@ and normal to vector @v@.
-reflectionAbout :: P3 -> R3 -> T3
-reflectionAbout p v =
-  conjugate (translation (origin .-. p)) reflect where
-    reflect = fromLinear t (linv t)
-    t = f v <-> f (negateV v)
-    f u w = w ^-^ 2 *^ project u w
-
--- | @reflectAbout p v@ reflects a diagram in the line determined by
---   the point @p@ and the vector @v@.
-reflectAbout :: (Transformable t, V t ~ R3) => P3 -> R3 -> t -> t
-reflectAbout p v = transform (reflectionAbout p v)
-
--- Utilities ----------------------------------------
+-- | @reflectionAcross p v@ is a reflection across the plane through
+--   the point @p@ and normal to vector @v@. This also works as a 2D
+--   transform where @v@ is the normal to the line passing through point
+--   @p@.
+reflectionAcross :: (Metric v, Fractional n)
+  => Point v n -> v n -> Transformation v n
+reflectionAcross p v =
+  conjugate (translation (origin .-. p)) reflect
+    where
+      reflect = fromLinear t (linv t)
+      t       = f v <-> f (negated v)
+      f u w   = w ^-^ 2 *^ project u w
 
--- | Get the matrix equivalent of an affine transform, as a triple of
---   columns paired with the translation vector.  This is mostly
---   useful for implementing backends.
-onBasis :: T3 -> ((R3, R3, R3), R3)
-onBasis t = ((x, y, z), v)
-  where (x:y:z:[], v) = T.onBasis t
+-- | @reflectAcross p v@ reflects a diagram across the plane though
+--   the point @p@ and the vector @v@. This also works as a 2D transform
+--   where @v@ is the normal to the line passing through point @p@.
+reflectAcross :: (InSpace v n t, Metric v, Fractional n, Transformable t)
+  => Point v n -> v n -> t -> t
+reflectAcross p v = transform (reflectionAcross p v)
diff --git a/src/Diagrams/ThreeD/Types.hs b/src/Diagrams/ThreeD/Types.hs
--- a/src/Diagrams/ThreeD/Types.hs
+++ b/src/Diagrams/ThreeD/Types.hs
@@ -1,12 +1,5 @@
-{-# LANGUAGE FlexibleInstances          #-}
-{-# LANGUAGE GeneralizedNewtypeDeriving #-}
-{-# LANGUAGE MultiParamTypeClasses      #-}
-{-# LANGUAGE RankNTypes                 #-}
-{-# LANGUAGE TypeFamilies               #-}
-{-# LANGUAGE TypeOperators              #-}
-{-# LANGUAGE TypeSynonymInstances       #-}
-{-# LANGUAGE UndecidableInstances       #-}
-{-# LANGUAGE ViewPatterns               #-}
+{-# LANGUAGE TypeFamilies #-}
+{-# OPTIONS_GHC -fno-warn-orphans #-}
 
 -----------------------------------------------------------------------------
 -- |
@@ -21,203 +14,85 @@
 
 module Diagrams.ThreeD.Types
        ( -- * 3D Euclidean space
-         R3(..), r3, unr3, mkR3
-       , P3, p3, unp3, mkP3
-       , T3
-       , r3Iso, p3Iso
+         r3, unr3, mkR3
+       , p3, unp3, mkP3
+       , r3Iso, p3Iso, project
+       , r3SphericalIso, r3CylindricalIso
+       , V3 (..), P3,      T3
+       , R1 (..), R2 (..), R3 (..)
 
-         -- * Directions in 3D
-       , Direction, direction, fromDirection, angleBetweenDirs
-       -- * other coördinate systems
-       , Spherical(..), Cylindrical(..), HasPhi(..)
        ) where
 
-import           Control.Lens           (Iso', Lens', iso, over
-                                        , _1, _2, _3, (^.))
+import           Control.Lens        (Iso', iso, _1, _2, _3)
 
-import           Diagrams.Core
 import           Diagrams.Angle
-import           Diagrams.TwoD.Types    (R2)
-import           Diagrams.Coordinates
+import           Diagrams.Core
+import           Diagrams.Points
+import           Diagrams.TwoD.Types
 
-import           Data.AffineSpace.Point
-import           Data.Basis
-import           Data.Cross
-import           Data.VectorSpace
+import           Linear.Metric
+import           Linear.V3           as V
 
 ------------------------------------------------------------
 -- 3D Euclidean space
 
--- | The three-dimensional Euclidean vector space R^3.
-data R3 = R3 !Double !Double !Double
-  deriving (Eq, Ord, Show, Read)
+-- Basic R3 types
 
-r3Iso :: Iso' R3 (Double, Double, Double)
+type P3 = Point V3
+type T3 = Transformation V3
+
+r3Iso :: Iso' (V3 n) (n, n, n)
 r3Iso = iso unr3 r3
 
 -- | Construct a 3D vector from a triple of components.
-r3 :: (Double, Double, Double) -> R3
-r3 (x,y,z) = R3 x y z
+r3 :: (n, n, n) -> V3 n
+r3 (x,y,z) = V3 x y z
 
 -- | Curried version of `r3`.
-mkR3 :: Double -> Double -> Double -> R3
-mkR3 = R3
+mkR3 :: n -> n -> n -> V3 n
+mkR3 = V3
 
 -- | Convert a 3D vector back into a triple of components.
-unr3 :: R3 -> (Double, Double, Double)
-unr3 (R3 x y z) = (x,y,z)
-
-instance AdditiveGroup R3 where
-    zeroV = R3 0 0 0
-    R3 x1 y1 z1 ^+^ R3 x2 y2 z2 = R3 (x1 + x2) (y1 + y2) (z1 + z2)
-    negateV (R3 x y z) = R3 (-x) (-y) (-z)
-
-type instance V R3 = R3
-
-instance VectorSpace R3 where
-  type Scalar R3 = Double
-  (*^) = over r3Iso . (*^)
-
-instance HasBasis R3 where
-  type Basis R3 = Either () (Either () ()) -- = Basis (Double, Double, Double)
-  basisValue = r3 . basisValue
-  decompose  = decompose  . unr3
-  decompose' = decompose' . unr3
-
-instance InnerSpace R3 where
-    (R3 x1 y1 z1) <.> (R3 x2 y2 z2) = x1*x2 + y1*y2 + z1*z2
-
-instance Coordinates R3 where
-  type FinalCoord R3       = Double
-  type PrevDim R3          = R2
-  type Decomposition R3    = Double :& Double :& Double
-
-  (coords -> x :& y) ^& z   = R3 x y z
-  coords (R3 x y z) = x :& y :& z
-
--- | Points in R^3.
-type P3 = Point R3
+unr3 :: V3 n -> (n, n, n)
+unr3 (V3 x y z) = (x,y,z)
 
 -- | Construct a 3D point from a triple of coordinates.
-p3 :: (Double, Double, Double) -> P3
+p3 :: (n, n, n) -> P3 n
 p3 = P . r3
 
 -- | Convert a 3D point back into a triple of coordinates.
-unp3 :: P3 -> (Double, Double, Double)
-unp3 = unr3 . unPoint
+unp3 :: P3 n -> (n, n, n)
+unp3 (P (V3 x y z)) = (x,y,z)
 
-p3Iso :: Iso' P3 (Double, Double, Double)
+p3Iso :: Iso' (P3 n) (n, n, n)
 p3Iso = iso unp3 p3
 
 -- | Curried version of `r3`.
-mkP3 :: Double -> Double -> Double -> P3
+mkP3 :: n -> n -> n -> P3 n
 mkP3 x y z = p3 (x, y, z)
 
--- | Transformations in R^3.
-type T3 = Transformation R3
+type instance V (V3 n) = V3
+type instance N (V3 n) = n
 
-instance Transformable R3 where
+instance Transformable (V3 n) where
   transform = apply
 
-instance HasCross3 R3 where
-  cross3 u v = r3 $ cross3 (unr3 u) (unr3 v)
-
---------------------------------------------------------------------------------
--- Direction
-
--- | A @Direction@ represents directions in R3.  The constructor is
--- not exported; @Direction@s can be used with 'fromDirection' and the
--- lenses provided by its instances.
-data Direction = Direction R3
-
--- | Not exported
-_Dir :: Iso' Direction R3
-_Dir = iso (\(Direction v) -> v) Direction
-
-instance HasX R3 where
-    _x = r3Iso . _1
-
-instance HasX P3 where
-    _x = p3Iso . _1
-
-instance HasY R3 where
-    _y = r3Iso . _2
-
-instance HasY P3 where
-    _y = p3Iso . _2
-
-instance HasZ R3 where
-    _z = r3Iso . _3
-
-instance HasZ P3 where
-    _z = p3Iso . _3
-
--- | Types which can be expressed in spherical 3D coordinates, as a
--- triple (r,θ,φ), where θ is rotation about the Z axis, and φ is the
--- angle from the Z axis.
-class Spherical t where
-    spherical :: Iso' t (Double, Angle, Angle)
-
--- | Types which can be expressed in cylindrical 3D coordinates.
-class Cylindrical t where
-    cylindrical :: Iso' t (Double, Angle, Double) -- r, θ, z
-
-instance Cylindrical R3 where
-    cylindrical = iso (\(R3 x y z) -> (sqrt (x^(2::Int)+y^(2::Int)), atanA (y/x), z))
-                      (\(r,θ,z) -> R3 (r*cosA θ) (r*sinA θ) z)
-
-instance Spherical R3 where
-    spherical = iso
-      (\v@(R3 x y z) -> (magnitude v, atanA (y/x), atanA (v^._r/z)))
-      (\(r,θ,φ) -> R3 (r*cosA θ*sinA φ) (r*sinA θ*sinA φ) (r*cosA φ))
-
--- We'd like to write: instance Spherical t => HasR t
--- But GHC can't work out that the instance won't overlap.  Just write them explicitly:
-
-instance HasR R3 where
-    _r = spherical . _1
-
-instance HasR P3 where
-    _r = spherical . _1
-
-instance HasTheta R3 where
-    _theta = cylindrical . _2
-
-instance HasTheta P3 where
-    _theta = cylindrical . _2
-
--- | The class of types with at least two angle coordinates, the
--- second called _phi.
-class HasPhi t where
-    _phi :: Lens' t Angle
-
-instance HasPhi R3 where
-    _phi = spherical . _3
-
-instance HasPhi P3 where
-    _phi = spherical . _3
-
-instance Cylindrical P3 where
-    cylindrical = _relative origin . cylindrical
-
-instance Spherical P3 where
-    spherical = _relative origin . spherical
+r3SphericalIso :: RealFloat n => Iso' (V3 n) (n, Angle n, Angle n)
+r3SphericalIso = iso
+  (\v@(V3 x y z) -> (norm v, atan2A y x, acosA (z / norm v)))
+  (\(r,θ,φ)   -> V3 (r * cosA θ * sinA φ) (r * sinA θ * sinA φ) (r * cosA φ))
 
-instance HasTheta Direction where
-    _theta = _Dir . _theta
+r3CylindricalIso :: RealFloat n => Iso' (V3 n) (n, Angle n, n)
+r3CylindricalIso = iso
+  (\(V3 x y z) -> (sqrt $ x*x + y*y, atan2A y x, z))
+  (\(r,θ,z)    -> V3 (r*cosA θ) (r*sinA θ) z)
 
-instance HasPhi Direction where
-    _phi = _Dir . _phi
+instance HasR V3 where
+  _r = r3SphericalIso . _1
 
--- | @direction v@ is the direction in which @v@ points.  Returns an
---   unspecified value when given the zero vector as input.
-direction :: R3 -> Direction
-direction = Direction
+instance HasTheta V3 where
+  _theta = r3CylindricalIso . _2
 
--- | @fromDirection d@ is the unit vector in the direction @d@.
-fromDirection :: Direction -> R3
-fromDirection (Direction v) = normalized v
+instance HasPhi V3 where
+  _phi = r3SphericalIso . _3
 
--- | compute the positive angle between the two directions in their common plane
-angleBetweenDirs  :: Direction -> Direction -> Angle
-angleBetweenDirs d1 d2 = angleBetween (fromDirection d1) (fromDirection d2)
diff --git a/src/Diagrams/ThreeD/Vector.hs b/src/Diagrams/ThreeD/Vector.hs
--- a/src/Diagrams/ThreeD/Vector.hs
+++ b/src/Diagrams/ThreeD/Vector.hs
@@ -1,7 +1,3 @@
-{-# LANGUAGE FlexibleContexts
-           , TypeFamilies
-           , ViewPatterns
-  #-}
 -----------------------------------------------------------------------------
 -- |
 -- Module      :  Diagrams.ThreeD.Vector
@@ -13,34 +9,27 @@
 --
 -----------------------------------------------------------------------------
 module Diagrams.ThreeD.Vector
-       ( -- * Special 2D vectors
-         unitX, unitY, unitZ, unit_X, unit_Y, unit_Z,
+       ( -- * Special 3D vectors
+         unitX, unitY, unitZ, unit_X, unit_Y, unit_Z
+       , xDir, yDir, zDir
        ) where
 
-import Diagrams.Coordinates
-import Diagrams.ThreeD.Types
+import           Control.Lens          ((&), (.~))
 
+import           Diagrams.ThreeD.Types
+import           Diagrams.TwoD.Vector
+import           Diagrams.Direction
 
--- | The unit vector in the positive X direction.
-unitX :: R3
-unitX = 1 ^& 0 ^& 0
+import           Linear.Vector
 
 -- | The unit vector in the positive Y direction.
-unitY :: R3
-unitY = 0 ^& 1 ^& 0
-
--- | The unit vector in the positive Z direction.
-unitZ :: R3
-unitZ = 0 ^& 0 ^& 1
+unitZ :: (R3 v, Additive v, Num n) => v n
+unitZ = zero & _z .~ 1
 
 -- | The unit vector in the negative X direction.
-unit_X :: R3
-unit_X = (-1) ^& 0 ^& 0
-
--- | The unit vector in the negative Y direction.
-unit_Y :: R3
-unit_Y = 0 ^& (-1) ^& 0
+unit_Z :: (R3 v, Additive v, Num n) => v n
+unit_Z = zero & _z .~ (-1)
 
--- | The unit vector in the negative Z direction.
-unit_Z :: R3
-unit_Z = 0 ^& 0 ^& (-1)
+-- | A 'Direction' pointing in the Z direction.
+zDir :: (R3 v, Additive v, Num n) => Direction v n
+zDir = dir unitZ
diff --git a/src/Diagrams/Trace.hs b/src/Diagrams/Trace.hs
--- a/src/Diagrams/Trace.hs
+++ b/src/Diagrams/Trace.hs
@@ -1,4 +1,10 @@
+{-# LANGUAGE ConstraintKinds #-}
 {-# LANGUAGE FlexibleContexts #-}
+{-# LANGUAGE MonoLocalBinds   #-}
+
+{-# OPTIONS_GHC -fno-warn-unused-imports #-}
+  -- for Data.Semigroup
+
 -----------------------------------------------------------------------------
 -- |
 -- Module      :  Diagrams.Trace
@@ -27,28 +33,30 @@
 
     ) where
 
-import           Diagrams.Core        (HasLinearMap, Point, Subdiagram
-                                      , location, origin, setTrace, trace
-                                      , OrderedField)
+import           Diagrams.Core        (OrderedField, Point, Subdiagram, location,
+                                       origin, setTrace, trace)
 import           Diagrams.Core.Trace
 
 import           Data.Maybe
 import           Data.Semigroup
-import           Data.VectorSpace     (Scalar, negateV, InnerSpace)
 import           Diagrams.Combinators (withTrace)
 
+import           Linear.Metric
+import           Linear.Vector
+
 -- | Compute the furthest point on the boundary of a subdiagram,
 --   beginning from the location (local origin) of the subdiagram and
 --   moving in the direction of the given vector.  If there is no such
 --   point, the origin is returned; see also 'boundaryFromMay'.
-boundaryFrom :: (HasLinearMap v, OrderedField (Scalar v), InnerSpace v, Semigroup m)
-                => Subdiagram b v m -> v -> Point v
+boundaryFrom :: (OrderedField n, Metric v, Semigroup m)
+              => Subdiagram b v n m -> v n -> Point v n
 boundaryFrom s v = fromMaybe origin $ boundaryFromMay s v
 
 -- | Compute the furthest point on the boundary of a subdiagram,
 --   beginning from the location (local origin) of the subdiagram and
 --   moving in the direction of the given vector, or @Nothing@ if
 --   there is no such point.
-boundaryFromMay :: (HasLinearMap v, OrderedField (Scalar v), Semigroup m, InnerSpace v)
-                   => Subdiagram b v m -> v -> Maybe (Point v)
-boundaryFromMay s v = traceP (location s) (negateV v) s
+boundaryFromMay :: (Metric v, OrderedField n, Semigroup m)
+                => Subdiagram b v n m -> v n -> Maybe (Point v n)
+boundaryFromMay s v = traceP (location s) (negated v) s
+
diff --git a/src/Diagrams/Trail.hs b/src/Diagrams/Trail.hs
--- a/src/Diagrams/Trail.hs
+++ b/src/Diagrams/Trail.hs
@@ -1,25 +1,27 @@
-{-# LANGUAGE DeriveFunctor              #-}
+{-# LANGUAGE ConstraintKinds #-}
+{-# LANGUAGE CPP                        #-}
 {-# LANGUAGE EmptyDataDecls             #-}
 {-# LANGUAGE FlexibleContexts           #-}
 {-# LANGUAGE FlexibleInstances          #-}
 {-# LANGUAGE GADTs                      #-}
 {-# LANGUAGE GeneralizedNewtypeDeriving #-}
+{-# LANGUAGE LambdaCase                 #-}
 {-# LANGUAGE MultiParamTypeClasses      #-}
 {-# LANGUAGE ScopedTypeVariables        #-}
 {-# LANGUAGE StandaloneDeriving         #-}
-{-# LANGUAGE TemplateHaskell            #-}
 {-# LANGUAGE TypeFamilies               #-}
 {-# LANGUAGE TypeOperators              #-}
 {-# LANGUAGE UndecidableInstances       #-}
 {-# LANGUAGE ViewPatterns               #-}
 
 {-# OPTIONS_GHC -fno-warn-orphans #-}
+{-# OPTIONS_GHC -fno-warn-name-shadowing #-}
 -- We have an orphan Transformable FingerTree instance here.
 
 -----------------------------------------------------------------------------
 -- |
 -- Module      :  Diagrams.Trail
--- Copyright   :  (c) 2013 diagrams-lib team (see LICENSE)
+-- Copyright   :  (c) 2013-2015 diagrams-lib team (see LICENSE)
 -- License     :  BSD-style (see LICENSE)
 -- Maintainer  :  diagrams-discuss@googlegroups.com
 --
@@ -55,6 +57,8 @@
          -- ** Generic trails
 
        , Trail(..)
+       , _Line, _Loop
+       , _LocLine, _LocLoop
        , wrapTrail, wrapLine, wrapLoop
        , onTrail, onLine
 
@@ -66,6 +70,7 @@
        , lineFromVertices, trailFromVertices
        , lineFromOffsets,  trailFromOffsets
        , lineFromSegments, trailFromSegments
+       , loopFromSegments
 
          -- * Eliminating trails
 
@@ -76,8 +81,10 @@
        , onLineSegments
        , trailOffsets, trailOffset
        , lineOffsets, lineOffset, loopOffsets
+       , trailPoints, linePoints, loopPoints
+       , trailVertices', lineVertices', loopVertices'
        , trailVertices, lineVertices, loopVertices
-       , trailLocSegments, fixTrail
+       , trailLocSegments, fixTrail, unfixTrail
 
          -- * Modifying trails
 
@@ -98,27 +105,34 @@
 
          -- ** Extracting segments
 
-       , GetSegment(..), getSegment
+       , GetSegment(..), getSegment, GetSegmentCodomain(..)
 
        ) where
 
-import           Control.Arrow       ((***))
-import           Control.Lens        (AnIso', iso, view, op, Wrapped(..), Rewrapped)
-import           Data.AffineSpace
-import           Data.FingerTree     (FingerTree, ViewL (..), ViewR (..), (<|),
-                                      (|>))
-import qualified Data.FingerTree     as FT
-import qualified Data.Foldable       as F
+import           Control.Arrow            ((***))
+import           Control.Lens             hiding (at, transform, (<|), (|>))
+import           Data.FingerTree          (FingerTree, ViewL (..), ViewR (..),
+                                           viewl, (<|), (|>))
+import qualified Data.FingerTree          as FT
+import           Data.Fixed
+import qualified Data.Foldable            as F
 import           Data.Monoid.MList
 import           Data.Semigroup
-import           Data.VectorSpace    hiding (Sum (..))
-import qualified Numeric.Interval.Kaucher    as I
+import qualified Numeric.Interval.Kaucher as I
 
-import           Diagrams.Core       hiding ((|>))
+import           Diagrams.Core
 import           Diagrams.Located
 import           Diagrams.Parametric
 import           Diagrams.Segment
+import           Diagrams.Tangent
 
+import           Linear.Affine
+import           Linear.Metric
+import           Linear.Vector
+
+import           Data.Serialize            (Serialize)
+import qualified Data.Serialize            as Serialize
+
 -- $internals
 --
 -- Most users of diagrams should not need to use anything in this
@@ -130,13 +144,26 @@
 ------------------------------------------------------------
 
 type instance V (FingerTree m a) = V a
+type instance N (FingerTree m a) = N a
 
-instance ( HasLinearMap (V a), InnerSpace (V a), OrderedField (Scalar (V a))
-         , FT.Measured m a, Transformable a
-         )
+instance (FT.Measured m a, Transformable a)
     => Transformable (FingerTree m a) where
   transform = FT.fmap' . transform
 
+instance (FT.Measured m a, FT.Measured n b)
+  => Cons (FingerTree m a) (FingerTree n b) a b where
+  _Cons = prism (uncurry (FT.<|)) $ \aas -> case FT.viewl aas of
+    a FT.:< as -> Right (a, as)
+    EmptyL     -> Left mempty
+  {-# INLINE _Cons #-}
+
+instance (FT.Measured m a, FT.Measured n b)
+  => Snoc (FingerTree m a) (FingerTree n b) a b where
+  _Snoc = prism (uncurry (FT.|>)) $ \aas -> case FT.viewr aas of
+    as FT.:> a -> Right (as, a)
+    EmptyR  -> Left mempty
+  {-# INLINE _Snoc #-}
+
 ------------------------------------------------------------
 --  Segment trees  -----------------------------------------
 ------------------------------------------------------------
@@ -148,72 +175,95 @@
 --   (/e.g./, split off the smallest number of segments from the
 --   beginning which have a combined arc length of at least 5).
 
-newtype SegTree v = SegTree (FingerTree (SegMeasure v) (Segment Closed v))
-  deriving (Eq, Ord, Show)
+newtype SegTree v n = SegTree (FingerTree (SegMeasure v n) (Segment Closed v n))
+  deriving (Eq, Ord, Show, Monoid, Transformable, FT.Measured (SegMeasure v n))
 
-instance Wrapped (SegTree v) where
-    type Unwrapped (SegTree v) = FingerTree (SegMeasure v) (Segment Closed v)
-    _Wrapped' = iso (\(SegTree x) -> x) SegTree
+-- Only derive the Semigroup instance for versions of base that
+-- include Semigroup.  This is because the fingertree package has
+-- similar CPP to only export a Semigroup instance for those versions
+-- of base, so for GHC 7.10 and earlier we get a 'no instance found'
+-- error when trying to derive the Semigroup instance for SegTree.  It
+-- would also be possible to depend on the 'semigroups' package in
+-- order to get the Semigroup class regardless of base version, but
+-- presumably fingertree didn't want to add a dependency.
+#if MIN_VERSION_base(4,9,0)
+deriving instance (Ord n, Floating n, Metric v) => Semigroup (SegTree v n)
+#endif
 
-instance Rewrapped (SegTree v) (SegTree v')
+instance Wrapped (SegTree v n) where
+  type Unwrapped (SegTree v n) = FingerTree (SegMeasure v n) (Segment Closed v n)
+  _Wrapped' = iso (\(SegTree x) -> x) SegTree
+  {-# INLINE _Wrapped' #-}
 
-type instance V (SegTree v) = v
+instance (Metric v, OrderedField n, Metric u, OrderedField n')
+  => Cons (SegTree v n) (SegTree u n') (Segment Closed v n) (Segment Closed u n') where
+  _Cons = _Wrapped . _Cons . bimapping id _Unwrapped
+  {-# INLINE _Cons #-}
 
-deriving instance (OrderedField (Scalar v), InnerSpace v)
-  => Monoid (SegTree v)
-deriving instance (OrderedField (Scalar v), InnerSpace v)
-  => FT.Measured (SegMeasure v) (SegTree v)
-deriving instance (HasLinearMap v, InnerSpace v, OrderedField (Scalar v))
-  => Transformable (SegTree v)
+instance (Metric v, OrderedField n, Metric u, OrderedField n')
+  => Snoc (SegTree v n) (SegTree u n') (Segment Closed v n) (Segment Closed u n') where
+  _Snoc = _Wrapped . _Snoc . bimapping _Unwrapped id
+  {-# INLINE _Snoc #-}
 
-type instance Codomain (SegTree v) = v
+instance Rewrapped (SegTree v n) (SegTree v' n')
 
-instance (InnerSpace v, OrderedField (Scalar v), RealFrac (Scalar v))
-    => Parametric (SegTree v) where
+type instance V (SegTree v n) = v
+type instance N (SegTree v n) = n
+
+type instance Codomain (SegTree v n) = v
+
+instance (Metric v, OrderedField n, Real n)
+    => Parametric (SegTree v n) where
   atParam t p = offset . fst $ splitAtParam t p
 
-instance Num (Scalar v) => DomainBounds (SegTree v)
+instance Num n => DomainBounds (SegTree v n)
 
-instance (InnerSpace v, OrderedField (Scalar v), RealFrac (Scalar v), Num (Scalar v))
-    => EndValues (SegTree v)
+instance (Metric v, OrderedField n, Real n)
+    => EndValues (SegTree v n)
 
-instance (InnerSpace v, RealFrac (Scalar v), Floating (Scalar v))
-    => Sectionable (SegTree v) where
-  splitAtParam (SegTree t) p
-    | p < 0     = case FT.viewl t of
-                    EmptyL    -> emptySplit
-                    seg :< t' ->
-                      case seg `splitAtParam` (p * tSegs) of
-                        (seg1, seg2) -> ( SegTree $ FT.singleton seg1
-                                        , SegTree $ seg2 <| t'
-                                        )
-    | p >= 1    = case FT.viewr t of
-                    EmptyR    -> emptySplit
-                    t' :> seg ->
-                      case seg `splitAtParam` (1 - (1 - p)*tSegs) of
-                        (seg1, seg2) -> ( SegTree $ t' |> seg1
-                                        , SegTree $ FT.singleton seg2
-                                        )
-    | otherwise = case FT.viewl after of
-                    EmptyL    -> emptySplit
-                    seg :< after' ->
-                      case seg `splitAtParam` (snd . propFrac $ p * tSegs) of
-                        (seg1, seg2) -> ( SegTree $ before |> seg1
-                                        , SegTree $ seg2   <| after'
-                                        )
-    where
-      (before, after) = FT.split ((p * tSegs <) . numSegs) t
-      tSegs           = numSegs t
-      emptySplit      = (SegTree t, SegTree t)
+splitAtParam' :: (Metric v, OrderedField n, Real n)
+              => SegTree v n -> n -> ((SegTree v n, SegTree v n), n -> n)
+splitAtParam' (SegTree t) p
+  | tSegs == 0 = ((mempty       , mempty       ), id)
+  | otherwise  = ((SegTree treeL, SegTree treeR), rescale)
+  where
+    tSegs  = numSegs t
+    splitParam q | q <  0    = (0        , q           * tSegs)
+                 | q >= 1    = (tSegs - 1, 1 + (q - 1) * tSegs)
+                 | otherwise = propFrac $  q           * tSegs
+      where propFrac x = let m = mod1 x in (x - m, m)
+    (pSegs, pParam) = splitParam p
+    (before, viewl -> seg FT.:< after) = FT.split ((pSegs <) . numSegs) t
+    (segL, segR) = seg `splitAtParam` pParam
+    (treeL, treeR) | pParam == 0 = (before        , seg  <| after)
+                   | pParam == 1 = (before |> seg ,         after)
+                   | otherwise   = (before |> segL, segR <| after)
+    -- section uses rescale to find the new value of p1 after the split at p2
+    rescale u | pSegs' == uSegs = (uSegs + uParam / pParam' {-'1-}) / (pSegs' + 1) {-'2-}
+              | otherwise       = u * tSegs / (pSegs' + 1) {-'3-}
+      where
+        -- param 0 on a segment is param 1 on the previous segment
+        (pSegs', pParam') | pParam == 0 = (pSegs-1, 1)
+                          | otherwise   = (pSegs  , pParam)
+        (uSegs , uParam ) = splitParam u
+        -- '1 (pParam ≠ 0 → pParam' = pParam) ∧ (pParam = 0 → pParam' = 1) → pParam' ≠ 0
+        -- '2 uSegs ≥ 0 ∧ pSegs' = uSegs → pSegs' ≥ 0 → pSegs' + 1 > 0
+        -- '3 pSegs' + 1 = 0 → pSegs' = -1 → pSegs = 0 ∧ pParam = 0 → p = 0
+        --    → rescale is not called
 
+instance (Metric v, OrderedField n, Real n) => Sectionable (SegTree v n) where
+  splitAtParam tree p = fst $ splitAtParam' tree p
+
   reverseDomain (SegTree t) = SegTree $ FT.reverse t'
     where t' = FT.fmap' reverseSegment t
 
-  -- XXX seems like it should be possible to collapse some of the
-  -- above cases into one?
+  section x p1 p2 | p2 == 0   = reverseDomain . fst $ splitAtParam x p1
+                  | p1 <= p2  = let ((a, _), rescale) = splitAtParam' x p2
+                                in  snd $ splitAtParam a (rescale p1)
+                  | otherwise = reverseDomain $ section x p2 p1
 
-instance (InnerSpace v, OrderedField (Scalar v), RealFrac (Scalar v))
-    => HasArcLength (SegTree v) where
+instance (Metric v, OrderedField n, Real n)
+    => HasArcLength (SegTree v n) where
   arcLengthBounded eps t
     -- Use the cached value if it is accurate enough; otherwise fall
     -- back to recomputing a more accurate value
@@ -221,60 +271,61 @@
     | otherwise        = fun (eps / numSegs t)
     where
       i   = trailMeasure (I.singleton 0)
-              (getArcLengthCached :: ArcLength v -> I.Interval (Scalar v))
+              getArcLengthCached
               t
       fun = trailMeasure (const 0)
-              (getArcLengthFun :: ArcLength v -> Scalar v -> I.Interval (Scalar v))
+              getArcLengthFun
               t
 
   arcLengthToParam eps st@(SegTree t) l
     | l < 0        = case FT.viewl t of
                        EmptyL   -> 0
-                       seg :< _ -> arcLengthToParam eps seg l / tSegs
+                       seg FT.:< _ -> arcLengthToParam eps seg l / tSegs
     | l >= totalAL = case FT.viewr t of
                        EmptyR    -> 0
-                       t' :> seg ->
+                       t' FT.:> seg ->
                          let p = arcLengthToParam (eps/2) seg
                                    (l - arcLength (eps/2) (SegTree t'))
                          in  (p - 1)/tSegs + 1
     | otherwise    = case FT.viewl after of
                        EmptyL    -> 0
-                       seg :< _  ->
+                       seg FT.:< _  ->
                          let p = arcLengthToParam (eps/2) seg
                                    (l - arcLength (eps/2) (SegTree before))
                          in  (numSegs before + p) / tSegs
     where
       totalAL         = arcLength eps st
       tSegs           = numSegs t
-      before, after :: FingerTree (SegMeasure v) (Segment Closed v)
-      (before, after) = FT.split ((>= l) . trailMeasure 0 (I.midpoint . (getArcLengthBounded eps :: ArcLength v -> I.Interval (Scalar v)))) t
+      before, after :: FingerTree (SegMeasure v n) (Segment Closed v n)
+      (before, after) =
+        FT.split ((>= l)
+                 . trailMeasure
+                 0
+                 (I.midpoint . getArcLengthBounded eps))
+                 t
 
 -- | Given a default result (to be used in the case of an empty
 --   trail), and a function to map a single measure to a result,
 --   extract the given measure for a trail and use it to compute a
 --   result.  Put another way, lift a function on a single measure
 --   (along with a default value) to a function on an entire trail.
-trailMeasure :: ( InnerSpace v, OrderedField (Scalar v)
-                , SegMeasure v :>: m, FT.Measured (SegMeasure v) t
-                )
+trailMeasure :: ( SegMeasure v n :>: m, FT.Measured (SegMeasure v n) t )
              => a -> (m -> a) -> t -> a
-trailMeasure d f = option d f . get . FT.measure
+trailMeasure d f = maybe d f . get . FT.measure
 
 -- | Compute the number of segments of anything measured by
 --   'SegMeasure' (/e.g./ @SegMeasure@ itself, @Segment@, @SegTree@,
 --   @Trail@s...)
-numSegs :: ( Floating (Scalar v), Num c, Ord (Scalar v), InnerSpace v,
-             FT.Measured (SegMeasure v) a
-           )
+numSegs :: (Num c, FT.Measured (SegMeasure v n) a)
         => a -> c
 numSegs = fromIntegral . trailMeasure 0 (getSum . op SegCount)
 
 -- | Compute the total offset of anything measured by 'SegMeasure'.
-offset :: ( Floating (Scalar v), Ord (Scalar v), InnerSpace v,
-            FT.Measured (SegMeasure v) t
+offset :: ( OrderedField n, Metric v,
+            FT.Measured (SegMeasure v n) t
           )
-       => t -> v
-offset = trailMeasure zeroV (op TotalOffset . view oeOffset)
+       => t -> v n
+offset = trailMeasure zero (op TotalOffset . view oeOffset)
 
 ------------------------------------------------------------
 --  Trails  ------------------------------------------------
@@ -342,85 +393,125 @@
 --   To extract information from trails, see 'withLine', 'isLoop',
 --   'trailSegments', 'trailOffsets', 'trailVertices', and friends.
 
-data Trail' l v where
-  Line :: SegTree v                   -> Trail' Line v
-  Loop :: SegTree v -> Segment Open v -> Trail' Loop v
+data Trail' l v n where
+  Line :: SegTree v n                     -> Trail' Line v n
+  Loop :: SegTree v n -> Segment Open v n -> Trail' Loop v n
 
 -- | A generic eliminator for 'Trail'', taking functions specifying
 --   what to do in the case of a line or a loop.
-withTrail' :: (Trail' Line v -> r) -> (Trail' Loop v -> r) -> Trail' l v -> r
+withTrail' :: (Trail' Line v n -> r) -> (Trail' Loop v n -> r) -> Trail' l v n -> r
 withTrail' line _    t@(Line{}) = line t
 withTrail' _    loop t@(Loop{}) = loop t
 
-deriving instance Show v => Show (Trail' l v)
-deriving instance Eq   v => Eq   (Trail' l v)
-deriving instance Ord  v => Ord  (Trail' l v)
+deriving instance Eq  (v n) => Eq   (Trail' l v n)
+deriving instance Ord (v n) => Ord  (Trail' l v n)
 
-type instance V (Trail' l v) = v
+instance Show (v n) => Show (Trail' l v n) where
+  showsPrec d (Line (SegTree ft)) = showParen (d > 10) $
+    showString "lineFromSegments " . showList (F.toList ft)
 
-type instance Codomain (Trail' l v) = v
+  showsPrec d (Loop (SegTree ft) o) = showParen (d > 10) $
+    showString "loopFromSegments " . showList (F.toList ft) .
+    showChar ' ' . showsPrec 11 o
 
-instance (OrderedField (Scalar v), InnerSpace v) => Semigroup (Trail' Line v) where
+type instance V (Trail' l v n) = v
+type instance N (Trail' l v n) = n
+
+type instance Codomain (Trail' l v n) = v
+
+instance (OrderedField n, Metric v) => Semigroup (Trail' Line v n) where
   (Line t1) <> (Line t2) = Line (t1 `mappend` t2)
 
 -- | The empty trail is constantly the zero vector.  Trails are
 --   composed via concatenation.  Note that only lines have a monoid
 --   instance (and not loops).
-instance (OrderedField (Scalar v), InnerSpace v) => Monoid (Trail' Line v) where
+instance (Metric v, OrderedField n) => Monoid (Trail' Line v n) where
   mempty  = emptyLine
   mappend = (<>)
 
-instance (HasLinearMap v, InnerSpace v, OrderedField (Scalar v))
-    => Transformable (Trail' l v) where
+instance (Metric v, OrderedField n) => AsEmpty (Trail' Line v n) where
+  _Empty = nearly emptyLine isLineEmpty
+
+instance (HasLinearMap v, Metric v, OrderedField n)
+    => Transformable (Trail' l v n) where
   transform tr (Line t  ) = Line (transform tr t)
   transform tr (Loop t s) = Loop (transform tr t) (transform tr s)
 
 -- | The envelope for a trail is based at the trail's start.
-instance (InnerSpace v, OrderedField (Scalar v)) => Enveloped (Trail' l v) where
+instance (Metric v, OrderedField n) => Enveloped (Trail' l v n) where
   getEnvelope = withTrail' ftEnv (ftEnv . cutLoop)
     where
-      ftEnv :: Trail' Line v -> Envelope v
-      ftEnv (Line t) = trailMeasure mempty (view oeEnvelope) $ t
+      ftEnv :: Trail' Line v n -> Envelope v n
+      ftEnv (Line t) = trailMeasure mempty (view oeEnvelope) t
 
-instance (HasLinearMap v, InnerSpace v, OrderedField (Scalar v))
-    => Renderable (Trail' o v) NullBackend where
+instance (HasLinearMap v, Metric v, OrderedField n)
+    => Renderable (Trail' o v n) NullBackend where
   render _ _ = mempty
 
-instance (InnerSpace v, OrderedField (Scalar v), RealFrac (Scalar v))
-    => Parametric (Trail' l v) where
+instance (Metric v, OrderedField n, Real n)
+    => Parametric (Trail' l v n) where
   atParam t p = withTrail'
                   (\(Line segT) -> segT `atParam` p)
                   (\l -> cutLoop l `atParam` mod1 p)
                   t
 
+instance (Parametric (GetSegment (Trail' c v n)), Additive v, Num n)
+    => Parametric (Tangent (Trail' c v n)) where
+  Tangent tr `atParam` p =
+    case GetSegment tr `atParam` p of
+      GetSegmentCodomain Nothing                  -> zero
+      GetSegmentCodomain (Just (_, seg, reparam)) -> Tangent seg `atParam` (p ^. cloneIso reparam)
+
+instance ( Parametric (GetSegment (Trail' c v n))
+         , EndValues (GetSegment (Trail' c v n))
+         , Additive v
+         , Num n
+         )
+    => EndValues (Tangent (Trail' c v n)) where
+  atStart (Tangent tr) =
+    case atStart (GetSegment tr) of
+      GetSegmentCodomain Nothing            -> zero
+      GetSegmentCodomain (Just (_, seg, _)) -> atStart (Tangent seg)
+  atEnd (Tangent tr) =
+    case atEnd (GetSegment tr) of
+      GetSegmentCodomain Nothing            -> zero
+      GetSegmentCodomain (Just (_, seg, _)) -> atEnd (Tangent seg)
+
+instance (Metric v , OrderedField n, Real n)
+    => Parametric (Tangent (Trail v n)) where
+  Tangent tr `atParam` p
+    = withTrail
+        ((`atParam` p) . Tangent)
+        ((`atParam` p) . Tangent)
+        tr
+
+instance (Metric v, OrderedField n, Real n)
+    => EndValues (Tangent (Trail v n)) where
+  atStart (Tangent tr) = withTrail (atStart . Tangent) (atStart . Tangent) tr
+  atEnd   (Tangent tr) = withTrail (atEnd   . Tangent) (atEnd   . Tangent) tr
+
 -- | Compute the remainder mod 1.  Convenient for constructing loop
 --   parameterizations that wrap around.
-mod1 :: RealFrac a => a -> a
-mod1 p = p'
- where
-   pf = snd . propFrac $ p
-   p' | p >= 0    = pf
-      | otherwise = 1 + pf
-
--- Get rid of defaulting warnings
-propFrac :: RealFrac a => a -> (Int, a)
-propFrac = properFraction
+mod1 :: Real a => a -> a
+mod1 = (`mod'` 1)
 
-instance Num (Scalar v) => DomainBounds (Trail' l v)
+instance Num n => DomainBounds (Trail' l v n)
 
-instance (InnerSpace v, OrderedField (Scalar v), RealFrac (Scalar v))
-  => EndValues (Trail' l v)
+instance (Metric v, OrderedField n, Real n)
+  => EndValues (Trail' l v n)
 
-instance (InnerSpace v, RealFrac (Scalar v), Floating (Scalar v))
-    => Sectionable (Trail' Line v) where
+instance (Metric v, OrderedField n, Real n)
+    => Sectionable (Trail' Line v n) where
   splitAtParam (Line t) p = (Line t1, Line t2)
     where
       (t1, t2) = splitAtParam t p
 
+  section (Line t) p1 p2 = Line (section t p1 p2)
+
   reverseDomain = reverseLine
 
-instance (InnerSpace v, OrderedField (Scalar v), RealFrac (Scalar v))
-    => HasArcLength (Trail' l v) where
+instance (Metric v, OrderedField n, Real n)
+    => HasArcLength (Trail' l v n) where
   arcLengthBounded eps =
     withTrail'
       (\(Line t) -> arcLengthBounded eps t)
@@ -432,6 +523,33 @@
       (\lp -> arcLengthToParam eps (cutLoop lp) l)
       tr
 
+instance Rewrapped (Trail' Line v n) (Trail' Line v' n')
+instance Wrapped (Trail' Line v n) where
+  type Unwrapped (Trail' Line v n) = SegTree v n
+  _Wrapped' = iso (\(Line x) -> x) Line
+  {-# INLINE _Wrapped' #-}
+
+instance (Metric v, OrderedField n, Metric u, OrderedField n')
+  => Cons (Trail' Line v n) (Trail' Line u n') (Segment Closed v n) (Segment Closed u n') where
+  _Cons = _Wrapped . _Cons . bimapping id _Unwrapped
+  {-# INLINE _Cons #-}
+
+instance (Metric v, OrderedField n, Metric u, OrderedField n')
+  => Snoc (Trail' Line v n) (Trail' Line u n') (Segment Closed v n) (Segment Closed u n') where
+  _Snoc = _Wrapped . _Snoc . bimapping _Unwrapped id
+  {-# INLINE _Snoc #-}
+
+-- | Compose two Located trails by adding a segment joining the endpoint
+--   of the first to the starting point of the second.  Note, if you have
+--   two located trails such that the end of the first coincides with the
+--   start of the second, this will still add a trivial zero-length segment
+--   between them; in that case you are probably better off with something
+--   like @mapLoc (<> unLoc t2) t1@.
+instance (Real n, Floating n, Metric v)
+  => Semigroup (Located (Trail' Line v n)) where
+    a@(Loc aLoc aLine) <> b@(Loc _ bLine) =
+      Loc aLoc (aLine <> lineFromOffsets [atStart b .-. atEnd a] <> bLine)
+
 --------------------------------------------------
 -- Extracting segments
 
@@ -453,9 +571,10 @@
 --   trail, respectively.
 --
 --   The codomain for 'GetSegment', /i.e./ the result you get from
---   calling 'atParam', 'atStart', or 'atEnd', is @Maybe (v, Segment
---   Closed v, AnIso' (Scalar v) (Scalar v))@.  @Nothing@ results if
---   the trail is empty; otherwise, you get:
+--   calling 'atParam', 'atStart', or 'atEnd', is
+--   'GetSegmentCodomain', which is a newtype wrapper around @Maybe
+--   (v, Segment Closed v, AnIso' n n)@.  @Nothing@ results if the
+--   trail is empty; otherwise, you get:
 --
 --   * the offset from the start of the trail to the beginning of the
 --     segment,
@@ -469,41 +588,42 @@
 --     you can use.
 newtype GetSegment t = GetSegment t
 
+newtype GetSegmentCodomain v n =
+  GetSegmentCodomain
+    (Maybe ( v n                -- offset from trail start to segment start
+           , Segment Closed v n -- the segment
+           , AnIso' n n         -- reparameterization, trail <-> segment
+           ))
+
 -- | Create a 'GetSegment' wrapper around a trail, after which you can
 --   call 'atParam', 'atStart', or 'atEnd' to extract a segment.
 getSegment :: t -> GetSegment t
 getSegment = GetSegment
 
 type instance V (GetSegment t) = V t
-type instance Codomain (GetSegment t)
-  = Maybe
-    ( V t                                   -- offset from trail start to segment start
-    , Segment Closed (V t)                  -- the segment
-    , AnIso' (Scalar (V t)) (Scalar (V t))  -- reparameterization, trail <-> segment
-    )
+type instance N (GetSegment t) = N t
 
+type instance Codomain (GetSegment t) = GetSegmentCodomain (V t)
+
 -- | Parameters less than 0 yield the first segment; parameters
 --   greater than 1 yield the last.  A parameter exactly at the
 --   junction of two segments yields the second segment (/i.e./ the
 --   one with higher parameter values).
-instance (InnerSpace v, OrderedField (Scalar v))
-    => Parametric (GetSegment (Trail' Line v)) where
+instance (Metric v, OrderedField n) => Parametric (GetSegment (Trail' Line v n)) where
   atParam (GetSegment (Line (SegTree ft))) p
-    | p <= 0
-    = case FT.viewl ft of
-        EmptyL    -> Nothing
-        seg :< _  -> Just (zeroV, seg, reparam 0)
+    | p <= 0 = case FT.viewl ft of
+        EmptyL   -> GetSegmentCodomain Nothing
+        seg FT.:< _ -> GetSegmentCodomain $ Just (zero, seg, reparam 0)
 
-    | p >= 1
-    = case FT.viewr ft of
-        EmptyR     -> Nothing
-        ft' :> seg -> Just (offset ft', seg, reparam (n-1))
+    | p >= 1 = case FT.viewr ft of
+        EmptyR     -> GetSegmentCodomain Nothing
+        ft' FT.:> seg -> GetSegmentCodomain $ Just (offset ft', seg, reparam (n-1))
 
     | otherwise
-    = let (before, after) = FT.split ((p*n <) . numSegs) $ ft
+    = let (before, after) = FT.split ((p*n <) . numSegs) ft
       in  case FT.viewl after of
-            EmptyL   -> Nothing
-            seg :< _ -> Just (offset before, seg, reparam (numSegs before))
+            EmptyL   -> GetSegmentCodomain Nothing
+            seg FT.:< _ -> GetSegmentCodomain $ Just (offset before, seg, reparam (numSegs before))
     where
       n = numSegs ft
       reparam k = iso (subtract k . (*n))
@@ -511,12 +631,11 @@
 
 -- | The parameterization for loops wraps around, /i.e./ parameters
 --   are first reduced \"mod 1\".
-instance (InnerSpace v, OrderedField (Scalar v), RealFrac (Scalar v))
-    => Parametric (GetSegment (Trail' Loop v)) where
+instance (Metric v, OrderedField n, Real n) => Parametric (GetSegment (Trail' Loop v n)) where
   atParam (GetSegment l) p = atParam (GetSegment (cutLoop l)) (mod1 p)
 
-instance (InnerSpace v, OrderedField (Scalar v), RealFrac (Scalar v))
-    => Parametric (GetSegment (Trail v)) where
+instance (Metric v, OrderedField n, Real n)
+    => Parametric (GetSegment (Trail v n)) where
   atParam (GetSegment t) p
     = withTrail
       ((`atParam` p) . GetSegment)
@@ -527,40 +646,41 @@
   domainLower (GetSegment t) = domainLower t
   domainUpper (GetSegment t) = domainUpper t
 
-instance (InnerSpace v, OrderedField (Scalar v))
-    => EndValues (GetSegment (Trail' Line v)) where
+instance (Metric v, OrderedField n)
+    => EndValues (GetSegment (Trail' Line v n)) where
   atStart (GetSegment (Line (SegTree ft)))
     = case FT.viewl ft of
-        EmptyL   -> Nothing
-        seg :< _ ->
+        EmptyL   -> GetSegmentCodomain Nothing
+        seg FT.:< _ ->
           let n = numSegs ft
-          in  Just (zeroV, seg, iso (*n) (/n))
+          in  GetSegmentCodomain $ Just (zero, seg, iso (*n) (/n))
 
   atEnd (GetSegment (Line (SegTree ft)))
     = case FT.viewr ft of
-        EmptyR     -> Nothing
-        ft' :> seg ->
+        EmptyR     -> GetSegmentCodomain Nothing
+        ft' FT.:> seg ->
           let n = numSegs ft
-          in  Just (offset ft', seg, iso (subtract (n-1) . (*n))
+          in  GetSegmentCodomain $
+                Just (offset ft', seg, iso (subtract (n-1) . (*n))
                                          ((/n) . (+ (n-1)))
-                   )
+                     )
 
-instance (InnerSpace v, OrderedField (Scalar v), RealFrac (Scalar v))
-    => EndValues (GetSegment (Trail' Loop v)) where
+instance (Metric v, OrderedField n, Real n)
+    => EndValues (GetSegment (Trail' Loop v n)) where
   atStart (GetSegment l) = atStart (GetSegment (cutLoop l))
   atEnd   (GetSegment l) = atEnd   (GetSegment (cutLoop l))
 
-instance (InnerSpace v, OrderedField (Scalar v), RealFrac (Scalar v))
-    => EndValues (GetSegment (Trail v)) where
+instance (Metric v, OrderedField n, Real n)
+    => EndValues (GetSegment (Trail v n)) where
   atStart (GetSegment t)
     = withTrail
-      (\l -> atStart (GetSegment l))
-      (\l -> atStart (GetSegment l))
+      (atStart . GetSegment)
+      (atStart . GetSegment)
       t
   atEnd (GetSegment t)
     = withTrail
-      (\l -> atEnd (GetSegment l))
-      (\l -> atEnd (GetSegment l))
+      (atEnd . GetSegment)
+      (atEnd . GetSegment)
       t
 
 --------------------------------------------------
@@ -569,23 +689,23 @@
 -- | @Trail@ is a wrapper around @Trail'@, hiding whether the
 --   underlying @Trail'@ is a line or loop (though which it is can be
 --   recovered; see /e.g./ 'withTrail').
-data Trail v where
-  Trail :: Trail' l v -> Trail v
+data Trail v n where
+  Trail :: Trail' l v n -> Trail v n
 
-deriving instance Show v => Show (Trail v)
+deriving instance Show (v n) => Show (Trail v n)
 
-instance Eq v => Eq (Trail v) where
+instance Eq (v n) => Eq (Trail v n) where
   t1 == t2 =
     withTrail
       (\ln1 -> withTrail (\ln2 -> ln1 == ln2) (const False) t2)
       (\lp1 -> withTrail (const False) (\lp2 -> lp1 == lp2) t2)
       t1
 
-instance Ord v => Ord (Trail v) where
+instance Ord (v n) => Ord (Trail v n) where
   compare t1 t2 =
     withTrail
-      (\ln1 -> withTrail (\ln2 -> compare ln1 ln2) (const LT) t2)
-      (\lp1 -> withTrail (const GT) (\lp2 -> compare lp1 lp2) t2)
+      (\ln1 -> withTrail (compare ln1) (const LT) t2)
+      (\lp1 -> withTrail (const GT) (compare lp1) t2)
       t1
 
 -- | Two @Trail@s are combined by first ensuring they are both lines
@@ -593,7 +713,7 @@
 --   result, in general, is a line.  However, there is a special case
 --   for the empty line, which acts as the identity (so combining the
 --   empty line with a loop results in a loop).
-instance (OrderedField (Scalar v), InnerSpace v) => Semigroup (Trail v) where
+instance (OrderedField n, Metric v) => Semigroup (Trail v n) where
   (Trail (Line (SegTree ft))) <> t2 | FT.null ft = t2
   t1 <> (Trail (Line (SegTree ft))) | FT.null ft = t1
   t1 <> t2 = flip withLine t1 $ \l1 ->
@@ -608,29 +728,32 @@
 --   strange.  Mostly it is provided for convenience, so one can work
 --   directly with @Trail@s instead of working with @Trail' Line@s and
 --   then wrapping.
-instance (OrderedField (Scalar v), InnerSpace v) => Monoid (Trail v) where
+instance (Metric v, OrderedField n) => Monoid (Trail v n) where
   mempty  = wrapLine emptyLine
   mappend = (<>)
 
-type instance V (Trail v) = v
+instance (Metric v, OrderedField n) => AsEmpty (Trail v n) where
+  _Empty = nearly emptyTrail isTrailEmpty
 
-type instance Codomain (Trail v) = v
+type instance V (Trail v n) = v
+type instance N (Trail v n) = n
 
-instance (HasLinearMap v, InnerSpace v, OrderedField (Scalar v))
-    => Transformable (Trail v) where
+type instance Codomain (Trail v n) = v
+
+instance (HasLinearMap v, Metric v, OrderedField n)
+    => Transformable (Trail v n) where
   transform t = onTrail (transform t) (transform t)
 
-instance (InnerSpace v, OrderedField (Scalar v)) => Enveloped (Trail v) where
+instance (Metric v, OrderedField n) => Enveloped (Trail v n) where
   getEnvelope = withTrail getEnvelope getEnvelope
 
-instance (InnerSpace v, OrderedField (Scalar v), RealFrac (Scalar v))
-    => Parametric (Trail v) where
+instance (Metric v, OrderedField n, Real n)
+    => Parametric (Trail v n) where
   atParam t p = withTrail (`atParam` p) (`atParam` p) t
 
-instance Num (Scalar v) => DomainBounds (Trail v)
+instance Num n => DomainBounds (Trail v n)
 
-instance (InnerSpace v, OrderedField (Scalar v), RealFrac (Scalar v))
-  => EndValues (Trail v)
+instance (Metric v, OrderedField n, Real n) => EndValues (Trail v n)
 
 -- | Note that there is no @Sectionable@ instance for @Trail' Loop@,
 --   because it does not make sense (splitting a loop at a parameter
@@ -641,29 +764,57 @@
 --   semantically a bit silly, so please don't rely on it. (*E.g.* if
 --   this is really the behavior you want, consider first calling
 --   'cutLoop' yourself.)
-instance (InnerSpace v, RealFrac (Scalar v), Floating (Scalar v))
-    => Sectionable (Trail v) where
+instance (Metric v, OrderedField n, Real n) => Sectionable (Trail v n) where
   splitAtParam t p = withLine ((wrapLine *** wrapLine) . (`splitAtParam` p)) t
 
+  section t p1 p2 = withLine (wrapLine . (\l -> section l p1 p2)) t
+
   reverseDomain = reverseTrail
 
-instance (InnerSpace v, OrderedField (Scalar v), RealFrac (Scalar v))
-    => HasArcLength (Trail v) where
+instance (Metric v, OrderedField n, Real n)
+    => HasArcLength (Trail v n) where
   arcLengthBounded = withLine . arcLengthBounded
   arcLengthToParam eps tr al = withLine (\ln -> arcLengthToParam eps ln al) tr
 
+-- lens instrances -----------------------------------------------------
+
+-- | Prism onto a 'Line'.
+_Line :: Prism' (Trail v n) (Trail' Line v n)
+_Line = _Wrapped' . _Left
+
+-- | Prism onto a 'Loop'.
+_Loop :: Prism' (Trail v n) (Trail' Loop v n)
+_Loop = _Wrapped' . _Right
+
+-- | Prism onto a 'Located' 'Line'.
+_LocLine :: Prism' (Located (Trail v n)) (Located (Trail' Line v n))
+_LocLine = prism' (mapLoc Trail) $ located (preview _Line)
+
+-- | Prism onto a 'Located' 'Loop'.
+_LocLoop :: Prism' (Located (Trail v n)) (Located (Trail' Loop v n))
+_LocLoop = prism' (mapLoc Trail) $ located (preview _Loop)
+
+instance Rewrapped (Trail v n) (Trail v' n')
+instance Wrapped (Trail v n) where
+  type Unwrapped (Trail v n) = Either (Trail' Line v n) (Trail' Loop v n)
+  _Wrapped' = iso getTrail (either Trail Trail)
+    where
+      getTrail :: Trail v n -> Either (Trail' Line v n) (Trail' Loop v n)
+      getTrail (Trail t@(Line {})) = Left t
+      getTrail (Trail t@(Loop {})) = Right t
+
 --------------------------------------------------
 -- Constructors and eliminators for Trail
 
 -- | A generic eliminator for 'Trail', taking functions specifying
 --   what to do in the case of a line or a loop.
-withTrail :: (Trail' Line v -> r) -> (Trail' Loop v -> r) -> Trail v -> r
+withTrail :: (Trail' Line v n -> r) -> (Trail' Loop v n -> r) -> Trail v n -> r
 withTrail line loop (Trail t) = withTrail' line loop t
 
 -- | Modify a @Trail@, specifying two separate transformations for the
 --   cases of a line or a loop.
-onTrail :: (Trail' Line v -> Trail' l1 v) -> (Trail' Loop v -> Trail' l2 v)
-        -> (Trail v -> Trail v)
+onTrail :: (Trail' Line v n -> Trail' l1 v n) -> (Trail' Loop v n -> Trail' l2 v n)
+        -> Trail v n -> Trail v n
 onTrail o c = withTrail (wrapTrail . o) (wrapTrail . c)
 
 -- | An eliminator for @Trail@ based on eliminating lines: if the
@@ -673,8 +824,8 @@
 -- @
 -- withLine f === 'withTrail' f (f . 'cutLoop')
 -- @
-withLine :: (InnerSpace v, OrderedField (Scalar v))
-              => (Trail' Line v -> r) -> Trail v -> r
+withLine :: (Metric v, OrderedField n)
+              => (Trail' Line v n -> r) -> Trail v n -> r
 withLine f = withTrail f (f . cutLoop)
 
 -- | Modify a @Trail@ by specifying a transformation on lines.  If the
@@ -690,25 +841,25 @@
 --   Note that there is no corresponding @onLoop@ function, because
 --   there is no nice way in general to convert a line into a loop,
 --   operate on it, and then convert back.
-onLine :: (InnerSpace v, OrderedField (Scalar v))
-            => (Trail' Line v -> Trail' Line v) -> Trail v -> Trail v
+onLine :: (Metric v, OrderedField n)
+       => (Trail' Line v n -> Trail' Line v n) -> Trail v n -> Trail v n
 onLine f = onTrail f (glueLine . f . cutLoop)
 
 -- | Convert a 'Trail'' into a 'Trail', hiding the type-level
 --   distinction between lines and loops.
-wrapTrail :: Trail' l v -> Trail v
+wrapTrail :: Trail' l v n -> Trail v n
 wrapTrail = Trail
 
 -- | Convert a line into a 'Trail'.  This is the same as 'wrapTrail',
 --   but with a more specific type, which can occasionally be
 --   convenient for fixing the type of a polymorphic expression.
-wrapLine :: Trail' Line v -> Trail v
+wrapLine :: Trail' Line v n -> Trail v n
 wrapLine = wrapTrail
 
 -- | Convert a loop into a 'Trail'.  This is the same as 'wrapTrail',
 --   but with a more specific type, which can occasionally be
 --   convenient for fixing the type of a polymorphic expression.
-wrapLoop :: Trail' Loop v -> Trail v
+wrapLoop :: Trail' Loop v n -> Trail v n
 wrapLoop = wrapTrail
 
 ------------------------------------------------------------
@@ -716,22 +867,28 @@
 ------------------------------------------------------------
 
 -- | The empty line, which is the identity for concatenation of lines.
-emptyLine :: (InnerSpace v, OrderedField (Scalar v)) => Trail' Line v
+emptyLine :: (Metric v, OrderedField n) => Trail' Line v n
 emptyLine = Line mempty
 
 -- | A wrapped variant of 'emptyLine'.
-emptyTrail :: (InnerSpace v, OrderedField (Scalar v)) => Trail v
+emptyTrail :: (Metric v, OrderedField n) => Trail v n
 emptyTrail = wrapLine emptyLine
 
 -- | Construct a line from a list of closed segments.
-lineFromSegments :: (InnerSpace v, OrderedField (Scalar v))
-                   => [Segment Closed v] -> Trail' Line v
+lineFromSegments :: (Metric v, OrderedField n)
+                   => [Segment Closed v n] -> Trail' Line v n
 lineFromSegments = Line . SegTree . FT.fromList
 
+-- | Construct a loop from a list of closed segments and an open segment
+--   that completes the loop.
+loopFromSegments :: (Metric v, OrderedField n)
+                  => [Segment Closed v n] -> Segment Open v n -> Trail' Loop v n
+loopFromSegments segs = Loop (SegTree (FT.fromList segs))
+
 -- | @trailFromSegments === 'wrapTrail' . 'lineFromSegments'@, for
 --   conveniently constructing a @Trail@ instead of a @Trail'@.
-trailFromSegments :: (InnerSpace v, OrderedField (Scalar v))
-                  => [Segment Closed v] -> Trail v
+trailFromSegments :: (Metric v, OrderedField n)
+                  => [Segment Closed v n] -> Trail v n
 trailFromSegments = wrapTrail . lineFromSegments
 
 -- | Construct a line containing only linear segments from a list of
@@ -742,14 +899,12 @@
 --
 --   > import Diagrams.Coordinates
 --   > lineFromOffsetsEx = strokeLine $ lineFromOffsets [ 2 ^& 1, 2 ^& (-1), 2 ^& 0.5 ]
-lineFromOffsets :: (InnerSpace v, OrderedField (Scalar v))
-                  => [v] -> Trail' Line v
+lineFromOffsets :: (Metric v, OrderedField n) => [v n] -> Trail' Line v n
 lineFromOffsets = lineFromSegments . map straight
 
 -- | @trailFromOffsets === 'wrapTrail' . 'lineFromOffsets'@, for
 --   conveniently constructing a @Trail@ instead of a @Trail' Line@.
-trailFromOffsets :: (InnerSpace v, OrderedField (Scalar v))
-                 => [v] -> Trail v
+trailFromOffsets :: (Metric v, OrderedField n) => [v n] -> Trail v n
 trailFromOffsets = wrapTrail . lineFromOffsets
 
 -- | Construct a line containing only linear segments from a list of
@@ -771,8 +926,8 @@
 --   > import Diagrams.Coordinates
 --   > lineFromVerticesEx = pad 1.1 . centerXY . strokeLine
 --   >   $ lineFromVertices [origin, 0 ^& 1, 1 ^& 2, 5 ^& 1]
-lineFromVertices :: (InnerSpace v, OrderedField (Scalar v))
-                   => [Point v] -> Trail' Line v
+lineFromVertices :: (Metric v, OrderedField n)
+                   => [Point v n] -> Trail' Line v n
 lineFromVertices []  = emptyLine
 lineFromVertices [_] = emptyLine
 lineFromVertices ps  = lineFromSegments . map straight $ zipWith (.-.) (tail ps) ps
@@ -780,8 +935,8 @@
 
 -- | @trailFromVertices === 'wrapTrail' . 'lineFromVertices'@, for
 --   conveniently constructing a @Trail@ instead of a @Trail' Line@.
-trailFromVertices :: (InnerSpace v, OrderedField (Scalar v))
-                  => [Point v] -> Trail v
+trailFromVertices :: (Metric v, OrderedField n)
+                  => [Point v n] -> Trail v n
 trailFromVertices = wrapTrail . lineFromVertices
 
 ------------------------------------------------------------
@@ -797,10 +952,10 @@
 --
 --   <<diagrams/src_Diagrams_Trail_glueLineEx.svg#diagram=glueLineEx&width=500>>
 --
---   > glueLineEx = pad 1.1 . hcat' (with & sep .~ 1)
+--   > glueLineEx = pad 1.1 . hsep 1
 --   >   $ [almostClosed # strokeLine, almostClosed # glueLine # strokeLoop]
 --   >
---   > almostClosed :: Trail' Line R2
+--   > almostClosed :: Trail' Line V2 Double
 --   > almostClosed = fromOffsets $ map r2 [(2, -1), (-3, -0.5), (-2, 1), (1, 0.5)]
 --
 --   @glueLine@ is left inverse to 'cutLoop', that is,
@@ -808,16 +963,16 @@
 --   @
 --   glueLine . cutLoop === id
 --   @
-glueLine :: (InnerSpace v, OrderedField (Scalar v)) => Trail' Line v -> Trail' Loop v
+glueLine :: (Metric v, OrderedField n) => Trail' Line v n -> Trail' Loop v n
 glueLine (Line (SegTree t)) =
   case FT.viewr t of
-    FT.EmptyR             -> Loop mempty (Linear OffsetOpen)
-    t' :> (Linear _)      -> Loop (SegTree t') (Linear OffsetOpen)
-    t' :> (Cubic c1 c2 _) -> Loop (SegTree t') (Cubic c1 c2 OffsetOpen)
+    FT.EmptyR           -> Loop mempty (Linear OffsetOpen)
+    t' FT.:> Linear _      -> Loop (SegTree t') (Linear OffsetOpen)
+    t' FT.:> Cubic c1 c2 _ -> Loop (SegTree t') (Cubic c1 c2 OffsetOpen)
 
 -- | @glueTrail@ is a variant of 'glueLine' which works on 'Trail's.
 --   It performs 'glueLine' on lines and is the identity on loops.
-glueTrail :: (InnerSpace v, OrderedField (Scalar v)) => Trail v -> Trail v
+glueTrail :: (Metric v, OrderedField n) => Trail v n -> Trail v n
 glueTrail = onTrail glueLine id
 
 -- | Make a line into a loop by adding a new linear segment from the
@@ -843,12 +998,12 @@
 --
 --   > closeLineEx = pad 1.1 . centerXY . hcat' (with & sep .~ 1)
 --   >   $ [almostClosed # strokeLine, almostClosed # closeLine # strokeLoop]
-closeLine :: Trail' Line v -> Trail' Loop v
+closeLine :: Trail' Line v n -> Trail' Loop v n
 closeLine (Line t) = Loop t (Linear OffsetOpen)
 
 -- | @closeTrail@ is a variant of 'closeLine' for 'Trail', which
 --   performs 'closeLine' on lines and is the identity on loops.
-closeTrail :: Trail v -> Trail v
+closeTrail :: Trail v n -> Trail v n
 closeTrail = onTrail closeLine id
 
 -- | Turn a loop into a line by \"cutting\" it at the common start/end
@@ -860,22 +1015,22 @@
 --   @
 --   glueLine . cutLoop === id
 --   @
-cutLoop :: forall v. (InnerSpace v, OrderedField (Scalar v))
-         => Trail' Loop v -> Trail' Line v
+cutLoop :: forall v n. (Metric v, OrderedField n)
+         => Trail' Loop v n -> Trail' Line v n
 cutLoop (Loop (SegTree t) c) =
   case (FT.null t, c) of
     (True, Linear OffsetOpen)      -> emptyLine
     (_   , Linear OffsetOpen)      -> Line (SegTree (t |> Linear off))
     (_   , Cubic c1 c2 OffsetOpen) -> Line (SegTree (t |> Cubic c1 c2 off))
   where
-    offV :: v
-    offV = negateV . trailMeasure zeroV (op TotalOffset .view oeOffset) $ t
+    offV :: v n
+    offV = negated . trailMeasure zero (op TotalOffset .view oeOffset) $ t
     off = OffsetClosed offV
 
 -- | @cutTrail@ is a variant of 'cutLoop' for 'Trail'; it is the is
 --   the identity on lines and performs 'cutLoop' on loops.
-cutTrail :: (InnerSpace v, OrderedField (Scalar v))
-         => Trail v -> Trail v
+cutTrail :: (Metric v, OrderedField n)
+         => Trail v n -> Trail v n
 cutTrail = onTrail id cutLoop
 
 ------------------------------------------------------------
@@ -883,45 +1038,45 @@
 ------------------------------------------------------------
 
 -- | Test whether a line is empty.
-isLineEmpty :: (InnerSpace v, OrderedField (Scalar v)) => Trail' Line v -> Bool
+isLineEmpty :: (Metric v, OrderedField n) => Trail' Line v n -> Bool
 isLineEmpty (Line (SegTree t)) = FT.null t
 
 -- | Test whether a trail is empty.  Note that loops are never empty.
-isTrailEmpty :: (InnerSpace v, OrderedField (Scalar v)) => Trail v -> Bool
+isTrailEmpty :: (Metric v, OrderedField n) => Trail v n -> Bool
 isTrailEmpty = withTrail isLineEmpty (const False)
 
 -- | Determine whether a trail is a line.
-isLine :: Trail v -> Bool
+isLine :: Trail v n -> Bool
 isLine = not . isLoop
 
 -- | Determine whether a trail is a loop.
-isLoop :: Trail v -> Bool
+isLoop :: Trail v n -> Bool
 isLoop = withTrail (const False) (const True)
 
 -- | Extract the segments comprising a line.
-lineSegments :: Trail' Line v -> [Segment Closed v]
+lineSegments :: Trail' Line v n -> [Segment Closed v n]
 lineSegments (Line (SegTree t)) = F.toList t
 
 -- | Modify a line by applying a function to its list of segments.
 onLineSegments
-  :: (InnerSpace v, OrderedField (Scalar v))
-  => ([Segment Closed v] -> [Segment Closed v])
-  -> Trail' Line v -> Trail' Line v
+  :: (Metric v, OrderedField n)
+  => ([Segment Closed v n] -> [Segment Closed v n])
+  -> Trail' Line v n -> Trail' Line v n
 onLineSegments f = lineFromSegments . f . lineSegments
 
 -- | Extract the segments comprising a loop: a list of closed
 --   segments, and one final open segment.
-loopSegments :: Trail' Loop v -> ([Segment Closed v], Segment Open v)
+loopSegments :: Trail' Loop v n -> ([Segment Closed v n], Segment Open v n)
 loopSegments (Loop (SegTree t) c) = (F.toList t, c)
 
 -- | Extract the segments of a trail.  If the trail is a loop it will
 --   first have 'cutLoop' applied.
-trailSegments :: (InnerSpace v, OrderedField (Scalar v))
-              => Trail v -> [Segment Closed v]
+trailSegments :: (Metric v, OrderedField n)
+              => Trail v n -> [Segment Closed v n]
 trailSegments = withLine lineSegments
 
 -- | Extract the offsets of the segments of a trail.
-trailOffsets :: (InnerSpace v, OrderedField (Scalar v)) => Trail v -> [v]
+trailOffsets :: (Metric v, OrderedField n) => Trail v n -> [v n]
 trailOffsets = withLine lineOffsets
 
 -- | Compute the offset from the start of a trail to the end.  Satisfies
@@ -936,67 +1091,208 @@
 --
 --   > trailOffsetEx = (strokeLine almostClosed <> showOffset) # centerXY # pad 1.1
 --   >   where showOffset = fromOffsets [trailOffset (wrapLine almostClosed)]
---   >                    # stroke # lc red
-trailOffset :: (InnerSpace v, OrderedField (Scalar v)) => Trail v -> v
+--   >                    # strokeP # lc red
+trailOffset :: (Metric v, OrderedField n) => Trail v n -> v n
 trailOffset = withLine lineOffset
 
 -- | Extract the offsets of the segments of a line.
-lineOffsets :: (InnerSpace v, OrderedField (Scalar v)) => Trail' Line v -> [v]
+lineOffsets :: Trail' Line v n -> [v n]
 lineOffsets = map segOffset . lineSegments
 
 -- | Extract the offsets of the segments of a loop.
-loopOffsets :: (InnerSpace v, OrderedField (Scalar v)) => Trail' Loop v -> [v]
+loopOffsets :: (Metric v, OrderedField n) => Trail' Loop v n -> [v n]
 loopOffsets = lineOffsets . cutLoop
 
 -- | Compute the offset from the start of a line to the end.  (Note,
 --   there is no corresponding @loopOffset@ function because by
 --   definition it would be constantly zero.)
-lineOffset :: (InnerSpace v, OrderedField (Scalar v)) => Trail' Line v -> v
-lineOffset (Line t) = trailMeasure zeroV (op TotalOffset . view oeOffset) t
+lineOffset :: (Metric v, OrderedField n) => Trail' Line v n -> v n
+lineOffset (Line t) = trailMeasure zero (op TotalOffset . view oeOffset) t
 
--- | Extract the vertices of a concretely located trail.  Note that
---   for loops, the starting vertex will /not/ be repeated at the end.
---   If you want this behavior, you can use 'cutTrail' to make the
---   loop into a line first, which happens to repeat the same vertex
---   at the start and end, /e.g./ with @trailVertices . mapLoc
+-- | Extract the points of a concretely located trail, /i.e./ the points
+--   where one segment ends and the next begins. Note that for loops,
+--   the starting point will /not/ be repeated at the end.  If you
+--   want this behavior, you can use 'cutTrail' to make the loop into
+--   a line first, which happens to repeat the same point at the start
+--   and end, /e.g./ with @trailPoints . mapLoc cutTrail@.
+--
+--   Note that it does not make sense to ask for the points of a
+--   'Trail' by itself; if you want the points of a trail
+--   with the first point at, say, the origin, you can use
+--   @trailPoints . (\`at\` origin)@.
+--
+--   This function allows you "observe" the fact that trails are
+--   implemented as lists of segments, which may be problematic if we
+--   want to think of trails as parametric vector functions. This also
+--   means that the behavior of this function may not be stable under
+--   future changes to the implementation of trails.  For an
+--   unproblematic version which only yields vertices at which there
+--   is a sharp corner, excluding points where the trail is
+--   differentiable, see 'trailVertices'.
+--
+--   This function is not re-exported from "Diagrams.Prelude"; to use
+--   it, import "Diagrams.Trail".
+trailPoints :: (Metric v, OrderedField n)
+              => Located (Trail v n) -> [Point v n]
+trailPoints (viewLoc -> (p,t))
+  = withTrail (linePoints . (`at` p)) (loopPoints . (`at` p)) t
+
+-- | Extract the segment join points of a concretely located line.  See
+--   'trailPoints' for more information.
+--
+--   This function allows you "observe" the fact that lines are
+--   implemented as lists of segments, which may be problematic if we
+--   want to think of lines as parametric vector functions. This also
+--   means that the behavior of this function may not be stable under
+--   future changes to the implementation of trails.  For an
+--   unproblematic version which only yields vertices at which there
+--   is a sharp corner, excluding points where the trail is
+--   differentiable, see 'lineVertices'.
+--
+--   This function is not re-exported from "Diagrams.Prelude"; to use
+--   it, import "Diagrams.Trail".
+linePoints :: (Metric v, OrderedField n)
+             => Located (Trail' Line v n) -> [Point v n]
+linePoints (viewLoc -> (p,t))
+  = segmentPoints p . lineSegments $ t
+
+-- | Extract the segment join points of a concretely located loop.  Note that the
+--   initial vertex is not repeated at the end.  See 'trailPoints' for
+--   more information.
+--
+--   This function allows you "observe" the fact that lines are
+--   implemented as lists of segments, which may be problematic if we
+--   want to think of lines as parametric vector functions. This also
+--   means that the behavior of this function may not be stable under
+--   future changes to the implementation of trails.  For an
+--   unproblematic version which only yields vertices at which there
+--   is a sharp corner, excluding points where the trail is
+--   differentiable, see 'lineVertices'.
+--
+--   This function is not re-exported from "Diagrams.Prelude"; to use
+--   it, import "Diagrams.Trail".
+loopPoints :: (Metric v, OrderedField n)
+             => Located (Trail' Loop v n) -> [Point v n]
+loopPoints (viewLoc -> (p,t))
+  = segmentPoints p . fst . loopSegments $ t
+
+segmentPoints :: (Additive v, Num n) => Point v n -> [Segment Closed v n] -> [Point v n]
+segmentPoints p = scanl (.+^) p . map segOffset
+
+tolerance :: OrderedField a => a
+tolerance = 10e-16
+
+-- | Extract the vertices of a concretely located trail.  Here a /vertex/
+--   is defined as a non-differentiable point on the trail, /i.e./ a
+--   sharp corner.  (Vertices are thus a subset of the places where
+--   segments join; if you want all joins between segments, see
+--   'trailPoints'.)  The tolerance determines how close the tangents
+--   of two segments must be at their endpoints to consider the
+--   transition point to be differentiable.
+--
+--   Note that for loops, the starting vertex will /not/ be repeated
+--   at the end.  If you want this behavior, you can use 'cutTrail' to
+--   make the loop into a line first, which happens to repeat the same
+--   vertex at the start and end, /e.g./ with @trailVertices . mapLoc
 --   cutTrail@.
 --
---   Note that it does not make sense to ask for the vertices of a
---   'Trail' by itself; if you want the vertices of a trail
---   with the first vertex at, say, the origin, you can use
---   @trailVertices . (\`at\` origin)@.
-trailVertices :: (InnerSpace v, OrderedField (Scalar v))
-              => Located (Trail v) -> [Point v]
-trailVertices (viewLoc -> (p,t))
-  = withTrail (lineVertices . (`at` p)) (loopVertices . (`at` p)) t
+--   It does not make sense to ask for the vertices of a 'Trail' by
+--   itself; if you want the vertices of a trail with the first vertex
+--   at, say, the origin, you can use @trailVertices . (\`at\`
+--   origin)@.
+trailVertices' :: (Metric v, OrderedField n)
+              => n ->  Located (Trail v n) -> [Point v n]
+trailVertices' toler (viewLoc -> (p,t))
+  = withTrail (lineVertices' toler . (`at` p)) (loopVertices' toler . (`at` p)) t
 
+-- | Like 'trailVertices'', with a default tolerance.
+trailVertices :: (Metric v, OrderedField n)
+              => Located (Trail v n) -> [Point v n]
+trailVertices = trailVertices' tolerance
+
 -- | Extract the vertices of a concretely located line.  See
 --   'trailVertices' for more information.
-lineVertices :: (InnerSpace v, OrderedField (Scalar v))
-             => Located (Trail' Line v) -> [Point v]
-lineVertices (viewLoc -> (p,t))
-  = segmentVertices p . lineSegments $ t
+lineVertices' :: (Metric v, OrderedField n)
+             => n -> Located (Trail' Line v n) -> [Point v n]
+lineVertices' toler (viewLoc -> (p,t))
+  = segmentVertices' toler p . lineSegments $ t
 
+-- | Like 'lineVertices'', with a default tolerance.
+lineVertices :: (Metric v, OrderedField n)
+             => Located (Trail' Line v n) -> [Point v n]
+lineVertices = lineVertices' tolerance
+
 -- | Extract the vertices of a concretely located loop.  Note that the
 --   initial vertex is not repeated at the end.  See 'trailVertices' for
 --   more information.
-loopVertices :: (InnerSpace v, OrderedField (Scalar v))
-             => Located (Trail' Loop v) -> [Point v]
-loopVertices (viewLoc -> (p,t))
-  = segmentVertices p . fst . loopSegments $ t
+loopVertices' :: (Metric v, OrderedField n)
+             => n -> Located (Trail' Loop v n) -> [Point v n]
+loopVertices' toler (viewLoc -> (p,t))
+  | length segs > 1 = if far > toler  then init ps else init . drop 1 $ ps
+  | otherwise       = ps
+  where
+    far = quadrance ((signorm . tangentAtStart . head $ segs) ^-^
+                       (signorm . tangentAtEnd   . last $ segs))
+    segs = lineSegments . cutLoop $ t
+    ps = segmentVertices' toler p segs
 
-segmentVertices :: AdditiveGroup v => Point v -> [Segment Closed v] -> [Point v]
-segmentVertices p = scanl (.+^) p . map segOffset
+-- | Same as 'loopVertices'', with a default tolerance.
+loopVertices :: (Metric v, OrderedField n)
+             => Located (Trail' Loop v n) -> [Point v n]
+loopVertices = loopVertices' tolerance
 
+-- | The vertices of a list of segments laid end to end.
+--   The start and end points are always included in the list of
+--   vertices.  The other points connecting segments are included if
+--   the slope at the end of a segment is not equal to the slope at
+--   the beginning of the next.  The 'toler' parameter is used to
+--   control how close the slopes need to be in order to declare them
+--   equal.
+segmentVertices' :: (Metric v, OrderedField n)
+             => n -> Point v n -> [Segment Closed v n] -> [Point v n]
+segmentVertices' toler p ts  =
+  case ps of
+    (x:_:_) -> x : select (drop 1 ps) ds ++ [last ps]
+    _       -> ps
+    where
+      ds = zipWith far tans (drop 1 tans)
+      tans = [(signorm . tangentAtStart $ s
+              ,signorm . tangentAtEnd   $ s) | s <- ts]
+      ps = scanl (.+^) p . map segOffset $ ts
+      far p2 q2 = quadrance (snd p2 ^-^ fst q2) > toler
+
+select :: [a] -> [Bool] -> [a]
+select xs bs = map fst $ filter snd (zip xs bs)
+
 -- | Convert a concretely located trail into a list of fixed segments.
-fixTrail :: (InnerSpace v, OrderedField (Scalar v))
-         => Located (Trail v) -> [FixedSegment v]
+--   'unfixTrail' is almost its left inverse.
+fixTrail :: (Metric v, OrderedField n)
+         => Located (Trail v n) -> [FixedSegment v n]
 fixTrail t = map mkFixedSeg (trailLocSegments t)
 
+-- | Convert a list of fixed segments into a located trail.  Note that
+--   this may lose information: it throws away the locations of all
+--   but the first @FixedSegment@.  This does not matter precisely
+--   when each @FixedSegment@ begins where the previous one ends.
+--
+--   This is almost left inverse to 'fixTrail', that is, @unfixTrail
+--   . fixTrail == id@, except for the fact that @unfixTrail@ will
+--   never yield a @Loop@.  In the case of a loop, we instead have
+--   @glueTrail . unfixTrail . fixTrail == id@.  On the other hand, it
+--   is not the case that @fixTrail . unfixTrail == id@ since
+--   @unfixTrail@ may lose information.
+unfixTrail
+  :: (Metric v, Ord n, Floating n)
+  => [FixedSegment v n] -> Located (Trail v n)
+unfixTrail = mapLoc trailFromSegments . takeLoc . map fromFixedSeg
+  where
+    takeLoc []       = [] `at` origin
+    takeLoc xs@(x:_) = map unLoc xs `at` loc x
+
 -- | Convert a concretely located trail into a list of located segments.
-trailLocSegments :: (InnerSpace v, OrderedField (Scalar v))
-                  => Located (Trail v) -> [Located (Segment Closed v)]
-trailLocSegments t = zipWith at (trailSegments (unLoc t)) (trailVertices t)
+trailLocSegments :: (Metric v, OrderedField n)
+                  => Located (Trail v n) -> [Located (Segment Closed v n)]
+trailLocSegments t = zipWith at (trailSegments (unLoc t)) (trailPoints t)
 
 ------------------------------------------------------------
 --  Modifying trails  --------------------------------------
@@ -1009,7 +1305,7 @@
 --   @
 --   reverseTrail . reverseTrail === id
 --   @
-reverseTrail :: (InnerSpace v, OrderedField (Scalar v)) => Trail v -> Trail v
+reverseTrail :: (Metric v, OrderedField n) => Trail v n -> Trail v n
 reverseTrail = onTrail reverseLine reverseLoop
 
 -- | Reverse a concretely located trail.  The endpoint of the original
@@ -1020,27 +1316,81 @@
 --   @
 --   reverseLocTrail . reverseLocTrail === id
 --   @
-reverseLocTrail :: (InnerSpace v, OrderedField (Scalar v))
-                => Located (Trail v) -> Located (Trail v)
+reverseLocTrail :: (Metric v, OrderedField n)
+                => Located (Trail v n) -> Located (Trail v n)
 reverseLocTrail (viewLoc -> (p, t)) = reverseTrail t `at` (p .+^ trailOffset t)
 
 -- | Reverse a line.  See 'reverseTrail'.
-reverseLine :: (InnerSpace v, OrderedField (Scalar v))
-            => Trail' Line v -> Trail' Line v
+reverseLine :: (Metric v, OrderedField n)
+            => Trail' Line v n -> Trail' Line v n
 reverseLine = onLineSegments (reverse . map reverseSegment)
 
 -- | Reverse a concretely located line.  See 'reverseLocTrail'.
-reverseLocLine :: (InnerSpace v, OrderedField (Scalar v))
-               => Located (Trail' Line v) -> Located (Trail' Line v)
+reverseLocLine :: (Metric v, OrderedField n)
+               => Located (Trail' Line v n) -> Located (Trail' Line v n)
 reverseLocLine (viewLoc -> (p,l)) = reverseLine l `at` (p .+^ lineOffset l)
 
 -- | Reverse a loop.  See 'reverseTrail'.
-reverseLoop :: (InnerSpace v, OrderedField (Scalar v))
-            => Trail' Loop v -> Trail' Loop v
+reverseLoop :: (Metric v, OrderedField n)
+            => Trail' Loop v n -> Trail' Loop v n
 reverseLoop = glueLine . reverseLine . cutLoop
 
 -- | Reverse a concretely located loop.  See 'reverseLocTrail'.  Note
 --   that this is guaranteed to preserve the location.
-reverseLocLoop :: (InnerSpace v, OrderedField (Scalar v))
-               => Located (Trail' Loop v) -> Located (Trail' Loop v)
+reverseLocLoop :: (Metric v, OrderedField n)
+               => Located (Trail' Loop v n) -> Located (Trail' Loop v n)
 reverseLocLoop = mapLoc reverseLoop
+
+-- | Same as 'reverseLine' or 'reverseLoop'.
+instance (Metric v, OrderedField n) => Reversing (Trail' l v n) where
+  reversing t@(Line _)   = onLineSegments (reverse . map reversing) t
+  reversing t@(Loop _ _) = glueLine . reversing . cutLoop $ t
+
+-- | Same as 'reverseTrail'.
+instance (Metric v, OrderedField n) => Reversing (Trail v n) where
+  reversing (Trail t) = Trail (reversing t)
+
+-- | Same as 'reverseLocLine' or 'reverseLocLoop'.
+instance (Metric v, OrderedField n) => Reversing (Located (Trail' l v n)) where
+  reversing l@(Loc _ Line {}) = reverseLocLine l
+  reversing l@(Loc _ Loop {}) = reverseLocLoop l
+
+-- | Same as 'reverseLocTrail'.
+instance (Metric v, OrderedField n) => Reversing (Located (Trail v n)) where
+  reversing = reverseLocTrail
+
+------------------------------------------------------------
+--  Serialize instances
+------------------------------------------------------------
+
+instance (Serialize (v n), OrderedField n, Metric v) => Serialize (Trail v n) where
+  {-# INLINE get #-}
+  get = do
+    isLine <- Serialize.get
+    case isLine of
+      True  -> do
+        segTree <- Serialize.get
+        return (Trail (Line segTree))
+      False -> do
+        segTree <- Serialize.get
+        segment <- Serialize.get
+        return (Trail (Loop segTree segment))
+
+  {-# INLINE put #-}
+  put (Trail (Line segTree)) = do
+    Serialize.put True
+    Serialize.put segTree
+
+  put (Trail (Loop segTree segment)) = do
+    Serialize.put False
+    Serialize.put segTree
+    Serialize.put segment
+
+instance (OrderedField n, Metric v, Serialize (v n)) => Serialize (SegTree v n) where
+  {-# INLINE put #-}
+  put (SegTree fingerTree) = Serialize.put (F.toList fingerTree)
+
+  {-# INLINE get #-}
+  get = do
+    fingerTree <- Serialize.get
+    return (SegTree (FT.fromList fingerTree))
diff --git a/src/Diagrams/TrailLike.hs b/src/Diagrams/TrailLike.hs
--- a/src/Diagrams/TrailLike.hs
+++ b/src/Diagrams/TrailLike.hs
@@ -1,6 +1,8 @@
+{-# LANGUAGE ConstraintKinds      #-}
 {-# LANGUAGE FlexibleContexts     #-}
 {-# LANGUAGE FlexibleInstances    #-}
 {-# LANGUAGE TypeFamilies         #-}
+{-# LANGUAGE TypeOperators        #-}
 {-# LANGUAGE UndecidableInstances #-}
 -----------------------------------------------------------------------------
 -- |
@@ -28,15 +30,17 @@
 
        ) where
 
-import           Data.AffineSpace ((.-.))
-import           Data.VectorSpace
-import           Control.Lens (view, _Unwrapped')
+import           Control.Lens     (view, _Unwrapped')
 
 import           Diagrams.Core
 import           Diagrams.Located
 import           Diagrams.Segment
 import           Diagrams.Trail
 
+import           Linear.Affine
+import           Linear.Metric
+import           Linear.Vector
+
 ------------------------------------------------------------
 --  TrailLike class
 ------------------------------------------------------------
@@ -61,36 +65,36 @@
 --   course call 'trailLike' directly; more typically, one would use
 --   one of the provided functions like 'fromOffsets', 'fromVertices',
 --   'fromSegments', or '~~'.
-class (InnerSpace (V t), OrderedField (Scalar (V t))) => TrailLike t where
+class (Metric (V t), OrderedField (N t)) => TrailLike t where
 
   trailLike
-    :: Located (Trail (V t))  -- ^ The concretely located trail.  Note
-                              --   that some trail-like things
-                              --   (e.g. 'Trail's) may ignore the
-                              --   location.
+    :: Located (Trail (V t) (N t)) -- ^ The concretely located trail.  Note
+                                   --   that some trail-like things
+                                   --   (e.g. 'Trail's) may ignore the
+                                   --   location.
     -> t
 
 ------------------------------------------------------------
 --  Instances  ---------------------------------------------
 
 -- | A list of points is trail-like; this instance simply
---   computes the vertices of the trail, using 'trailVertices'.
-instance (InnerSpace v, OrderedField (Scalar v)) => TrailLike [Point v] where
-  trailLike = trailVertices
+--   computes the vertices of the trail, using 'trailPoints'.
+instance (Metric v, OrderedField n) => TrailLike [Point v n] where
+  trailLike = trailPoints
 
 -- | Lines are trail-like.  If given a 'Trail' which contains a loop,
 --   the loop will be cut with 'cutLoop'.  The location is ignored.
-instance (InnerSpace v, OrderedField (Scalar v)) => TrailLike (Trail' Line v) where
+instance (Metric v, OrderedField n) => TrailLike (Trail' Line v n) where
   trailLike = withTrail id cutLoop . unLoc
 
 -- | Loops are trail-like.  If given a 'Trail' containing a line, the
 --   line will be turned into a loop using 'glueLine'.  The location
 --   is ignored.
-instance (InnerSpace v, OrderedField (Scalar v)) => TrailLike (Trail' Loop v) where
+instance (Metric v, OrderedField n) => TrailLike (Trail' Loop v n) where
   trailLike = withTrail glueLine id . unLoc
 
 -- | 'Trail's are trail-like; the location is simply ignored.
-instance (InnerSpace v, OrderedField (Scalar v)) => TrailLike (Trail v) where
+instance (Metric v, OrderedField n) => TrailLike (Trail v n) where
   trailLike = unLoc
 
 -- | Translationally invariant things are trail-like as long as the
@@ -119,11 +123,11 @@
 --   >   , straight unit_X
 --   >   ]
 --   >   # centerXY # pad 1.1
-fromSegments :: TrailLike t => [Segment Closed (V t)] -> t
+fromSegments :: TrailLike t => [Segment Closed (V t) (N t)] -> t
 fromSegments = fromLocSegments . (`at` origin)
 
 -- | Construct a trail-like thing from a located list of segments.
-fromLocSegments :: TrailLike t => Located [Segment Closed (V t)] -> t
+fromLocSegments :: TrailLike t => Located [Segment Closed (V t) (N t)] -> t
 fromLocSegments = trailLike . mapLoc trailFromSegments
 
 -- | Construct a trail-like thing of linear segments from a list
@@ -138,12 +142,12 @@
 --   >   , unitX
 --   >   ]
 --   >   # centerXY # pad 1.1
-fromOffsets :: TrailLike t => [V t] -> t
+fromOffsets :: TrailLike t => [Vn t] -> t
 fromOffsets = trailLike . (`at` origin) . trailFromOffsets
 
 -- | Construct a trail-like thing of linear segments from a located
 --   list of offsets.
-fromLocOffsets :: (V (V t) ~ V t, TrailLike t) => Located [V t] -> t
+fromLocOffsets :: (V t ~ v, N t ~ n, V (v n) ~ v, N (v n) ~ n, TrailLike t) => Located [v n] -> t
 fromLocOffsets = trailLike . mapLoc trailFromOffsets
 
 -- | Construct a trail-like thing connecting the given vertices with
@@ -166,11 +170,11 @@
 --   >   # fromVertices
 --   >   # closeTrail # strokeTrail
 --   >   # centerXY # pad 1.1
-fromVertices :: TrailLike t => [Point (V t)] -> t
+fromVertices :: TrailLike t => [Point (V t) (N t)] -> t
 fromVertices []       = trailLike (emptyTrail `at` origin)
 fromVertices ps@(p:_) = trailLike (trailFromSegments (segmentsFromVertices ps) `at` p)
 
-segmentsFromVertices :: AdditiveGroup v => [Point v] -> [Segment Closed v]
+segmentsFromVertices :: (Additive v, Num n) => [Point v n] -> [Segment Closed v n]
 segmentsFromVertices []         = []
 segmentsFromVertices vvs@(_:vs) = map straight (zipWith (flip (.-.)) vvs vs)
 
@@ -181,7 +185,7 @@
 --   > twiddleEx
 --   >   = mconcat ((~~) <$> hexagon 1 <*> hexagon 1)
 --   >   # centerXY # pad 1.1
-(~~) :: TrailLike t => Point (V t) -> Point (V t) -> t
+(~~) :: (V t ~ v, N t ~ n, TrailLike t) => Point v n -> Point v n -> t
 p1 ~~ p2 = fromVertices [p1, p2]
 
 -- | Given a concretely located trail, \"explode\" it by turning each
@@ -195,7 +199,7 @@
 --   >   # explodeTrail  -- generate a list of diagrams
 --   >   # zipWith lc [orange, green, yellow, red, blue]
 --   >   # mconcat # centerXY # pad 1.1
-explodeTrail :: (VectorSpace (V t), TrailLike t) => Located (Trail (V t)) -> [t]
+explodeTrail :: (V t ~ v, N t ~ n, TrailLike t) => Located (Trail v n) -> [t]
 explodeTrail = map (mkTrail . fromFixedSeg) . fixTrail
   where
     mkTrail = trailLike . mapLoc (trailFromSegments . (:[]))
diff --git a/src/Diagrams/Transform.hs b/src/Diagrams/Transform.hs
--- a/src/Diagrams/Transform.hs
+++ b/src/Diagrams/Transform.hs
@@ -1,7 +1,15 @@
+{-# LANGUAGE ConstraintKinds #-}
+{-# LANGUAGE MultiParamTypeClasses #-}
+{-# LANGUAGE RankNTypes            #-}
+{-# LANGUAGE TypeFamilies          #-}
+
+{-# OPTIONS_GHC -fno-warn-unused-imports #-}
+  -- for Data.Semigroup
+
 -----------------------------------------------------------------------------
 -- |
 -- Module      :  Diagrams.Transform
--- Copyright   :  (c) 2011-13 diagrams-lib team (see LICENSE)
+-- Copyright   :  (c) 2011-15 diagrams-lib team (see LICENSE)
 -- License     :  BSD-style (see LICENSE)
 -- Maintainer  :  diagrams-discuss@googlegroups.com
 --
@@ -11,7 +19,6 @@
 --
 -----------------------------------------------------------------------------
 
-{-# LANGUAGE TypeFamilies #-}
 
 module Diagrams.Transform
     ( -- * Transformations
@@ -24,7 +31,7 @@
     , translation, translate, moveTo, place, scaling, scale
 
       -- * Miscellaneous transformation-related utilities
-    , conjugate, under
+    , conjugate, underT, transformed, translated, movedTo, movedFrom
 
       -- * The HasOrigin class
 
@@ -32,27 +39,90 @@
 
     ) where
 
+import           Control.Lens   hiding (transform)
 import           Data.Semigroup
 import           Diagrams.Core
 
+import           Linear.Vector
+
 -- | Conjugate one transformation by another. @conjugate t1 t2@ is the
 --   transformation which performs first @t1@, then @t2@, then the
 --   inverse of @t1@.
-conjugate :: HasLinearMap v => Transformation v -> Transformation v -> Transformation v
-conjugate t1 t2  = inv t1 <> t2 <> t1
+conjugate :: (Additive v, Num n)
+          => Transformation v n -> Transformation v n -> Transformation v n
+conjugate t1 t2 = inv t1 <> t2 <> t1
 
--- | Carry out some transformation \"under\" another one: @f ``under``
+-- | Carry out some transformation \"under\" another one: @f ``underT``
 --   t@ first applies @t@, then @f@, then the inverse of @t@.  For
---   example, @'scaleX' 2 ``under`` 'rotation' (-1/8 \@\@ Turn)@
+--   example, @'scaleX' 2 ``underT`` 'rotation' (-1/8 \@\@ Turn)@
 --   is the transformation which scales by a factor of 2 along the
 --   diagonal line y = x.
 --
 --   Note that
 --
---   @
---   (transform t2) `under` t1 == transform (conjugate t1 t2)
---   @
+-- @
+-- (transform t2) `underT` t1 == transform (conjugate t1 t2)
+-- @
 --
 --   for all transformations @t1@ and @t2@.
-under :: (Transformable a, Transformable b, V a ~ V b) => (a -> b) -> Transformation (V a) -> a -> b
-f `under` t = transform (inv t) . f . transform t
+--
+--   See also the isomorphisms like 'transformed', 'movedTo',
+--   'movedFrom', and 'translated'.
+underT :: (InSpace v n a, SameSpace a b, Transformable a, Transformable b)
+      => (a -> b) -> Transformation v n -> a -> b
+f `underT` t = transform (inv t) . f . transform t
+
+-- | Use a 'Transformation' to make an 'Iso' between an object
+--   transformed and untransformed. This is useful for carrying out
+--   functions 'under' another transform:
+--
+-- @
+-- under (transformed t) f               == transform (inv t) . f . transform t
+-- under (transformed t1) (transform t2) == transform (conjugate t1 t2)
+-- transformed t ## a                    == transform t a
+-- a ^. transformed t                    == transform (inv t) a
+-- @
+transformed :: (InSpace v n a, SameSpace a b, Transformable a, Transformable b)
+            => Transformation v n -> Iso a b a b
+transformed t = iso (transform $ inv t) (transform t)
+
+-- | Use a 'Point' to make an 'Iso' between an object
+--   moved to and from that point:
+--
+-- @
+-- under (movedTo p) f == moveTo (-p) . f . moveTo p
+-- over (movedTo p) f  == moveTo p . f . moveTo (-p)
+-- movedTo p           == from (movedFrom p)
+-- movedTo p ## a      == moveTo p a
+-- a ^. movedTo p      == moveOriginTo p a
+-- @
+movedTo :: (InSpace v n a, SameSpace a b, HasOrigin a, HasOrigin b)
+        => Point v n -> Iso a b a b
+movedTo p = iso (moveTo (negated p)) (moveTo p)
+
+-- | Use a 'Transformation' to make an 'Iso' between an object
+--   transformed and untransformed. We have
+--
+-- @
+-- under (movedFrom p) f == moveTo p . f . moveTo (-p)
+-- movedFrom p           == from (movedTo p)
+-- movedFrom p ## a      == moveOriginTo p a
+-- a ^. movedFrom p      == moveTo p a
+-- over (movedFrom p) f  == moveTo (-p) . f . moveTo p
+-- @
+movedFrom :: (InSpace v n a, SameSpace a b, HasOrigin a, HasOrigin b)
+          => Point v n -> Iso a b a b
+movedFrom p = iso (moveOriginTo (negated p)) (moveOriginTo p)
+
+-- | Use a vector to make an 'Iso' between an object translated and
+--   untranslated.
+--
+-- @
+-- under (translated v) f == translate (-v) . f . translate v
+-- translated v ## a      == translate v a
+-- a ^. translated v      == translate (-v) a
+-- over (translated v) f  == translate v . f . translate (-v)
+-- @
+translated :: (InSpace v n a, SameSpace a b, Transformable a, Transformable b)
+           => v n -> Iso a b a b
+translated v = transformed $ translation v
diff --git a/src/Diagrams/Transform/Matrix.hs b/src/Diagrams/Transform/Matrix.hs
new file mode 100644
--- /dev/null
+++ b/src/Diagrams/Transform/Matrix.hs
@@ -0,0 +1,73 @@
+{-# LANGUAGE ConstraintKinds #-}
+{-# LANGUAGE MonoLocalBinds  #-}
+{-# LANGUAGE TypeFamilies    #-}
+
+-----------------------------------------------------------------------------
+-- |
+-- Module      :  Diagrams.Transform.Matrix
+-- Copyright   :  (c) 2014 diagrams team (see LICENSE)
+-- License     :  BSD-style (see LICENSE)
+-- Maintainer  :  diagrams-discuss@googlegroups.com
+--
+-- Functions for converting between 'Transformation's and matricies.
+--
+-----------------------------------------------------------------------------
+
+module Diagrams.Transform.Matrix where
+
+import           Control.Arrow           ((&&&))
+import           Control.Lens
+import           Data.Distributive
+import qualified Data.Foldable           as F
+import           Data.Functor.Rep
+
+import           Diagrams.Core.Transform as D
+import           Diagrams.ThreeD.Types
+import           Diagrams.TwoD.Types
+
+import           Linear.Matrix
+import           Linear.Vector
+
+-- | Build a matrix from a 'Transformation', ignoring the translation.
+mkMat :: (HasBasis v, Num n) => Transformation v n -> v (v n)
+mkMat t = distribute . tabulate $ apply t . unit . (\x -> el x)
+
+-- | Build a 3D transformation matrix in homogeneous coordinates from
+--   a 'Transformation V3'.
+mkMatHomo :: Num n => Transformation V3 n -> M44 n
+mkMatHomo t = mkTransformationMat (mkMat t) (transl t)
+
+-- | Make a 2D transformation from a 2x2 transform matrix and a
+--   translation vector. Does not check if the matrix is not invertible
+--   (in which case the 'T2' will be invalid).
+fromMat22 :: Floating n => M22 n -> V2 n -> T2 n
+fromMat22 m v = fromMatWithInv m (inv22 m) v
+
+-- | Make a 3D transformation from a 3x3 transform matrix and a
+--   translation vector. Does not check if the matrix is not invertible
+--   (in which case the 'T3' will be invalid).
+fromMat33 :: Floating n => M33 n -> V3 n -> T3 n
+fromMat33 m v = fromMatWithInv m (inv33 m) v
+
+-- | Build a transform with a maxtrix along with its inverse.
+fromMatWithInv :: (Additive v, Distributive v, F.Foldable v, Num n)
+  => v (v n) -- ^ matrix
+  -> v (v n) -- ^ inverse
+  -> v n     -- ^ translation
+  -> Transformation v n
+fromMatWithInv m m_ v =
+  Transformation ((m !*)            <-> (m_ !*))
+                 ((distribute m !*) <-> (distribute m_ !*))
+                 v
+
+-- | Prism onto a 2D transformation from a 2x2 transform matrix and
+--   translation vector. Does not check if the matrix is invertible (in
+--   which case the 'T2' will be invalid).
+mat22 :: Floating n => Iso' (M22 n, V2 n) (T2 n)
+mat22 = iso (uncurry fromMat22) (mkMat &&& transl)
+
+-- | Prism onto a 3D transformation from a 3x3 transform matrix and
+--   translation vector. Does not check if the matrix is invertible
+--   (in which case the 'T3' will be invalid).
+mat33 :: Floating n => Iso' (M33 n, V3 n) (T3 n)
+mat33 = iso (uncurry fromMat33) (mkMat &&& transl)
diff --git a/src/Diagrams/Transform/ScaleInv.hs b/src/Diagrams/Transform/ScaleInv.hs
new file mode 100644
--- /dev/null
+++ b/src/Diagrams/Transform/ScaleInv.hs
@@ -0,0 +1,185 @@
+{-# LANGUAGE ConstraintKinds       #-}
+{-# LANGUAGE DeriveDataTypeable    #-}
+{-# LANGUAGE FlexibleContexts      #-}
+{-# LANGUAGE FlexibleInstances     #-}
+{-# LANGUAGE MultiParamTypeClasses #-}
+{-# LANGUAGE ScopedTypeVariables   #-}
+{-# LANGUAGE StandaloneDeriving    #-}
+{-# LANGUAGE TemplateHaskell       #-}
+{-# LANGUAGE TypeFamilies          #-}
+{-# LANGUAGE TypeOperators         #-}
+{-# LANGUAGE UndecidableInstances  #-}
+-----------------------------------------------------------------------------
+-- |
+-- Module      :  Diagrams.TwoD.Transform.ScaleInv
+-- Copyright   :  (c) 2012-2013 diagrams-lib team (see LICENSE)
+-- License     :  BSD-style (see LICENSE)
+-- Maintainer  :  diagrams-discuss@googlegroups.com
+--
+-- Wrapper for creating scale-invariant objects in two dimensions.
+--
+-----------------------------------------------------------------------------
+
+module Diagrams.Transform.ScaleInv
+    ( ScaleInv(..)
+    , scaleInvObj, scaleInvDir, scaleInvLoc
+    , scaleInv, scaleInvPrim)
+    where
+
+import           Control.Lens            (makeLenses, view, (^.))
+import           Data.Typeable
+
+import           Diagrams.Angle
+import           Diagrams.Core
+import           Diagrams.TwoD.Transform
+import           Diagrams.TwoD.Types
+
+import           Linear.Affine
+import           Linear.Vector
+
+-- | The @ScaleInv@ wrapper creates two-dimensional /scale-invariant/
+--   objects.  Intuitively, a scale-invariant object is affected by
+--   transformations like translations and rotations, but not by scales.
+--
+--   However, this is problematic when it comes to /non-uniform/
+--   scales (/e.g./ @scaleX 2 . scaleY 3@) since they can introduce a
+--   perceived rotational component.  The prototypical example is an
+--   arrowhead on the end of a path, which should be scale-invariant.
+--   However, applying a non-uniform scale to the path but not the
+--   arrowhead would leave the arrowhead pointing in the wrong
+--   direction.
+--
+--   Moreover, for objects whose local origin is not at the local
+--   origin of the parent diagram, any scale can result in a
+--   translational component as well.
+--
+--   The solution is to also store a point (indicating the location,
+--   /i.e./ the local origin) and a unit vector (indicating the
+--   /direction/) along with a scale-invariant object.  A
+--   transformation to be applied is decomposed into rotational and
+--   translational components as follows:
+--
+--   * The transformation is applied to the direction vector, and the
+--   difference in angle between the original direction vector and its
+--   image under the transformation determines the rotational
+--   component.  The rotation is applied with respect to the stored
+--   location, rather than the global origin.
+--
+--   * The vector from the location to the image of the location under
+--   the transformation determines the translational component.
+
+data ScaleInv t =
+  ScaleInv
+  { _scaleInvObj :: t
+  , _scaleInvDir :: Vn t
+  , _scaleInvLoc :: Point (V t) (N t)
+  }
+  deriving Typeable
+
+deriving instance (Show t, Show (Vn t)) => Show (ScaleInv t)
+
+makeLenses ''ScaleInv
+
+-- | Create a scale-invariant object pointing in the given direction,
+--   located at the origin.
+scaleInv :: (V t ~ v, N t ~ n, Additive v, Num n) => t -> v n -> ScaleInv t
+scaleInv t d = ScaleInv t d origin
+
+type instance V (ScaleInv t) = V t
+type instance N (ScaleInv t) = N t
+
+instance (V t ~ v, N t ~ n, Additive v, Num n, HasOrigin t) => HasOrigin (ScaleInv t) where
+  moveOriginTo p (ScaleInv t v l) = ScaleInv (moveOriginTo p t) v (moveOriginTo p l)
+
+instance (V t ~ V2, N t ~ n, RealFloat n, Transformable t) => Transformable (ScaleInv t) where
+  transform tr (ScaleInv t v l) = ScaleInv (trans . rot $ t) (rot v) l'
+    where
+      angle = transform tr v ^. _theta
+
+      rot :: (V k ~ V t, N k ~ N t, Transformable k) => k -> k
+      rot = rotateAround l angle
+
+      l'  = transform tr l
+
+      trans = translate (l' .-. l)
+
+{- Proof that the above satisfies the monoid action laws.
+
+   1. transform mempty (ScaleInv t v l)
+      = ScaleInv (trans . rot $ t) (rot v) l'
+        { l'    = transform mempty l = l }
+        { trans = translate (l' .-. l)
+                = translate (l .-. l)
+                = translate zeroV
+                = id
+        }
+        { rot   = rotateAround l angle
+                = rotateAround l (direction (transform mempty v) - direction v)
+                = rotateAround l (direction v - direction v)
+                = rotateAround l 0
+                = id
+        }
+      = ScaleInv t v l
+
+  2. transform t1 (transform t2 (ScaleInv t v l))
+     = let angle = direction (transform t2 v) - direction v
+           rot   = rotateAround l angle
+           l'    = transform t2 l
+           trans = translate (l' .-. l)
+       in
+           transform t1 (ScaleInv (trans . rot $ t) (rot v) l')
+
+     = let angle  = direction (transform t2 v) - direction v
+           rot    = rotateAround l angle
+           l'     = transform t2 l
+           trans  = translate (l' .-. l)
+           angle2 = direction (transform t1 (rot v)) - direction (rot v)
+           rot2   = rotateAround l' angle2
+           l'2    = transform t1 l'
+           trans2 = translate (l'2 .-. l')
+       in
+           ScaleInv (trans2 . rot2 . trans . rot $ t) (rot2 . rot $ v) l'2
+
+       { l'2 = transform t1 l'
+             = transform t1 (transform t2 l)
+             = transform (t1 <> t2) l
+       }
+       { trans2 = translate (l'2 .-. l')
+                = translate (transform (t1 <> t2) l .-. transform t2 l)
+                = translate (transform t1 l .-. l)
+       }
+       { rot v  = rotateAround l angle v
+                = rotate angle `under` translation (origin .-. l) $ v
+                = rotate angle v
+       }
+       { angle2 = direction (transform t1 (rot v)) - direction (rot v)
+                = direction (transform t1 (rotate angle v)) - direction (rotate angle v)
+                = direction (transform t1 (rotate angle v)) - direction v - angle
+       }
+       { rot2   = rotateAround l' angle2
+                = ???
+       }
+
+-}
+
+instance (V t ~ V2, N t ~ n, RealFloat n, Renderable t b) => Renderable (ScaleInv t) b where
+  render b = render b . view scaleInvObj
+
+-- | Create a diagram from a single scale-invariant primitive.  The
+--   vector argument specifies the direction in which the primitive is
+--   \"pointing\" (for the purpose of keeping it rotated correctly
+--   under non-uniform scaling).  The primitive is assumed to be
+--   \"located\" at the origin (for the purpose of translating it
+--   correctly under scaling).
+--
+--   Note that the resulting diagram will have an /empty/ envelope,
+--   trace, and query.  The reason is that the envelope, trace, and
+--   query cannot be cached---applying a transformation would cause
+--   the cached envelope, etc. to get \"out of sync\" with the
+--   scale-invariant object.  The intention, at any rate, is that
+--   scale-invariant things will be used only as \"decorations\" (/e.g./
+--   arrowheads) which should not affect the envelope, trace, and
+--   query.
+scaleInvPrim :: (V t ~ V2, N t ~ n, RealFloat n, Typeable t, Renderable t b, Monoid m)
+             => t -> V2 n -> QDiagram b (V t) (N t) m
+scaleInvPrim t d = mkQD (Prim $ scaleInv t d) mempty mempty mempty mempty
diff --git a/src/Diagrams/TwoD.hs b/src/Diagrams/TwoD.hs
--- a/src/Diagrams/TwoD.hs
+++ b/src/Diagrams/TwoD.hs
@@ -4,7 +4,7 @@
 -----------------------------------------------------------------------------
 -- |
 -- Module      :  Diagrams.TwoD
--- Copyright   :  (c) 2011 diagrams-lib team (see LICENSE)
+-- Copyright   :  (c) 2011-2015 diagrams-lib team (see LICENSE)
 -- License     :  BSD-style (see LICENSE)
 -- Maintainer  :  diagrams-discuss@googlegroups.com
 --
@@ -25,10 +25,17 @@
 --     specialized to two dimensions (see also "Diagrams.Combinators"
 --     for more general combining).
 --
+--   * "Diagrams.TwoD.Attributes" defines attributes specific to two
+--     dimensions, *e.g.* fill color, line color, and gradients.
+--
 --   * "Diagrams.TwoD.Transform" defines R^2-specific transformations
 --     such as rotation by an angle, and scaling, translation, and
 --     reflection in the X and Y directions.
 --
+--   * "Diagrams.TwoD.Deform" defines some non-affine transformations
+--     specific to two dimensions, *e.g.* parallel and perspective
+--     projections.
+--
 --   * "Diagrams.TwoD.Ellipse" defines circles and ellipses.
 --
 --   * "Diagrams.TwoD.Arc" defines circular arcs.
@@ -43,7 +50,8 @@
 --     e.g. various polygons.
 --
 --   * "Diagrams.TwoD.Arrow" contains tools for drawing arrows between
---     things.
+--     things, and "Diagrams.TwoD.Arrowheads" defines a collection of
+--     arrowheads.
 --
 --   * "Diagrams.TwoD.Text" defines primitive text diagrams.
 --
@@ -61,25 +69,38 @@
 -----------------------------------------------------------------------------
 module Diagrams.TwoD
        ( -- * R^2
-         R2, r2, unr2, mkR2
-       , P2, p2, unp2, mkP2
-       , T2
+         V2 (..), R1 (..), R2 (..)
+       , P2, T2
+       , r2, unr2, mkR2
+       , p2, unp2, mkP2
        , unitX, unitY, unit_X, unit_Y
-       , direction, fromDirection
+       , perp, leftTurn
+       , xDir, yDir
 
          -- * Angles
        , tau
+       , angleV
+       , angleDir
+       , signedAngleBetween , signedAngleBetweenDirs
 
+       -- * Polar Coördinates
+       , HasR(..), r2PolarIso
+
          -- * Paths
          -- ** Stroking
-       , stroke, stroke', strokeTrail, strokeT, strokeTrail', strokeT'
+       , stroke, stroke'
+       , strokePath, strokeP, strokePath', strokeP'
+       , strokeTrail, strokeT, strokeTrail', strokeT'
        , strokeLine, strokeLoop
        , strokeLocTrail, strokeLocT, strokeLocLine, strokeLocLoop
-       , FillRule(..), fillRule
+       , FillRule(..), fillRule, _fillRule
        , StrokeOpts(..), vertexNames, queryFillRule
+       , intersectPoints, intersectPoints'
+       , intersectPointsP, intersectPointsP'
+       , intersectPointsT, intersectPointsT'
 
          -- ** Clipping
-       , clipBy, clipTo, clipped
+       , clipBy, clipTo, clipped, _Clip, _clip
 
          -- * Shapes
          -- ** Rules
@@ -93,6 +114,7 @@
        , arc
        , arc'
        , arcCW
+       , arcCCW
        , wedge
        , arcBetween
        , annularWedge
@@ -159,12 +181,15 @@
 
          -- * Text
        , text, topLeftText, alignedText, baselineText
-       , font, italic, oblique, bold, fontSize
+       , font, italic, oblique, fontSize
+       , bold, bolder, lighter, thinWeight
+       , ultraLight, light, mediumWeight, heavy, semiBold, ultraBold
+       , _font, _fontSizeR, _fontSize
        , fontSizeO, fontSizeL, fontSizeN, fontSizeG
 
          -- * Images
        , DImage(..), ImageData(..)
-       , Embedded, External
+       , Embedded, External, Native
        , image
        , loadImageEmb
        , loadImageExt
@@ -174,8 +199,9 @@
 
          -- * Transformations
          -- ** Rotation
-       , rotation, rotate, rotateBy
-       , rotationAbout, rotateAbout
+       , rotation, rotate, rotateBy, rotated
+       , rotationAround, rotateAround
+       , rotationTo, rotateTo
          -- ** Scaling
        , scalingX, scaleX
        , scalingY, scaleY
@@ -186,9 +212,12 @@
        , translationX, translateX
        , translationY, translateY
        , translation, translate
+         -- ** Conformal affine maps
+       , scalingRotationTo, scaleRotateTo
          -- ** Reflection
        , reflectionX, reflectX
        , reflectionY, reflectY
+       , reflectionXY, reflectXY
        , reflectionAbout, reflectAbout
          -- ** Shears
        , shearingX, shearX
@@ -200,21 +229,22 @@
 
          -- * Combinators
          -- ** Combining multiple diagrams
-       , (===), (|||), atAngle
-       , hcat, hcat'
-       , vcat, vcat'
 
+       , (===), (|||)
+       , hcat, hcat', hsep
+       , vcat, vcat', vsep
+
          -- ** Spacing and envelopes
        , strutX, strutY
        , padX, padY
 
        , extrudeLeft, extrudeRight, extrudeBottom, extrudeTop
 
-       , view
+       , rectEnvelope, crop
 
          -- ** Background
 
-       , boundingRect, bg
+       , boundingRect, bg, bgFrame
 
          -- * Alignment
        , alignL, alignR, alignT, alignB, alignTL, alignTR, alignBL, alignBR
@@ -222,53 +252,49 @@
        , centerX, centerY, centerXY
 
          -- * Snugging
-       , snugL, snugR, snugT, snugB, snugTL, snugTR, snugBL, snugBR
+       , snugL, snugR, snugT, snugB
        , snugX, snugY
        , snugCenterX, snugCenterY, snugCenterXY
 
          -- * Size
          -- ** Computing size
-       , width, height, size2D, sizeSpec2D
-       , extentX, extentY, center2D
+       , width, height
+       , extentX, extentY
 
          -- ** Specifying size
-       , SizeSpec2D(..)
-       , mkSizeSpec
-
-         -- ** Adjusting size
-       , sized, sizedAs
-
-        -- * Textures
-      , Texture(..), solid 
-      , SpreadMethod(..), GradientStop(..), mkStops, getFillTexture
-      , fillTexture, getLineTexture, lineTexture, lineTextureA
-      , stopFraction, stopColor
-
-      , LGradient(..), lGradStops, lGradTrans, lGradStart, lGradEnd
-      , lGradSpreadMethod, defaultLG, _LG, mkLinearGradient
+       , mkSizeSpec2D
+       , mkWidth
+       , mkHeight
+       , dims2D
 
-      , RGradient(..)
-      , rGradStops, rGradCenter0, rGradRadius0, rGradCenter1, rGradRadius1
-      , rGradTrans, rGradSpreadMethod, defaultRG, _RG, mkRadialGradient
+         -- * Textures
+       , Texture(..), solid
+       , SpreadMethod(..), GradientStop(..)
+       , _FillTexture, fillTexture, _fillTexture, getFillTexture
+       , _LineTexture, lineTexture, _lineTexture, lineTextureA, getLineTexture
+       , stopFraction, stopColor, mkStops
 
-        -- ** Colors
-      , fillColor, fc, fcA, recommendFillColor
-      , lineColor, lc, lcA, _SC
+       , LGradient(..), _LG, lGradStops, lGradTrans, lGradStart, lGradEnd
+       , lGradSpreadMethod, defaultLG, mkLinearGradient
 
-       -- ** Width
-       , LineWidth, getLineWidth, lineWidth, lineWidthA
-       , lw, lwN, lwO, lwL, lwG
-       , ultraThin, veryThin, thin, medium, thick, veryThick, ultraThick, none
-       , tiny, verySmall, small, normal, large, veryLarge, huge
+       , RGradient(..)
+       , rGradStops, rGradCenter0, rGradRadius0, rGradCenter1, rGradRadius1
+       , rGradTrans, rGradSpreadMethod, defaultRG, _RG, mkRadialGradient
 
-       -- ** Dashing
-       , Dashing(..), DashingA, getDashing
-       , dashing, dashingO, dashingL, dashingN, dashingG
+         -- ** Colors
+       , fillColor, _SC, _AC, fc, fcA, recommendFillColor
+       , lineColor, lc, lcA
 
          -- * Visual aids for understanding the internal model
        , showOrigin
        , showOrigin'
        , OriginOpts(..), oColor, oScale, oMinSize
+       , showEnvelope
+       , showEnvelope'
+       , EnvelopeOpts(..), eColor, eLineWidth, ePoints
+       , showTrace
+       , showTrace'
+       , TraceOpts(..), tColor, tScale, tMinSize, tPoints
        , showLabels
 
        ) where
diff --git a/src/Diagrams/TwoD/Adjust.hs b/src/Diagrams/TwoD/Adjust.hs
--- a/src/Diagrams/TwoD/Adjust.hs
+++ b/src/Diagrams/TwoD/Adjust.hs
@@ -1,5 +1,11 @@
-{-# LANGUAGE Rank2Types #-}
+{-# LANGUAGE ConstraintKinds #-}
+{-# LANGUAGE FlexibleContexts #-}
+{-# LANGUAGE Rank2Types       #-}
+{-# LANGUAGE TypeFamilies     #-}
 
+{-# OPTIONS_GHC -fno-warn-unused-imports #-}
+  -- for Data.Semigroup
+
 -----------------------------------------------------------------------------
 -- |
 -- Module      :  Diagrams.TwoD.Adjust
@@ -13,45 +19,44 @@
 -----------------------------------------------------------------------------
 
 module Diagrams.TwoD.Adjust
-    (
-      setDefault2DAttributes
-    , adjustDiaSize2D
+    ( setDefault2DAttributes
+    , adjustSize2D
     , adjustDia2D
     ) where
 
-import           Diagrams.Attributes      (lineCap, lineJoin,
-                                           lineMiterLimitA)
+import           Diagrams.Attributes
+import           Diagrams.BoundingBox
 import           Diagrams.Core
-import           Diagrams.TwoD.Attributes (lineWidthA, lineTextureA)
-import           Diagrams.TwoD.Size       (SizeSpec2D (..), center2D,
-                                           requiredScale, size2D)
-import           Diagrams.TwoD.Text       (fontSizeA)
-import           Diagrams.TwoD.Types      (R2, T2, p2)
+import           Diagrams.Size
+import           Diagrams.TwoD.Attributes (lineTextureA)
+import           Diagrams.TwoD.Types
 import           Diagrams.Util            (( # ))
 
-import           Control.Lens             (Lens', (&), (.~), (^.))
-import           Data.AffineSpace         ((.-.))
-import           Data.Default.Class
+import           Control.Lens             (Lens', set, (^.))
+import           Data.Default
 import           Data.Semigroup
 
+
 -- | Set default attributes of a 2D diagram (in case they have not
 --   been set):
 --
---       * Line width 0.01
---
---       * Line color black
+--       * 'LineWidth':  0.01
 --
---       * Font size 1
+--       * 'LineTexture': solid black
 --
---       * Line cap LineCapButt
+--       * 'LineCap': LineCapButt
 --
---       * line join miter
+--       * 'LineJoin': miter
 --
---       * Miter limit 10
-setDefault2DAttributes :: Semigroup m => QDiagram b R2 m -> QDiagram b R2 m
-setDefault2DAttributes d = d # lineWidthA def # lineTextureA def # fontSizeA def
-                             # lineCap def # lineJoin def # lineMiterLimitA def
-
+--       * 'MiterLimit': 10
+setDefault2DAttributes :: (TypeableFloat n, Semigroup m)
+  => QDiagram b V2 n m -> QDiagram b V2 n m
+setDefault2DAttributes d
+  = d # lineWidthM def
+      # lineTextureA def
+      # lineCap def
+      # lineJoin def
+      # lineMiterLimitA def
 
 -- | Adjust the size and position of a 2D diagram to fit within the
 --   requested size. The first argument is a lens into the output
@@ -60,25 +65,17 @@
 --   inverse of which can be used, say, to translate output/device
 --   coordinates back into local diagram coordinates), and the
 --   modified diagram itself.
-adjustDiaSize2D :: Monoid' m
-                => Lens' (Options b R2) SizeSpec2D
-                -> b -> Options b R2 -> QDiagram b R2 m
-                -> (Options b R2, T2, QDiagram b R2 m)
-adjustDiaSize2D szL _ opts d =
-  ( case spec of
-     Dims _ _ -> opts
-     _        -> opts & szL .~ (uncurry Dims . scale s $ size)
-  , adjustT
-  , d # transform adjustT
-  )
-  where spec = opts ^. szL
-        size = size2D d
-        s    = requiredScale spec size
-        finalSz = case spec of
-                    Dims w h -> (w,h)
-                    _        -> scale s size
-        tr = (0.5 *. p2 finalSz) .-. (s *. center2D d)
-        adjustT = translation tr <> scaling s
+adjustSize2D
+  :: (TypeableFloat n, Monoid' m)
+  => Lens' (Options b V2 n) (SizeSpec V2 n)
+  -> b
+  -> Options b V2 n
+  -> QDiagram b V2 n m
+  -> (Options b V2 n, Transformation V2 n, QDiagram b V2 n m)
+adjustSize2D szL _ opts d = (set szL spec opts, t, d # transform t)
+  where
+    spec    = dims sz
+    (sz, t) = sizeAdjustment (opts ^. szL) (boundingBox d)
 
 -- | @adjustDia2D@ provides a useful default implementation of
 --   the 'adjustDia' method from the 'Backend' type class.
@@ -97,10 +94,10 @@
 --   to the diagram (the inverse of which can be used, say, to
 --   translate output/device coordinates back into local diagram
 --   coordinates), and the modified diagram itself.
-adjustDia2D :: Monoid' m
-            => Lens' (Options b R2) SizeSpec2D
-            -> b -> Options b R2 -> QDiagram b R2 m
-            -> (Options b R2, T2, QDiagram b R2 m)
+adjustDia2D :: (TypeableFloat n, Monoid' m)
+            => Lens' (Options b V2 n) (SizeSpec V2 n)
+            -> b -> Options b V2 n -> QDiagram b V2 n m
+            -> (Options b V2 n, Transformation V2 n, QDiagram b V2 n m)
 adjustDia2D szL b opts d
-  = adjustDiaSize2D szL b opts (d # setDefault2DAttributes)
+  = adjustSize2D szL b opts (d # setDefault2DAttributes)
 
diff --git a/src/Diagrams/TwoD/Align.hs b/src/Diagrams/TwoD/Align.hs
--- a/src/Diagrams/TwoD/Align.hs
+++ b/src/Diagrams/TwoD/Align.hs
@@ -1,5 +1,7 @@
+{-# LANGUAGE ConstraintKinds #-}
 {-# LANGUAGE FlexibleContexts #-}
 {-# LANGUAGE TypeFamilies     #-}
+
 -----------------------------------------------------------------------------
 -- |
 -- Module      :  Diagrams.TwoD.Align
@@ -28,7 +30,6 @@
 
       -- ** Align by trace
     , snugL, snugR, snugT, snugB
-    , snugTL, snugTR, snugBL, snugBR
 
       -- * Relative alignment
     , alignX, snugX, alignY, snugY
@@ -45,57 +46,43 @@
 import           Diagrams.TwoD.Types
 import           Diagrams.TwoD.Vector
 
-import           Data.VectorSpace
-
 -- | Align along the left edge, i.e. translate the diagram in a
 --   horizontal direction so that the local origin is on the left edge
 --   of the envelope.
-alignL :: (Alignable a, HasOrigin a, V a ~ R2) => a -> a
-alignL = align (negateV unitX)
+alignL :: (InSpace V2 n a, Fractional n, Alignable a, HasOrigin a) => a -> a
+alignL = align unit_X
 
-snugL :: (Fractional (Scalar (V a)), Alignable a, Traced a,
-      HasOrigin a, V a ~ R2) => a -> a
-snugL = snug (negateV unitX)
+snugL :: (InSpace V2 n a, Fractional n, Alignable a, Traced a, HasOrigin a) => a -> a
+snugL = snug unit_X
 
 -- | Align along the right edge.
-alignR :: (Alignable a, HasOrigin a, V a ~ R2) => a -> a
+alignR :: (InSpace V2 n a, Fractional n, Alignable a, HasOrigin a) => a -> a
 alignR = align unitX
 
-snugR :: (Fractional (Scalar (V a)), Alignable a, Traced a,
-      HasOrigin a, V a ~ R2) => a -> a
+snugR :: (InSpace V2 n a, Fractional n, Alignable a, Traced a, HasOrigin a) => a -> a
 snugR = snug unitX
 
 
 -- | Align along the top edge.
-alignT :: (Alignable a, HasOrigin a, V a ~ R2) => a -> a
+alignT :: (InSpace V2 n a, Fractional n, Alignable a, HasOrigin a) => a -> a
 alignT = align unitY
 
-snugT:: (Fractional (Scalar (V a)), Alignable a, Traced a,
-      HasOrigin a, V a ~ R2) => a -> a
+snugT:: (InSpace V2 n a, Fractional n, Alignable a, Traced a, HasOrigin a) => a -> a
 snugT = snug unitY
 
 -- | Align along the bottom edge.
-alignB :: (Alignable a, HasOrigin a, V a ~ R2) => a -> a
-alignB = align (negateV unitY)
+alignB :: (InSpace V2 n a, Fractional n, Alignable a, HasOrigin a) => a -> a
+alignB = align unit_Y
 
-snugB :: (Fractional (Scalar (V a)), Alignable a, Traced a,
-      HasOrigin a, V a ~ R2) => a -> a
-snugB = snug (negateV unitY)
+snugB :: (InSpace V2 n a, Fractional n, Alignable a, Traced a, HasOrigin a) => a -> a
+snugB = snug unit_Y
 
-alignTL, alignTR, alignBL, alignBR :: (Alignable a, HasOrigin a, V a ~ R2) => a -> a
+alignTL, alignTR, alignBL, alignBR :: (InSpace V2 n a, Fractional n, Alignable a, HasOrigin a) => a -> a
 alignTL = alignT . alignL
 alignTR = alignT . alignR
 alignBL = alignB . alignL
 alignBR = alignB . alignR
 
-snugTL, snugTR, snugBL, snugBR
-  :: (Fractional (Scalar (V a)), Alignable a, Traced a, HasOrigin a, V a ~ R2)
-   => a -> a
-snugTL = snugT . snugL
-snugTR = snugT . snugR
-snugBL = snugB . snugL
-snugBR = snugB . snugR
-
 -- | @alignX@ and @snugX@ move the local origin horizontally as follows:
 --
 --   * @alignX (-1)@ moves the local origin to the left edge of the boundary;
@@ -108,44 +95,40 @@
 --
 --   * @snugX@ works the same way.
 
-alignX :: (Alignable a, HasOrigin a, V a ~ R2) => Double -> a -> a
+alignX :: (InSpace v n a, R1 v, Fractional n, Alignable a, HasOrigin a) => n -> a -> a
 alignX = alignBy unitX
 
 -- | See the documentation for 'alignX'.
-snugX :: (Fractional (Scalar (V a)), Alignable a, Traced a,
-      HasOrigin a, V a ~ R2) => Double -> a -> a
+snugX :: (InSpace v n a, R1 v, Fractional n, Alignable a, Traced a, HasOrigin a) => n -> a -> a
 snugX = snugBy unitX
 
 -- | Like 'alignX', but moving the local origin vertically, with an
 --   argument of @1@ corresponding to the top edge and @(-1)@ corresponding
 --   to the bottom edge.
-alignY :: (Alignable a, HasOrigin a, V a ~ R2) => Double -> a -> a
+alignY :: (InSpace v n a, R2 v, Fractional n, Alignable a, HasOrigin a) => n -> a -> a
 alignY = alignBy unitY
 
-snugY :: (Fractional (Scalar (V a)), Alignable a, Traced a,
-      HasOrigin a, V a ~ R2) => Double -> a -> a
+-- | See the documentation for 'alignY'.
+snugY :: (InSpace v n a, R2 v, Fractional n, Alignable a, Traced a, HasOrigin a) => n -> a -> a
 snugY = snugBy unitY
 
 -- | Center the local origin along the X-axis.
-centerX  :: (Alignable a, HasOrigin a, V a ~ R2) => a -> a
-centerX  = alignBy unitX 0
+centerX :: (InSpace v n a, R1 v, Fractional n, Alignable a, HasOrigin a) => a -> a
+centerX = alignBy unitX 0
 
-snugCenterX :: (Fractional (Scalar (V a)), Alignable a, Traced a,
-      HasOrigin a, V a ~ R2) => a -> a
+snugCenterX :: (InSpace v n a, R1 v, Fractional n, Alignable a, Traced a, HasOrigin a) => a -> a
 snugCenterX = snugBy unitX 0
 
 -- | Center the local origin along the Y-axis.
-centerY  :: (Alignable a, HasOrigin a, V a ~ R2) => a -> a
-centerY  = alignBy unitY 0
+centerY :: (InSpace v n a, R2 v, Fractional n, Alignable a, HasOrigin a) => a -> a
+centerY = alignBy unitY 0
 
-snugCenterY :: (Fractional (Scalar (V a)), Alignable a, Traced a,
-      HasOrigin a, V a ~ R2) => a -> a
+snugCenterY :: (InSpace v n a, R2 v, Fractional n, Alignable a, Traced a, HasOrigin a) => a -> a
 snugCenterY = snugBy unitY 0
 
 -- | Center along both the X- and Y-axes.
-centerXY :: (Alignable a, HasOrigin a, V a ~ R2) => a -> a
-centerXY = center
+centerXY :: (InSpace v n a, R2 v, Fractional n, Alignable a, HasOrigin a) => a -> a
+centerXY = centerX . centerY
 
-snugCenterXY :: (Fractional (Scalar (V a)), Alignable a, Traced a,
-      HasOrigin a, V a ~ R2) => a -> a
-snugCenterXY = snugCenter
+snugCenterXY :: (InSpace v n a, R2 v, Fractional n, Alignable a, Traced a, HasOrigin a) => a -> a
+snugCenterXY = snugCenterX . snugCenterY
diff --git a/src/Diagrams/TwoD/Arc.hs b/src/Diagrams/TwoD/Arc.hs
--- a/src/Diagrams/TwoD/Arc.hs
+++ b/src/Diagrams/TwoD/Arc.hs
@@ -1,5 +1,12 @@
-{-# LANGUAGE TypeFamilies #-}
-{-# LANGUAGE ViewPatterns #-}
+{-# LANGUAGE ConstraintKinds  #-}
+{-# LANGUAGE FlexibleContexts #-}
+{-# LANGUAGE TypeFamilies     #-}
+{-# LANGUAGE TypeOperators    #-}
+{-# LANGUAGE ViewPatterns     #-}
+
+{-# OPTIONS_GHC -fno-warn-unused-imports #-}
+  -- for Data.Semigroup
+
 -----------------------------------------------------------------------------
 -- |
 -- Module      :  Diagrams.TwoD.Arc
@@ -14,8 +21,11 @@
 module Diagrams.TwoD.Arc
     ( arc
     , arc'
-    , arcCW
     , arcT
+
+    , arcCCW
+    , arcCW
+
     , bezierFromSweep
 
     , wedge
@@ -25,49 +35,49 @@
 
 import           Diagrams.Angle
 import           Diagrams.Core
+import           Diagrams.Direction
 import           Diagrams.Located        (at)
 import           Diagrams.Segment
 import           Diagrams.Trail
 import           Diagrams.TrailLike
 import           Diagrams.TwoD.Transform
 import           Diagrams.TwoD.Types
-import           Diagrams.TwoD.Vector    (direction, e, unitX)
+import           Diagrams.TwoD.Vector    (e, unitX, unitY, unit_Y)
 import           Diagrams.Util           (( # ))
 
-import           Control.Lens            ((^.))
-import           Data.AffineSpace        ((.-.))
-import           Data.Semigroup          ((<>))
-import           Data.VectorSpace
-import           Diagrams.Coordinates
+import           Control.Lens            ((&), (<>~), (^.))
+import           Data.Semigroup
 
+import           Linear.Affine
+import           Linear.Metric
+import           Linear.Vector
+
 -- For details of this approximation see:
 --   http://www.tinaja.com/glib/bezcirc2.pdf
 
 -- | @bezierFromSweepQ1 s@ constructs a 'Cubic' segment that starts in
---   the positive y direction and sweeps counterclockwise through @s@
---   radians.  The approximation is only valid for angles in the first
---   quadrant.
-bezierFromSweepQ1 :: Angle -> Segment Closed R2
-bezierFromSweepQ1 s = fmap (^-^ v) . rotate (s ^/ 2) $ bezier3 c2 c1 p0
-  where p0@(coords -> x :& y) = rotate (s ^/ 2) v
-        c1                    = ((4-x)/3)  ^&  ((1-x)*(3-x)/(3*y))
-        c2                    = reflectY c1
-        v                     = unitX
+--  the positive y direction and sweeps counterclockwise through an
+--  angle @s@.  The approximation is only valid for angles in the
+--  first quadrant.
+bezierFromSweepQ1 :: Floating n => Angle n -> Segment Closed V2 n
+bezierFromSweepQ1 s = mapSegmentVectors (^-^ unitX) . rotate (s ^/ 2) $ bezier3 c2 c1 p0
+  where p0@(V2 x y) = e (s ^/ 2)
+        c1          = V2 ((4-x)/3) ((1-x)*(3-x)/(3*y))
+        c2          = reflectY c1
 
 -- | @bezierFromSweep s@ constructs a series of 'Cubic' segments that
 --   start in the positive y direction and sweep counter clockwise
 --   through the angle @s@.  If @s@ is negative, it will start in the
 --   negative y direction and sweep clockwise.  When @s@ is less than
---   0.0001 the empty list results.  If the sweep is greater than tau
---   radians then it is truncated to one full revolution.
-bezierFromSweep :: Angle -> [Segment Closed R2]
+--   0.0001 the empty list results.  If the sweep is greater than @fullTurn@
+--   later segments will overlap earlier segments.
+bezierFromSweep :: OrderedField n => Angle n -> [Segment Closed V2 n]
 bezierFromSweep s
-  | s > fullTurn = bezierFromSweep fullTurn
-  | s < zeroV      = fmap reflectY . bezierFromSweep $ (negateV s)
-  | s < 0.0001 @@ rad     = []
-  | s < fullTurn^/4      = [bezierFromSweepQ1 s]
-  | otherwise      = bezierFromSweepQ1 (fullTurn^/4)
-          : map (rotateBy (1/4)) (bezierFromSweep (max (s ^-^ fullTurn^/4) zeroV))
+  | s < zero          = fmap reflectY . bezierFromSweep $ negated s
+  | s < 0.0001 @@ rad = []
+  | s < fullTurn^/4   = [bezierFromSweepQ1 s]
+  | otherwise         = bezierFromSweepQ1 (fullTurn^/4)
+          : map (rotateBy (1/4)) (bezierFromSweep (max (s ^-^ fullTurn^/4) zero))
 
 {-
 ~~~~ Note [segment spacing]
@@ -89,72 +99,71 @@
 the approximation error.
 -}
 
--- | Given a start angle @s@ and an end angle @e@, @'arcT' s e@ is the
---   'Trail' of a radius one arc counterclockwise between the two angles.
-arcT :: Angle -> Angle -> Trail R2
-arcT start end
-    | end' < start' = arcT start (end ^+^ (fromIntegral d @@ turn))
-    | otherwise     = (if sweep >= fullTurn then glueTrail else id)
-                    $ trailFromSegments bs
-  where sweep = end ^-^ start
-        bs    = map (rotate start) . bezierFromSweep $ sweep
-
-        -- We want to compare the start and the end and in case
-        -- there isn't some law about 'Angle' ordering, we use a
-        -- known 'Angle' for that.
-        start' = start^.turn
-        end'   = end^.turn
-        d      = ceiling (start' - end') :: Integer
-
--- | Given a start angle @s@ and an end angle @e@, @'arc' s e@ is the
---   path of a radius one arc counterclockwise between the two angles.
---   The origin of the arc is its center.
-arc :: (TrailLike t, V t ~ R2) => Angle -> Angle -> t
-arc start end = trailLike $ arcT start end `at` (rotate start $ p2 (1,0))
+-- | Given a start direction @d@ and a sweep angle @s@, @'arcT' d s@
+--   is the 'Trail' of a radius one arc starting at @d@ and sweeping out
+--   the angle @s@ counterclockwise (for positive s).  The resulting
+--   @Trail@ is allowed to wrap around and overlap itself.
+arcT :: OrderedField n => Direction V2 n -> Angle n -> Trail V2 n
+arcT start sweep = trailFromSegments bs
+  where
+    bs = map (rotateTo start) . bezierFromSweep $ sweep
 
--- | Like 'arc' but clockwise.
-arcCW :: (TrailLike t, V t ~ R2) => Angle -> Angle -> t
-arcCW start end = trailLike $
-                            -- flipped arguments to get the path we want
-                            -- then reverse the trail to get the cw direction.
-                            (reverseTrail $ arcT end start)
-                            `at`
-                            (rotate start $ p2 (1,0))
-                   -- We could just have `arcCW = reversePath . flip arc`
-                   -- but that wouldn't be `TrailLike`.
+-- | Given a start direction @d@ and a sweep angle @s@, @'arc' d s@ is the
+--   path of a radius one arc starting at @d@ and sweeping out the angle
+--   @s@ counterclockwise (for positive s).  The resulting
+--   @Trail@ is allowed to wrap around and overlap itself.
+arc :: (InSpace V2 n t, OrderedField n, TrailLike t) => Direction V2 n -> Angle n -> t
+arc start sweep = trailLike $ arcT start sweep `at` P (fromDirection start)
 
--- | Given a radus @r@, a start angle @s@ and an end angle @e@,
---   @'arc'' r s e@ is the path of a radius @(abs r)@ arc between
---   the two angles.  If a negative radius is given, the arc will
---   be clockwise, otherwise it will be counterclockwise. The origin
---   of the arc is its center.
+-- | Given a radus @r@, a start direction @d@ and an angle @s@,
+--   @'arc'' r d s@ is the path of a radius @(abs r)@ arc starting at
+--   @d@ and sweeping out the angle @s@ counterclockwise (for positive
+--   s).  The origin of the arc is its center.
 --
 --   <<diagrams/src_Diagrams_TwoD_Arc_arc'Ex.svg#diagram=arc'Ex&width=300>>
 --
---   > arc'Ex = mconcat [ arc' r (0 @@ turn) (1/4 @@ turn) | r <- [0.5,-1,1.5] ]
+--   > arc'Ex = mconcat [ arc' r xDir (1/4 @@ turn) | r <- [0.5,-1,1.5] ]
 --   >        # centerXY # pad 1.1
-arc' :: (TrailLike p, V p ~ R2) => Double -> Angle -> Angle -> p
-arc' r start end = trailLike $ scale (abs r) ts `at` (rotate start $ p2 (abs r,0))
-  where ts | r < 0     = reverseTrail $ arcT end start
-           | otherwise = arcT start end
+arc' :: (InSpace V2 n t, OrderedField n, TrailLike t) => n -> Direction V2 n -> Angle n -> t
+arc' (abs -> r) start sweep = trailLike $ scale r ts `at` P (r *^ fromDirection start)
+  where ts = arcT start sweep
 
+arcCCWT :: RealFloat n => Direction V2 n -> Direction V2 n -> Trail V2 n
+arcCCWT start end = trailFromSegments bs
+  where
+    bs    = map (rotateTo start) . bezierFromSweep $ sweep
+    sweep = normalizeAngle $ end ^. _theta ^-^ start ^. _theta
+
+-- | Given a start direction @s@ and end direction @e@, @arcCCW s e@ is the
+--   path of a radius one arc counterclockwise between the two directions.
+--   The origin of the arc is its center.
+arcCCW :: (InSpace V2 n t, RealFloat n, TrailLike t) => Direction V2 n -> Direction V2 n -> t
+arcCCW start end = trailLike $ arcCCWT start end `at` P (fromDirection start)
+
+-- | Like 'arcAngleCCW' but clockwise.
+arcCW :: (InSpace V2 n t, RealFloat n, TrailLike t) => Direction V2 n -> Direction V2 n -> t
+arcCW start end = trailLike $
+  -- flipped arguments to get the path we want
+  -- then reverse the trail to get the cw direction.
+  reverseTrail (arcCCWT end start) `at` P (fromDirection start)
+
 -- | Create a circular wedge of the given radius, beginning at the
---   first angle and extending counterclockwise to the second.
+--   given direction and extending through the given angle.
 --
 --   <<diagrams/src_Diagrams_TwoD_Arc_wedgeEx.svg#diagram=wedgeEx&width=400>>
 --
 --   > wedgeEx = hcat' (with & sep .~ 0.5)
---   >   [ wedge 1 (0 @@ turn) (1/4 @@ turn)
---   >   , wedge 1 (7/30 @@ turn) (11/30 @@ turn)
---   >   , wedge 1 (1/8 @@ turn) (7/8 @@ turn)
+--   >   [ wedge 1 xDir (1/4 @@ turn)
+--   >   , wedge 1 (rotate (7/30 @@ turn) xDir) (4/30 @@ turn)
+--   >   , wedge 1 (rotate (1/8 @@ turn) xDir) (3/4 @@ turn)
 --   >   ]
 --   >   # fc blue
 --   >   # centerXY # pad 1.1
-wedge :: (TrailLike p, V p ~ R2) => Double -> Angle -> Angle -> p
-wedge r a1 a2 = trailLike . (`at` origin) . glueTrail . wrapLine
-              $ fromOffsets [r *^ e a1]
-                <> arc a1 a2 # scale r
-                <> fromOffsets [r *^ negateV (e a2)]
+wedge :: (InSpace V2 n t, OrderedField n, TrailLike t) => n -> Direction V2 n -> Angle n -> t
+wedge r d s = trailLike . (`at` origin) . glueTrail . wrapLine
+              $ fromOffsets [r *^ fromDirection d]
+                <> arc d s # scale r
+                <> fromOffsets [r *^ negated (rotate s $ fromDirection d)]
 
 -- | @arcBetween p q height@ creates an arc beginning at @p@ and
 --   ending at @q@, with its midpoint at a distance of @abs height@
@@ -167,45 +176,47 @@
 --   > arcBetweenEx = mconcat
 --   >   [ arcBetween origin (p2 (2,1)) ht | ht <- [-0.2, -0.1 .. 0.2] ]
 --   >   # centerXY # pad 1.1
-arcBetween :: (TrailLike t, V t ~ R2) => P2 -> P2 -> Double -> t
-arcBetween p q ht = trailLike (a # rotate (direction v) # moveTo p)
+arcBetween :: (TrailLike t, V t ~ V2, N t ~ n, RealFloat n) => Point V2 n -> Point V2 n -> n -> t
+arcBetween p q ht = trailLike (a # rotate (v^._theta) # moveTo p)
   where
     h = abs ht
     isStraight = h < 0.00001
     v = q .-. p
-    d = magnitude (q .-. p)
-    th  = acos ((d*d - 4*h*h)/(d*d + 4*h*h))
-    r = d/(2*sin th)
-    mid | ht >= 0    = fullTurn ^/ 4
-        | otherwise = 3 *^ fullTurn ^/ 4
-    st  = mid ^-^ (th @@ rad)
-    end = mid ^+^ (th @@ rad)
+    d = norm (q .-. p)
+    th  = acosA ((d*d - 4*h*h)/(d*d + 4*h*h))
+    r = d/(2*sinA th)
+    mid | ht >= 0    = direction unitY
+        | otherwise  = direction unit_Y
+    st  = mid & _theta <>~ negated th
     a | isStraight
       = fromOffsets [d *^ unitX]
       | otherwise
-      = arc st end
+      = arc st (2 *^ th)
         # scale r
-        # translateY ((if ht > 0 then negate else id) (r-h))
+        # translateY ((if ht > 0 then negate else id) (r - h))
         # translateX (d/2)
         # (if ht > 0 then reverseLocTrail else id)
 
 -- | Create an annular wedge of the given radii, beginning at the
---   first angle and extending counterclockwise to the second.
+--   first direction and extending through the given sweep angle.
 --   The radius of the outer circle is given first.
 --
 --   <<diagrams/src_Diagrams_TwoD_Arc_annularWedgeEx.svg#diagram=annularWedgeEx&width=400>>
 --
---   > annularWedgeEx = hcat' (with & sep .~ 0.50)
---   >   [ annularWedge 1 0.5 (0 @@ turn) (1/4 @@ turn)
---   >   , annularWedge 1 0.3 (7/30 @@ turn) (11/30 @@ turn)
---   >   , annularWedge 1 0.7 (1/8 @@ turn) (7/8 @@ turn)
+--   > annularWedgeEx = hsep 0.50
+--   >   [ annularWedge 1 0.5 xDir (1/4 @@ turn)
+--   >   , annularWedge 1 0.3 (rotate (7/30 @@ turn) xDir) (4/30 @@ turn)
+--   >   , annularWedge 1 0.7 (rotate (1/8 @@ turn) xDir) (3/4 @@ turn)
 --   >   ]
 --   >   # fc blue
 --   >   # centerXY # pad 1.1
-annularWedge :: (TrailLike p, V p ~ R2) => Double -> Double -> Angle -> Angle -> p
-annularWedge r1' r2' a1 a2 = trailLike . (`at` o) . glueTrail . wrapLine
-              $ fromOffsets [(r1'-r2') *^ e a1]
-                <> arc a1 a2 # scale r1'
-                <> fromOffsets [(r1'-r2') *^ negateV (e a2)]
-                <> arcCW a2 a1 # scale r2'
-  where o = origin # translate (r2' *^ e a1)
+annularWedge :: (TrailLike t, V t ~ V2, N t ~ n, RealFloat n) =>
+                n -> n -> Direction V2 n -> Angle n -> t
+annularWedge r1' r2' d1 s = trailLike . (`at` o) . glueTrail . wrapLine
+              $ fromOffsets [(r1' - r2') *^ fromDirection d1]
+                <> arc d1 s # scale r1'
+                <> fromOffsets [(r1' - r2') *^ negated (fromDirection d2)]
+                <> arc d2 (negated s) # scale r2'
+  where o = origin # translate (r2' *^ fromDirection d1)
+        d2 = d1 & _theta <>~ s
+
diff --git a/src/Diagrams/TwoD/Arrow.hs b/src/Diagrams/TwoD/Arrow.hs
--- a/src/Diagrams/TwoD/Arrow.hs
+++ b/src/Diagrams/TwoD/Arrow.hs
@@ -1,21 +1,25 @@
+{-# LANGUAGE ConstraintKinds            #-}
 {-# LANGUAGE DeriveDataTypeable         #-}
 {-# LANGUAGE FlexibleContexts           #-}
-{-# LANGUAGE GADTs                      #-}
 {-# LANGUAGE GeneralizedNewtypeDeriving #-}
 {-# LANGUAGE MultiParamTypeClasses      #-}
+{-# LANGUAGE RankNTypes                 #-}
+{-# LANGUAGE ScopedTypeVariables        #-}
 {-# LANGUAGE TemplateHaskell            #-}
 {-# LANGUAGE TypeFamilies               #-}
+{-# LANGUAGE TypeOperators              #-}
+{-# LANGUAGE UndecidableInstances       #-}
 
 -----------------------------------------------------------------------------
 -- |
 -- Module      :  Diagrams.TwoD.Arrow
--- Copyright   :  (c) 2013 diagrams-lib team (see LICENSE)
+-- Copyright   :  (c) 2013-2015 diagrams-lib team (see LICENSE)
 -- License     :  BSD-style (see LICENSE)
 -- Maintainer  :  diagrams-discuss@googlegroups.com
 --
 -- Drawing arrows in two dimensions.  For a tutorial on drawing arrows
 -- using this module, see the diagrams website:
--- <http://projects.haskell.org/diagrams/doc/arrow.html>.
+-- <https://diagrams.github.io/doc/arrow.html>.
 --
 -----------------------------------------------------------------------------
 
@@ -73,6 +77,9 @@
        , arrow
        , arrow'
 
+       , arrowFromLocatedTrail
+       , arrowFromLocatedTrail'
+
          -- * Options
        , ArrowOpts(..)
 
@@ -98,57 +105,62 @@
        , module Diagrams.TwoD.Arrowheads
        ) where
 
-import           Control.Applicative      ((<*>))
-import           Control.Lens             (Lens', Setter', Traversal',
-                                           generateSignatures, lensRules,
-                                           makeLensesWith, (%~), (&), (.~),
-                                           (^.))
-import           Data.AffineSpace
-import           Data.Default.Class
-import           Data.Functor             ((<$>))
-import           Data.Maybe               (fromMaybe)
-import           Data.Monoid.Coproduct    (untangle)
+import           Control.Lens              (Lens', Traversal',
+                                            generateSignatures, lensRules,
+                                            makeLensesWith, view, (%~), (&),
+                                            (.~), (^.))
+import           Data.Default
+import           Data.Maybe                (fromMaybe)
+import           Data.Monoid.Coproduct     (untangle)
 import           Data.Semigroup
-import           Data.VectorSpace
+import           Data.Typeable
 
-import           Data.Colour              hiding (atop)
+import           Data.Colour               hiding (atop)
 import           Diagrams.Core
-import           Diagrams.Core.Types      (QDiaLeaf (..), mkQD')
+import           Diagrams.Core.Style       (unmeasureAttrs)
+import           Diagrams.Core.Types       (QDiaLeaf (..), mkQD')
 
 import           Diagrams.Angle
 import           Diagrams.Attributes
+import           Diagrams.Direction        hiding (dir)
+import           Diagrams.Located          (Located (..), unLoc)
 import           Diagrams.Parametric
 import           Diagrams.Path
-import           Diagrams.Solve           (quadForm)
-import           Diagrams.Tangent         (tangentAtEnd, tangentAtStart)
+import           Diagrams.Solve.Polynomial (quadForm)
+import           Diagrams.Tangent          (tangentAtEnd, tangentAtStart)
 import           Diagrams.Trail
 import           Diagrams.TwoD.Arrowheads
 import           Diagrams.TwoD.Attributes
-import           Diagrams.TwoD.Path       (stroke, strokeT)
-import           Diagrams.TwoD.Transform  (rotate, translateX)
+import           Diagrams.TwoD.Path        (stroke, strokeT)
+import           Diagrams.TwoD.Transform   (reflectY, translateX)
 import           Diagrams.TwoD.Types
-import           Diagrams.TwoD.Vector     (direction, unitX, unit_X)
-import           Diagrams.Util            (( # ))
+import           Diagrams.TwoD.Vector      (unitX, unit_X)
+import           Diagrams.Util             (( # ))
 
-data ArrowOpts
+import           Linear.Affine
+import           Linear.Metric
+import           Linear.Vector
+
+
+data ArrowOpts n
   = ArrowOpts
-    { _arrowHead  :: ArrowHT
-    , _arrowTail  :: ArrowHT
-    , _arrowShaft :: Trail R2
-    , _headGap    :: Measure R2
-    , _tailGap    :: Measure R2
-    , _headStyle  :: Style R2
-    , _headLength :: Measure R2
-    , _tailStyle  :: Style R2
-    , _tailLength :: Measure R2
-    , _shaftStyle :: Style R2
+    { _arrowHead  :: ArrowHT n
+    , _arrowTail  :: ArrowHT n
+    , _arrowShaft :: Trail V2 n
+    , _headGap    :: Measure n
+    , _tailGap    :: Measure n
+    , _headStyle  :: Style V2 n
+    , _headLength :: Measure n
+    , _tailStyle  :: Style V2 n
+    , _tailLength :: Measure n
+    , _shaftStyle :: Style V2 n
     }
 
 -- | Straight line arrow shaft.
-straightShaft :: Trail R2
+straightShaft :: OrderedField n => Trail V2 n
 straightShaft = trailFromOffsets [unitX]
 
-instance Default ArrowOpts where
+instance TypeableFloat n => Default (ArrowOpts n) where
   def = ArrowOpts
         { _arrowHead    = dart
         , _arrowTail    = noTail
@@ -158,61 +170,63 @@
 
         -- See note [Default arrow style attributes]
         , _headStyle    = mempty
-        , _headLength     = normal
+        , _headLength   = normal
         , _tailStyle    = mempty
-        , _tailLength     = normal
+        , _tailLength   = normal
         , _shaftStyle   = mempty
         }
 
 makeLensesWith (lensRules & generateSignatures .~ False) ''ArrowOpts
 
 -- | A shape to place at the head of the arrow.
-arrowHead :: Lens' ArrowOpts ArrowHT
+arrowHead :: Lens' (ArrowOpts n) (ArrowHT n)
 
 -- | A shape to place at the tail of the arrow.
-arrowTail :: Lens' ArrowOpts ArrowHT
+arrowTail :: Lens' (ArrowOpts n) (ArrowHT n)
 
 -- | The trail to use for the arrow shaft.
-arrowShaft :: Lens' ArrowOpts (Trail R2)
+arrowShaft :: Lens' (ArrowOpts n) (Trail V2 n)
 
 -- | Distance to leave between the head and the target point.
-headGap :: Lens' ArrowOpts (Measure R2)
+headGap :: Lens' (ArrowOpts n) (Measure n)
 
 -- | Distance to leave between the starting point and the tail.
-tailGap :: Lens' ArrowOpts (Measure R2)
+tailGap :: Lens' (ArrowOpts n) (Measure n)
 
 -- | Set both the @headGap@ and @tailGap@ simultaneously.
-gaps :: Traversal' ArrowOpts (Measure R2) 
+gaps :: Traversal' (ArrowOpts n) (Measure n)
 gaps f opts = (\h t -> opts & headGap .~ h & tailGap .~ t)
         <$> f (opts ^. headGap)
         <*> f (opts ^. tailGap)
 
 -- | Same as gaps, provided for backward compatiiblity.
-gap :: Traversal' ArrowOpts (Measure R2)
+gap :: Traversal' (ArrowOpts n) (Measure n)
 gap = gaps
 
 -- | Style to apply to the head. @headStyle@ is modified by using the lens
 --   combinator @%~@ to change the current style. For example, to change
 --   an opaque black arrowhead to translucent orange:
 --   @(with & headStyle %~ fc orange .  opacity 0.75)@.
-headStyle :: Lens' ArrowOpts (Style R2)
+headStyle :: Lens' (ArrowOpts n) (Style V2 n)
 
 -- | Style to apply to the tail. See `headStyle`.
-tailStyle :: Lens' ArrowOpts (Style R2)
+tailStyle :: Lens' (ArrowOpts n) (Style V2 n)
 
 -- | Style to apply to the shaft. See `headStyle`.
-shaftStyle :: Lens' ArrowOpts (Style R2)
+shaftStyle :: Lens' (ArrowOpts n) (Style V2 n)
 
 -- | The length from the start of the joint to the tip of the head.
-headLength :: Lens' ArrowOpts (Measure R2)
+headLength :: Lens' (ArrowOpts n) (Measure n)
 
--- | The length of the tail plus its joint. 
-tailLength :: Lens' ArrowOpts (Measure R2)
+-- | The length of the tail plus its joint.
+tailLength :: Lens' (ArrowOpts n) (Measure n)
 
 -- | Set both the @headLength@ and @tailLength@ simultaneously.
-lengths :: Traversal' ArrowOpts (Measure R2)
-lengths f opts = (\h t -> opts & headLength .~ h & tailLength .~ t) <$> f (opts ^. headLength)
-             <*> f (opts ^. tailLength)
+lengths :: Traversal' (ArrowOpts n) (Measure n)
+lengths f opts =
+  (\h t -> opts & headLength .~ h & tailLength .~ t)
+    <$> f (opts ^. headLength)
+    <*> f (opts ^. tailLength)
 
 -- | A lens for setting or modifying the texture of an arrowhead. For
 --   example, one may write @... (with & headTexture .~ grad)@ to get an
@@ -220,108 +234,107 @@
 --   defined. Or @... (with & headTexture .~ solid blue@ to set the head
 --   color to blue. For more general control over the style of arrowheads,
 --   see 'headStyle'.
-headTexture :: Setter' ArrowOpts Texture
-headTexture = headStyle . styleFillTexture
+headTexture :: TypeableFloat n => Lens' (ArrowOpts n) (Texture n)
+headTexture = headStyle . _fillTexture
 
 -- | A lens for setting or modifying the texture of an arrow
---   tail.
-tailTexture :: Setter' ArrowOpts Texture
-tailTexture = tailStyle . styleFillTexture
+--   tail. This is *not* a valid lens (see 'committed').
+tailTexture :: TypeableFloat n => Lens' (ArrowOpts n) (Texture n)
+tailTexture = tailStyle . _fillTexture
 
 -- | A lens for setting or modifying the texture of an arrow
 --   shaft.
-shaftTexture :: Setter' ArrowOpts Texture
-shaftTexture = shaftStyle . styleLineTexture
+shaftTexture :: TypeableFloat n => Lens' (ArrowOpts n) (Texture n)
+shaftTexture = shaftStyle . _lineTexture
 
 -- Set the default shaft style of an `ArrowOpts` record by applying the
 -- default style after all other styles have been applied.
 -- The semigroup stucture of the lw attribute will insure that the default
 -- is only used if it has not been set in @opts@.
-shaftSty :: ArrowOpts -> Style R2
+shaftSty :: ArrowOpts n -> Style V2 n
 shaftSty opts = opts^.shaftStyle
 
 -- Set the default head style. See `shaftSty`.
-headSty :: ArrowOpts -> Style R2
+headSty :: TypeableFloat n => ArrowOpts n -> Style V2 n
 headSty opts = fc black (opts^.headStyle)
 
 -- Set the default tail style. See `shaftSty`.
-tailSty :: ArrowOpts -> Style R2
+tailSty :: TypeableFloat n => ArrowOpts n -> Style V2 n
 tailSty opts = fc black (opts^.tailStyle)
 
-fromMeasure :: Double -> Double -> Measure R2 -> Double
-fromMeasure g n m = u
-  where Output u = toOutput g n m
-
 -- | Calculate the length of the portion of the horizontal line that passes
 --   through the origin and is inside of p.
-xWidth :: (Traced t, V t ~ R2) => t -> Double
+xWidth :: Floating n => (Traced t, V t ~ V2, N t ~ n) => t -> n
 xWidth p = a + b
   where
-    a = fromMaybe 0 (magnitude <$> traceV origin unitX p)
-    b = fromMaybe 0 (magnitude <$> traceV origin unit_X p)
+    a = fromMaybe 0 (norm <$> traceV origin unitX p)
+    b = fromMaybe 0 (norm <$> traceV origin unit_X p)
 
 -- | Get the line color from the shaft to use as the fill color for the joint.
 --   And set the opacity of the shaft to the current opacity.
-colorJoint :: Style R2 -> Style R2
+colorJoint :: TypeableFloat n => Style V2 n -> Style V2 n
 colorJoint sStyle =
-    let c = fmap getLineTexture . getAttr $ sStyle
-        o = fmap getOpacity . getAttr $ sStyle
-    in
-    case (c, o) of
-        (Nothing, Nothing) -> fillColor (black :: Colour Double) $ mempty
-        (Just t, Nothing) -> fillTexture t $ mempty
-        (Nothing, Just o') -> opacity o' . fillColor (black :: Colour Double)  $ mempty
-        (Just t, Just o') -> opacity o' . fillTexture t $ mempty
+  let c = fmap getLineTexture . getAttr $ sStyle
+      o = fmap getOpacity . getAttr $ sStyle
+  in
+  case (c, o) of
+      (Nothing, Nothing) -> fillColor black mempty
+      (Just t, Nothing)  -> fillTexture t mempty
+      (Nothing, Just o') -> opacity o' . fillColor black $ mempty
+      (Just t, Just o')  -> opacity o' . fillTexture t $ mempty
 
 -- | Get line width from a style.
-widthOfJoint :: Style v -> Double -> Double  -> Double
+widthOfJoint :: forall n. TypeableFloat n => Style V2 n -> n -> n -> n
 widthOfJoint sStyle gToO nToO =
-  maybe (fromMeasure gToO nToO (Output 1)) -- Should be same as default line width
-        (fromMeasure gToO nToO)
-        (fmap getLineWidth . getAttr $ sStyle)
+  fromMaybe
+    (fromMeasured gToO nToO medium) -- should be same as default line width
+    (fmap getLineWidth . getAttr . unmeasureAttrs gToO nToO $ sStyle)
 
 -- | Combine the head and its joint into a single scale invariant diagram
 --   and move the origin to the attachment point. Return the diagram
 --   and its width.
-mkHead :: Renderable (Path R2) b =>
-          Double -> ArrowOpts -> Double -> Double -> (Diagram b R2, Double)
-mkHead size opts gToO nToO = ((j <> h) # moveOriginBy (jWidth *^ unit_X) # lwO 0
-              , hWidth + jWidth)
-  where
-    (h', j') = (opts^.arrowHead) size
-               (widthOfJoint (shaftSty opts) gToO nToO)
-    hWidth = xWidth h'
-    jWidth = xWidth j'
-    h = stroke h' # applyStyle (headSty opts)
-    j = stroke j' # applyStyle (colorJoint (opts^.shaftStyle))
+mkHead :: (TypeableFloat n, Renderable (Path V2 n) b) =>
+          n -> ArrowOpts n -> n -> n -> Bool -> (QDiagram b V2 n Any, n)
+mkHead = mkHT unit_X arrowHead headSty
 
--- | Just like mkHead only the attachment point is on the right.
-mkTail :: Renderable (Path R2) b =>
-          Double -> ArrowOpts -> Double -> Double -> (Diagram b R2, Double)
-mkTail size opts gToO nToO = ((t <> j) # moveOriginBy (jWidth *^ unitX) # lwO 0
-              , tWidth + jWidth)
+mkTail :: (TypeableFloat n, Renderable (Path V2 n) b) =>
+          n -> ArrowOpts n -> n -> n -> Bool -> (QDiagram b V2 n Any, n)
+mkTail = mkHT unitX arrowTail tailSty
+
+mkHT
+  :: (TypeableFloat n, Renderable (Path V2 n) b)
+  => V2 n -> Lens' (ArrowOpts n) (ArrowHT n) -> (ArrowOpts n -> Style V2 n)
+  -> n -> ArrowOpts n -> n -> n -> Bool -> (QDiagram b V2 n Any, n)
+mkHT xDir htProj styProj sz opts gToO nToO reflect
+    = ( (j <> ht)
+        # (if reflect then reflectY else id)
+        # moveOriginBy (jWidth *^ xDir) # lwO 0
+      , htWidth + jWidth
+      )
   where
-    (t', j') = (opts^.arrowTail) size
-               (widthOfJoint (shaftSty opts) gToO nToO)
-    tWidth = xWidth t'
-    jWidth = xWidth j'
-    t = stroke t' # applyStyle (tailSty opts)
-    j = stroke j' # applyStyle (colorJoint (opts^.shaftStyle))
+    (ht', j') = (opts^.htProj) sz
+                (widthOfJoint (shaftSty opts) gToO nToO)
+    htWidth = xWidth ht'
+    jWidth  = xWidth j'
+    ht = stroke ht' # applyStyle (styProj opts)
+    j  = stroke j'  # applyStyle (colorJoint (opts^.shaftStyle))
 
--- | Make a trail with the same angles and offset as an arrow with tail width
---   tw, head width hw and shaft of tr, such that the magnituted of the shaft
---   offset is size. Used for calculating the offset of an arrow.
-spine :: Trail R2 -> Double -> Double -> Double -> Trail R2
-spine tr tw hw size = tS <> tr # scale size <> hS
+-- | @spine tr tw hw sz@ makes a trail with the same angles and offset
+--   as an arrow with tail width @t@w, head width @hw@ and shaft @tr@,
+--   such that the magnitude of the shaft offset is @sz@. Used for
+--   calculating the offset of an arrow.
+spine :: TypeableFloat n => Trail V2 n -> n -> n -> n -> Trail V2 n
+spine tr tw hw sz = tS <> tr # scale sz <> hS
   where
-    tSpine = trailFromOffsets [(normalized . tangentAtStart) $ tr] # scale tw
-    hSpine = trailFromOffsets [(normalized . tangentAtEnd) $ tr] # scale hw
+    tSpine = trailFromOffsets [signorm . tangentAtStart $ tr] # scale tw
+    hSpine = trailFromOffsets [signorm . tangentAtEnd $ tr] # scale hw
     hS = if hw > 0 then hSpine else mempty
     tS = if tw > 0 then tSpine else mempty
 
---  | Calculate the amount required to scale a shaft trail so that an arrow with
---    head width hw and tail width tw has offset t.
-scaleFactor :: Trail R2 -> Double -> Double -> Double -> Double
+-- | @scaleFactor tr tw hw t@ calculates the amount required to scale
+--   a shaft trail @tr@ so that an arrow with head width @hw@ and tail
+--   width @tw@ has offset @t@.
+scaleFactor :: TypeableFloat n => Trail V2 n -> n -> n -> n -> n
 scaleFactor tr tw hw t
 
   -- Let tv be a vector representing the tail width, i.e. a vector
@@ -336,9 +349,9 @@
   -- dot product, resulting in a quadratic in k.
 
   = case quadForm
-             (magnitudeSq v)
-             (2* (v <.> (tv ^+^ hv)))
-             (magnitudeSq (tv ^+^ hv) - t*t)
+             (quadrance v)
+             (2* (v `dot` (tv ^+^ hv)))
+             (quadrance (tv ^+^ hv) - t*t)
     of
       []  -> 1   -- no scale works, just return 1
       [s] -> s   -- single solution
@@ -346,34 +359,35 @@
         -- we will usually get both a positive and a negative solution;
         -- return the maximum (i.e. positive) solution
   where
-    tv = tw *^ (tangentAtStart tr # normalized)
-    hv = hw *^ (tangentAtEnd   tr # normalized)
+    tv = tw *^ (tangentAtStart tr # signorm)
+    hv = hw *^ (tangentAtEnd   tr # signorm)
     v  = trailOffset tr
 
 -- Calculate the approximate envelope of a horizontal arrow
 -- as if the arrow were made only of a shaft.
-arrowEnv :: ArrowOpts -> Double -> Envelope R2
+arrowEnv :: TypeableFloat n => ArrowOpts n -> n -> Envelope V2 n
 arrowEnv opts len = getEnvelope horizShaft
   where
-    horizShaft = shaft # rotate (negateV direction v) # scale (len / m)
-    m = magnitude v
+    horizShaft = shaft # rotate (negated (v ^. _theta)) # scale (len / m)
+    m = norm v
     v = trailOffset shaft
     shaft = opts ^. arrowShaft
 
 -- | @arrow len@ creates an arrow of length @len@ with default
 --   parameters, starting at the origin and ending at the point
 --   @(len,0)@.
-arrow :: Renderable (Path R2) b => Double -> Diagram b R2
-arrow len = arrow' def len
+arrow :: (TypeableFloat n, Renderable (Path V2 n) b) => n -> QDiagram b V2 n Any
+arrow = arrow' def
 
 -- | @arrow' opts len@ creates an arrow of length @len@ using the
 --   given options, starting at the origin and ending at the point
 --   @(len,0)@.  In particular, it scales the given 'arrowShaft' so
 --   that the entire arrow has length @len@.
-arrow' :: Renderable (Path R2) b => ArrowOpts -> Double -> Diagram b R2
+arrow' :: (TypeableFloat n, Renderable (Path V2 n) b) => ArrowOpts n -> n -> QDiagram b V2 n Any
 arrow' opts len = mkQD' (DelayedLeaf delayedArrow)
 
-      -- Currently arrows have an empty envelope and trace.
+      -- Currently we approximate the envelope of an arrow by using the
+      -- envelope of its shaft (see 'arrowEnv'). The trace of an arrow is empty.
       (arrowEnv opts len) mempty mempty mempty
 
   where
@@ -388,13 +402,13 @@
     -- uniformly as the transformation applied to the entire arrow.
     -- See https://github.com/diagrams/diagrams-lib/issues/112.
     delayedArrow da g n =
-      let (trans, globalSty) = option mempty untangle . fst $ da
+      let (trans, globalSty) = maybe mempty untangle . fst $ da
       in  dArrow globalSty trans len g n
 
     -- Build an arrow and set its endpoints to the image under tr of origin and (len,0).
     dArrow sty tr ln gToO nToO = (h' <> t' <> shaft)
                # moveOriginBy (tWidth *^ (unit_X # rotate tAngle))
-               # rotate (direction (q .-. p) ^-^ dir)
+               # rotate (((q .-. p)^._theta) ^-^ (dir^._theta))
                # moveTo p
       where
 
@@ -403,29 +417,31 @@
 
         -- Use the existing line color for head, tail, and shaft by
         -- default (can be overridden by explicitly setting headStyle,
-        -- tailStyle, or shaftStyle).
+        -- tailStyle, or shaftStyle).  Also use existing global line width
+        -- for shaft if not explicitly set in shaftStyle.
         globalLC = getLineTexture <$> getAttr sty
         opts' = opts
           & headStyle  %~ maybe id fillTexture globalLC
           & tailStyle  %~ maybe id fillTexture globalLC
-          & shaftStyle %~ maybe id lineTexture globalLC
+          & shaftStyle %~ applyStyle sty . transform tr
 
         -- The head size, tail size, head gap, and tail gap are obtained
         -- from the style and converted to output units.
-        hSize = fromMeasure gToO nToO . transform tr $ opts ^. headLength
-        tSize = fromMeasure gToO nToO . transform tr $ opts ^. tailLength
-        hGap = fromMeasure gToO nToO . transform tr $ opts ^. headGap
-        tGap = fromMeasure gToO nToO . transform tr $ opts ^. tailGap
+        scaleFromMeasure = fromMeasured gToO nToO . scaleLocal (avgScale tr)
+        hSize = scaleFromMeasure $ opts ^. headLength
+        tSize = scaleFromMeasure $ opts ^. tailLength
+        hGap  = scaleFromMeasure $ opts ^. headGap
+        tGap  = scaleFromMeasure $ opts ^. tailGap
 
         -- Make the head and tail and save their widths.
-        (h, hWidth') = mkHead hSize opts' gToO nToO
-        (t, tWidth') = mkTail tSize opts' gToO nToO
+        (h, hWidth') = mkHead hSize opts' gToO nToO (isReflection tr)
+        (t, tWidth') = mkTail tSize opts' gToO nToO (isReflection tr)
 
         rawShaftTrail = opts^.arrowShaft
         shaftTrail
           = rawShaftTrail
             -- rotate it so it is pointing in the positive X direction
-          # rotate (negateV direction (trailOffset rawShaftTrail))
+          # rotate (negated . view _theta . trailOffset $ rawShaftTrail)
             -- apply the context transformation -- in case it includes
             -- things like flips and shears (the possibility of shears
             -- is why we must rotate it to a neutral position first)
@@ -436,15 +452,15 @@
         hWidth = hWidth' + hGap
 
         -- Calculate the angles that the head and tail should point.
-        tAngle = direction . tangentAtStart $ shaftTrail
-        hAngle = direction . tangentAtEnd $ shaftTrail
+        tAngle = tangentAtStart shaftTrail ^. _theta
+        hAngle = tangentAtEnd shaftTrail ^. _theta
 
         -- Calculte the scaling factor to apply to the shaft shaftTrail so that the entire
         -- arrow will be of length len. Then apply it to the shaft and make the
         -- shaft into a Diagram with using its style.
-        sf = scaleFactor shaftTrail tWidth hWidth (magnitude (q .-. p))
+        sf = scaleFactor shaftTrail tWidth hWidth (norm (q .-. p))
         shaftTrail' = shaftTrail # scale sf
-        shaft = strokeT shaftTrail' # applyStyle (shaftSty opts)
+        shaft = strokeT shaftTrail' # applyStyle (shaftSty opts')
 
         -- Adjust the head and tail to point in the directions of the shaft ends.
         h' = h # rotate hAngle
@@ -457,7 +473,7 @@
 
 -- | @arrowBetween s e@ creates an arrow pointing from @s@ to @e@
 --   with default parameters.
-arrowBetween :: Renderable (Path R2) b => P2 -> P2 -> Diagram b R2
+arrowBetween :: (TypeableFloat n, Renderable (Path V2 n) b) => Point V2 n -> Point V2 n -> QDiagram b V2 n Any
 arrowBetween = arrowBetween' def
 
 -- | @arrowBetween' opts s e@ creates an arrow pointing from @s@ to
@@ -465,47 +481,64 @@
 --   rotates @arrowShaft@ to go between @s@ and @e@, taking head,
 --   tail, and gaps into account.
 arrowBetween'
-  :: Renderable (Path R2) b =>
-     ArrowOpts -> P2 -> P2 -> Diagram b R2
+  :: (TypeableFloat n, Renderable (Path V2 n) b) =>
+     ArrowOpts n -> Point V2 n -> Point V2 n -> QDiagram b V2 n Any
 arrowBetween' opts s e = arrowAt' opts s (e .-. s)
 
 -- | Create an arrow starting at s with length and direction determined by
 --   the vector v.
-arrowAt :: Renderable (Path R2) b => P2 -> R2 -> Diagram b R2
-arrowAt s v = arrowAt' def s v
+arrowAt :: (TypeableFloat n, Renderable (Path V2 n) b) => Point V2 n -> V2 n -> QDiagram b V2 n Any
+arrowAt = arrowAt' def
 
 arrowAt'
-  :: Renderable (Path R2) b =>
-     ArrowOpts -> P2 -> R2 -> Diagram b R2
+  :: (TypeableFloat n, Renderable (Path V2 n) b) =>
+     ArrowOpts n -> Point V2 n -> V2 n -> QDiagram b V2 n Any
 arrowAt' opts s v = arrow' opts len
                   # rotate dir # moveTo s
   where
-    len = magnitude v
-    dir = direction v
+    len = norm v
+    dir = v ^. _theta
 
--- | @arrowV v@ creates an arrow with the direction and magnitude of
+-- | @arrowV v@ creates an arrow with the direction and norm of
 --   the vector @v@ (with its tail at the origin), using default
 --   parameters.
-arrowV :: Renderable (Path R2) b => R2 -> Diagram b R2
+arrowV :: (TypeableFloat n, Renderable (Path V2 n) b) => V2 n -> QDiagram b V2 n Any
 arrowV = arrowV' def
 
--- | @arrowV' v@ creates an arrow with the direction and magnitude of
+-- | @arrowV' v@ creates an arrow with the direction and norm of
 --   the vector @v@ (with its tail at the origin).
 arrowV'
-  :: Renderable (Path R2) b
-  => ArrowOpts -> R2 -> Diagram b R2
+  :: (TypeableFloat n, Renderable (Path V2 n) b)
+  => ArrowOpts n -> V2 n -> QDiagram b V2 n Any
 arrowV' opts = arrowAt' opts origin
 
+-- | Turn a located trail into a default arrow by putting an
+--   arrowhead at the end of the trail.
+arrowFromLocatedTrail
+  :: (Renderable (Path V2 n) b, RealFloat n, Typeable n)
+  => Located (Trail V2 n) -> QDiagram b V2 n Any
+arrowFromLocatedTrail = arrowFromLocatedTrail' def
+
+-- | Turn a located trail into an arrow using the given options.
+arrowFromLocatedTrail'
+  :: (Renderable (Path V2 n) b, RealFloat n, Typeable n)
+  => ArrowOpts n -> Located (Trail V2 n) -> QDiagram b V2 n Any
+arrowFromLocatedTrail' opts trail = arrowBetween' opts' start end
+  where
+    opts' = opts & arrowShaft .~ unLoc trail
+    start = atStart trail
+    end   = atEnd trail
+
 -- | Connect two diagrams with a straight arrow.
 connect
-  :: (Renderable (Path R2) b, IsName n1, IsName n2)
-  => n1 -> n2 -> (Diagram b R2 -> Diagram b R2)
+  :: (TypeableFloat n, Renderable (Path V2 n) b, IsName n1, IsName n2)
+  => n1 -> n2 -> QDiagram b V2 n Any -> QDiagram b V2 n Any
 connect = connect' def
 
 -- | Connect two diagrams with an arbitrary arrow.
 connect'
-  :: (Renderable (Path R2) b, IsName n1, IsName n2)
-  => ArrowOpts -> n1 -> n2 -> (Diagram b R2 -> Diagram b R2)
+  :: (TypeableFloat n, Renderable (Path V2 n) b, IsName n1, IsName n2)
+  => ArrowOpts n -> n1 -> n2 -> QDiagram b V2 n Any -> QDiagram b V2 n Any
 connect' opts n1 n2 =
   withName n1 $ \sub1 ->
   withName n2 $ \sub2 ->
@@ -515,15 +548,15 @@
 -- | Connect two diagrams at point on the perimeter of the diagrams, choosen
 --   by angle.
 connectPerim
-  :: (Renderable (Path R2) b, IsName n1, IsName n2)
- => n1 -> n2 -> Angle -> Angle
-  -> (Diagram b R2 -> Diagram b R2)
+  :: (TypeableFloat n, Renderable (Path V2 n) b, IsName n1, IsName n2)
+ => n1 -> n2 -> Angle n -> Angle n
+  -> QDiagram b V2 n Any -> QDiagram b V2 n Any
 connectPerim = connectPerim' def
 
 connectPerim'
-  :: (Renderable (Path R2) b, IsName n1, IsName n2)
-  => ArrowOpts -> n1 -> n2 -> Angle -> Angle
-  -> (Diagram b R2 -> Diagram b R2)
+  :: (TypeableFloat n, Renderable (Path V2 n) b, IsName n1, IsName n2)
+  => ArrowOpts n -> n1 -> n2 -> Angle n -> Angle n
+  -> QDiagram b V2 n Any -> QDiagram b V2 n Any
 connectPerim' opts n1 n2 a1 a2 =
   withName n1 $ \sub1 ->
   withName n2 $ \sub2 ->
@@ -537,19 +570,19 @@
 --   drawn so that it stops at the boundaries of the diagrams, using traces
 --   to find the intersection points.
 connectOutside
-  :: (Renderable (Path R2) b, IsName n1, IsName n2)
-  => n1 -> n2 -> (Diagram b R2 -> Diagram b R2)
+  :: (TypeableFloat n, Renderable (Path V2 n) b, IsName n1, IsName n2)
+  => n1 -> n2 -> QDiagram b V2 n Any -> QDiagram b V2 n Any
 connectOutside = connectOutside' def
 
 connectOutside'
-  :: (Renderable (Path R2) b, IsName n1, IsName n2)
-  => ArrowOpts -> n1 -> n2 -> (Diagram b R2 -> Diagram b R2)
+  :: (TypeableFloat n, Renderable (Path V2 n) b, IsName n1, IsName n2)
+  => ArrowOpts n -> n1 -> n2 -> QDiagram b V2 n Any -> QDiagram b V2 n Any
 connectOutside' opts n1 n2 =
   withName n1 $ \b1 ->
   withName n2 $ \b2 ->
     let v = location b2 .-. location b1
-        midpoint = location b1 .+^ (v/2)
-        s' = fromMaybe (location b1) $ traceP midpoint (-v) b1
+        midpoint = location b1 .+^ (v ^/ 2)
+        s' = fromMaybe (location b1) $ traceP midpoint (negated v) b1
         e' = fromMaybe (location b2) $ traceP midpoint v b2
     in
       atop (arrowBetween' opts s' e')
diff --git a/src/Diagrams/TwoD/Arrowheads.hs b/src/Diagrams/TwoD/Arrowheads.hs
--- a/src/Diagrams/TwoD/Arrowheads.hs
+++ b/src/Diagrams/TwoD/Arrowheads.hs
@@ -1,6 +1,9 @@
+{-# LANGUAGE ConstraintKinds #-}
 {-# LANGUAGE FlexibleContexts          #-}
 {-# LANGUAGE NoMonomorphismRestriction #-}
+{-# LANGUAGE ScopedTypeVariables       #-}
 {-# LANGUAGE TypeFamilies              #-}
+{-# OPTIONS_GHC -fno-warn-unused-imports       #-}
 -----------------------------------------------------------------------------
 -- |
 -- Module      :  Diagrams.TwoD.Arrowheads
@@ -20,6 +23,7 @@
        -- ** Standard arrowheads
          tri
        , dart
+       , halfDart
        , spike
        , thorn
        , lineHead
@@ -31,6 +35,7 @@
        --   left point of the arrowhead.
        , arrowheadTriangle
        , arrowheadDart
+       , arrowheadHalfDart
        , arrowheadSpike
        , arrowheadThorn
 
@@ -38,6 +43,7 @@
        -- ** Standard arrow tails
        , tri'
        , dart'
+       , halfDart'
        , spike'
        , thorn'
        , lineTail
@@ -54,16 +60,13 @@
        , ArrowHT
        ) where
 
-import           Control.Lens            ((&), (.~), (^.))
-import           Data.AffineSpace
-import           Data.Default.Class
+import           Control.Lens            ((&), (.~), (<>~), (^.))
+import           Data.Default
 import           Data.Monoid             (mempty, (<>))
-import           Data.VectorSpace
 
 import           Diagrams.Angle
 import           Diagrams.Core
 
-import           Diagrams.Coordinates    ((^&))
 import           Diagrams.Path
 import           Diagrams.Segment
 import           Diagrams.Trail
@@ -75,66 +78,91 @@
 import           Diagrams.TwoD.Shapes
 import           Diagrams.TwoD.Transform
 import           Diagrams.TwoD.Types
-import           Diagrams.TwoD.Vector    (fromDirection, direction, unit_X)
+import           Diagrams.TwoD.Vector    (unitX, unit_X, xDir)
 import           Diagrams.Util           (( # ))
 
+import           Linear.Affine
+import           Linear.Metric
+import           Linear.Vector
+
 -----------------------------------------------------------------------------
 
-type ArrowHT = Double -> Double -> (Path R2, Path R2)
+type ArrowHT n = n -> n -> (Path V2 n, Path V2 n)
 
-closedPath :: (Floating (Scalar v), Ord (Scalar v), InnerSpace v) => Trail v -> Path v
+closedPath :: OrderedField n => Trail V2 n -> Path V2 n
 closedPath = pathFromTrail . closeTrail
 
 -- Heads ------------------------------------------------------------------
---   > drawHead h = arrowAt' (with & arrowHead .~ h & shaftStyle %~ lw none)
---   >         origin (r2 (0.001, 0))
---   >      <> square 0.5 # alignL # lw none
+--   > drawHead h = arrowAt' (with & arrowHead .~ h & shaftStyle %~ lw none
+--   >                             & headLength .~ local 0.5)
+--   >         origin (r2 (1, 0))
+--   >      <> square 0.5 # alignL # lw none # frame 0.1
 
 -- | Isoceles triangle style. The above example specifies an angle of `2/5 Turn`.
 
 -- | <<diagrams/src_Diagrams_TwoD_Arrowheads_tri25Ex.svg#diagram=tri25Ex&width=120>>
 
---   > tri25Ex = arrowAt' (with & arrowHead .~ arrowheadTriangle (2/5 @@ turn) & shaftStyle %~ lw none)
---   >           origin (r2 (0.001, 0))
---   >        <> square 0.6 # alignL # lw none
-arrowheadTriangle :: Angle -> ArrowHT
+--   > tri25Ex = arrowAt' (with & arrowHead .~ arrowheadTriangle (2/5 @@ turn)
+--   >                          & shaftStyle %~ lw none & headLength .~ local 0.5)
+--   >           origin (r2 (0.5, 0))
+--   >        <> square 0.6 # alignL # lw none # frame 0.1
+arrowheadTriangle :: RealFloat n => Angle n -> ArrowHT n
 arrowheadTriangle theta = aHead
   where
     aHead len _ = (p, mempty)
       where
         psi = pi - (theta ^. rad)
         r = len / (1 + cos psi)
-        p = polygon (def & polyType .~ PolyPolar [theta, (negateV 2 *^ theta)]
+        p = polygon (def & polyType .~ PolyPolar [theta, (-2) *^ theta]
             (repeat r) & polyOrient .~ NoOrient)  # alignL
 
 
 -- | Isoceles triangle with linear concave base. Inkscape type 1 - dart like.
-arrowheadDart :: Angle -> ArrowHT
-arrowheadDart theta len shaftWidth = (hd # scale size, jt)
+arrowheadDart :: RealFloat n => Angle n -> ArrowHT n
+arrowheadDart theta len shaftWidth = (hd # scale sz, jt)
   where
     hd = snugL . pathFromTrail . glueTrail $ fromOffsets [t1, t2, b2, b1]
     jt = pathFromTrail . glueTrail $ j <> reflectY j
-    j = closeTrail $ fromOffsets [(-jLength ^& 0), (0 ^& shaftWidth / 2)]
-    v = fromDirection theta
-    (t1, t2) = (unit_X ^+^ v, (-0.5 ^& 0) ^-^ v)
-    [b1, b2] = map (reflectY . negateV) [t1, t2]
-    psi = pi - (direction . negateV $ t2) ^. rad
+    j = closeTrail $ fromOffsets [V2 (-jLength) 0, V2 0 (shaftWidth / 2)]
+    v = rotate theta unitX
+    (t1, t2) = (unit_X ^+^ v, V2 (-0.5) 0 ^-^ v)
+    [b1, b2] = map (reflectY . negated) [t1, t2]
+    psi = pi - negated t2 ^. _theta . rad
     jLength = shaftWidth / (2 * tan psi)
 
-    -- If the shaft if too wide, set the size to a default value of 1.
-    size = max 1 ((len - jLength) / (1.5))
+    -- If the shaft is too wide, set the size to a default value of 1.
+    sz = max 1 ((len - jLength) / 1.5)
 
+-- | Top half of an 'arrowheadDart'.
+arrowheadHalfDart :: RealFloat n => Angle n -> ArrowHT n
+arrowheadHalfDart theta len shaftWidth = (hd, jt)
+  where
+    hd = fromOffsets [t1, t2]
+       # closeTrail # pathFromTrail
+       # translateX 1.5 # scale sz
+       # translateY (-shaftWidth/2)
+       # snugL
+    jt = snugR . translateY (-shaftWidth/2) . pathFromTrail . closeTrail $ fromOffsets [V2 (-jLength) 0, V2 0 shaftWidth]
+    v = rotate theta unitX
+    (t1, t2) = (unit_X ^+^ v, (0.5 *^ unit_X) ^-^ v)
+    psi = pi - negated t2 ^. _theta . rad
+    jLength = shaftWidth / tan psi
+
+    -- If the shaft is too wide, set the size to a default value of 1.
+    sz = max 1 ((len - jLength) / 1.5)
+
 -- | Isoceles triangle with curved concave base. Inkscape type 2.
-arrowheadSpike :: Angle -> ArrowHT
+arrowheadSpike :: RealFloat n => Angle n -> ArrowHT n
 arrowheadSpike theta len shaftWidth  = (hd # scale r, jt # scale r)
   where
     hd = snugL . closedPath $ l1 <> c <> l2
     jt = alignR . centerY . pathFromTrail
-                . closeTrail $ arc' 1 (negateV phi) phi
+                . closeTrail $ arc' 1 (xDir & _theta <>~ negated phi) (2 *^ phi)
     l1 = trailFromSegments [straight $ unit_X ^+^ v]
-    l2 = trailFromSegments [reverseSegment . straight $ (unit_X ^+^ (reflectY v))]
-    c = reflectX $ arc' 1 theta (negateV theta)
-    v = fromDirection theta
+    l2 = trailFromSegments [reverseSegment . straight $ (unit_X ^+^ reflectY v)]
+    c = arc' 1 (rotate α xDir) ((-2) *^ α)
+    α = (1/2 @@ turn) ^-^ theta
+    v = rotate theta unitX
 
     -- The length of the head without its joint is, -2r cos theta and
     -- the length of the joint is r - sqrt (r^2 - y^2). So the total
@@ -149,157 +177,170 @@
     -- 2/3 * len by setting d=1 and phi=pi/2.
     d = max 1 (len**2 + (1 - a**2) * y**2)
     r = (a * len + sqrt d) / (a**2 -1)
-    phi = asin (min 1 (y/r)) @@ rad
+    phi = asinA (min 1 (y/r))
 
 -- | Curved sides, linear concave base. Illustrator CS5 #3
-arrowheadThorn :: Angle -> ArrowHT
-arrowheadThorn theta len shaftWidth = (hd # scale size, jt)
+arrowheadThorn :: RealFloat n => Angle n -> ArrowHT n
+arrowheadThorn theta len shaftWidth = (hd # scale sz, jt)
   where
     hd = snugL . pathFromTrail . glueTrail $ hTop <> reflectY hTop
     hTop = closeTrail . trailFromSegments $ [c, l]
     jt = pathFromTrail . glueTrail $ j <> reflectY j
-    j = closeTrail $ fromOffsets [(-jLength ^& 0), (0 ^& shaftWidth / 2)]
+    j = closeTrail $ fromOffsets [V2 (-jLength) 0, V2 0 (shaftWidth / 2)]
     c = curvedSide theta
-    v = fromDirection theta
+    v = rotate theta unitX
     l = reverseSegment . straight $ t
-    t = v ^-^ (-0.5 ^& 0)
-    psi = pi - (direction . negateV $ t) ^. rad
-    jLength = shaftWidth / (2 * tan psi)
+    t = v ^-^ V2 (-0.5) 0
+    psi = fullTurn ^/ 2 ^-^ (negated t ^. _theta)
+    jLength = shaftWidth / (2 * tanA psi)
 
-    -- If the shaft if too wide, set the size to a default value of 1.    
-    size = max 1 ((len - jLength) / (1.5))
+    -- If the shaft if too wide, set the size to a default value of 1.
+    sz = max 1 ((len - jLength) / 1.5)
 
 -- | Make a side for the thorn head.
-curvedSide :: Angle -> Segment Closed R2
+curvedSide :: Floating n => Angle n -> Segment Closed V2 n
 curvedSide theta = bezier3 ctrl1 ctrl2 end
   where
     v0    = unit_X
-    v1    = fromDirection theta
+    v1    = rotate theta unitX
     ctrl1 = v0
     ctrl2 = v0 ^+^ v1
     end   = v0 ^+^ v1
 
 -- Standard heads ---------------------------------------------------------
 -- | A line the same width as the shaft.
-lineHead :: ArrowHT
+lineHead :: RealFloat n => ArrowHT n
 lineHead s w = (square 1 # scaleX s # scaleY w # alignL, mempty)
 
-noHead :: ArrowHT
+noHead :: ArrowHT n
 noHead _ _ = (mempty, mempty)
 
 -- | <<diagrams/src_Diagrams_TwoD_Arrowheads_triEx.svg#diagram=triEx&width=100>>
 
 --   > triEx = drawHead tri
-tri :: ArrowHT
+tri :: RealFloat n => ArrowHT n
 tri = arrowheadTriangle (1/3 @@ turn)
 
 -- | <<diagrams/src_Diagrams_TwoD_Arrowheads_spikeEx.svg#diagram=spikeEx&width=100>>
 
 --   > spikeEx = drawHead spike
-spike :: ArrowHT
+spike :: RealFloat n => ArrowHT n
 spike = arrowheadSpike (3/8 @@ turn)
 
 -- | <<diagrams/src_Diagrams_TwoD_Arrowheads_thornEx.svg#diagram=thornEx&width=100>>
 
 --   > thornEx = drawHead thorn
-thorn :: ArrowHT
-thorn = arrowheadThorn (3/8 @@ turn) 
+thorn :: RealFloat n => ArrowHT n
+thorn = arrowheadThorn (3/8 @@ turn)
 
 -- | <<diagrams/src_Diagrams_TwoD_Arrowheads_dartEx.svg#diagram=dartEx&width=100>>
 
 --   > dartEx = drawHead dart
-dart :: ArrowHT
+dart :: RealFloat n => ArrowHT n
 dart = arrowheadDart (2/5 @@ turn)
 
+-- | <<diagrams/src_Diagrams_TwoD_Arrowheads_halfDartEx.svg#diagram=halfDartEx&width=100>>
+
+--   > halfDartEx = drawHead halfDart
+halfDart :: RealFloat n => ArrowHT n
+halfDart = arrowheadHalfDart (2/5 @@ turn)
+
 -- Tails ------------------------------------------------------------------
---   > drawTail t = arrowAt' (with  & arrowTail .~ t & shaftStyle %~ lw none & arrowHead .~ noHead)
---   >         origin (r2 (0.001, 0))
---   >      <> square 0.5 # alignL # lw none
+--   > drawTail t = arrowAt' (with  & arrowTail .~ t & shaftStyle %~ lw none
+--   >                              & arrowHead .~ noHead & tailLength .~ local 0.5)
+--   >         origin (r2 (1, 0))
+--   >      <> square 0.5 # alignL # lw none # frame 0.1
 
 -- | Utility function to convert any arrowhead to an arrowtail, i.e.
 --   attached at the start of the trail.
-headToTail :: ArrowHT -> ArrowHT
+headToTail :: OrderedField n => ArrowHT n -> ArrowHT n
 headToTail hd = tl
   where
-    tl size shaftWidth = (t, j)
+    tl sz shaftWidth = (t, j)
       where
-        (t', j') = hd size shaftWidth
+        (t', j') = hd sz shaftWidth
         t = reflectX t'
         j = reflectX j'
 
-arrowtailBlock :: Angle -> ArrowHT
+arrowtailBlock :: forall n. (RealFloat n) => Angle n -> ArrowHT n
 arrowtailBlock theta = aTail
   where
    aTail len _ = (t, mempty)
       where
-        t = rect len (len * x) # alignR
-        a'  = fromDirection theta
-        a = a' ^-^ (reflectY a')
-        x = magnitude a
+        t  = rect len (len * x) # alignR
+        a' :: V2 n
+        a' = rotate theta unitX
+        a  = a' ^-^ reflectY a'
+        x  = norm a
 
 -- | The angle is where the top left corner intersects the circle.
-arrowtailQuill :: Angle -> ArrowHT
+arrowtailQuill :: OrderedField n => Angle n -> ArrowHT n
 arrowtailQuill theta = aTail
   where
    aTail len shaftWidth = (t, j)
       where
-        t = ( closedPath $ trailFromVertices [v0, v1, v2, v3, v4, v5, v0] )
-            # scale size # alignR
-        size = len / 0.6
+        t = closedPath (trailFromVertices [v0, v1, v2, v3, v4, v5, v0])
+              # scale sz # alignR
+        sz = len / 0.6
         v0 = p2 (0.5, 0)
-        v2 = p2 (unr2 $ fromDirection theta # scale 0.5)
+        v2 = origin .+^ (rotate theta unitX # scale 0.5)
         v1 = v2 # translateX (5/8)
         v3 = p2 (-0.1, 0)
         v4 = v2 # reflectY
         v5 = v4 # translateX (5/8)
-        s = 1 - shaftWidth / magnitude (v1 .-. v5)
+        s = 1 - shaftWidth / norm (v1 .-. v5)
         n1 = v0 # translateY (0.5 * shaftWidth)
         n2 = v1 .-^ ((v1 .-. v0) # scale s)
         n3 = v5 .-^ ((v5 .-. v0) # scale s)
         n4 = n1 # reflectY
-        j = ( closedPath $ trailFromVertices
-                [ v0, n1, n2, v0, n3, n4, v0 ])
+        j  = closedPath $ trailFromVertices [v0, n1, n2, v0, n3, n4, v0]
 
 -- Standard tails ---------------------------------------------------------
 -- | A line the same width as the shaft.
-lineTail :: ArrowHT
+lineTail :: RealFloat n => ArrowHT n
 lineTail s w = (square 1 # scaleY w # scaleX s # alignR, mempty)
 
-noTail :: ArrowHT
+noTail :: ArrowHT n
 noTail _ _ = (mempty, mempty)
 
 -- | <<diagrams/src_Diagrams_TwoD_Arrowheads_tri'Ex.svg#diagram=tri'Ex&width=100>>
 
 --   > tri'Ex = drawTail tri'
-tri' :: ArrowHT
+tri' :: RealFloat n => ArrowHT n
 tri' = headToTail tri
 
 -- | <<diagrams/src_Diagrams_TwoD_Arrowheads_spike'Ex.svg#diagram=spike'Ex&width=100>>
 
 --   > spike'Ex = drawTail spike'
-spike' :: ArrowHT
+spike' :: RealFloat n => ArrowHT n
 spike' = headToTail spike
 
 -- | <<diagrams/src_Diagrams_TwoD_Arrowheads_thorn'Ex.svg#diagram=thorn'Ex&width=100>>
 
 --   > thorn'Ex = drawTail thorn'
-thorn' :: ArrowHT
+thorn' :: RealFloat n => ArrowHT n
 thorn' = headToTail thorn
 
 -- | <<diagrams/src_Diagrams_TwoD_Arrowheads_dart'Ex.svg#diagram=dart'Ex&width=100>>
 
 --   > dart'Ex = drawTail dart'
-dart' :: ArrowHT
+dart' :: RealFloat n => ArrowHT n
 dart' = headToTail dart
 
+-- | <<diagrams/src_Diagrams_TwoD_Arrowheads_halfDart'Ex.svg#diagram=halfDart'Ex&width=100>>
+
+--   > halfDart'Ex = drawTail halfDart'
+halfDart' :: RealFloat n => ArrowHT n
+halfDart' = headToTail halfDart
+
 -- | <<diagrams/src_Diagrams_TwoD_Arrowheads_quillEx.svg#diagram=quillEx&width=100>>
 
 --   > quillEx = drawTail quill
-quill :: ArrowHT
+quill :: (Floating n, Ord n) => ArrowHT n
 quill = arrowtailQuill (2/5 @@ turn)
 
 -- | <<diagrams/src_Diagrams_TwoD_Arrowheads_blockEx.svg#diagram=blockEx&width=100>>
 
 --   > blockEx = drawTail block
-block :: ArrowHT
+block :: RealFloat n => ArrowHT n
 block = arrowtailBlock (7/16 @@ turn)
diff --git a/src/Diagrams/TwoD/Attributes.hs b/src/Diagrams/TwoD/Attributes.hs
--- a/src/Diagrams/TwoD/Attributes.hs
+++ b/src/Diagrams/TwoD/Attributes.hs
@@ -1,21 +1,26 @@
+{-# LANGUAGE ConstraintKinds            #-}
 {-# LANGUAGE DeriveDataTypeable         #-}
-{-# LANGUAGE ExistentialQuantification  #-}
+{-# LANGUAGE DeriveFunctor              #-}
+{-# LANGUAGE FlexibleContexts           #-}
 {-# LANGUAGE FlexibleInstances          #-}
 {-# LANGUAGE GeneralizedNewtypeDeriving #-}
+{-# LANGUAGE MultiParamTypeClasses      #-}
 {-# LANGUAGE ScopedTypeVariables        #-}
+{-# LANGUAGE StandaloneDeriving         #-}
 {-# LANGUAGE TemplateHaskell            #-}
 {-# LANGUAGE TypeFamilies               #-}
+{-# LANGUAGE UndecidableInstances       #-}
 
 -----------------------------------------------------------------------------
 -- |
 -- Module      :  Diagrams.TwoD.Attributes
--- Copyright   :  (c) 2013 diagrams-lib team (see LICENSE)
+-- Copyright   :  (c) 2013-2015 diagrams-lib team (see LICENSE)
 -- License     :  BSD-style (see LICENSE)
 -- Maintainer  :  diagrams-discuss@googlegroups.com
 --
 -- Diagrams may have /attributes/ which affect the way they are
 -- rendered. This module defines /Textures/ (Gradients and Colors) in two
--- dimensions. Like the attriubtes defined in the Diagrams.Attributes module,
+-- dimensions. Like the attributes defined in the Diagrams.Attributes module,
 -- all attributes defined here use the 'Last' or 'Recommend' /semigroup/ structure.
 -- 'FillColor' and 'LineColor' attributes are provided so that backends that
 -- don't support gradients need not be concerned with using textures. Backends
@@ -24,18 +29,8 @@
 -----------------------------------------------------------------------------
 
 module Diagrams.TwoD.Attributes (
-    -- ** Width
-    LineWidth, getLineWidth, lineWidth, lineWidthA
-  , lw, lwN, lwO, lwL, lwG
-  , ultraThin, veryThin, thin, medium, thick, veryThick, ultraThick, none
-  , tiny, verySmall, small, normal, large, veryLarge, huge
-
-    -- ** Dashing
-  , Dashing(..), DashingA, getDashing
-  , dashing, dashingN, dashingO, dashingL, dashingG
-
   -- * Textures
-  , Texture(..), solid, _SC, _LG, _RG, defaultLG, defaultRG
+    Texture(..), solid, _SC, _AC, _LG, _RG, defaultLG, defaultRG
   , GradientStop(..), stopColor, stopFraction, mkStops
   , SpreadMethod(..), lineLGradient, lineRGradient
 
@@ -49,15 +44,15 @@
   , rGradSpreadMethod, mkRadialGradient
 
   -- ** Line texture
-  ,  LineTexture(..), getLineTexture, lineTexture, lineTextureA
-  ,  mkLineTexture, styleLineTexture
+  , LineTexture(..), _LineTexture, getLineTexture, lineTexture, lineTextureA
+  , mkLineTexture, _lineTexture
 
   -- ** Line color
   , lineColor, lc, lcA
 
   -- ** Fill texture
-  , FillTexture(..), getFillTexture, fillTexture
-  , mkFillTexture, styleFillTexture
+  , FillTexture(..), _FillTexture, getFillTexture, fillTexture
+  , mkFillTexture, _fillTexture, _fillTextureR
 
   -- ** Fill color
   , fillColor, fc, fcA, recommendFillColor
@@ -67,160 +62,41 @@
 
   ) where
 
-import           Diagrams.Core
-import           Diagrams.Core.Style         (setAttr)
+import           Control.Lens                hiding (transform)
+import           Data.Colour                 hiding (AffineSpace, over)
+import           Data.Data
+import           Data.Default
+import           Data.Monoid.Recommend
+import           Data.Semigroup
+
 import           Diagrams.Attributes
 import           Diagrams.Attributes.Compile
-import           Diagrams.TwoD.Types
-
+import           Diagrams.Core
 import           Diagrams.Core.Types         (RTree)
 import           Diagrams.Located            (unLoc)
 import           Diagrams.Path               (Path, pathTrails)
 import           Diagrams.Trail              (isLoop)
+import           Diagrams.TwoD.Types
+import           Diagrams.Util
 
-import           Control.Lens ( makeLensesWith, generateSignatures, lensRules
-                              , makePrisms, Lens', (&), (%~), (.~), Setter', sets)
 
-import           Data.Colour hiding (AffineSpace)
-import           Data.Data
-import           Data.Default.Class
-import           Data.Maybe                  (fromMaybe)
-
-import           Data.Monoid.Recommend
-import           Data.Semigroup
-
--- | Standard 'Measures'.
-none, ultraThin, veryThin, thin, medium, thick, veryThick, ultraThick,
-  tiny, verySmall, small, normal, large, veryLarge, huge :: Measure R2
-none       = Output 0
-ultraThin  = Normalized 0.0005 `atLeast` Output 0.5
-veryThin   = Normalized 0.001  `atLeast` Output 0.5
-thin       = Normalized 0.002  `atLeast` Output 0.5
-medium     = Normalized 0.004  `atLeast` Output 0.5
-thick      = Normalized 0.0075 `atLeast` Output 0.5
-veryThick  = Normalized 0.01   `atLeast` Output 0.5
-ultraThick = Normalized 0.02   `atLeast` Output 0.5
-
-tiny      = Normalized 0.01
-verySmall = Normalized 0.015
-small     = Normalized 0.023
-normal    = Normalized 0.035
-large     = Normalized 0.05
-veryLarge = Normalized 0.07
-huge      = Normalized 0.10
-
 -----------------------------------------------------------------
---  Line Width  -------------------------------------------------
------------------------------------------------------------------
-
--- | Line widths specified on child nodes always override line widths
---   specified at parent nodes.
-newtype LineWidth = LineWidth (Last (Measure R2))
-  deriving (Typeable, Data, Semigroup)
-instance AttributeClass LineWidth
-
-type instance V LineWidth = R2
-
-instance Transformable LineWidth where
-  transform t (LineWidth (Last w)) =
-    LineWidth (Last (transform t w))
-
-instance Default LineWidth where
-    def = LineWidth (Last medium)
-
-getLineWidth :: LineWidth -> Measure R2
-getLineWidth (LineWidth (Last w)) = w
-
--- | Set the line (stroke) width.
-lineWidth :: (HasStyle a, V a ~ R2) => Measure R2 -> a -> a
-lineWidth = applyGTAttr . LineWidth . Last
-
--- | Apply a 'LineWidth' attribute.
-lineWidthA ::  (HasStyle a, V a ~ R2) => LineWidth -> a -> a
-lineWidthA = applyGTAttr
-
--- | Default for 'lineWidth'.
-lw :: (HasStyle a, V a ~ R2) => Measure R2 -> a -> a
-lw = lineWidth
-
--- | A convenient synonym for 'lineWidth (Global w)'.
-lwG :: (HasStyle a, V a ~ R2) => Double -> a -> a
-lwG w = lineWidth (Global w)
-
--- | A convenient synonym for 'lineWidth (Normalized w)'.
-lwN :: (HasStyle a, V a ~ R2) => Double -> a -> a
-lwN w = lineWidth (Normalized w)
-
--- | A convenient synonym for 'lineWidth (Output w)'.
-lwO :: (HasStyle a, V a ~ R2) => Double -> a -> a
-lwO w = lineWidth (Output w)
-
--- | A convenient sysnonym for 'lineWidth (Local w)'.
-lwL :: (HasStyle a, V a ~ R2) => Double -> a -> a
-lwL w = lineWidth (Local w)
-
------------------------------------------------------------------
---  Dashing  ----------------------------------------------------
+--  Gradients  --------------------------------------------------
 -----------------------------------------------------------------
 
--- | Create lines that are dashing... er, dashed.
-data Dashing = Dashing [Measure R2] (Measure R2)
-  deriving (Typeable, Data, Eq)
-
-newtype DashingA = DashingA (Last Dashing)
-  deriving (Typeable, Data, Semigroup, Eq)
-instance AttributeClass DashingA
-
-type instance V DashingA = R2
-
-instance Transformable DashingA where
-  transform t (DashingA (Last (Dashing w v))) =
-    DashingA (Last (Dashing r s))
-    where
-      r = map (transform t) w
-      s = transform t v
-
-getDashing :: DashingA -> Dashing
-getDashing (DashingA (Last d)) = d
-
--- | Set the line dashing style.
-dashing :: (HasStyle a, V a ~ R2) =>
-           [Measure R2]  -- ^ A list specifying alternate lengths of on
-                         --   and off portions of the stroke.  The empty
-                         --   list indicates no dashing.
-        -> Measure R2    -- ^ An offset into the dash pattern at which the
-                         --   stroke should start.
-        -> a -> a
-dashing ds offs = applyGTAttr (DashingA (Last (Dashing ds offs)))
-
--- | A convenient synonym for 'dashing (Global w)'.
-dashingG :: (HasStyle a, V a ~ R2) => [Double] -> Double -> a -> a
-dashingG w v = dashing (map Global w) (Global v)
-
--- | A convenient synonym for 'dashing (Normalized w)'.
-dashingN :: (HasStyle a, V a ~ R2) => [Double] -> Double -> a -> a
-dashingN w v = dashing (map Normalized w) (Normalized v)
-
--- | A convenient synonym for 'dashing (Output w)'.
-dashingO :: (HasStyle a, V a ~ R2) => [Double] -> Double -> a -> a
-dashingO w v = dashing (map Output w) (Output v)
-
--- | A convenient sysnonym for 'dashing (Local w)'.
-dashingL :: (HasStyle a, V a ~ R2) => [Double] -> Double -> a -> a
-dashingL w v = dashing (map Local w) (Local v)
-
 -- | A gradient stop contains a color and fraction (usually between 0 and 1)
-data GradientStop = GradientStop
-     { _stopColor    :: SomeColor
-     , _stopFraction :: Double}
+data GradientStop d = GradientStop
+  { _stopColor    :: SomeColor
+  , _stopFraction :: d
+  }
 
 makeLensesWith (lensRules & generateSignatures .~ False) ''GradientStop
 
 -- | A color for the stop.
-stopColor :: Lens' GradientStop SomeColor
+stopColor :: Lens' (GradientStop n) SomeColor
 
 -- | The fraction for stop.
-stopFraction :: Lens' GradientStop Double
+stopFraction :: Lens' (GradientStop n) n
 
 -- | The 'SpreadMethod' determines what happens before 'lGradStart' and after
 --   'lGradEnd'. 'GradPad' fills the space before the start of the gradient
@@ -230,278 +106,309 @@
 data SpreadMethod = GradPad | GradReflect | GradRepeat
 
 -- | Linear Gradient
-data LGradient = LGradient
-    { _lGradStops        :: [GradientStop]
-    , _lGradStart        :: P2
-    , _lGradEnd          :: P2
-    , _lGradTrans        :: T2
-    , _lGradSpreadMethod :: SpreadMethod }
+data LGradient n = LGradient
+  { _lGradStops        :: [GradientStop n]
+  , _lGradStart        :: Point V2 n
+  , _lGradEnd          :: Point V2 n
+  , _lGradTrans        :: Transformation V2 n
+  , _lGradSpreadMethod :: SpreadMethod }
 
+type instance V (LGradient n) = V2
+type instance N (LGradient n) = n
+
 makeLensesWith (lensRules & generateSignatures .~ False) ''LGradient
 
+instance Fractional n => Transformable (LGradient n) where
+  transform = over lGradTrans . transform
+
 -- | A list of stops (colors and fractions).
-lGradStops :: Lens' LGradient [GradientStop]
+lGradStops :: Lens' (LGradient n) [GradientStop n]
 
 -- | A transformation to be applied to the gradient. Usually this field will
 --   start as the identity transform and capture the transforms that are applied
 --   to the gradient.
-lGradTrans :: Lens' LGradient T2
+lGradTrans :: Lens' (LGradient n) (Transformation V2 n)
 
 -- | The starting point for the first gradient stop. The coordinates are in
---   'Local' units and the default is (-0.5, 0).
-lGradStart :: Lens' LGradient P2
+--   'local' units and the default is (-0.5, 0).
+lGradStart :: Lens' (LGradient n) (Point V2 n)
 
 -- | The ending point for the last gradient stop.The coordinates are in
---   'Local' units and the default is (0.5, 0).
-lGradEnd :: Lens' LGradient P2
+--   'local' units and the default is (0.5, 0).
+lGradEnd :: Lens' (LGradient n) (Point V2 n)
 
 -- | For setting the spread method.
-lGradSpreadMethod :: Lens' LGradient SpreadMethod
+lGradSpreadMethod :: Lens' (LGradient n) SpreadMethod
 
 -- | Radial Gradient
-data RGradient = RGradient
-    { _rGradStops        :: [GradientStop]
-    , _rGradCenter0      :: P2
-    , _rGradRadius0      :: Double
-    , _rGradCenter1      :: P2
-    , _rGradRadius1      :: Double
-    , _rGradTrans        :: T2
-    , _rGradSpreadMethod :: SpreadMethod }
+data RGradient n = RGradient
+  { _rGradStops        :: [GradientStop n]
+  , _rGradCenter0      :: Point V2 n
+  , _rGradRadius0      :: n
+  , _rGradCenter1      :: Point V2 n
+  , _rGradRadius1      :: n
+  , _rGradTrans        :: Transformation V2 n
+  , _rGradSpreadMethod :: SpreadMethod }
 
 makeLensesWith (lensRules & generateSignatures .~ False) ''RGradient
 
+type instance V (RGradient n) = V2
+type instance N (RGradient n) = n
+
+instance Fractional n => Transformable (RGradient n) where
+  transform = over rGradTrans . transform
+
 -- | A list of stops (colors and fractions).
-rGradStops :: Lens' RGradient [GradientStop]
+rGradStops :: Lens' (RGradient n) [GradientStop n]
 
 -- | The center point of the inner circle.
-rGradCenter0 :: Lens' RGradient P2
+rGradCenter0 :: Lens' (RGradient n) (Point V2 n)
 
--- | The radius of the inner cirlce in 'Local' coordinates.
-rGradRadius0 :: Lens' RGradient Double
+-- | The radius of the inner cirlce in 'local' coordinates.
+rGradRadius0 :: Lens' (RGradient n) n
 
 -- | The center of the outer circle.
-rGradCenter1  :: Lens' RGradient P2
+rGradCenter1  :: Lens' (RGradient n) (Point V2 n)
 
--- | The radius of the outer circle in 'Local' coordinates.
-rGradRadius1 :: Lens' RGradient Double
+-- | The radius of the outer circle in 'local' coordinates.
+rGradRadius1 :: Lens' (RGradient n) n
 
 -- | A transformation to be applied to the gradient. Usually this field will
 --   start as the identity transform and capture the transforms that are applied
 --   to the gradient.
-rGradTrans :: Lens' RGradient T2
+rGradTrans :: Lens' (RGradient n) (Transformation V2 n)
 
 -- | For setting the spread method.
-rGradSpreadMethod :: Lens' RGradient SpreadMethod
+rGradSpreadMethod :: Lens' (RGradient n) SpreadMethod
 
+-----------------------------------------------------------------
+--  Textures  ---------------------------------------------------
+-----------------------------------------------------------------
+
 -- | A Texture is either a color 'SC', linear gradient 'LG', or radial gradient 'RG'.
 --   An object can have only one texture which is determined by the 'Last'
 --   semigroup structure.
-data Texture = SC SomeColor | LG LGradient | RG RGradient
-  deriving (Typeable)
+data Texture n = SC SomeColor | LG (LGradient n) | RG (RGradient n)
+  deriving Typeable
 
+type instance V (Texture n) = V2
+type instance N (Texture n) = n
+
 makePrisms ''Texture
 
+-- | Prism onto an 'AlphaColour' 'Double' of a 'SC' texture.
+_AC :: Prism' (Texture n) (AlphaColour Double)
+_AC = _SC . _SomeColor
+
+instance Floating n => Transformable (Texture n) where
+  transform t (LG lg) = LG $ transform t lg
+  transform t (RG rg) = RG $ transform t rg
+  transform _ sc      = sc
+
 -- | Convert a solid colour into a texture.
-solid :: Color a => a -> Texture
+solid :: Color a => a -> Texture n
 solid = SC . SomeColor
 
 -- | A default is provided so that linear gradients can easily be created using
 --   lenses. For example, @lg = defaultLG & lGradStart .~ (0.25 ^& 0.33)@. Note that
 --   no default value is provided for @lGradStops@, this must be set before
 --   the gradient value is used, otherwise the object will appear transparent.
-defaultLG :: Texture
-defaultLG = LG (LGradient
-    { _lGradStops        = []
-    , _lGradStart        = mkP2 (-0.5) 0
-    , _lGradEnd          = mkP2 (0.5)  0
-    , _lGradTrans        = mempty
-    , _lGradSpreadMethod = GradPad
-    })
+defaultLG :: Fractional n => Texture n
+defaultLG = LG LGradient
+  { _lGradStops        = []
+  , _lGradStart        = mkP2 (-0.5) 0
+  , _lGradEnd          = mkP2 0.5 0
+  , _lGradTrans        = mempty
+  , _lGradSpreadMethod = GradPad
+  }
 
 -- | A default is provided so that radial gradients can easily be created using
 --   lenses. For example, @rg = defaultRG & rGradRadius1 .~ 0.25@. Note that
 --   no default value is provided for @rGradStops@, this must be set before
 --   the gradient value is used, otherwise the object will appear transparent.
-defaultRG :: Texture
-defaultRG = RG (RGradient
-    { _rGradStops        = []
-    , _rGradCenter0      = mkP2 0 0
-    , _rGradRadius0      = 0.0
-    , _rGradCenter1      = mkP2 0 0
-    , _rGradRadius1      = 0.5
-    , _rGradTrans        = mempty
-    , _rGradSpreadMethod = GradPad
-    })
+defaultRG :: Fractional n => Texture n
+defaultRG = RG RGradient
+  { _rGradStops        = []
+  , _rGradCenter0      = mkP2 0 0
+  , _rGradRadius0      = 0.0
+  , _rGradCenter1      = mkP2 0 0
+  , _rGradRadius1      = 0.5
+  , _rGradTrans        = mempty
+  , _rGradSpreadMethod = GradPad
+  }
 
 -- | A convenient function for making gradient stops from a list of triples.
 --   (An opaque color, a stop fraction, an opacity).
-mkStops :: [(Colour Double, Double, Double)] -> [GradientStop]
+mkStops :: [(Colour Double, d, Double)] -> [GradientStop d]
 mkStops = map (\(x, y, z) -> GradientStop (SomeColor (withOpacity x z)) y)
 
 -- | Make a linear gradient texture from a stop list, start point, end point,
 --   and 'SpreadMethod'. The 'lGradTrans' field is set to the identity
 --   transfrom, to change it use the 'lGradTrans' lens.
-mkLinearGradient :: [GradientStop]  -> P2 -> P2 -> SpreadMethod -> Texture
+mkLinearGradient :: Num n => [GradientStop n] -> Point V2 n -> Point V2 n -> SpreadMethod -> Texture n
 mkLinearGradient stops  start end spreadMethod
   = LG (LGradient stops start end mempty spreadMethod)
 
 -- | Make a radial gradient texture from a stop list, radius, start point,
 --   end point, and 'SpreadMethod'. The 'rGradTrans' field is set to the identity
 --   transfrom, to change it use the 'rGradTrans' lens.
-mkRadialGradient :: [GradientStop] -> P2 -> Double
-                  -> P2 -> Double -> SpreadMethod -> Texture
+mkRadialGradient :: Num n => [GradientStop n] -> Point V2 n -> n
+                  -> Point V2 n -> n -> SpreadMethod -> Texture n
 mkRadialGradient stops c0 r0 c1 r1 spreadMethod
   = RG (RGradient stops c0 r0 c1 r1 mempty spreadMethod)
 
+-- Line Texture --------------------------------------------------------
+
 -- | The texture with which lines are drawn.  Note that child
 --   textures always override parent textures.
 --   More precisely, the semigroup structure on line texture attributes
 --   is that of 'Last'.
-newtype LineTexture = LineTexture (Last Texture)
+newtype LineTexture n = LineTexture (Last (Texture n))
   deriving (Typeable, Semigroup)
-instance AttributeClass LineTexture
+instance (Typeable n) => AttributeClass (LineTexture n)
 
-type instance V LineTexture = R2
+type instance V (LineTexture n) = V2
+type instance N (LineTexture n) = n
 
+_LineTexture :: Iso (LineTexture n) (LineTexture n')
+                    (Texture n)     (Texture n')
+_LineTexture = iso getLineTexture (LineTexture . Last)
+
 -- Only gradients get transformed. The transform is applied to the gradients
 -- transform field. Colors are left unchanged.
-instance Transformable LineTexture where
-  transform t (LineTexture (Last texture)) = LineTexture (Last tx)
-    where
-      tx = texture & lgt . rgt
-      lgt = _LG . lGradTrans %~ f
-      rgt = _RG . rGradTrans %~ f
-      f = transform t
+instance Floating n => Transformable (LineTexture n) where
+  transform t (LineTexture (Last tx)) = LineTexture (Last $ transform t tx)
 
-instance Default LineTexture where
-    def = LineTexture (Last (SC (SomeColor (black :: Colour Double))))
+instance Default (LineTexture n) where
+  def = _LineTexture . _SC ## SomeColor black
 
-getLineTexture :: LineTexture -> Texture
+mkLineTexture :: Texture n -> LineTexture n
+mkLineTexture = LineTexture . Last
+
+getLineTexture :: LineTexture n -> Texture n
 getLineTexture (LineTexture (Last t)) = t
 
-lineTexture :: (HasStyle a, V a ~ R2) => Texture-> a -> a
+lineTexture :: (InSpace V2 n a, Typeable n, Floating n, HasStyle a) => Texture n -> a -> a
 lineTexture = applyTAttr . LineTexture . Last
 
-lineTextureA :: (HasStyle a, V a ~ R2) => LineTexture -> a -> a
+lineTextureA :: (InSpace V2 n a, Typeable n, Floating n, HasStyle a) => LineTexture n -> a -> a
 lineTextureA = applyTAttr
 
-mkLineTexture :: Texture  -> LineTexture
-mkLineTexture = LineTexture . Last
-
-styleLineTexture :: Setter' (Style v) Texture
-styleLineTexture = sets modifyLineTexture
+_lineTexture :: (Floating n, Typeable n) => Lens' (Style V2 n) (Texture n)
+_lineTexture = atTAttr . anon def isDef . _LineTexture
   where
-    modifyLineTexture f s
-      = flip setAttr s
-      . mkLineTexture
-      . f
-      . getLineTexture
-      . fromMaybe def . getAttr
-      $ s
+    isDef = anyOf (_LineTexture . _AC) (== opaque black)
 
 -- | Set the line (stroke) color.  This function is polymorphic in the
 --   color type (so it can be used with either 'Colour' or
 --   'AlphaColour'), but this can sometimes create problems for type
 --   inference, so the 'lc' and 'lcA' variants are provided with more
 --   concrete types.
-lineColor :: (Color c, HasStyle a, V a ~ R2) => c -> a -> a
+lineColor :: (InSpace V2 n a, Color c, Typeable n, Floating n, HasStyle a) => c -> a -> a
 lineColor = lineTexture . SC . SomeColor
 
 -- | A synonym for 'lineColor', specialized to @'Colour' Double@
 --   (i.e. opaque colors).  See comment in 'lineColor' about backends.
-lc :: (HasStyle a, V a ~ R2) => Colour Double -> a -> a
+lc :: (InSpace V2 n a, Typeable n, Floating n, HasStyle a) => Colour Double -> a -> a
 lc = lineColor
 
 -- | A synonym for 'lineColor', specialized to @'AlphaColour' Double@
 --   (i.e. colors with transparency).  See comment in 'lineColor'
 --   about backends.
-lcA :: (HasStyle a, V a ~ R2) => AlphaColour Double -> a -> a
+lcA :: (InSpace V2 n a, Typeable n, Floating n, HasStyle a) => AlphaColour Double -> a -> a
 lcA = lineColor
 
 -- | Apply a linear gradient.
-lineLGradient :: (HasStyle a, V a ~ R2) => LGradient -> a -> a
+lineLGradient :: (InSpace V2 n a, Typeable n, Floating n, HasStyle a) => LGradient n -> a -> a
 lineLGradient g = lineTexture (LG g)
 
 -- | Apply a radial gradient.
-lineRGradient :: (HasStyle a, V a ~ R2) => RGradient -> a -> a
+lineRGradient :: (InSpace V2 n a, Typeable n, Floating n, HasStyle a) => RGradient n -> a -> a
 lineRGradient g = lineTexture (RG g)
 
+-- Fill Texture --------------------------------------------------------
+
 -- | The texture with which objects are filled.
 --   The semigroup structure on fill texture attributes
 --   is that of 'Recommed . Last'.
-newtype FillTexture = FillTexture (Recommend (Last Texture))
+newtype FillTexture n = FillTexture (Recommend (Last (Texture n)))
   deriving (Typeable, Semigroup)
 
-instance AttributeClass FillTexture
+instance Typeable n => AttributeClass (FillTexture n)
 
-type instance V FillTexture = R2
+_FillTexture :: Iso' (FillTexture n) (Recommend (Texture n))
+_FillTexture = iso getter setter
+  where
+    getter (FillTexture (Recommend (Last t))) = Recommend t
+    getter (FillTexture (Commit    (Last t))) = Commit t
+    setter (Recommend t) = FillTexture (Recommend (Last t))
+    setter (Commit t)    = FillTexture (Commit (Last t))
+  -- = iso (\(FillTexture a) -> a) FillTexture . mapping _Wrapped
+  -- -- once we depend on monoid-extras-0.4
 
+type instance V (FillTexture n) = V2
+type instance N (FillTexture n) = n
+
 -- Only gradients get transformed. The transform is applied to the gradients
 -- transform field. Colors are left unchanged.
-instance Transformable FillTexture where
-  transform _ tx@(FillTexture (Recommend _)) = tx
-  transform t (FillTexture (Commit (Last texture))) = FillTexture (Commit (Last tx))
-    where
-      tx = texture & lgt . rgt
-      lgt = _LG . lGradTrans %~ f
-      rgt = _RG . rGradTrans %~ f
-      f = transform t
+instance Floating n => Transformable (FillTexture n) where
+  transform = over (_FillTexture . _recommend) . transform
 
-instance Default FillTexture where
-    def = FillTexture (Recommend (Last (SC
-                      (SomeColor (transparent :: AlphaColour Double)))))
+instance Default (FillTexture n) where
+  def = mkFillTexture $ _AC ## transparent
 
-getFillTexture :: FillTexture -> Texture
+getFillTexture :: FillTexture n -> Texture n
 getFillTexture (FillTexture tx) = getLast . getRecommend $ tx
 
-fillTexture :: (HasStyle a, V a ~ R2) => Texture -> a -> a
-fillTexture = applyTAttr . FillTexture . Commit . Last
+fillTexture :: (InSpace V2 n a, Typeable n, Floating n, HasStyle a) => Texture n -> a -> a
+fillTexture = applyTAttr . mkFillTexture
 
-mkFillTexture :: Texture  -> FillTexture
+mkFillTexture :: Texture n -> FillTexture n
 mkFillTexture = FillTexture . Commit . Last
 
-styleFillTexture :: Setter' (Style v) Texture
-styleFillTexture = sets modifyFillTexture
+-- | Lens onto the 'Recommend' of a fill texture in a style.
+_fillTextureR :: (Typeable n, Floating n) => Lens' (Style V2 n) (Recommend (Texture n))
+_fillTextureR = atTAttr . anon def isDef . _FillTexture
   where
-    modifyFillTexture f s
-      = flip setAttr s
-      . mkFillTexture
-      . f
-      . getFillTexture
-      . fromMaybe def . getAttr
-      $ s
+    isDef = anyOf (_FillTexture . _Recommend . _AC) (== transparent)
 
+-- | Commit a fill texture in a style. This is /not/ a valid setter
+--   because it doesn't abide the functor law (see 'committed').
+_fillTexture :: (Typeable n, Floating n) => Lens' (Style V2 n) (Texture n)
+_fillTexture = _fillTextureR . committed
+
 -- | Set the fill color.  This function is polymorphic in the color
 --   type (so it can be used with either 'Colour' or 'AlphaColour'),
 --   but this can sometimes create problems for type inference, so the
 --   'fc' and 'fcA' variants are provided with more concrete types.
-fillColor :: (Color c, HasStyle a, V a ~ R2) => c -> a -> a
+fillColor :: (InSpace V2 n a, Color c, Typeable n, Floating n, HasStyle a) => c -> a -> a
 fillColor = fillTexture . SC . SomeColor
 
 -- | Set a \"recommended\" fill color, to be used only if no explicit
 --   calls to 'fillColor' (or 'fc', or 'fcA') are used.
 --   See comment after 'fillColor' about backends.
-recommendFillColor :: (Color c, HasStyle a, V a ~ R2) => c -> a -> a
+recommendFillColor :: (InSpace V2 n a, Color c, Typeable n, Floating n, HasStyle a) => c -> a -> a
 recommendFillColor =
   applyTAttr . FillTexture . Recommend . Last . SC . SomeColor
 
 -- | A synonym for 'fillColor', specialized to @'Colour' Double@
 --   (i.e. opaque colors). See comment after 'fillColor' about backends.
-fc :: (HasStyle a, V a ~ R2) => Colour Double -> a -> a
+fc :: (InSpace V2 n a, Floating n, Typeable n, HasStyle a) => Colour Double -> a -> a
 fc = fillColor
 
 -- | A synonym for 'fillColor', specialized to @'AlphaColour' Double@
 --   (i.e. colors with transparency). See comment after 'fillColor' about backends.
-fcA :: (HasStyle a, V a ~ R2) => AlphaColour Double -> a -> a
+fcA :: (InSpace V2 n a, Floating n, Typeable n, HasStyle a) => AlphaColour Double -> a -> a
 fcA = fillColor
-------------------------------------------------------------
 
-data FillTextureLoops v = FillTextureLoops
+-- Split fills ---------------------------------------------------------
 
-instance Typeable v => SplitAttribute (FillTextureLoops v) where
-  type AttrType (FillTextureLoops v) = FillTexture
-  type PrimType (FillTextureLoops v) = Path v
+data FillTextureLoops n = FillTextureLoops
 
+instance Typeable n => SplitAttribute (FillTextureLoops n) where
+  type AttrType (FillTextureLoops n) = FillTexture n
+  type PrimType (FillTextureLoops n) = Path V2 n
+
   primOK _ = all (isLoop . unLoc) . pathTrails
 
 -- | Push fill attributes down until they are at the root of subtrees
@@ -510,5 +417,7 @@
 --   applied to lines/non-closed paths as well as loops/closed paths,
 --   whereas in the semantics of diagrams, fill attributes only apply
 --   to loops.
-splitTextureFills :: forall b v a. Typeable v => RTree b v a -> RTree b v a
-splitTextureFills = splitAttr (FillTextureLoops :: FillTextureLoops v)
+splitTextureFills
+  :: forall b v n a. (
+                     Typeable n) => RTree b v n a -> RTree b v n a
+splitTextureFills = splitAttr (FillTextureLoops :: FillTextureLoops n)
diff --git a/src/Diagrams/TwoD/Combinators.hs b/src/Diagrams/TwoD/Combinators.hs
--- a/src/Diagrams/TwoD/Combinators.hs
+++ b/src/Diagrams/TwoD/Combinators.hs
@@ -1,7 +1,12 @@
+{-# LANGUAGE ConstraintKinds       #-}
 {-# LANGUAGE FlexibleContexts      #-}
 {-# LANGUAGE MultiParamTypeClasses #-}
+{-# LANGUAGE ScopedTypeVariables   #-}
 {-# LANGUAGE TypeFamilies          #-}
-{-# LANGUAGE ViewPatterns          #-}
+
+{-# OPTIONS_GHC -fno-warn-unused-imports #-}
+  -- for Data.Semigroup
+
 -----------------------------------------------------------------------------
 -- |
 -- Module      :  Diagrams.TwoD.Combinators
@@ -18,11 +23,11 @@
     (
       -- * Binary combinators
 
-      (===), (|||), atAngle
+      (===), (|||)
 
       -- * n-ary combinators
-    , hcat, hcat'
-    , vcat, vcat'
+    , hcat, hcat', hsep
+    , vcat, vcat', vsep
 
       -- * Spacing/envelopes
     , strutR2
@@ -31,36 +36,38 @@
 
     , extrudeLeft, extrudeRight, extrudeBottom, extrudeTop
 
-    , view
+    , rectEnvelope, crop
 
-    , boundingRect, bg
+    , boundingRect, bg, bgFrame
 
     ) where
 
-import           Data.AffineSpace
+import           Control.Lens             ((&), (.~))
 import           Data.Colour
-import           Data.Default.Class
+import           Data.Default
 import           Data.Semigroup
-import           Data.VectorSpace
 
 import           Diagrams.Core
 
-import           Diagrams.Angle
+import           Diagrams.Attributes      (lwO)
 import           Diagrams.BoundingBox
 import           Diagrams.Combinators
-import           Diagrams.Coordinates
 import           Diagrams.Path
+import           Diagrams.Query           (value)
 import           Diagrams.Segment
 import           Diagrams.TrailLike
 import           Diagrams.TwoD.Align
-import           Diagrams.TwoD.Attributes (lineWidth, fc)
+import           Diagrams.TwoD.Attributes (fc)
 import           Diagrams.TwoD.Path       ()
 import           Diagrams.TwoD.Shapes
 import           Diagrams.TwoD.Transform  (scaleX, scaleY)
 import           Diagrams.TwoD.Types
-import           Diagrams.TwoD.Vector     (fromDirection, unitX, unitY)
+import           Diagrams.TwoD.Vector
 import           Diagrams.Util            (( # ))
 
+import           Linear.Affine
+import           Linear.Metric
+import           Linear.Vector
 
 infixl 6 ===
 infixl 6 |||
@@ -79,8 +86,8 @@
 --   combined diagram is the same as the local origin of the first.
 --   @(===)@ is associative and has 'mempty' as an identity.  See the
 --   documentation of 'beside' for more information.
-(===) :: (Juxtaposable a, V a ~ R2, Semigroup a) => a -> a -> a
-(===) = beside (negateV unitY)
+(===) :: (InSpace V2 n a, Juxtaposable a, Semigroup a) => a -> a -> a
+(===) = beside unit_Y
 
 -- | Place two diagrams (or other juxtaposable objects) horizontally
 --   adjacent to one another, with the first diagram to the left of
@@ -88,17 +95,9 @@
 --   is the same as the local origin of the first.  @(|||)@ is
 --   associative and has 'mempty' as an identity.  See the
 --   documentation of 'beside' for more information.
-(|||) :: (Juxtaposable a, V a ~ R2, Semigroup a) => a -> a -> a
+(|||) :: (InSpace V2 n a, Juxtaposable a, Semigroup a) => a -> a -> a
 (|||) = beside unitX
 
--- | Place two diagrams (or other juxtaposable objects) adjacent to one
---   another, with the second diagram placed along a line at angle
---   'th' from the first.  The local origin of the resulting combined
---   diagram is the same as the local origin of the first.
---   See the documentation of 'beside' for more information.
-atAngle :: (Juxtaposable a, V a ~ R2, Semigroup a) => Angle -> a -> a -> a
-atAngle th = beside (fromDirection th)
-
 -- | Lay out a list of juxtaposable objects in a row from left to right,
 --   so that their local origins lie along a single horizontal line,
 --   with successive envelopes tangent to one another.
@@ -110,17 +109,24 @@
 --     "Diagrams.TwoD.Align" before applying 'hcat'.
 --
 --   * For non-axis-aligned layout, see 'cat'.
-hcat :: (Juxtaposable a, HasOrigin a, Monoid' a, V a ~ R2)
+hcat :: (InSpace V2 n a, Floating n, Juxtaposable a, HasOrigin a, Monoid' a)
      => [a] -> a
 hcat = hcat' def
 
 -- | A variant of 'hcat' taking an extra 'CatOpts' record to control
 --   the spacing.  See the 'cat'' documentation for a description of
---   the possibilities.
-hcat' :: (Juxtaposable a, HasOrigin a, Monoid' a, V a ~ R2)
-      => CatOpts R2 -> [a] -> a
+--   the possibilities. For the common case of setting just a
+--   separation amount, see 'hsep'.
+hcat' :: (InSpace V2 n a, Floating n, Juxtaposable a, HasOrigin a, Monoid' a)
+      => CatOpts n -> [a] -> a
 hcat' = cat' unitX
 
+-- | A convenient synonym for horizontal concatenation with
+--   separation: @hsep s === hcat' (with & sep .~ s)@.
+hsep :: (InSpace V2 n a, Floating n, Juxtaposable a, HasOrigin a, Monoid' a)
+     => n -> [a] -> a
+hsep s = hcat' (def & sep .~ s)
+
 -- | Lay out a list of juxtaposable objects in a column from top to
 --   bottom, so that their local origins lie along a single vertical
 --   line, with successive envelopes tangent to one another.
@@ -132,24 +138,31 @@
 --     "Diagrams.TwoD.Align" before applying 'vcat'.
 --
 --   * For non-axis-aligned layout, see 'cat'.
-vcat :: (Juxtaposable a, HasOrigin a, Monoid' a, V a ~ R2)
+vcat :: (InSpace V2 n a, Floating n, Juxtaposable a, HasOrigin a, Monoid' a)
      => [a] -> a
 vcat = vcat' def
 
 -- | A variant of 'vcat' taking an extra 'CatOpts' record to control
---   the spacing.  See the 'cat'' documentation for a description of the
---   possibilities.
-vcat' :: (Juxtaposable a, HasOrigin a, Monoid' a, V a ~ R2)
-      => CatOpts R2 -> [a] -> a
-vcat' = cat' (negateV unitY)
+--   the spacing.  See the 'cat'' documentation for a description of
+--   the possibilities.  For the common case of setting just a
+--   separation amount, see 'vsep'.
+vcat' :: (InSpace V2 n a, Floating n, Juxtaposable a, HasOrigin a, Monoid' a)
+      => CatOpts n -> [a] -> a
+vcat' = cat' unit_Y
 
+-- | A convenient synonym for vertical concatenation with
+--   separation: @vsep s === vcat' (with & sep .~ s)@.
+vsep :: (InSpace V2 n a, Floating n, Juxtaposable a, HasOrigin a, Monoid' a)
+     => n -> [a] -> a
+vsep s = vcat' (def & sep .~ s)
+
 -- | @strutR2 v@ is a two-dimensional diagram which produces no
 --   output, but with respect to alignment, envelope, /and trace/ acts
 --   like a 1-dimensional segment oriented along the vector @v@, with
 --   local origin at its center.  If you don't care about the trace
 --   then there's no difference between @strutR2@ and the more general
 --   'strut'.
-strutR2 :: (Backend b R2, Monoid' m) => R2 -> QDiagram b R2 m
+strutR2 :: (RealFloat n, Monoid' m) => V2 n -> QDiagram b V2 n m
 strutR2 v = phantom seg
   where
     seg = FLinear (origin .+^ 0.5 *^ v) (origin .+^ (-0.5) *^ v)
@@ -157,14 +170,14 @@
 -- | @strutX w@ is an empty diagram with width @w@, height 0, and a
 --   centered local origin.  Note that @strutX (-w)@ behaves the same as
 --   @strutX w@.
-strutX :: (Backend b R2, Monoid' m) => Double -> QDiagram b R2 m
-strutX d = strut (d ^& 0)
+strutX :: (Metric v, R1 v, OrderedField n) => n -> QDiagram b v n m
+strutX d = strut (zero & _x .~ d)
 
 -- | @strutY h@ is an empty diagram with height @h@, width 0, and a
 --   centered local origin. Note that @strutY (-h)@ behaves the same as
 --   @strutY h@.
-strutY :: (Backend b R2, Monoid' m) => Double -> QDiagram b R2 m
-strutY d = strut (0 ^& d)
+strutY :: (Metric v, R2 v, OrderedField n) => n -> QDiagram b v n m
+strutY d = strut (zero & _y .~ d)
 
 -- | @padX s@ \"pads\" a diagram in the x-direction, expanding its
 --   envelope horizontally by a factor of @s@ (factors between 0 and 1
@@ -173,8 +186,8 @@
 --   centered horizontally the padding may appear \"uneven\".  If this
 --   is not desired, the origin can be centered (using 'centerX')
 --   before applying @padX@.
-padX :: ( Backend b R2, Monoid' m )
-     => Double -> QDiagram b R2 m -> QDiagram b R2 m
+padX :: (Metric v, R2 v, OrderedField n, Monoid' m)
+     => n -> QDiagram b v n m -> QDiagram b v n m
 padX s d = withEnvelope (d # scaleX s) d
 
 -- | @padY s@ \"pads\" a diagram in the y-direction, expanding its
@@ -184,8 +197,8 @@
 --   so if the origin is not centered vertically the padding may appear
 --   \"uneven\".  If this is not desired, the origin can be centered
 --   (using 'centerY') before applying @padY@.
-padY :: ( Backend b R2, Monoid' m )
-     => Double -> QDiagram b R2 m -> QDiagram b R2 m
+padY :: (Metric v, R2 v, Monoid' m, OrderedField n)
+     => n -> QDiagram b v n m -> QDiagram b v n m
 padY s d = withEnvelope (d # scaleY s) d
 
 -- | @extrudeLeft s@ \"extrudes\" a diagram in the negative x-direction,
@@ -193,7 +206,7 @@
 --   the envelope is inset instead.
 --
 --   See the documentation for 'extrudeEnvelope' for more information.
-extrudeLeft :: Monoid' m => Double -> QDiagram b R2 m -> QDiagram b R2 m
+extrudeLeft :: (OrderedField n, Monoid' m) => n -> QDiagram b V2 n m -> QDiagram b V2 n m
 extrudeLeft s
   | s >= 0    = extrudeEnvelope $ unitX ^* negate s
   | otherwise = intrudeEnvelope $ unitX ^* negate s
@@ -203,7 +216,7 @@
 --   the envelope is inset instead.
 --
 --   See the documentation for 'extrudeEnvelope' for more information.
-extrudeRight :: Monoid' m => Double -> QDiagram b R2 m -> QDiagram b R2 m
+extrudeRight :: (OrderedField n, Monoid' m) => n -> QDiagram b V2 n m -> QDiagram b V2 n m
 extrudeRight s
   | s >= 0    = extrudeEnvelope $ unitX ^* s
   | otherwise = intrudeEnvelope $ unitX ^* s
@@ -213,7 +226,7 @@
 --   the envelope is inset instead.
 --
 --   See the documentation for 'extrudeEnvelope' for more information.
-extrudeBottom :: Monoid' m => Double -> QDiagram b R2 m -> QDiagram b R2 m
+extrudeBottom :: (OrderedField n, Monoid' m) => n -> QDiagram b V2 n m -> QDiagram b V2 n m
 extrudeBottom s
   | s >= 0    = extrudeEnvelope $ unitY ^* negate s
   | otherwise = intrudeEnvelope $ unitY ^* negate s
@@ -223,29 +236,44 @@
 --   the envelope is inset instead.
 --
 --   See the documentation for 'extrudeEnvelope' for more information.
-extrudeTop :: Monoid' m => Double -> QDiagram b R2 m -> QDiagram b R2 m
+extrudeTop :: (OrderedField n, Monoid' m) => n -> QDiagram b V2 n m -> QDiagram b V2 n m
 extrudeTop s
   | s >= 0    = extrudeEnvelope $ unitY ^* s
   | otherwise = intrudeEnvelope $ unitY ^* s
 
--- | @view p v@ sets the envelope of a diagram to a rectangle whose
+-- | @rectEnvelope p v@ sets the envelope of a diagram to a rectangle whose
 --   lower-left corner is at @p@ and whose upper-right corner is at @p
 --   .+^ v@.  Useful for selecting the rectangular portion of a
 --   diagram which should actually be \"viewed\" in the final render,
 --   if you don't want to see the entire diagram.
-view :: ( Backend b R2, Monoid' m )
-     => P2 -> R2 -> QDiagram b R2 m -> QDiagram b R2 m
-view p (coords -> w :& h) = withEnvelope (rect w h # alignBL # moveTo p :: D R2)
+rectEnvelope :: forall b n m. (OrderedField n, Monoid' m)
+     => Point V2 n -> V2 n -> QDiagram b V2 n m -> QDiagram b V2 n m
+rectEnvelope p (V2 w h) = withEnvelope (rect w h # alignBL # moveTo p :: Path V2 n)
 
+-- | A synonym for 'rectEnvelope'.
+crop :: forall b n m. (OrderedField n, Monoid' m)
+     => Point V2 n -> V2 n -> QDiagram b V2 n m -> QDiagram b V2 n m
+crop = rectEnvelope
+
 -- | Construct a bounding rectangle for an enveloped object, that is,
 --   the smallest axis-aligned rectangle which encloses the object.
-boundingRect :: ( Enveloped t, Transformable t, TrailLike t, Monoid t, V t ~ R2
-                , Enveloped a, V a ~ R2
-                )
+boundingRect :: ( InSpace V2 n a, SameSpace a t
+                , Enveloped t, Transformable t, TrailLike t, Monoid t
+                , Enveloped a)
              => a -> t
 boundingRect = (`boxFit` rect 1 1) . boundingBox
 
 -- | \"Set the background color\" of a diagram.  That is, place a
 --   diagram atop a bounding rectangle of the given color.
-bg :: (Renderable (Path R2) b) => Colour Double -> Diagram b R2 -> Diagram b R2
-bg c d = d <> boundingRect d # lineWidth (Output 0) # fc c
+--   The background does not change the result of queries.
+bg :: (TypeableFloat n, Renderable (Path V2 n) b, Monoid' q)
+    => Colour Double -> QDiagram b V2 n q -> QDiagram b V2 n q
+bg c d = d <> boundingRect d # lwO 0 # fc c # value mempty
+
+-- | Similar to 'bg' but makes the colored background rectangle larger than
+--   the diagram. The first parameter is used to set how far the background
+--   extends beyond the diagram.
+--   The background does not change the result of queries.
+bgFrame :: (TypeableFloat n, Renderable (Path V2 n) b, Monoid' q)
+    => n -> Colour Double -> QDiagram b V2 n q -> QDiagram b V2 n q
+bgFrame f c d = d <> boundingRect (frame f d) # lwO 0 # fc c # value mempty
diff --git a/src/Diagrams/TwoD/Curvature.hs b/src/Diagrams/TwoD/Curvature.hs
--- a/src/Diagrams/TwoD/Curvature.hs
+++ b/src/Diagrams/TwoD/Curvature.hs
@@ -19,16 +19,16 @@
     , squaredRadiusOfCurvature
     ) where
 
+import           Control.Lens        (over)
+import           Control.Monad
 import           Data.Monoid.Inf
-import           Data.VectorSpace
 
-import           Control.Arrow        (first, second)
-import           Control.Monad        (join)
-
 import           Diagrams.Segment
 import           Diagrams.Tangent
 import           Diagrams.TwoD.Types
 
+import           Linear.Vector
+
 -- | Curvature measures how curved the segment is at a point.  One intuition
 -- for the concept is how much you would turn the wheel when driving a car
 -- along the curve.  When the wheel is held straight there is zero curvature.
@@ -68,9 +68,10 @@
 -- > import Data.Monoid.Inf
 -- > import Diagrams.Coordinates
 -- >
+-- > segmentA :: Segment Closed V2 Double
 -- > segmentA = Cubic (12 ^& 0) (8 ^& 10) (OffsetClosed (20 ^& 8))
 -- >
--- > curveA = lw thick . stroke . fromSegments $ [segmentA]
+-- > curveA = lw thick . strokeP . fromSegments $ [segmentA]
 -- >
 -- > diagramA = pad 1.1 . centerXY $ curveA
 -- >
@@ -83,9 +84,10 @@
 -- > diagramWithRadius t = pad 1.1 . centerXY
 -- >          $ curveA
 -- >         <> showCurvature segmentA t
--- >          # withEnvelope (curveA :: D R2)
+-- >          # withEnvelope (curveA :: D V2 Double)
 -- >          # lc red
 -- >
+-- > showCurvature :: Segment Closed V2 Double -> Double -> Diagram SVG
 -- > showCurvature bez@(Cubic b c (OffsetClosed d)) t
 -- >   | v == (0,0) = mempty
 -- >   | otherwise  = go (radiusOfCurvature bez t)
@@ -97,41 +99,41 @@
 -- >
 -- >     go Infinity   = mempty
 -- >     go (Finite r) = (circle (abs r) # translate vpr
--- >                  <> stroke (origin ~~ (origin .+^ vpr)))
+-- >                  <> strokeP (origin ~~ (origin .+^ vpr)))
 -- >                   # moveTo (origin .+^ atParam bez t)
 -- >       where
--- >         vpr = r2 (normalized vp ^* r)
+-- >         vpr = signorm vp ^* r
 -- >
 --
-curvature :: Segment Closed R2  -- ^ Segment to measure on.
-          -> Double           -- ^ Parameter to measure at.
-          -> PosInf Double    -- ^ Result is a @PosInf@ value where @PosInfty@ represents
-                              -- infinite curvature or zero radius of curvature.
-curvature s = toPosInf . second sqrt . curvaturePair (fmap unr2 s) -- TODO: Use the generalized unr2
+curvature :: RealFloat n
+          => Segment Closed V2 n  -- ^ Segment to measure on.
+          -> n                    -- ^ Parameter to measure at.
+          -> PosInf n             -- ^ Result is a @PosInf@ value where @PosInfty@ represents
+                                  --   infinite curvature or zero radius of curvature.
+curvature s = toPosInf . over _y sqrt . curvaturePair s
 
 -- | With @squaredCurvature@ we can compute values in spaces that do not support
 -- 'sqrt' and it is just as useful for relative ordering of curvatures or looking
 -- for zeros.
-squaredCurvature :: Segment Closed R2 -> Double -> PosInf Double
-squaredCurvature s = toPosInf . first (join (*)) . curvaturePair (fmap unr2 s) -- TODO: Use the generalized unr2
-
+squaredCurvature :: RealFloat n => Segment Closed V2 n -> n -> PosInf n
+squaredCurvature s = toPosInf . over _x (join (*)) . curvaturePair s
 
 -- | Reciprocal of @curvature@.
-radiusOfCurvature :: Segment Closed R2  -- ^ Segment to measure on.
-                  -> Double           -- ^ Parameter to measure at.
-                  -> PosInf Double    -- ^ Result is a @PosInf@ value where @PosInfty@ represents
-                                      -- infinite radius of curvature or zero curvature.
-radiusOfCurvature s = toPosInf . (\(p,q) -> (q,p)) . second sqrt . curvaturePair (fmap unr2 s)
+radiusOfCurvature :: RealFloat n
+                  => Segment Closed V2 n -- ^ Segment to measure on.
+                  -> n                   -- ^ Parameter to measure at.
+                  -> PosInf n            -- ^ Result is a @PosInf@ value where @PosInfty@ represents
+                                         --   infinite radius of curvature or zero curvature.
+radiusOfCurvature s = toPosInf . (\(V2 p q) -> V2 (sqrt q) p) . curvaturePair s
 
 -- | Reciprocal of @squaredCurvature@
-squaredRadiusOfCurvature :: Segment Closed R2 -> Double -> PosInf Double
-squaredRadiusOfCurvature s = toPosInf . (\(p,q) -> (q,p)) . first (join (*)) . curvaturePair (fmap unr2 s)
-
+squaredRadiusOfCurvature :: RealFloat n => Segment Closed V2 n -> n -> PosInf n
+squaredRadiusOfCurvature s = toPosInf . (\(V2 p q) -> (V2 q (p * p))) . curvaturePair s
 
 -- Package up problematic values with the appropriate infinity.
-toPosInf :: RealFloat a => (a,a) -> PosInf a
-toPosInf (_,0) = Infinity
-toPosInf (p,q)
+toPosInf :: RealFloat a => V2 a -> PosInf a
+toPosInf (V2 _ 0) = Infinity
+toPosInf (V2 p q)
   | isInfinite r || isNaN r = Infinity
   | otherwise               = Finite r
   where r = p / q
@@ -139,13 +141,14 @@
 -- Internal function that is not quite curvature or squaredCurvature but lets
 -- us get there by either taking the square root of the numerator or squaring
 -- the denominator respectively.
-curvaturePair :: (Num t, Num (Scalar t), VectorSpace t)
-    => Segment Closed (t, t) -> Scalar t -> (t, t)
-curvaturePair (Linear _) _ = (0,1) -- Linear segments always have zero curvature (infinite radius).
-curvaturePair seg@(Cubic b c (OffsetClosed d)) t = ((x'*y'' - y'*x''), (x'*x' + y'*y')^(3 :: Integer))
+curvaturePair :: Num n
+    => Segment Closed V2 n -> n -> V2 n
+curvaturePair (Linear _) _ = V2 0 1 -- Linear segments always have zero curvature (infinite radius).
+curvaturePair seg@(Cubic b c (OffsetClosed d)) t
+  = V2 (x'*y'' - y'*x'') ((x'*x' + y'*y')^(3 :: Int))
   where
-    (x' ,y' ) = seg `tangentAtParam` t
-    (x'',y'') = secondDerivative
+    (V2 x'  y' )     = seg `tangentAtParam` t
+    (V2 x'' y'')     = secondDerivative
     secondDerivative = (6*(3*t-2))*^b ^+^ (6-18*t)*^c ^+^ (6*t)*^d
 
 -- TODO: We should be able to generalize this to higher dimensions.  See
@@ -153,3 +156,11 @@
 --
 -- TODO: I'm not sure what the best way to generalize squaredCurvature to other spaces is.
 
+-- curvaturePair :: (Num t, Num (Scalar t), VectorSpace t)
+--     => Segment Closed (t, t) -> Scalar t -> (t, t)
+-- curvaturePair (Linear _) _ = (0,1) -- Linear segments always have zero curvature (infinite radius).
+-- curvaturePair seg@(Cubic b c (OffsetClosed d)) t = ((x'*y'' - y'*x''), (x'*x' + y'*y')^(3 :: Integer))
+--   where
+--     (x' ,y' ) = seg `tangentAtParam` t
+--     (x'',y'') = secondDerivative
+--     secondDerivative = (6*(3*t-2))*^b ^+^ (6-18*t)*^c ^+^ (6*t)*^d
diff --git a/src/Diagrams/TwoD/Deform.hs b/src/Diagrams/TwoD/Deform.hs
--- a/src/Diagrams/TwoD/Deform.hs
+++ b/src/Diagrams/TwoD/Deform.hs
@@ -1,36 +1,41 @@
 module Diagrams.TwoD.Deform where
 
-import Control.Lens
+import           Control.Lens
 
-import Diagrams.Deform
+import           Diagrams.Deform
 
-import Diagrams.Coordinates
-import Diagrams.TwoD.Types
+import           Linear.V2
+import           Linear.Vector
 
--- | The parallel projection onto the line x=0
-parallelX0 :: Deformation R2
-parallelX0 = Deformation (& _x .~ 0)
+-- | The parallel projection onto the plane x=0
+parallelX0 :: (R1 v, Num n) => Deformation v v n
+parallelX0 = Deformation (_x .~ 0)
 
--- | The perspective division onto the line x=1 along lines going
+-- | The perspective division onto the plane x=1 along lines going
 -- through the origin.
-perspectiveX1 :: Deformation R2
-perspectiveX1 = Deformation (\p -> p & _y //~ (p^._x) & _x .~ 1)
+perspectiveX1 :: (R1 v, Functor v, Fractional n) => Deformation v v n
+perspectiveX1 = Deformation $ \p -> p ^/ (p ^. _x)
 
--- | The parallel projection onto the line y=0
-parallelY0 :: Deformation R2
-parallelY0 = Deformation (& _y .~ 0)
+-- | The parallel projection onto the plane y=0
+parallelY0 :: (R2 v, Num n) => Deformation v v n
+parallelY0 = Deformation (_y .~ 0)
 
--- | The perspective division onto the line y=1 along lines going
+-- | The perspective division onto the plane y=1 along lines going
 -- through the origin.
-perspectiveY1 :: Deformation R2
-perspectiveY1 = Deformation (\p -> p & _x //~ (p^._y) & _y .~ 1)
+perspectiveY1 :: (R2 v, Functor v, Floating n) => Deformation v v n
+perspectiveY1 = Deformation $ \p -> p ^/ (p ^. _y)
 
 -- | The viewing transform for a viewer facing along the positive X
 -- axis.  X coördinates stay fixed, while Y coördinates are compressed
 -- with increasing distance.  @asDeformation (translation unitX) <>
 -- parallelX0 <> frustrumX = perspectiveX1@
-facingX :: Deformation R2
-facingX = Deformation (\v -> v & _y //~ (v^._x))
+facingX :: (R1 v, Functor v, Fractional n) => Deformation v v n
+facingX = Deformation $
+  \p -> let x = p ^. _x
+        in  p ^/ x & _x .~ x
 
-facingY :: Deformation R2
-facingY = Deformation (\v -> v & _x //~ (v^._y))
+facingY :: (R2 v, Functor v, Fractional n) => Deformation v v n
+facingY = Deformation $
+  \p -> let y = p ^. _y
+        in  p ^/ y & _y .~ y
+
diff --git a/src/Diagrams/TwoD/Ellipse.hs b/src/Diagrams/TwoD/Ellipse.hs
--- a/src/Diagrams/TwoD/Ellipse.hs
+++ b/src/Diagrams/TwoD/Ellipse.hs
@@ -1,6 +1,7 @@
 {-# LANGUAGE FlexibleContexts      #-}
 {-# LANGUAGE MultiParamTypeClasses #-}
 {-# LANGUAGE TypeFamilies          #-}
+{-# LANGUAGE TypeOperators         #-}
 {-# LANGUAGE TypeSynonymInstances  #-}
 -----------------------------------------------------------------------------
 -- |
@@ -22,31 +23,31 @@
     , ellipseXY
     ) where
 
-import           Data.AdditiveGroup
-
 import           Diagrams.Core
 
 import           Diagrams.Angle
 import           Diagrams.Located        (at)
+import           Diagrams.Trail          (glueTrail)
 import           Diagrams.TrailLike
 import           Diagrams.TwoD.Arc
 import           Diagrams.TwoD.Transform
 import           Diagrams.TwoD.Types
+import           Diagrams.TwoD.Vector    (xDir)
 import           Diagrams.Util
 
 -- | A circle of radius 1, with center at the origin.
-unitCircle :: (TrailLike t, V t ~ R2) => t
-unitCircle = trailLike $ arcT zeroV fullTurn `at` (p2 (1,0))
+unitCircle :: (TrailLike t, V t ~ V2, N t ~ n) => t
+unitCircle = trailLike $ glueTrail (arcT xDir fullTurn) `at` p2 (1,0)
 
 -- | A circle of the given radius, centered at the origin.  As a path,
 --   it begins at (r,0).
-circle :: (TrailLike t, V t ~ R2, Transformable t) => Double -> t
+circle :: (TrailLike t, V t ~ V2, N t ~ n, Transformable t) => n -> t
 circle d = unitCircle # scale d
 
 -- | @ellipse e@ constructs an ellipse with eccentricity @e@ by
 --   scaling the unit circle in the X direction.  The eccentricity must
 --   be within the interval [0,1).
-ellipse :: (TrailLike t, V t ~ R2, Transformable t) => Double -> t
+ellipse :: (TrailLike t, V t ~ V2, N t ~ n, Transformable t) => n -> t
 ellipse e
     | e >= 0 && e < 1  = scaleX (sqrt (1 - e*e)) unitCircle
     | otherwise        = error "Eccentricity of ellipse must be >= 0 and < 1."
@@ -54,5 +55,5 @@
 -- | @ellipseXY x y@ creates an axis-aligned ellipse, centered at the
 --   origin, with radius @x@ along the x-axis and radius @y@ along the
 --   y-axis.
-ellipseXY :: (TrailLike t, V t ~ R2, Transformable t) => Double -> Double -> t
+ellipseXY :: (TrailLike t, V t ~ V2, N t ~ n, Transformable t) => n -> n -> t
 ellipseXY x y = unitCircle # scaleX x # scaleY y
diff --git a/src/Diagrams/TwoD/Image.hs b/src/Diagrams/TwoD/Image.hs
--- a/src/Diagrams/TwoD/Image.hs
+++ b/src/Diagrams/TwoD/Image.hs
@@ -1,9 +1,12 @@
+{-# LANGUAGE ConstraintKinds       #-}
 {-# LANGUAGE DeriveDataTypeable    #-}
 {-# LANGUAGE EmptyDataDecls        #-}
 {-# LANGUAGE FlexibleContexts      #-}
 {-# LANGUAGE GADTs                 #-}
 {-# LANGUAGE MultiParamTypeClasses #-}
 {-# LANGUAGE TypeFamilies          #-}
+{-# LANGUAGE UndecidableInstances  #-}
+
 -----------------------------------------------------------------------------
 -- |
 -- Module      :  Diagrams.TwoD.Image
@@ -11,93 +14,121 @@
 -- License     :  BSD-style (see LICENSE)
 -- Maintainer  :  diagrams-discuss@googlegroups.com
 --
--- Importing external images into diagrams.
--- Usage: To create a diagram from an embedded image with width 1 and height
---   set according to the aspect ratio: 'image img # scaleUToX 1`
---   where 'img' is a 'DImage Embedded'
+-- Importing external images into diagrams.  Usage example: To create
+-- a diagram from an embedded image with width 1 and height set
+-- according to the aspect ratio, use @image img # scaleUToX 1@, where
+-- @img@ is a value of type @DImage n e@, created with a function like
+-- 'loadImageEmb', 'loadImageExt', or 'raster'.
 -----------------------------------------------------------------------------
 
 module Diagrams.TwoD.Image
     (
       DImage(..), ImageData(..)
-    , Embedded, External
+    , Embedded, External, Native
     , image
+    , embeddedImage
     , loadImageEmb
+    , loadImageEmbBS
     , loadImageExt
     , uncheckedImageRef
     , raster
     , rasterDia
     ) where
 
-
 import           Codec.Picture
-import           Codec.Picture.Types  (dynamicMap)
 
-import           Data.Typeable        (Typeable)
 import           Data.Colour          (AlphaColour)
+import           Data.Kind            (Type)
+import           Data.Semigroup
+import           Data.Typeable        (Typeable)
 
 import           Diagrams.Core
 
 import           Diagrams.Attributes  (colorToSRGBA)
 import           Diagrams.Path        (Path)
+import           Diagrams.Query
 import           Diagrams.TwoD.Path   (isInsideEvenOdd)
 import           Diagrams.TwoD.Shapes (rect)
-import           Diagrams.TwoD.Types  (R2, T2)
+import           Diagrams.TwoD.Types
 
-import           Data.AffineSpace     ((.-.))
-import           Data.Semigroup
+import           Data.ByteString
 
+import           Linear.Affine
+
 data Embedded deriving Typeable
 data External deriving Typeable
+data Native (t :: Type) deriving Typeable
 
 -- | 'ImageData' is either a JuicyPixels @DynamicImage@ tagged as 'Embedded' or
---   a reference tagged as 'External'.
-data ImageData :: * -> * where
+--   a reference tagged as 'External'. Additionally 'Native' is provided for
+--   external libraries to hook into.
+data ImageData :: Type -> Type where
   ImageRaster :: DynamicImage -> ImageData Embedded
-  ImageRef :: FilePath -> ImageData External
+  ImageRef    :: FilePath -> ImageData External
+  ImageNative :: t -> ImageData (Native t)
 
 -------------------------------------------------------------------------------
 -- | An image primitive, the two ints are width followed by height.
 --   Will typically be created by @loadImageEmb@ or @loadImageExt@ which,
---   will handle setting the width and heigh to the actual width and height
+--   will handle setting the width and height to the actual width and height
 --   of the image.
-data DImage :: * -> * where
-  DImage :: ImageData t -> Int -> Int -> T2 -> DImage t
+data DImage :: Type -> Type -> Type where
+  DImage :: ImageData t -> Int -> Int -> Transformation V2 n -> DImage n t
   deriving Typeable
 
-type instance V (DImage a) = R2
+type instance V (DImage n a) = V2
+type instance N (DImage n a) = n
 
-instance Transformable (DImage a) where
+instance RealFloat n => HasQuery (DImage n a) Any where
+  getQuery (DImage _ w h _) = -- transform t $
+    Query $ \p -> Any (isInsideEvenOdd r p)
+    where
+    r = rectPath (fromIntegral w) (fromIntegral h)
+
+instance Fractional n => Transformable (DImage n a) where
   transform t1 (DImage iD w h t2) = DImage iD w h (t1 <> t2)
 
-instance HasOrigin (DImage a) where
+instance Fractional n => HasOrigin (DImage n a) where
   moveOriginTo p = translate (origin .-. p)
 
 -- | Make a 'DImage' into a 'Diagram'.
-image :: (Typeable a, Renderable (DImage a) b) => DImage a -> Diagram b R2
-image img = mkQD (Prim (img)) (getEnvelope r) (getTrace r) mempty
-                  (Query $ \p -> Any (isInsideEvenOdd p r))
+image :: (TypeableFloat n, Typeable a, Renderable (DImage n a) b)
+      => DImage n a -> QDiagram b V2 n Any
+image img
+  = mkQD (Prim img)
+         (getEnvelope r)
+         (getTrace r)
+         mempty
+         (Query $ \p -> Any (isInsideEvenOdd r p))
   where
-    r :: Path R2
-    r = rect (fromIntegral w) (fromIntegral h)
+    r = rectPath (fromIntegral w) (fromIntegral h)
+    -- should we use the transform here?
     DImage _ w h _ = img
 
--- | Use JuicyPixels to read an image in any format and wrap it in a 'DImage'.
+rectPath :: RealFloat n => n -> n -> Path V2 n
+rectPath = rect
+
+-- | Read a JuicyPixels @DynamicImage@ and wrap it in a 'DImage'.
 --   The width and height of the image are set to their actual values.
-loadImageEmb :: FilePath -> IO (Either String (DImage Embedded))
-loadImageEmb path = do
-    dImg <- readImage path
-    return $ case dImg of
-      Left msg  -> Left msg
-      Right img -> Right (DImage (ImageRaster img) w h mempty)
-        where
-          w = dynamicMap imageWidth img
-          h = dynamicMap imageHeight img
+embeddedImage :: Num n => DynamicImage -> DImage n Embedded
+embeddedImage img = DImage (ImageRaster img) w h mempty
+  where
+    w = dynamicMap imageWidth img
+    h = dynamicMap imageHeight img
 
+-- | Use JuicyPixels to read a file in any format and wrap it in a 'DImage'.
+--   The width and height of the image are set to their actual values.
+loadImageEmb :: Num n => FilePath -> IO (Either String (DImage n Embedded))
+loadImageEmb path = fmap embeddedImage `fmap` readImage path
+
+-- | A pure variant of 'loadImageEmb'
+loadImageEmbBS :: Num n => ByteString -> Either String (DImage n Embedded)
+loadImageEmbBS bs = embeddedImage `fmap` decodeImage bs
+
 -- | Check that a file exists, and use JuicyPixels to figure out
 --   the right size, but save a reference to the image instead
 --   of the raster data
-loadImageExt :: FilePath -> IO (Either String (DImage External))
+loadImageExt :: Num n => FilePath -> IO (Either String (DImage n External))
 loadImageExt path = do
   dImg <- readImage path
   return $ case dImg of
@@ -110,16 +141,16 @@
 -- | Make an "unchecked" image reference; have to specify a
 --   width and height. Unless the aspect ratio of the external
 --   image is the w :: h, then the image will be distorted.
-uncheckedImageRef :: FilePath -> Int -> Int -> DImage External
+uncheckedImageRef :: Num n => FilePath -> Int -> Int -> DImage n External
 uncheckedImageRef path w h = DImage (ImageRef path) w h mempty
 
 -- | Crate a diagram from raw raster data.
-rasterDia :: Renderable (DImage Embedded) b
-          => (Int -> Int -> AlphaColour Double) -> Int -> Int -> Diagram b R2
+rasterDia :: (TypeableFloat n, Renderable (DImage n Embedded) b)
+          => (Int -> Int -> AlphaColour Double) -> Int -> Int -> QDiagram b V2 n Any
 rasterDia f w h = image $ raster f w h
 
 -- | Create an image "from scratch" by specifying the pixel data
-raster :: (Int -> Int -> AlphaColour Double) -> Int -> Int -> DImage Embedded
+raster :: Num n => (Int -> Int -> AlphaColour Double) -> Int -> Int -> DImage n Embedded
 raster f w h = DImage (ImageRaster (ImageRGBA8 img)) w h mempty
   where
     img = generateImage g w h
@@ -132,5 +163,6 @@
     (r', g', b', a') = colorToSRGBA c
     int x = round (255 * x)
 
-instance Renderable (DImage a) NullBackend where
+instance Fractional n => (Renderable (DImage n a) NullBackend) where
   render _ _ = mempty
+
diff --git a/src/Diagrams/TwoD/Model.hs b/src/Diagrams/TwoD/Model.hs
--- a/src/Diagrams/TwoD/Model.hs
+++ b/src/Diagrams/TwoD/Model.hs
@@ -1,6 +1,8 @@
+{-# LANGUAGE ConstraintKinds #-}
 {-# LANGUAGE FlexibleContexts      #-}
 {-# LANGUAGE MultiParamTypeClasses #-}
 {-# LANGUAGE TemplateHaskell       #-}
+{-# LANGUAGE TypeFamilies          #-}
 -----------------------------------------------------------------------------
 -- |
 -- Module      :  Diagrams.TwoD.Model
@@ -9,7 +11,7 @@
 -- Maintainer  :  diagrams-discuss@googlegroups.com
 --
 -- Tools for visualizing diagrams' internal model: local origins,
--- envelopes, /etc./
+-- envelopes, traces, /etc./
 --
 -----------------------------------------------------------------------------
 module Diagrams.TwoD.Model
@@ -17,72 +19,155 @@
          showOrigin
        , showOrigin'
        , OriginOpts(..), oColor, oScale, oMinSize
+
+         -- * Showing an approximation of the envelope
+       , showEnvelope
+       , showEnvelope'
+       , EnvelopeOpts(..), eColor, eLineWidth, ePoints
+
+         -- * Showing an approximation of the trace
+       , showTrace
+       , showTrace'
+       , TraceOpts(..), tColor, tScale, tMinSize, tPoints
+
+         -- * Showing labels of all named subdiagrams
        , showLabels
        ) where
 
-import           Control.Lens          (makeLenses, (^.))
+import           Control.Arrow            (second)
+import           Control.Lens             (makeLenses, (^.))
+import           Data.Colour              (Colour)
+import           Data.Colour.Names
+import           Data.Default
+import           Data.List                (intercalate)
+import qualified Data.Map                 as M
+import           Data.Maybe               (catMaybes)
+import           Data.Semigroup
 
+import           Diagrams.Attributes
+import           Diagrams.Combinators     (atPoints)
 import           Diagrams.Core
-import           Diagrams.TwoD.Attributes
+import           Diagrams.Core.Names
+import           Diagrams.CubicSpline
 import           Diagrams.Path
+import           Diagrams.TwoD.Attributes
 import           Diagrams.TwoD.Ellipse
 import           Diagrams.TwoD.Path
-import           Diagrams.TwoD.Size    (size2D)
 import           Diagrams.TwoD.Text
+import           Diagrams.TwoD.Transform  (rotateBy)
 import           Diagrams.TwoD.Types
+import           Diagrams.TwoD.Vector     (unitX)
 import           Diagrams.Util
 
-import           Control.Arrow         (second)
-import           Data.AffineSpace      ((.-.))
-import           Data.Default.Class
-import           Data.Semigroup
-import           Data.VectorSpace      ((^*))
-
-import qualified Data.Map              as M
-
-import           Data.Colour           (Colour)
-import           Data.Colour.Names
+import           Linear.Affine
+import           Linear.Vector
 
 ------------------------------------------------------------
 -- Marking the origin
 ------------------------------------------------------------
 
-data OriginOpts = OriginOpts { _oColor   :: Colour Double
-                             , _oScale   :: Double
-                             , _oMinSize :: Double
-                             }
+data OriginOpts n = OriginOpts
+  { _oColor   :: Colour Double
+  , _oScale   :: n
+  , _oMinSize :: n
+  }
 
 makeLenses ''OriginOpts
 
-instance Default OriginOpts where
+instance Fractional n => Default (OriginOpts n) where
   def = OriginOpts red (1/50) 0.001
 
+data EnvelopeOpts n = EnvelopeOpts
+  { _eColor     :: Colour Double
+  , _eLineWidth :: Measure n
+  , _ePoints    :: Int
+  }
+
+makeLenses ''EnvelopeOpts
+
+instance OrderedField n => Default (EnvelopeOpts n) where
+  def = EnvelopeOpts red medium 32
+
+data TraceOpts n = TraceOpts
+  { _tColor   :: Colour Double
+  , _tScale   :: n
+  , _tMinSize :: n
+  , _tPoints  :: Int
+  }
+
+makeLenses ''TraceOpts
+
+instance Floating n => Default (TraceOpts n) where
+  def = TraceOpts red (1/100) 0.001 64
+
 -- | Mark the origin of a diagram by placing a red dot 1/50th its size.
-showOrigin :: (Renderable (Path R2) b, Backend b R2, Monoid' m)
-           => QDiagram b R2 m -> QDiagram b R2 m
+showOrigin :: (TypeableFloat n, Renderable (Path V2 n) b, Monoid' m)
+           => QDiagram b V2 n m -> QDiagram b V2 n m
 showOrigin = showOrigin' def
 
 -- | Mark the origin of a diagram, with control over colour and scale
 -- of marker dot.
-showOrigin' :: (Renderable (Path R2) b, Backend b R2, Monoid' m)
-           => OriginOpts -> QDiagram b R2 m -> QDiagram b R2 m
+showOrigin' :: (TypeableFloat n, Renderable (Path V2 n) b, Monoid' m)
+           => OriginOpts n -> QDiagram b V2 n m -> QDiagram b V2 n m
 showOrigin' oo d = o <> d
-  where o     = stroke (circle sz)
-                # fc (oo^.oColor)
-                # lineWidth (Output 0)
-                # fmap (const mempty)
-        (w,h) = size2D d ^* oo^.oScale
-        sz = maximum [w, h, oo^.oMinSize]
+  where o      = strokeP (circle sz)
+                   # fc (oo^.oColor)
+                   # lw none
+                   # fmap (const mempty)
+        V2 w h = oo^.oScale *^ size d
+        sz     = maximum [w, h, oo^.oMinSize]
 
+-- | Mark the envelope with an approximating cubic spline with control 
+--   over the color, line width and number of points.
+showEnvelope' :: (Enum n, TypeableFloat n, Renderable (Path V2 n) b) 
+              => EnvelopeOpts n -> QDiagram b V2 n Any -> QDiagram b V2 n Any
+showEnvelope' opts d = cubicSpline True pts # lc (opts^.eColor)
+                                            # lw w <> d
+  where
+    pts = catMaybes [envelopePMay v d | v <- map (`rotateBy` unitX) [0,inc..top]]
+    w   = opts ^. eLineWidth
+    inc = 1 / fromIntegral (opts^.ePoints)
+    top = 1 - inc
+
+
+-- | Mark the envelope with an approximating cubic spline
+--   using 32 points, medium line width and red line color.
+showEnvelope :: (Enum n, TypeableFloat n, Renderable (Path V2 n) b)
+             => QDiagram b V2 n Any -> QDiagram b V2 n Any
+showEnvelope = showEnvelope' def
+
+-- | Mark the trace of a diagram, with control over colour and scale
+-- of marker dot and the number of points on the trace.
+showTrace' :: (Enum n, TypeableFloat n, Renderable (Path V2 n) b) 
+          => TraceOpts n -> QDiagram b V2 n Any -> QDiagram b V2 n Any
+showTrace' opts d =  atPoints ps (repeat pt) <> d
+  where
+    ps = concatMap p ts
+    ts = zip rs vs
+    p (r, v) = [origin .+^ (s *^ v) | s <- r]
+    vs = map (`rotateBy` unitX) [0, inc..top]
+    rs = [getSortedList $ (appTrace . getTrace) d origin v | v <- vs]
+    pt = circle sz # fc (opts^.tColor) # lw none
+    V2 w h = opts^.tScale *^ size d
+    sz     = maximum [w, h, opts^.tMinSize]
+    inc = 1 / fromIntegral (opts^.tPoints)
+    top = 1 - inc
+
+-- | Mark the trace of a diagram by placing 64 red dots 1/100th its size
+--   along the trace.
+showTrace :: (Enum n, TypeableFloat n, Renderable (Path V2 n) b) 
+          => QDiagram b V2 n Any -> QDiagram b V2 n Any
+showTrace = showTrace' def
+
 ------------------------------------------------------------
 -- Labeling named points
 ------------------------------------------------------------
 
-showLabels :: (Renderable Text b, Backend b R2, Semigroup m)
-           => QDiagram b R2 m -> QDiagram b R2 Any
+showLabels :: (TypeableFloat n, Renderable (Text n) b, Semigroup m)
+           => QDiagram b V2 n m -> QDiagram b V2 n Any
 showLabels d =
              ( mconcat
-             . map (\(n,p) -> text (show n) # translate (p .-. origin))
+             . map (\(n,p) -> text (simpleName n) # translate (p .-. origin))
              . concatMap (\(n,ps) -> zip (repeat n) ps)
              . (map . second . map) location
              . M.assocs
@@ -91,3 +176,5 @@
              fmap (const (Any False)) d
   where
     SubMap m = d^.subMap
+    simpleName (Name ns) = intercalate " .> " $ map simpleAName ns
+    simpleAName (AName n) = show n
diff --git a/src/Diagrams/TwoD/Offset.hs b/src/Diagrams/TwoD/Offset.hs
--- a/src/Diagrams/TwoD/Offset.hs
+++ b/src/Diagrams/TwoD/Offset.hs
@@ -1,8 +1,16 @@
-{-# LANGUAGE GADTs            #-}
-{-# LANGUAGE TemplateHaskell  #-}
-{-# LANGUAGE TypeFamilies     #-}
-{-# LANGUAGE FlexibleContexts #-}
-{-# LANGUAGE ViewPatterns     #-}
+{-# LANGUAGE ConstraintKinds      #-}
+{-# LANGUAGE FlexibleContexts     #-}
+{-# LANGUAGE GADTs                #-}
+{-# LANGUAGE StandaloneDeriving   #-}
+{-# LANGUAGE TemplateHaskell      #-}
+{-# LANGUAGE TypeFamilies         #-}
+{-# LANGUAGE TypeOperators        #-}
+{-# LANGUAGE UndecidableInstances #-}
+{-# LANGUAGE ViewPatterns         #-}
+
+{-# OPTIONS_GHC -fno-warn-unused-imports #-}
+  -- for Data.Semigroup
+
 -----------------------------------------------------------------------------
 -- |
 -- Module      :  Diagrams.TwoD.Offset
@@ -10,15 +18,15 @@
 -- License     :  BSD-style (see LICENSE)
 -- Maintainer  :  diagrams-discuss@googlegroups.com
 --
--- Compute offsets to segments in two dimensions.  More details can be 
--- found in the manual at 
--- <http://projects.haskell.org/diagrams/doc/manual.html#offsets-of-segments-trails-and-paths>.
+-- Compute offsets to segments in two dimensions.  More details can be
+-- found in the manual at
+-- <https://diagrams.github.io/doc/manual.html#offsets-of-segments-trails-and-paths>.
 --
 -----------------------------------------------------------------------------
 module Diagrams.TwoD.Offset
-    ( 
+    (
       -- * Offsets
-      
+
       offsetSegment
 
     , OffsetOpts(..), offsetJoin, offsetMiterLimit, offsetEpsilon
@@ -37,40 +45,44 @@
 
     ) where
 
-import Control.Applicative
-import Control.Lens            hiding (at)
+import           Control.Applicative
+import           Control.Lens            hiding (at)
+import           Prelude
 
-import Data.AffineSpace
-import Data.Maybe              (catMaybes)
-import Data.Monoid
-import Data.Monoid.Inf
-import Data.VectorSpace
+import           Data.Maybe              (catMaybes)
+import           Data.Monoid
+import           Data.Monoid.Inf
 
-import Data.Default.Class
+import           Data.Default
 
-import Diagrams.Core
+import           Diagrams.Core
 
-import Diagrams.Attributes
-import Diagrams.Located
-import Diagrams.Parametric
-import Diagrams.Path
-import Diagrams.Segment
-import Diagrams.Trail           hiding (offset, isLoop)
-import Diagrams.TrailLike
-import Diagrams.TwoD.Arc
-import Diagrams.TwoD.Curvature
-import Diagrams.TwoD.Path       ()
-import Diagrams.TwoD.Types
-import Diagrams.TwoD.Vector     (perp, direction)
+import           Diagrams.Attributes
+import           Diagrams.Direction
+import           Diagrams.Located
+import           Diagrams.Parametric
+import           Diagrams.Path
+import           Diagrams.Segment
+import           Diagrams.Trail          hiding (isLoop, offset)
+import           Diagrams.TrailLike
+import           Diagrams.TwoD.Arc
+import           Diagrams.TwoD.Curvature
+import           Diagrams.TwoD.Path      ()
+import           Diagrams.TwoD.Types
+import           Diagrams.TwoD.Vector    hiding (e)
 
-unitPerp :: R2 -> R2
-unitPerp = normalized . perp
+import           Linear.Affine
+import           Linear.Metric
+import           Linear.Vector
 
-perpAtParam :: Segment Closed R2 -> Double -> R2
-perpAtParam   (Linear (OffsetClosed a))  _ = -unitPerp a
-perpAtParam s@(Cubic _ _ _)              t = -unitPerp a
+unitPerp :: OrderedField n => V2 n -> V2 n
+unitPerp = signorm . perp
+
+perpAtParam :: OrderedField n => Segment Closed V2 n -> n -> V2 n
+perpAtParam (Linear (OffsetClosed a)) _ = negated $ unitPerp a
+perpAtParam cubic t                     = negated $ unitPerp a
   where
-    (Cubic a _ _) = snd $ splitAtParam s t
+    (Cubic a _ _) = snd $ splitAtParam cubic t
 
 -- | Compute the offset of a segment.  Given a segment compute the offset
 --   curve that is a fixed distance from the original curve.  For linear
@@ -101,59 +113,63 @@
 
 -- | Options for specifying line join and segment epsilon for an offset
 --   involving multiple segments.
-data OffsetOpts = OffsetOpts
-    { _offsetJoin :: LineJoin
-    , _offsetMiterLimit :: Double
-    , _offsetEpsilon :: Double
-    } deriving (Eq, Show)
+data OffsetOpts d = OffsetOpts
+    { _offsetJoin       :: LineJoin
+    , _offsetMiterLimit :: d
+    , _offsetEpsilon    :: d
+    }
 
+deriving instance Eq d => Eq (OffsetOpts d)
+deriving instance Show d => Show (OffsetOpts d)
+
 makeLensesWith (lensRules & generateSignatures .~ False) ''OffsetOpts
 
 -- | Specifies the style of join for between adjacent offset segments.
-offsetJoin :: Lens' OffsetOpts LineJoin
+offsetJoin :: Lens' (OffsetOpts d) LineJoin
 
 -- | Specifies the miter limit for the join.
-offsetMiterLimit :: Lens' OffsetOpts Double
+offsetMiterLimit :: Lens' (OffsetOpts d) d
 
 -- | Epsilon perimeter for 'offsetSegment'.
-offsetEpsilon :: Lens' OffsetOpts Double
+offsetEpsilon :: Lens' (OffsetOpts d) d
 
 -- | The default offset options use the default 'LineJoin' ('LineJoinMiter'), a
 --   miter limit of 10, and epsilon factor of 0.01.
-instance Default OffsetOpts where
+instance Fractional d => Default (OffsetOpts d) where
     def = OffsetOpts def 10 0.01
 
 -- | Options for specifying how a 'Trail' should be expanded.
-data ExpandOpts = ExpandOpts
-    { _expandJoin :: LineJoin
-    , _expandMiterLimit :: Double
-    , _expandCap  :: LineCap
-    , _expandEpsilon :: Double
+data ExpandOpts d = ExpandOpts
+    { _expandJoin       :: LineJoin
+    , _expandMiterLimit :: d
+    , _expandCap        :: LineCap
+    , _expandEpsilon    :: d
     } deriving (Eq, Show)
 
 makeLensesWith (lensRules & generateSignatures .~ False) ''ExpandOpts
 
 -- | Specifies the style of join for between adjacent offset segments.
-expandJoin :: Lens' ExpandOpts LineJoin
+expandJoin :: Lens' (ExpandOpts d) LineJoin
 
 -- | Specifies the miter limit for the join.
-expandMiterLimit :: Lens' ExpandOpts Double
+expandMiterLimit :: Lens' (ExpandOpts d) d
 
 -- | Specifies how the ends are handled.
-expandCap :: Lens' ExpandOpts LineCap
+expandCap :: Lens' (ExpandOpts d) LineCap
 
 -- | Epsilon perimeter for 'offsetSegment'.
-expandEpsilon :: Lens' ExpandOpts Double
+expandEpsilon :: Lens' (ExpandOpts d) d
 
 
 
 -- | The default 'ExpandOpts' is the default 'LineJoin' ('LineJoinMiter'),
 --   miter limit of 10, default 'LineCap' ('LineCapButt'), and epsilon factor
 --   of 0.01.
-instance Default ExpandOpts where
+instance (Fractional d) => Default (ExpandOpts d) where
     def = ExpandOpts def 10 def 0.01
 
-offsetSegment :: Double     -- ^ Epsilon factor that when multiplied to the
+offsetSegment :: RealFloat n
+              => n   -- ^ Epsilon factor that when multiplied to the
                             --   absolute value of the radius gives a
                             --   value that represents the maximum
                             --   allowed deviation from the true offset.  In
@@ -161,20 +177,20 @@
                             --   should be bounded by arcs that are plus or
                             --   minus epsilon factor from the radius of curvature of
                             --   the offset.
-              -> Double     -- ^ Offset from the original segment, positive is
+              -> n   -- ^ Offset from the original segment, positive is
                             --   on the right of the curve, negative is on the
                             --   left.
-              -> Segment Closed R2  -- ^ Original segment
-              -> Located (Trail R2) -- ^ Resulting located (at the offset) trail.
+              -> Segment Closed V2 n  -- ^ Original segment
+              -> Located (Trail V2 n) -- ^ Resulting located (at the offset) trail.
 offsetSegment _       r s@(Linear (OffsetClosed a))    = trailFromSegments [s] `at` origin .+^ va
-  where va = -r *^ unitPerp a
+  where va = (-r) *^ unitPerp a
 
 offsetSegment epsilon r s@(Cubic a b (OffsetClosed c)) = t `at` origin .+^ va
   where
     t = trailFromSegments (go (radiusOfCurvature s 0.5))
     -- Perpendiculars to handles.
-    va = -r *^ unitPerp a
-    vc = -r *^ unitPerp (c ^-^ b)
+    va = (-r) *^ unitPerp a
+    vc = (-r) *^ unitPerp (c ^-^ b)
     -- Split segments.
     ss = (\(x,y) -> [x,y]) $ splitAtParam s 0.5
     subdivided = concatMap (trailSegments . unLoc . offsetSegment epsilon r) ss
@@ -198,7 +214,7 @@
               Infinity  -> 1          -- Do the right thing.
               Finite sr -> 1 + r / sr
 
-        close = and [epsilon * abs r > (magnitude (p o ^+^ va ^-^ p s ^-^ pp s))
+        close = and [epsilon * abs r > norm (p o ^+^ va ^-^ p s ^-^ pp s)
                     | t' <- [0.25, 0.5, 0.75]
                     , let p = (`atParam` t')
                     , let pp = (r *^) . (`perpAtParam` t')
@@ -207,16 +223,16 @@
 
 -- > import Diagrams.TwoD.Offset
 -- >
--- > showExample :: Segment Closed R2 -> Diagram SVG R2
+-- > showExample :: Segment Closed V2 Double -> Diagram SVG
 -- > showExample s = pad 1.1 . centerXY $ d # lc blue # lw thick <> d' # lw thick
 -- >   where
--- >       d  = stroke . fromSegments $ [s]
--- >       d' = mconcat . zipWith lc colors . map stroke . explodeTrail
+-- >       d  = strokeP . fromSegments $ [s]
+-- >       d' = mconcat . zipWith lc colors . map strokeP . explodeTrail
 -- >          $ offsetSegment 0.1 (-1) s
 -- >
 -- >       colors = cycle [green, red]
 -- >
--- > cubicOffsetExample :: Diagram SVG R2
+-- > cubicOffsetExample :: Diagram SVG
 -- > cubicOffsetExample = hcat . map showExample $
 -- >         [ bezier3 (10 ^&  0) (  5  ^& 18) (10 ^& 20)
 -- >         , bezier3 ( 0 ^& 20) ( 10  ^& 10) ( 5 ^& 10)
@@ -229,16 +245,16 @@
 -- collapse the Located into the result.  This assumes that Located has the
 -- meaning of merely taking something that cannot be translated and lifting
 -- it into a space with translation.
-bindLoc :: (Transformable b, V a ~ V b) => (a -> b) -> Located a -> b
+bindLoc :: (Transformable b, V a ~ V b, N a ~ N b, V a ~ V2, N a ~ n, Num n) => (a -> b) -> Located a -> b
 bindLoc f = join' . mapLoc f
   where
     join' (viewLoc -> (p,a)) = translate (p .-. origin) a
 
--- While we build offsets and expansions we will use the [Located (Segment Closed R2)]
--- and [Located (Trail R2)] intermediate representations.
-locatedTrailSegments :: (InnerSpace v, OrderedField (Scalar v))
-                     => Located (Trail v) -> [Located (Segment Closed v)]
-locatedTrailSegments t = zipWith at (trailSegments (unLoc t)) (trailVertices t)
+-- While we build offsets and expansions we will use the [Located (Segment Closed v)]
+-- and [Located (Trail V2 n)] intermediate representations.
+locatedTrailSegments :: OrderedField n
+                     => Located (Trail V2 n) -> [Located (Segment Closed V2 n)]
+locatedTrailSegments t = zipWith at (trailSegments (unLoc t)) (trailPoints t)
 
 -- | Offset a 'Trail' with options and by a given radius.  This generates a new
 --   trail that is always radius 'r' away from the given 'Trail' (depending on
@@ -258,46 +274,47 @@
 --
 --   <<diagrams/src_Diagrams_TwoD_Offset_offsetTrailOuterExample.svg#diagram=offsetTrailOuterExample&width=300>>
 --
-offsetTrail' :: OffsetOpts
-             -> Double  -- ^ Radius of offset.  A negative value gives an offset on
-                        --   the left for a line and on the inside for a counter-clockwise
-                        --   loop.
-             -> Located (Trail R2)
-             -> Located (Trail R2)
+offsetTrail' :: RealFloat n
+             => OffsetOpts n
+             -> n -- ^ Radius of offset.  A negative value gives an offset on
+                         --   the left for a line and on the inside for a counter-clockwise
+                         --   loop.
+             -> Located (Trail V2 n)
+             -> Located (Trail V2 n)
 offsetTrail' opts r t = joinSegments eps j isLoop (opts^.offsetMiterLimit) r ends . offset $ t
     where
       eps = opts^.offsetEpsilon
       offset = map (bindLoc (offsetSegment eps r)) . locatedTrailSegments
-      ends | isLoop    = (\(a:as) -> as ++ [a]) . trailVertices $ t
-           | otherwise = tail . trailVertices $ t
+      ends | isLoop    = (\(a:as) -> as ++ [a]) . trailPoints $ t
+           | otherwise = tail . trailPoints $ t
       j = fromLineJoin (opts^.offsetJoin)
 
       isLoop = withTrail (const False) (const True) (unLoc t)
 
 -- | Offset a 'Trail' with the default options and a given radius.  See 'offsetTrail''.
-offsetTrail :: Double -> Located (Trail R2) -> Located (Trail R2)
+offsetTrail :: RealFloat n => n -> Located (Trail V2 n) -> Located (Trail V2 n)
 offsetTrail = offsetTrail' def
 
 -- | Offset a 'Path' by applying 'offsetTrail'' to each trail in the path.
-offsetPath' :: OffsetOpts -> Double -> Path R2 -> Path R2
+offsetPath' :: RealFloat n => OffsetOpts n -> n -> Path V2 n -> Path V2 n
 offsetPath' opts r = mconcat
                    . map (bindLoc (trailLike . offsetTrail' opts r) . (`at` origin))
                    . op Path
 
 -- | Offset a 'Path' with the default options and given radius.  See 'offsetPath''.
-offsetPath :: Double -> Path R2 -> Path R2
+offsetPath :: RealFloat n => n -> Path V2 n -> Path V2 n
 offsetPath = offsetPath' def
 
 -- TODO: Include arrowheads on examples to indicate direction so the "left" and
 -- "right" make sense.
 --
 -- > import Diagrams.TwoD.Offset
--- > import Data.Default.Class
+-- > import Data.Default
 -- >
--- > corner :: Located (Trail R2)
+-- > corner :: (OrderedField n) => Located (Trail V2 n)
 -- > corner = fromVertices (map p2 [(0, 0), (10, 0), (5, 6)]) `at` origin
 -- >
--- > offsetTrailExample :: Diagram SVG R2
+-- > offsetTrailExample :: Diagram SVG
 -- > offsetTrailExample = pad 1.1 . centerXY . lwO 3 . hcat' (def & sep .~ 1 )
 -- >                    . map (uncurry showStyle)
 -- >                    $ [ (LineJoinMiter, "LineJoinMiter")
@@ -309,7 +326,7 @@
 -- >               <> trailLike (offsetTrail' (def & offsetJoin .~ j) 2 corner) # lc green)
 -- >            === (strutY 3 <> text s # font "Helvetica" # bold)
 -- >
--- > offsetTrailLeftExample :: Diagram SVG R2
+-- > offsetTrailLeftExample :: Diagram SVG
 -- > offsetTrailLeftExample = pad 1.1 . centerXY . lwO 3
 -- >                        $ (trailLike c # lc blue)
 -- >                        <> (lc green . trailLike
@@ -317,7 +334,7 @@
 -- >   where
 -- >     c = reflectY corner
 -- >
--- > offsetTrailOuterExample :: Diagram SVG R2
+-- > offsetTrailOuterExample :: Diagram SVG
 -- > offsetTrailOuterExample = pad 1.1 . centerXY . lwO 3
 -- >                         $ (trailLike c # lc blue)
 -- >                         <> (lc green . trailLike
@@ -325,7 +342,7 @@
 -- >   where
 -- >     c = hexagon 5
 
-withTrailL :: (Located (Trail' Line v) -> r) -> (Located (Trail' Loop v) -> r) -> Located (Trail v) -> r
+withTrailL :: (Located (Trail' Line V2 n) -> r) -> (Located (Trail' Loop V2 n) -> r) -> Located (Trail V2 n) -> r
 withTrailL f g l = withTrail (f . (`at` p)) (g . (`at` p)) (unLoc l)
   where
     p = loc l
@@ -343,57 +360,58 @@
 --
 --   <<diagrams/src_Diagrams_TwoD_Offset_expandLoopExample.svg#diagram=expandLoopExample&width=300>>
 --
-expandTrail' :: ExpandOpts
-             -> Double  -- ^ Radius of offset.  Only non-negative values allowed.
+expandTrail' :: (OrderedField n, RealFloat n, RealFrac n)
+             => ExpandOpts n
+             -> n  -- ^ Radius of offset.  Only non-negative values allowed.
                         --   For a line this gives a loop of the offset.  For a
                         --   loop this gives two loops, the outer counter-clockwise
                         --   and the inner clockwise.
-             -> Located (Trail R2)
-             -> Path R2
+             -> Located (Trail V2 n)
+             -> Path V2 n
 expandTrail' o r t
   | r < 0     = error "expandTrail' with negative radius"
                 -- TODO: consider just reversing the path instead of this error.
   | otherwise = withTrailL (pathFromLocTrail . expandLine o r) (expandLoop o r) t
 
-expandLine :: ExpandOpts -> Double -> Located (Trail' Line R2) -> Located (Trail R2)
+expandLine :: RealFloat n => ExpandOpts n -> n -> Located (Trail' Line V2 n) -> Located (Trail V2 n)
 expandLine opts r (mapLoc wrapLine -> t) = caps cap r s e (f r) (f $ -r)
     where
       eps = opts^.expandEpsilon
       offset r' = map (bindLoc (offsetSegment eps r')) . locatedTrailSegments
-      f r' = joinSegments eps (fromLineJoin (opts^.expandJoin)) False (opts^.expandMiterLimit) r' ends 
+      f r' = joinSegments eps (fromLineJoin (opts^.expandJoin)) False (opts^.expandMiterLimit) r' ends
            . offset r' $ t
-      ends = tail . trailVertices $ t
+      ends = tail . trailPoints $ t
       s = atStart t
       e = atEnd t
       cap = fromLineCap (opts^.expandCap)
 
-expandLoop :: ExpandOpts -> Double -> Located (Trail' Loop R2) -> Path R2
-expandLoop opts r (mapLoc wrapLoop -> t) = (trailLike $ f r) <> (trailLike . reverseDomain . f $ -r)
+expandLoop :: RealFloat n => ExpandOpts n -> n -> Located (Trail' Loop V2 n) -> Path V2 n
+expandLoop opts r (mapLoc wrapLoop -> t) = trailLike (f r) <> (trailLike . reverseDomain . f $ -r)
     where
       eps = opts^.expandEpsilon
       offset r' = map (bindLoc (offsetSegment eps r')) . locatedTrailSegments
-      f r' = joinSegments eps (fromLineJoin (opts^.expandJoin)) True (opts^.expandMiterLimit) r' ends 
+      f r' = joinSegments eps (fromLineJoin (opts^.expandJoin)) True (opts^.expandMiterLimit) r' ends
            . offset r' $ t
-      ends = (\(a:as) -> as ++ [a]) . trailVertices $ t
+      ends = (\(a:as) -> as ++ [a]) . trailPoints $ t
 
 -- | Expand a 'Trail' with the given radius and default options.  See 'expandTrail''.
-expandTrail :: Double -> Located (Trail R2) -> Path R2
+expandTrail :: RealFloat n => n -> Located (Trail V2 n) -> Path V2 n
 expandTrail = expandTrail' def
 
 -- | Expand a 'Path' using 'expandTrail'' on each trail in the path.
-expandPath' :: ExpandOpts -> Double -> Path R2 -> Path R2
+expandPath' :: RealFloat n => ExpandOpts n -> n -> Path V2 n -> Path V2 n
 expandPath' opts r = mconcat
                    . map (bindLoc (expandTrail' opts r) . (`at` origin))
                    . op Path
 
 -- | Expand a 'Path' with the given radius and default options.  See 'expandPath''.
-expandPath :: Double -> Path R2 -> Path R2
+expandPath :: RealFloat n => n -> Path V2 n -> Path V2 n
 expandPath = expandPath' def
 
 -- > import Diagrams.TwoD.Offset
--- > import Data.Default.Class
+-- > import Data.Default
 -- >
--- > expandTrailExample :: Diagram SVG R2
+-- > expandTrailExample :: Diagram SVG
 -- > expandTrailExample = pad 1.1 . centerXY . hcat' (def & sep .~ 1)
 -- >                    . map (uncurry showStyle)
 -- >                    $ [ (LineCapButt,   "LineCapButt")
@@ -409,7 +427,7 @@
 -- >                                      # lw none # fc green)
 -- >               === (strutY 3 <> text s # font "Helvetica" # bold)
 -- >
--- > expandLoopExample :: Diagram SVG R2
+-- > expandLoopExample :: Diagram SVG
 -- > expandLoopExample = pad 1.1 . centerXY $ ((strokeLocT t # lw veryThick # lc white)
 -- >                                        <> (stroke t' # lw none # fc green))
 -- >   where
@@ -426,8 +444,8 @@
 --   caps  takes the radius and the start and end points of the original line and
 --   the offset trails going out and coming back.  The result is a new list of
 --   trails with the caps included.
-caps :: (Double -> P2 -> P2 -> P2 -> Trail R2)
-     -> Double -> P2 -> P2 -> Located (Trail R2) -> Located (Trail R2) -> Located (Trail R2)
+caps :: RealFloat n => (n -> Point V2 n -> Point V2 n -> Point V2 n -> Trail V2 n)
+     -> n -> Point V2 n -> Point V2 n -> Located (Trail V2 n) -> Located (Trail V2 n) -> Located (Trail V2 n)
 caps cap r s e fs bs = mapLoc glueTrail $ mconcat
     [ cap r s (atStart bs) (atStart fs)
     , unLoc fs
@@ -436,37 +454,29 @@
     ] `at` atStart bs
 
 -- | Take a LineCap style and give a function for building the cap from
-fromLineCap :: LineCap -> Double -> P2 -> P2 -> P2 -> Trail R2
+fromLineCap :: RealFloat n => LineCap -> n -> Point V2 n -> Point V2 n -> Point V2 n -> Trail V2 n
 fromLineCap c = case c of
     LineCapButt   -> capCut
     LineCapRound  -> capArc
     LineCapSquare -> capSquare
 
 -- | Builds a cap that directly connects the ends.
-capCut :: Double -> P2 -> P2 -> P2 -> Trail R2
+capCut :: RealFloat n => n -> Point V2 n -> Point V2 n -> Point V2 n -> Trail V2 n
 capCut _r _c a b = fromSegments [straight (b .-. a)]
 
 -- | Builds a cap with a square centered on the end.
-capSquare :: Double -> P2 -> P2 -> P2 -> Trail R2
+capSquare :: RealFloat n => n -> Point V2 n -> Point V2 n -> Point V2 n -> Trail V2 n
 capSquare _r c a b = unLoc $ fromVertices [ a, a .+^ v, b .+^ v, b ]
   where
     v = perp (a .-. c)
 
 -- | Builds an arc to fit with a given radius, center, start, and end points.
 --   A Negative r means a counter-clockwise arc
-capArc :: Double -> P2 -> P2 -> P2 -> Trail R2
+capArc :: RealFloat n => n -> Point V2 n -> Point V2 n -> Point V2 n -> Trail V2 n
 capArc r c a b = trailLike . moveTo c $ fs
   where
-    fs | r < 0     = scale (-r) $ arcVCW (a .-. c) (b .-. c)
-       | otherwise = scale r    $ arcV   (a .-. c) (b .-. c)
-
--- Arc helpers
-arcV :: (TrailLike t, V t ~ R2) => R2 -> R2 -> t
-arcV u v = arc (direction u) (direction v)
-
-arcVCW :: (TrailLike t, V t ~ R2) => R2 -> R2 -> t
-arcVCW u v = arcCW (direction u) (direction v)
-
+    fs | r < 0     = scale (-r) $ arcCW  (dirBetween c a) (dirBetween c b)
+       | otherwise = scale r    $ arcCCW (dirBetween c a) (dirBetween c b)
 
 -- | Join together a list of located trails with the given join style.  The
 --   style is given as a function to compute the join given the local information
@@ -476,14 +486,15 @@
 --   Note: this is not a general purpose join and assumes that we are joining an
 --   offset trail.  For instance, a fixed radius arc will not fit between arbitrary
 --   trails without trimming or extending.
-joinSegments :: Double
-             -> (Double -> Double -> P2 -> Located (Trail R2) -> Located (Trail R2) -> Trail R2)
+joinSegments :: RealFloat n
+             => n
+             -> (n -> n -> Point V2 n -> Located (Trail V2 n) -> Located (Trail V2 n) -> Trail V2 n)
              -> Bool
-             -> Double
-             -> Double
-             -> [Point R2]
-             -> [Located (Trail R2)]
-             -> Located (Trail R2)
+             -> n
+             -> n
+             -> [Point V2 n]
+             -> [Located (Trail V2 n)]
+             -> Located (Trail V2 n)
 joinSegments _ _ _ _ _ _ [] = mempty `at` origin
 joinSegments _ _ _ _ _ [] _ = mempty `at` origin
 joinSegments epsilon j isLoop ml r es ts@(t:_) = t'
@@ -498,7 +509,7 @@
 
 -- | Take a join style and give the join function to be used by joinSegments.
 fromLineJoin
-  :: LineJoin -> Double -> Double -> P2 -> Located (Trail R2) -> Located (Trail R2) -> Trail R2
+  :: RealFloat n => LineJoin -> n -> n -> Point V2 n -> Located (Trail V2 n) -> Located (Trail V2 n) -> Trail V2 n
 fromLineJoin j = case j of
     LineJoinMiter -> joinSegmentIntersect
     LineJoinRound -> joinSegmentArc
@@ -508,7 +519,7 @@
 -- how useful it is graphically, I mostly had it as it was useful for debugging
 {-
 -- | Join with segments going back to the original corner.
-joinSegmentCut :: Double -> Double -> P2 -> Located (Trail R2) -> Located (Trail R2) -> Trail R2
+joinSegmentCut :: (OrderedField n) => n -> n -> Point V2 n -> Located (Trail V2 n) -> Located (Trail V2 n) -> Trail V2 n
 joinSegmentCut _ _ e a b = fromSegments
     [ straight (e .-. atEnd a)
     , straight (atStart b .-. e)
@@ -518,19 +529,21 @@
 -- | Join by directly connecting the end points.  On an inside corner this
 --   creates negative space for even-odd fill.  Here is where we would want to
 --   use an arc or something else in the future.
-joinSegmentClip :: Double -> Double -> P2 -> Located (Trail R2) -> Located (Trail R2) -> Trail R2
+joinSegmentClip :: RealFloat n
+  => n -> n -> Point V2 n -> Located (Trail V2 n) -> Located (Trail V2 n) -> Trail V2 n
 joinSegmentClip _ _ _ a b = fromSegments [straight $ atStart b .-. atEnd a]
 
 -- | Join with a radius arc.  On an inside corner this will loop around the interior
 --   of the offset trail.  With a winding fill this will not be visible.
-joinSegmentArc :: Double -> Double -> P2 -> Located (Trail R2) -> Located (Trail R2) -> Trail R2
+joinSegmentArc :: RealFloat n
+  => n -> n -> Point V2 n -> Located (Trail V2 n) -> Located (Trail V2 n) -> Trail V2 n
 joinSegmentArc _ r e a b = capArc r e (atEnd a) (atStart b)
 
 -- | Join to the intersection of the incoming trails projected tangent to their ends.
 --   If the intersection is beyond the miter limit times the radius, stop at the limit.
 joinSegmentIntersect
-    :: Double -> Double -> P2 -> Located (Trail R2) -> Located (Trail R2) -> Trail R2
-joinSegmentIntersect miterLimit r e a b = 
+    :: RealFloat n => n -> n -> Point V2 n -> Located (Trail V2 n) -> Located (Trail V2 n) -> Trail V2 n
+joinSegmentIntersect miterLimit r e a b =
     if cross < 0.000001
       then clip
       else case traceP pa va t of
@@ -545,10 +558,9 @@
   where
     t = straight (miter vb) `at` pb
     va = unitPerp (pa .-. e)
-    vb = -unitPerp (pb .-. e)
+    vb = negated $ unitPerp (pb .-. e)
     pa = atEnd a
     pb = atStart b
-    miter v = (abs (miterLimit * r)) *^ v
+    miter v = abs (miterLimit * r) *^ v
     clip = joinSegmentClip miterLimit r e a b
     cross = let (xa,ya) = unr2 va; (xb,yb) = unr2 vb in abs (xa * yb - xb * ya)
-
diff --git a/src/Diagrams/TwoD/Path.hs b/src/Diagrams/TwoD/Path.hs
--- a/src/Diagrams/TwoD/Path.hs
+++ b/src/Diagrams/TwoD/Path.hs
@@ -1,17 +1,23 @@
+{-# LANGUAGE ConstraintKinds            #-}
 {-# LANGUAGE DeriveDataTypeable         #-}
 {-# LANGUAGE FlexibleContexts           #-}
 {-# LANGUAGE FlexibleInstances          #-}
 {-# LANGUAGE GeneralizedNewtypeDeriving #-}
 {-# LANGUAGE MultiParamTypeClasses      #-}
 {-# LANGUAGE Rank2Types                 #-}
+{-# LANGUAGE StandaloneDeriving         #-}
 {-# LANGUAGE TemplateHaskell            #-}
 {-# LANGUAGE TypeFamilies               #-}
+{-# LANGUAGE TypeOperators              #-}
+{-# LANGUAGE UndecidableInstances       #-}
 {-# LANGUAGE ViewPatterns               #-}
+
 {-# OPTIONS_GHC -fno-warn-orphans #-}
+
 -----------------------------------------------------------------------------
 -- |
 -- Module      :  Diagrams.TwoD.Path
--- Copyright   :  (c) 2011 diagrams-lib team (see LICENSE)
+-- Copyright   :  (c) 2011-2015 diagrams-lib team (see LICENSE)
 -- License     :  BSD-style (see LICENSE)
 -- Maintainer  :  diagrams-discuss@googlegroups.com
 --
@@ -23,54 +29,66 @@
 -----------------------------------------------------------------------------
 
 module Diagrams.TwoD.Path
-       ( -- * Constructing path-based diagrams
+  ( -- * Constructing path-based diagrams
 
-         stroke, stroke', strokeTrail, strokeT, strokeTrail', strokeT'
-       , strokeLine, strokeLoop
-       , strokeLocTrail, strokeLocT, strokeLocLine, strokeLocLoop
+    stroke, stroke'
+  , strokePath, strokeP, strokePath', strokeP'
+  , strokeTrail, strokeT, strokeTrail', strokeT'
+  , strokeLine, strokeLoop
+  , strokeLocTrail, strokeLocT, strokeLocLine, strokeLocLoop
 
-         -- ** Stroke options
+    -- ** Stroke options
 
-       , FillRule(..)
-       , FillRuleA(..), getFillRule, fillRule
-       , StrokeOpts(..), vertexNames, queryFillRule
+  , FillRule(..)
+  , getFillRule, fillRule, _fillRule
+  , StrokeOpts(..), vertexNames, queryFillRule
 
-         -- ** Inside/outside testing
+    -- ** Inside/outside testing
 
-       , isInsideWinding, isInsideEvenOdd
+  , Crossings (..)
+  , isInsideWinding
+  , isInsideEvenOdd
 
-         -- * Clipping
+    -- * Clipping
 
-       , Clip(..), clipBy, clipTo, clipped
-       ) where
+  , Clip(..), _Clip, _clip
+  , clipBy, clipTo, clipped
 
-import           Control.Applicative   (liftA2)
-import           Control.Lens          (Lens, Lens', generateSignatures,
-                                        lensRules, makeLensesWith, makeWrapped,
-                                        op, (.~), (^.), _Wrapped')
-import qualified Data.Foldable         as F
+    -- * Intersections
+
+  , intersectPoints, intersectPoints'
+  , intersectPointsP, intersectPointsP'
+  , intersectPointsT, intersectPointsT'
+  ) where
+
+import           Control.Applicative       (liftA2)
+import           Control.Lens              hiding (at, transform)
+import qualified Data.Foldable             as F
 import           Data.Semigroup
 import           Data.Typeable
 
-import           Data.AffineSpace
-import           Data.Default.Class
-import           Data.VectorSpace
+import           Data.Default
 
-import           Diagrams.Combinators  (withEnvelope, withTrace)
-import           Diagrams.Coordinates
+import           Diagrams.Angle
+import           Diagrams.Combinators      (withEnvelope, withTrace)
 import           Diagrams.Core
 import           Diagrams.Core.Trace
-import           Diagrams.Located      (Located, mapLoc, unLoc)
+import           Diagrams.Located          (Located, mapLoc, unLoc)
 import           Diagrams.Parametric
 import           Diagrams.Path
+import           Diagrams.Query
 import           Diagrams.Segment
-import           Diagrams.Solve
+import           Diagrams.Solve.Polynomial
 import           Diagrams.Trail
 import           Diagrams.TrailLike
-import           Diagrams.TwoD.Segment ()
+import           Diagrams.TwoD.Segment
 import           Diagrams.TwoD.Types
-import           Diagrams.Util         (tau)
+import           Diagrams.TwoD.Vector
+import           Diagrams.Util             (tau)
 
+import           Linear.Affine
+import           Linear.Vector
+
 ------------------------------------------------------------
 --  Trail and path traces  ---------------------------------
 ------------------------------------------------------------
@@ -79,14 +97,14 @@
 
 -- XXX can the efficiency of this be improved?  See the comment in
 -- Diagrams.Path on the Enveloped instance for Trail.
-instance Traced (Trail R2) where
+instance RealFloat n => Traced (Trail V2 n) where
   getTrace = withLine $
       foldr
-        (\seg bds -> moveOriginBy (negateV . atEnd $ seg) bds <> getTrace seg)
+        (\seg bds -> moveOriginBy (negated . atEnd $ seg) bds <> getTrace seg)
         mempty
     . lineSegments
 
-instance Traced (Path R2) where
+instance RealFloat n => Traced (Path V2 n) where
   getTrace = F.foldMap getTrace . op Path
 
 ------------------------------------------------------------
@@ -95,17 +113,21 @@
 
 -- | Enumeration of algorithms or \"rules\" for determining which
 --   points lie in the interior of a (possibly self-intersecting)
---   closed path.
-data FillRule = Winding  -- ^ Interior points are those with a nonzero
-                         --   /winding/ /number/.  See
-                         --   <http://en.wikipedia.org/wiki/Nonzero-rule>.
-              | EvenOdd  -- ^ Interior points are those where a ray
-                         --   extended infinitely in a particular
-                         --   direction crosses the path an odd number
-                         --   of times. See
-                         --   <http://en.wikipedia.org/wiki/Even-odd_rule>.
-    deriving (Eq, Show)
+--   path.
+data FillRule
+  = Winding  -- ^ Interior points are those with a nonzero
+             --   /winding/ /number/.  See
+             --   <http://en.wikipedia.org/wiki/Nonzero-rule>.
+  | EvenOdd  -- ^ Interior points are those where a ray
+             --   extended infinitely in a particular direction crosses
+             --   the path an odd number of times. See
+             --   <http://en.wikipedia.org/wiki/Even-odd_rule>.
+    deriving (Show, Typeable, Eq, Ord)
 
+instance AttributeClass FillRule
+instance Semigroup FillRule where
+  _ <> b = b
+
 instance Default FillRule where
   def = Winding
 
@@ -132,14 +154,13 @@
 --
 --   The default value is the empty list.
 
-vertexNames :: forall a a'. Lens (StrokeOpts a) (StrokeOpts a') [[a]] [[a']]
+vertexNames :: Lens (StrokeOpts a) (StrokeOpts a') [[a]] [[a']]
 
 -- | The fill rule used for determining which points are inside the path.
 --   The default is 'Winding'.  NOTE: for now, this only affects the resulting
 --   diagram's 'Query', /not/ how it will be drawn!  To set the fill rule
 --   determining how it is to be drawn, use the 'fillRule' function.
-queryFillRule :: forall a. Lens' (StrokeOpts a) FillRule
-
+queryFillRule :: Lens' (StrokeOpts a) FillRule
 
 instance Default (StrokeOpts a) where
   def = StrokeOpts
@@ -147,35 +168,54 @@
         , _queryFillRule = def
         }
 
--- | Convert a path into a diagram.  The resulting diagram has the
+-- | Convert a 'ToPath' object into a diagram.  The resulting diagram has the
 --   names 0, 1, ... assigned to each of the path's vertices.
 --
 --   See also 'stroke'', which takes an extra options record allowing
---   its behavior to be customized.
+--   its behaviour to be customized.
 --
---   Note that a bug in GHC 7.0.1 causes a context stack overflow when
---   inferring the type of @stroke@.  The solution is to give a type
---   signature to expressions involving @stroke@, or (recommended)
---   upgrade GHC (the bug is fixed in 7.0.2 onwards).
-stroke :: Renderable (Path R2) b
-       => Path R2 -> Diagram b R2
-stroke = stroke' (def :: StrokeOpts ())
-
-instance Renderable (Path R2) b => TrailLike (QDiagram b R2 Any) where
-  trailLike = stroke . trailLike
+-- @
+-- 'stroke' :: 'Path' 'V2' 'Double'                  -> 'Diagram' b
+-- 'stroke' :: 'Located' ('Trail' 'V2' 'Double')       -> 'Diagram' b
+-- 'stroke' :: 'Located' ('Trail'' 'Loop' 'V2' 'Double') -> 'Diagram' b
+-- 'stroke' :: 'Located' ('Trail'' 'Line' 'V2' 'Double') -> 'Diagram' b
+-- @
+stroke :: (InSpace V2 n t, ToPath t, TypeableFloat n, Renderable (Path V2 n) b)
+       => t -> QDiagram b V2 n Any
+stroke = strokeP . toPath
 
 -- | A variant of 'stroke' that takes an extra record of options to
---   customize its behavior.  In particular:
+--   customize its behaviour.  In particular:
 --
 --     * Names can be assigned to the path's vertices
 --
 --   'StrokeOpts' is an instance of 'Default', so @stroke' ('with' &
 --   ... )@ syntax may be used.
-stroke' :: (Renderable (Path R2) b, IsName a) => StrokeOpts a -> Path R2 -> Diagram b R2
-stroke' opts path
-  | null (pLines ^. _Wrapped') =           mkP pLoops
+stroke' :: (InSpace V2 n t, ToPath t, TypeableFloat n, Renderable (Path V2 n) b, IsName a)
+       => StrokeOpts a -> t -> QDiagram b V2 n Any
+stroke' opts = strokeP' opts . toPath
+
+-- | 'stroke' specialised to 'Path'.
+strokeP :: (TypeableFloat n, Renderable (Path V2 n) b)
+        => Path V2 n -> QDiagram b V2 n Any
+strokeP = strokeP' (def :: StrokeOpts ())
+
+-- | 'stroke' specialised to 'Path'.
+strokePath :: (TypeableFloat n, Renderable (Path V2 n) b)
+        => Path V2 n -> QDiagram b V2 n Any
+strokePath = strokeP
+
+instance (TypeableFloat n, Renderable (Path V2 n) b)
+    => TrailLike (QDiagram b V2 n Any) where
+  trailLike = strokeP . trailLike
+
+-- | 'stroke'' specialised to 'Path'.
+strokeP' :: (TypeableFloat n, Renderable (Path V2 n) b, IsName a)
+    => StrokeOpts a -> Path V2 n -> QDiagram b V2 n Any
+strokeP' opts path
+  | null (pLines ^. _Wrapped') = mkP pLoops
   | null (pLoops ^. _Wrapped') = mkP pLines
-  | otherwise                   = mkP pLines <> mkP pLoops
+  | otherwise                  = mkP pLines <> mkP pLoops
   where
     (pLines,pLoops) = partitionPath (isLine . unLoc) path
     mkP p
@@ -185,134 +225,176 @@
          (fromNames . concat $
            zipWith zip (opts^.vertexNames) ((map . map) subPoint (pathVertices p))
          )
-         (Query $ Any . flip (runFillRule (opts^.queryFillRule)) p)
+         (Query $ Any . (runFillRule (opts^.queryFillRule)) p)
 
+-- | 'stroke'' specialised to 'Path'.
+strokePath' :: (TypeableFloat n, Renderable (Path V2 n) b, IsName a)
+    => StrokeOpts a -> Path V2 n -> QDiagram b V2 n Any
+strokePath' = strokeP'
 
--- | A composition of 'stroke' and 'pathFromTrail' for conveniently
---   converting a trail directly into a diagram.
---
---   Note that a bug in GHC 7.0.1 causes a context stack overflow when
---   inferring the type of 'stroke' and hence of @strokeTrail@ as well.
---   The solution is to give a type signature to expressions involving
---   @strokeTrail@, or (recommended) upgrade GHC (the bug is fixed in 7.0.2
---   onwards).
-strokeTrail :: (Renderable (Path R2) b) => Trail R2 -> Diagram b R2
+-- | 'stroke' specialised to 'Trail'.
+strokeTrail :: (TypeableFloat n, Renderable (Path V2 n) b)
+            => Trail V2 n -> QDiagram b V2 n Any
 strokeTrail = stroke . pathFromTrail
 
--- | Deprecated synonym for 'strokeTrail'.
-strokeT :: (Renderable (Path R2) b) => Trail R2 -> Diagram b R2
+-- | 'stroke' specialised to 'Trail'.
+strokeT :: (TypeableFloat n, Renderable (Path V2 n) b)
+        => Trail V2 n -> QDiagram b V2 n Any
 strokeT = strokeTrail
 
 -- | A composition of 'stroke'' and 'pathFromTrail' for conveniently
 --   converting a trail directly into a diagram.
-strokeTrail' :: (Renderable (Path R2) b, IsName a)
-             => StrokeOpts a -> Trail R2 -> Diagram b R2
+strokeTrail' :: (TypeableFloat n, Renderable (Path V2 n) b, IsName a)
+             => StrokeOpts a -> Trail V2 n -> QDiagram b V2 n Any
 strokeTrail' opts = stroke' opts . pathFromTrail
 
 -- | Deprecated synonym for 'strokeTrail''.
-strokeT' :: (Renderable (Path R2) b, IsName a)
-         => StrokeOpts a -> Trail R2 -> Diagram b R2
+strokeT' :: (TypeableFloat n, Renderable (Path V2 n) b, IsName a)
+         => StrokeOpts a -> Trail V2 n -> QDiagram b V2 n Any
 strokeT' = strokeTrail'
 
 -- | A composition of 'strokeT' and 'wrapLine' for conveniently
 --   converting a line directly into a diagram.
-strokeLine :: (Renderable (Path R2) b) => Trail' Line R2 -> Diagram b R2
+strokeLine :: (TypeableFloat n, Renderable (Path V2 n) b)
+           => Trail' Line V2 n -> QDiagram b V2 n Any
 strokeLine = strokeT . wrapLine
 
 -- | A composition of 'strokeT' and 'wrapLoop' for conveniently
 --   converting a loop directly into a diagram.
-strokeLoop :: (Renderable (Path R2) b) => Trail' Loop R2 -> Diagram b R2
+strokeLoop :: (TypeableFloat n, Renderable (Path V2 n) b)
+           => Trail' Loop V2 n -> QDiagram b V2 n Any
 strokeLoop = strokeT . wrapLoop
 
 -- | A convenience function for converting a @Located Trail@ directly
 --   into a diagram; @strokeLocTrail = stroke . trailLike@.
-strokeLocTrail :: (Renderable (Path R2) b) => Located (Trail R2) -> Diagram b R2
-strokeLocTrail = stroke . trailLike
+strokeLocTrail :: (TypeableFloat n, Renderable (Path V2 n) b)
+               => Located (Trail V2 n) -> QDiagram b V2 n Any
+strokeLocTrail = strokeP . trailLike
 
 -- | Deprecated synonym for 'strokeLocTrail'.
-strokeLocT :: (Renderable (Path R2) b) => Located (Trail R2) -> Diagram b R2
+strokeLocT :: (TypeableFloat n, Renderable (Path V2 n) b)
+           => Located (Trail V2 n) -> QDiagram b V2 n Any
 strokeLocT = strokeLocTrail
 
 -- | A convenience function for converting a @Located@ line directly
 --   into a diagram; @strokeLocLine = stroke . trailLike . mapLoc wrapLine@.
-strokeLocLine :: (Renderable (Path R2) b) => Located (Trail' Line R2) -> Diagram b R2
-strokeLocLine = stroke . trailLike . mapLoc wrapLine
+strokeLocLine :: (TypeableFloat n, Renderable (Path V2 n) b)
+              => Located (Trail' Line V2 n) -> QDiagram b V2 n Any
+strokeLocLine = strokeP . trailLike . mapLoc wrapLine
 
 -- | A convenience function for converting a @Located@ loop directly
 --   into a diagram; @strokeLocLoop = stroke . trailLike . mapLoc wrapLoop@.
-strokeLocLoop :: (Renderable (Path R2) b) => Located (Trail' Loop R2) -> Diagram b R2
-strokeLocLoop = stroke . trailLike . mapLoc wrapLoop
+strokeLocLoop :: (TypeableFloat n, Renderable (Path V2 n) b)
+              => Located (Trail' Loop V2 n) -> QDiagram b V2 n Any
+strokeLocLoop = strokeP . trailLike . mapLoc wrapLoop
 
 ------------------------------------------------------------
 --  Inside/outside testing
 ------------------------------------------------------------
 
-
-
-runFillRule :: FillRule -> P2 -> Path R2 -> Bool
+runFillRule :: RealFloat n => FillRule -> Path V2 n -> Point V2 n -> Bool
 runFillRule Winding = isInsideWinding
 runFillRule EvenOdd = isInsideEvenOdd
 
-newtype FillRuleA = FillRuleA (Last FillRule)
-  deriving (Typeable, Semigroup, Show)
-instance AttributeClass FillRuleA
-
-instance Default FillRuleA where
-  def = FillRuleA $ Last $ def
-
 -- | Extract the fill rule from a 'FillRuleA' attribute.
-getFillRule :: FillRuleA -> FillRule
-getFillRule (FillRuleA (Last r)) = r
+getFillRule :: FillRule -> FillRule
+getFillRule = id
 
 -- | Specify the fill rule that should be used for determining which
 --   points are inside a path.
 fillRule :: HasStyle a => FillRule -> a -> a
-fillRule = applyAttr . FillRuleA . Last
+fillRule = applyAttr
 
-cross :: R2 -> R2 -> Double
-cross (coords -> x :& y) (coords -> x' :& y') = x * y' - y * x'
+-- | Lens onto the fill rule of a style.
+_fillRule :: Lens' (Style V2 n) FillRule
+_fillRule = atAttr . non def
 
--- XXX link to more info on this
+-- | The sum of /signed/ crossings of a path as we travel in the
+--   positive x direction from a given point.
+--
+--     - A point is filled according to the 'Winding' fill rule, if the
+--       number of 'Crossings' is non-zero (see 'isInsideWinding').
+--
+--     - A point is filled according to the 'EvenOdd' fill rule, if the
+--       number of 'Crossings' is odd (see 'isInsideEvenOdd').
+--
+--   This is the 'HasQuery' result for 'Path's, 'Located' 'Trail's and
+--   'Located' 'Loops'.
+--
+-- @
+-- 'sample' :: 'Path' 'V2' 'Double'                  -> 'Point' 'V2' 'Double' -> 'Crossings'
+-- 'sample' :: 'Located' ('Trail' 'V2' 'Double')       -> 'Point' 'V2' 'Double' -> 'Crossings'
+-- 'sample' :: 'Located' ('Trail'' 'Loop' 'V2' 'Double') -> 'Point' 'V2' 'Double' -> 'Crossings'
+-- @
+--
+--   Note that 'Line's have no inside or outside, so don't contribute
+--   crossings
+newtype Crossings = Crossings Int
+  deriving (Show, Eq, Ord, Num, Enum, Real, Integral)
 
--- | Test whether the given point is inside the given (closed) path,
+instance Semigroup Crossings where
+  Crossings a <> Crossings b = Crossings (a + b)
+
+instance Monoid Crossings where
+  mempty  = Crossings 0
+  mappend = (<>)
+
+instance RealFloat n => HasQuery (Located (Trail V2 n)) Crossings where
+  getQuery trail = Query $ \p -> trailCrossings p trail
+
+instance RealFloat n => HasQuery (Located (Trail' l V2 n)) Crossings where
+  getQuery trail' = getQuery (mapLoc Trail trail')
+
+instance RealFloat n => HasQuery (Path V2 n) Crossings where
+  getQuery = foldMapOf each getQuery
+
+-- | Test whether the given point is inside the given path,
 --   by testing whether the point's /winding number/ is nonzero. Note
---   that @False@ is /always/ returned for /open/ paths, regardless of
---   the winding number.
-isInsideWinding :: P2 -> Path R2 -> Bool
-isInsideWinding p = (/= 0) . crossings p
+--   that @False@ is /always/ returned for paths consisting of lines
+--   (as opposed to loops), regardless of the winding number.
+--
+-- @
+-- 'isInsideWinding' :: 'Path' 'V2' 'Double'                  -> 'Point' 'V2' 'Double' -> 'Bool'
+-- 'isInsideWinding' :: 'Located' ('Trail' 'V2' 'Double')       -> 'Point' 'V2' 'Double' -> 'Bool'
+-- 'isInsideWinding' :: 'Located' ('Trail'' 'Loop' 'V2' 'Double') -> 'Point' 'V2' 'Double' -> 'Bool'
+-- @
+isInsideWinding :: HasQuery t Crossings => t -> Point (V t) (N t) -> Bool
+isInsideWinding t = (/= 0) . sample t
 
--- | Test whether the given point is inside the given (closed) path,
+-- | Test whether the given point is inside the given path,
 --   by testing whether a ray extending from the point in the positive
 --   x direction crosses the path an even (outside) or odd (inside)
 --   number of times.  Note that @False@ is /always/ returned for
---   /open/ paths, regardless of the number of crossings.
-isInsideEvenOdd :: P2 -> Path R2 -> Bool
-isInsideEvenOdd p = odd . crossings p
-
--- | Compute the sum of /signed/ crossings of a path as we travel in the
---   positive x direction from a given point.
-crossings :: P2 -> Path R2 -> Int
-crossings p = F.sum . map (trailCrossings p) . op Path
+--   paths consisting of lines (as opposed to loops), regardless of
+--   the number of crossings.
+--
+-- @
+-- 'isInsideEvenOdd' :: 'Path' 'V2' 'Double'                  -> 'Point' 'V2' 'Double' -> 'Bool'
+-- 'isInsideEvenOdd' :: 'Located' ('Trail' 'V2' 'Double')       -> 'Point' 'V2' 'Double' -> 'Bool'
+-- 'isInsideEvenOdd' :: 'Located' ('Trail'' 'Loop' 'V2' 'Double') -> 'Point' 'V2' 'Double' -> 'Bool'
+-- @
+isInsideEvenOdd :: HasQuery t Crossings => t -> Point (V t) (N t) -> Bool
+isInsideEvenOdd t = odd . sample t
 
 -- | Compute the sum of signed crossings of a trail starting from the
 --   given point in the positive x direction.
-trailCrossings :: P2 -> Located (Trail R2) -> Int
+trailCrossings :: RealFloat n => Point V2 n -> Located (Trail V2 n) -> Crossings
 
   -- non-loop trails have no inside or outside, so don't contribute crossings
 trailCrossings _ t | not (isLoop (unLoc t)) = 0
 
 trailCrossings p@(unp2 -> (x,y)) tr
-  = sum . map test $ fixTrail tr
+  = F.foldMap test $ fixTrail tr
   where
     test (FLinear a@(unp2 -> (_,ay)) b@(unp2 -> (_,by)))
       | ay <= y && by > y && isLeft a b > 0 =  1
       | by <= y && ay > y && isLeft a b < 0 = -1
       | otherwise                           =  0
 
-    test c@(FCubic (unp2 -> x1@(_,x1y))
-                   (unp2 -> c1@(_,c1y))
-                   (unp2 -> c2@(_,c2y))
-                   (unp2 -> x2@(_,x2y))
+    test c@(FCubic (P x1@(V2 _ x1y))
+                   (P c1@(V2 _ c1y))
+                   (P c2@(V2 _ c2y))
+                   (P x2@(V2 _ x2y))
            ) =
         sum . map testT $ ts
       where ts = filter (liftA2 (&&) (>=0) (<=1))
@@ -323,15 +405,15 @@
             testT t = let (unp2 -> (px,_)) = c `atParam` t
                       in  if px > x then signFromDerivAt t else 0
             signFromDerivAt t =
-              let (dx,dy) = (3*t*t) *^ ((-1)*^x1 ^+^ 3*^c1 ^-^ 3*^c2 ^+^ x2)
-                        ^+^ (2*t)   *^ (3*^x1 ^-^ 6*^c1 ^+^ 3*^c2)
-                        ^+^            ((-3)*^x1 ^+^ 3*^c1)
-                  ang = atan2 dy dx
+              let v =  (3*t*t) *^ ((-1)*^x1 ^+^ 3*^c1 ^-^ 3*^c2 ^+^ x2)
+                   ^+^ (2*t)   *^ (3*^x1 ^-^ 6*^c1 ^+^ 3*^c2)
+                   ^+^            ((-3)*^x1 ^+^ 3*^c1)
+                  ang = v ^. _theta . rad
               in  case () of _ | 0      < ang && ang < tau/2 && t < 1 ->  1
                                | -tau/2 < ang && ang < 0     && t > 0 -> -1
                                | otherwise                            ->  0
 
-    isLeft a b = cross (b .-. a) (p .-. a)
+    isLeft a b = cross2 (b .-. a) (p .-. a)
 
 ------------------------------------------------------------
 --  Clipping  ----------------------------------------------
@@ -342,25 +424,42 @@
 --   concatenation, so applying multiple clipping paths is sensible.
 --   The clipping region is the intersection of all the applied
 --   clipping paths.
-newtype Clip = Clip [Path R2]
+newtype Clip n = Clip [Path V2 n]
   deriving (Typeable, Semigroup)
 
 makeWrapped ''Clip
 
-instance AttributeClass Clip
+instance Typeable n => AttributeClass (Clip n)
 
-type instance V Clip = R2
+instance AsEmpty (Clip n) where
+  _Empty = _Clip . _Empty
 
-instance Transformable Clip where
+type instance V (Clip n) = V2
+type instance N (Clip n) = n
+
+instance (OrderedField n) => Transformable (Clip n) where
   transform t (Clip ps) = Clip (transform t ps)
 
+-- | A point inside a clip if the point is in 'All' invididual clipping
+--   paths.
+instance RealFloat n => HasQuery (Clip n) All where
+  getQuery (Clip paths) = Query $ \p ->
+    F.foldMap (All . flip isInsideWinding p) paths
+
+_Clip :: Iso (Clip n) (Clip n') [Path V2 n] [Path V2 n']
+_Clip = _Wrapped
+
+-- | Lens onto the Clip in a style. An empty list means no clipping.
+_clip :: (Typeable n, OrderedField n) => Lens' (Style V2 n) [Path V2 n]
+_clip = atTAttr . non' _Empty . _Clip
+
 -- | Clip a diagram by the given path:
 --
 --   * Only the parts of the diagram which lie in the interior of the
 --     path will be drawn.
 --
 --   * The envelope of the diagram is unaffected.
-clipBy :: (HasStyle a, V a ~ R2) => Path R2 -> a -> a
+clipBy :: (HasStyle a, V a ~ V2, N a ~ n, TypeableFloat n) => Path V2 n -> a -> a
 clipBy = applyTAttr . Clip . (:[])
 
 -- | Clip a diagram to the given path setting its envelope to the
@@ -368,7 +467,8 @@
 --   trace consists of those parts of the original diagram's trace
 --   which fall within the clipping path, or parts of the path's trace
 --   within the original diagram.
-clipTo :: (Renderable (Path R2) b) => Path R2 ->  Diagram b R2 ->  Diagram b R2
+clipTo :: TypeableFloat n
+  => Path V2 n -> QDiagram b V2 n Any -> QDiagram b V2 n Any
 clipTo p d = setTrace intersectionTrace . toEnvelope $ clipBy p d
   where
     envP = appEnvelope . getEnvelope $ p
@@ -376,17 +476,56 @@
     toEnvelope = case (envP, envD) of
       (Just eP, Just eD) -> setEnvelope . mkEnvelope $ \v -> min (eP v) (eD v)
       (_, _)             -> id
-    intersectionTrace = Trace intersections
-    intersections pt v =
+    intersectionTrace = Trace traceIntersections
+    traceIntersections pt v =
         -- on boundary of d, inside p
         onSortedList (filter pInside) (appTrace (getTrace d) pt v) <>
         -- or on boundary of p, inside d
         onSortedList (filter dInside) (appTrace (getTrace p) pt v) where
           newPt dist = pt .+^ v ^* dist
-          pInside dDist = runFillRule Winding (newPt dDist) p
+          pInside dDist = runFillRule Winding p (newPt dDist)
           dInside pDist = getAny . sample d $ newPt pDist
 
 -- | Clip a diagram to the clip path taking the envelope and trace of the clip
 --   path.
-clipped :: (Renderable (Path R2) b) => Path R2 ->  Diagram b R2 ->  Diagram b R2
-clipped p = (withTrace p) . (withEnvelope p) . (clipBy p)
+clipped :: TypeableFloat n
+  => Path V2 n -> QDiagram b V2 n Any -> QDiagram b V2 n Any
+clipped p = withTrace p . withEnvelope p . clipBy p
+
+------------------------------------------------------------
+--  Intersections  -----------------------------------------
+------------------------------------------------------------
+
+-- | Find the intersect points of two objects that can be converted to a path.
+intersectPoints :: (InSpace V2 n t, SameSpace t s, ToPath t, ToPath s, OrderedField n)
+  => t -> s -> [P2 n]
+intersectPoints = intersectPoints' 1e-8
+
+-- | Find the intersect points of two objects that can be converted to a path
+--   within the given tolerance.
+intersectPoints' :: (InSpace V2 n t, SameSpace t s, ToPath t, ToPath s, OrderedField n)
+  => n -> t -> s -> [P2 n]
+intersectPoints' eps t s = intersectPointsP' eps (toPath t) (toPath s)
+
+-- | Compute the intersect points between two paths.
+intersectPointsP :: OrderedField n => Path V2 n -> Path V2 n -> [P2 n]
+intersectPointsP = intersectPointsP' 1e-8
+
+-- | Compute the intersect points between two paths within given tolerance.
+intersectPointsP' :: OrderedField n => n -> Path V2 n -> Path V2 n -> [P2 n]
+intersectPointsP' eps as bs = do
+  a <- pathTrails as
+  b <- pathTrails bs
+  intersectPointsT' eps a b
+
+-- | Compute the intersect points between two located trails.
+intersectPointsT :: OrderedField n => Located (Trail V2 n) -> Located (Trail V2 n) -> [P2 n]
+intersectPointsT = intersectPointsT' 1e-8
+
+-- | Compute the intersect points between two located trails within the given
+--   tolerance.
+intersectPointsT' :: OrderedField n => n -> Located (Trail V2 n) -> Located (Trail V2 n) -> [P2 n]
+intersectPointsT' eps as bs = do
+  a <- fixTrail as
+  b <- fixTrail bs
+  intersectPointsS' eps a b
diff --git a/src/Diagrams/TwoD/Points.hs b/src/Diagrams/TwoD/Points.hs
new file mode 100644
--- /dev/null
+++ b/src/Diagrams/TwoD/Points.hs
@@ -0,0 +1,60 @@
+{-# LANGUAGE ConstraintKinds #-}
+-----------------------------------------------------------------------------
+-- |
+-- Module      :  Diagrams.TwoD.Points
+-- Copyright   :  (c) 2014 diagrams-lib team (see LICENSE)
+-- License     :  BSD-style (see LICENSE)
+-- Maintainer  :  diagrams-discuss@googlegroups.com
+--
+-- Special functions for points in R2.
+--
+-----------------------------------------------------------------------------
+
+{-# LANGUAGE TypeFamilies #-}
+
+module Diagrams.TwoD.Points where
+
+import Data.List
+
+import Diagrams.Core
+import Diagrams.TwoD.Vector
+import Diagrams.TwoD.Types (P2)
+
+import Linear.Affine
+
+-- | Find the convex hull of a list of points using Andrew's monotone chain
+--   algorithm O(n log n).
+--   
+--   Returns clockwise list of points starting from the left-most point.
+convexHull2D :: OrderedField n => [P2 n] -> [P2 n]
+convexHull2D ps = init upper ++ reverse (tail lower)
+  where
+    (upper, lower) = sortedConvexHull (sort ps)
+
+-- | Find the convex hull of a set of points already sorted in the x direction. 
+--   The first list of the tuple is the upper hull going clockwise from 
+--   left-most to right-most point. The second is the lower hull from 
+--   right-most to left-most in the anti-clockwise direction.
+sortedConvexHull :: OrderedField n => [P2 n] -> ([P2 n], [P2 n])
+sortedConvexHull ps = (chain True ps, chain False ps)
+ where
+   chain upper (p1_:p2_:rest_) =
+     case go (p2_ .-. p1_) p2_ rest_ of
+       Right l -> p1_:l
+       Left l  -> chain upper (p1_:l)
+     where
+       test = if upper then (>0) else (<0)
+       -- find the convex hull by comparing the angles of the vectors with
+       -- the cross product and backtracking if necessary
+       go dir p1 l@(p2:rest)
+         -- backtrack if the direction is outward
+         | test $ dir `cross2` dir' = Left l
+         | otherwise                =
+             case go dir' p2 rest of
+               Left m  -> go dir p1 m
+               Right m -> Right (p1:m)
+         where
+           dir' = p2 .-. p1
+       go _ p1 p = Right (p1:p)
+
+   chain _ l = l
diff --git a/src/Diagrams/TwoD/Polygons.hs b/src/Diagrams/TwoD/Polygons.hs
--- a/src/Diagrams/TwoD/Polygons.hs
+++ b/src/Diagrams/TwoD/Polygons.hs
@@ -1,9 +1,10 @@
-{-# LANGUAGE DeriveFunctor             #-}
-{-# LANGUAGE ExistentialQuantification #-}
-{-# LANGUAGE ScopedTypeVariables       #-}
-{-# LANGUAGE TemplateHaskell           #-}
-{-# LANGUAGE TypeFamilies              #-}
-{-# LANGUAGE ViewPatterns              #-}
+{-# LANGUAGE ConstraintKinds     #-}
+{-# LANGUAGE DeriveFunctor       #-}
+{-# LANGUAGE FlexibleContexts    #-}
+{-# LANGUAGE ScopedTypeVariables #-}
+{-# LANGUAGE TemplateHaskell     #-}
+{-# LANGUAGE TypeFamilies        #-}
+{-# LANGUAGE ViewPatterns        #-}
 
 -----------------------------------------------------------------------------
 -- |
@@ -45,35 +46,34 @@
 
     ) where
 
-import           Control.Lens            (Lens', generateSignatures, lensRules,
-                                          makeLensesWith, (.~), (^.), view)
-import           Control.Monad           (forM, liftM)
-import           Control.Monad.ST        (ST, runST)
-import           Data.Array.ST           (STUArray, newArray, readArray,
-                                          writeArray)
-import           Data.List               (maximumBy, minimumBy)
-import           Data.Maybe              (catMaybes)
-import           Data.Monoid             (mconcat, mempty)
-import           Data.Ord                (comparing)
-
-import           Data.AffineSpace        ((.+^), (.-.))
-import           Data.Default.Class
-import           Data.VectorSpace
+import           Control.Lens         (Lens', generateSignatures, lensRules,
+                                       makeLensesWith, view, (.~), (^.))
+import           Control.Monad        (forM, liftM)
+import           Control.Monad.ST     (ST, runST)
+import           Data.Array.ST        (STUArray, newArray, readArray,
+                                       writeArray)
+import           Data.Default
+import           Data.List            (maximumBy, minimumBy)
+import           Data.Maybe           (catMaybes)
+import           Data.Ord             (comparing)
 
 import           Diagrams.Angle
 import           Diagrams.Core
 import           Diagrams.Located
 import           Diagrams.Path
-import           Diagrams.Points         (centroid)
+import           Diagrams.Points      (centroid)
 import           Diagrams.Trail
 import           Diagrams.TrailLike
-import           Diagrams.TwoD.Transform
 import           Diagrams.TwoD.Types
-import           Diagrams.TwoD.Vector    (leftTurn, unitX, unitY, unit_Y)
-import           Diagrams.Util           (tau, ( # ))
+import           Diagrams.TwoD.Vector (leftTurn, unitX, unitY, unit_Y)
+import           Diagrams.Util        (tau, ( # ))
 
+import           Linear.Affine
+import           Linear.Metric
+import           Linear.Vector
+
 -- | Method used to determine the vertices of a polygon.
-data PolyType = PolyPolar [Angle] [Double]
+data PolyType n = PolyPolar [Angle n] [n]
                 -- ^ A \"polar\" polygon.
                 --
                 --   * The first argument is a list of /central/
@@ -90,21 +90,21 @@
                 --   circle) can be constructed using a second
                 --   argument of @(repeat r)@.
 
-              | PolySides [Angle] [Double]
+              | PolySides [Angle n] [n]
                 -- ^ A polygon determined by the distance between
-                --   successive vertices and the angles formed by
-                --   each three successive vertices.  In other
+                --   successive vertices and the external angles formed
+                --   by each three successive vertices. In other
                 --   words, a polygon specified by \"turtle
                 --   graphics\": go straight ahead x1 units; turn by
-                --   angle a1; go straght ahead x2 units; turn by
-                --   angle a2; etc. The polygon will be centered at
-                --   the /centroid/ of its vertices.
+                --   external angle a1; go straight ahead x2 units; turn by
+                --   external angle a2; etc. The polygon will be centered
+                --   at the /centroid/ of its vertices.
                 --
                 --   * The first argument is a list of /vertex/
-                --     /angles/, giving the angle at each vertex
+                --     /angles/, giving the external angle at each vertex
                 --     from the previous vertex to the next.  The
-                --     first angle in the list is the angle at the
-                --     /second/ vertex; the first edge always starts
+                --     first angle in the list is the external angle at
+                --     the /second/ vertex; the first edge always starts
                 --     out heading in the positive y direction from
                 --     the first vertex.
                 --
@@ -115,54 +115,54 @@
                 --   angles and /n-1/ edge lengths.  Extra angles or
                 --   lengths are ignored.
 
-              | PolyRegular Int Double
+              | PolyRegular Int n
                 -- ^ A regular polygon with the given number of
                 --   sides (first argument) and the given radius
                 --   (second argument).
 
 -- | Determine how a polygon should be oriented.
-data PolyOrientation = NoOrient     -- ^ No special orientation; the first
-                                    --   vertex will be at (1,0).
-                                    --   This is the default.
-                     | OrientH      -- ^ Orient /horizontally/, so the
-                                    --   bottommost edge is parallel to
-                                    --   the x-axis.
-                     | OrientV      -- ^ Orient /vertically/, so the
-                                    --   leftmost edge is parallel to the
-                                    --   y-axis.
-                     | OrientTo R2  -- ^ Orient so some edge is
-                                    --   /facing/ /in/ /the/ /direction/
-                                    --   /of/, that is, perpendicular
-                                    --   to, the given vector.
-  deriving (Eq, Ord, Show, Read)
+data PolyOrientation n = NoOrient        -- ^ No special orientation; the first
+                                         --   vertex will be at (1,0).
+                       | OrientH         -- ^ Orient /horizontally/, so the
+                                         --   bottommost edge is parallel to
+                                         --   the x-axis.
+                                         --   This is the default.
+                       | OrientV         -- ^ Orient /vertically/, so the
+                                         --   leftmost edge is parallel to the
+                                         --   y-axis.
+                       | OrientTo (V2 n) -- ^ Orient so some edge is
+                                         --   /facing/ /in/ /the/ /direction/
+                                         --   /of/, that is, perpendicular
+                                         --   to, the given vector.
+                       deriving (Eq, Ord, Show, Read)
 
 -- | Options for specifying a polygon.
-data PolygonOpts = PolygonOpts
-                   { _polyType   :: PolyType
-                   , _polyOrient :: PolyOrientation
-                   , _polyCenter :: P2
+data PolygonOpts n = PolygonOpts
+                   { _polyType   :: PolyType n
+                   , _polyOrient :: PolyOrientation n
+                   , _polyCenter :: Point V2 n
                    }
 
 makeLensesWith (generateSignatures .~ False $ lensRules) ''PolygonOpts
 
 -- | Specification for the polygon's vertices.
-polyType :: Lens' PolygonOpts PolyType
+polyType :: Lens' (PolygonOpts n) (PolyType n)
 
 -- | Should a rotation be applied to the polygon in order to orient it in a
 --   particular way?
-polyOrient :: Lens' PolygonOpts PolyOrientation
+polyOrient :: Lens' (PolygonOpts n) (PolyOrientation n)
 
 -- | Should a translation be applied to the polygon in order to place the center
 --   at a particular location?
-polyCenter :: Lens' PolygonOpts P2
+polyCenter :: Lens' (PolygonOpts n) (Point V2 n)
 
 -- | The default polygon is a regular pentagon of radius 1, centered
 --   at the origin, aligned to the x-axis.
-instance Default PolygonOpts where
+instance Num n => Default (PolygonOpts n) where
     def = PolygonOpts (PolyRegular 5 1) OrientH origin
 
 -- | Generate a polygon.  See 'PolygonOpts' for more information.
-polyTrail :: PolygonOpts -> Located (Trail R2)
+polyTrail :: OrderedField n => PolygonOpts n -> Located (Trail V2 n)
 polyTrail po = transform ori tr
     where
         tr = case po^.polyType of
@@ -170,18 +170,18 @@
             PolySides ans szs -> polySidesTrail ans szs
             PolyRegular n r   -> polyRegularTrail n r
         ori = case po^.polyOrient of
-            OrientH      -> orient unit_Y tr
-            OrientV      -> orient unitX  tr
-            OrientTo v   -> orient v      tr
-            NoOrient     -> mempty
+            OrientH    -> orient unit_Y tr
+            OrientV    -> orient unitX  tr
+            OrientTo v -> orient v      tr
+            NoOrient   -> mempty
 
 -- | Generate the polygon described by the given options.
-polygon :: (TrailLike t, V t ~ R2) => PolygonOpts -> t
+polygon :: (InSpace V2 n t, TrailLike t) => PolygonOpts n -> t
 polygon = trailLike . polyTrail
 
 -- | Generate the located trail of a polygon specified by polar data
 --   (central angles and radii). See 'PolyPolar'.
-polyPolarTrail :: [Angle] -> [Double] -> Located (Trail R2)
+polyPolarTrail :: OrderedField n =>  [Angle n] -> [n] -> Located (Trail V2 n)
 polyPolarTrail [] _ = emptyTrail `at` origin
 polyPolarTrail _ [] = emptyTrail `at` origin
 polyPolarTrail ans (r:rs) = tr `at` p1
@@ -190,52 +190,54 @@
     tr = closeTrail . trailFromVertices $
            zipWith
              (\a l -> rotate a . scale l $ p2 (1,0))
-             (scanl (^+^) zeroV ans)
+             (scanl (^+^) zero ans)
              (r:rs)
 
 -- | Generate the vertices of a polygon specified by side length and
 --   angles, and a starting point for the trail such that the origin
 --   is at the centroid of the vertices.  See 'PolySides'.
-polySidesTrail :: [Angle] -> [Double] -> Located (Trail R2)
+polySidesTrail :: OrderedField n =>  [Angle n] -> [n] -> Located (Trail V2 n)
 polySidesTrail ans ls = tr `at` (centroid ps # scale (-1))
   where
-    ans'    = scanl (^+^) zeroV ans
+    ans'    = scanl (^+^) zero ans
     offsets = zipWith rotate ans' (map (unitY ^*) ls)
     ps      = scanl (.+^) origin offsets
     tr      = closeTrail . trailFromOffsets $ offsets
 
 -- | Generate the vertices of a regular polygon.  See 'PolyRegular'.
-polyRegularTrail :: Int -> Double -> Located (Trail R2)
+polyRegularTrail :: OrderedField n =>  Int -> n -> Located (Trail V2 n)
 polyRegularTrail n r = polyPolarTrail
-                         (take (n-1) . repeat $ fullTurn ^/ fromIntegral n)
+                         (replicate (n - 1) $ fullTurn ^/ fromIntegral n)
                          (repeat r)
 
 -- | Generate a transformation to orient a trail.  @orient v t@
 --   generates the smallest rotation such that one of the segments
 --   adjacent to the vertex furthest in the direction of @v@ is
 --   perpendicular to @v@.
-orient :: R2 -> Located (Trail R2) -> T2
+orient :: OrderedField n => V2 n -> Located (Trail V2 n) -> Transformation V2 n
 orient v = orientPoints v . trailVertices
 
-orientPoints :: R2 -> [P2] -> T2
+orientPoints :: OrderedField n => V2 n -> [Point V2 n] -> Transformation V2 n
+orientPoints _ [] = mempty
+orientPoints _ [_] = mempty
 orientPoints v xs = rotation a
   where
     (n1,x,n2) = maximumBy (comparing (distAlong v . sndOf3))
                   (zip3 (tail (cycle xs)) xs (last xs : init xs))
-    distAlong w ((.-. origin) -> p) = signum (w <.> p) * magnitude (project w p)
+    distAlong w ((.-. origin) -> p) = signum (w `dot` p) * norm (project w p)
     sndOf3 (_,b,_) = b
-    a :: Angle
+    -- a :: Angle (Scalar v)
     a = minimumBy (comparing $ abs . view rad)
         . map (angleFromNormal . (.-. x)) $ [n1,n2]
-    v' = normalized v
-    angleFromNormal :: R2 -> Angle
+    v' = signorm v
+    -- angleFromNormal :: v -> Angle (Scalar v)
     angleFromNormal o
       | leftTurn o' v' = phi
-      | otherwise      = negateV phi
+      | otherwise      = negated phi
       where
-        o' = normalized o
-        theta = acos (v' <.> o')
-        phi :: Angle
+        o' = signorm o
+        theta = acos (v' `dot` o')
+        -- phi :: Angle (Scalar v)
         phi
           | theta <= tau/4 = tau/4 - theta @@ rad
           | otherwise      = theta - tau/4 @@ rad
@@ -275,10 +277,10 @@
     markRho :: Int -> STUArray s Int Bool -> ST s [Int]
     markRho i marks = do
       isMarked <- readArray marks i
-      case isMarked of
-        True  -> return []
-        False -> writeArray marks i True >>
-                 liftM (i:) (markRho (f_n i) marks)
+      if isMarked
+        then return []
+        else writeArray marks i True >>
+               liftM (i:) (markRho (f_n i) marks)
 
     splitParts :: [Int] -> [GraphPart Int]
     splitParts tr = hair ++ cyc
@@ -317,13 +319,13 @@
 -- | Create a generalized /star/ /polygon/.  The 'StarOpts' are used
 --   to determine in which order the given vertices should be
 --   connected.  The intention is that the second argument of type
---   @[P2]@ could be generated by a call to 'polygon', 'regPoly', or
+--   @[Point v]@ could be generated by a call to 'polygon', 'regPoly', or
 --   the like, since a list of vertices is 'TrailLike'.  But of course
---   the list can be generated any way you like.  A @'Path' 'R2'@ is
+--   the list can be generated any way you like.  A @'Path' 'v'@ is
 --   returned (instead of any 'TrailLike') because the resulting path
 --   may have more than one component, for example if the vertices are
 --   to be connected in several disjoint cycles.
-star :: StarOpts -> [P2] -> Path R2
+star :: OrderedField n => StarOpts -> [Point V2 n] -> Path V2 n
 star sOpts vs = graphToPath $ mkGraph f vs
   where f = case sOpts of
               StarFun g  -> g
diff --git a/src/Diagrams/TwoD/Segment.hs b/src/Diagrams/TwoD/Segment.hs
--- a/src/Diagrams/TwoD/Segment.hs
+++ b/src/Diagrams/TwoD/Segment.hs
@@ -1,9 +1,12 @@
+{-# LANGUAGE ConstraintKinds #-}
 {-# LANGUAGE FlexibleContexts     #-}
 {-# LANGUAGE FlexibleInstances    #-}
+{-# LANGUAGE TypeFamilies         #-}
+{-# LANGUAGE ViewPatterns         #-}
 {-# LANGUAGE UndecidableInstances #-}
 
 {-# OPTIONS_GHC -fno-warn-orphans #-}
--- Orphan Traced instances for Segment Closed R2 and FixedSegment R2.
+-- Orphan Traced instances for Segment Closed V2 and FixedSegment V2.
 -- They can't go in Traced; but they shouldn't really go in
 -- Diagrams.Segment either because we only have Traced instances for
 -- the special case of R2.
@@ -19,89 +22,358 @@
 --
 -----------------------------------------------------------------------------
 
-module Diagrams.TwoD.Segment where
+module Diagrams.TwoD.Segment
+  ( -- * Segment intersections
 
-import           Control.Applicative     (liftA2)
+    intersectPointsS
+  , intersectPointsS'
 
-import           Data.AffineSpace
-import           Data.VectorSpace
+    -- * Closest point on a segment
 
+  , closestPoint
+  , closestPoint'
+  , closestDistance
+  , closestDistance'
+  , closestParam
+  , closestParam'
+
+    -- ** Low level functions
+  , segmentSegment
+  , lineSegment
+  )
+  where
+
+import           Control.Lens                    hiding (at, contains, transform, ( # ))
+import           Data.Maybe
+
 import           Diagrams.Core
 
+import           Diagrams.Direction
 import           Diagrams.Located
 import           Diagrams.Parametric
 import           Diagrams.Segment
-import           Diagrams.Solve
+import           Diagrams.TwoD.Points
+import           Diagrams.TwoD.Segment.Bernstein
 import           Diagrams.TwoD.Transform
-import           Diagrams.TwoD.Types
+import           Diagrams.TwoD.Types             hiding (p2)
 import           Diagrams.TwoD.Vector
-import           Diagrams.Util
 
+import           Linear.Affine
+import           Linear.Metric
+
 {- All instances of Traced should maintain the invariant that the list of
    traces is sorted in increasing order.
 -}
 
-instance Traced (Segment Closed R2) where
+instance OrderedField n => Traced (Segment Closed V2 n) where
   getTrace = getTrace . mkFixedSeg . (`at` origin)
 
-instance Traced (FixedSegment R2) where
+instance OrderedField n => Traced (FixedSegment V2 n) where
+  getTrace seg = mkTrace $ \p v ->
+    mkSortedList . map (view _1) $ lineSegment defEps (v `at` p) seg
 
-{- Given lines defined by p0 + t0 * v0 and p1 + t1 * v1, their point of
-   intersection in 2D is given by
+defEps :: Fractional n => n
+defEps = 1e-8
 
-     t_i = (v_(1-i)^ . (p1 - p0)) / (v1^ . v0)
+-- | Compute the intersections between two fixed segments.
+intersectPointsS :: OrderedField n => FixedSegment V2 n -> FixedSegment V2 n -> [P2 n]
+intersectPointsS = intersectPointsS' defEps
 
-   where v^ denotes the perpendicular to v, i.e. v rotated by
-   -tau/4.
+-- | Compute the intersections between two segments using the given tolerance.
+intersectPointsS' :: OrderedField n => n -> FixedSegment V2 n -> FixedSegment V2 n -> [P2 n]
+intersectPointsS' eps s1 s2 = map (view _3) $ segmentSegment eps s1 s2
 
-   This can be derived by starting with the parametric equation
+-- | Get the closest distance(s) from a point to a 'FixedSegment'.
+closestDistance :: OrderedField n => FixedSegment V2 n -> P2 n -> [n]
+closestDistance = closestDistance' defEps
 
-     p0 + v0 t0 = p1 + v1 t1
+-- | Get the closest distance(s) from a point to a 'FixedSegment' within given
+--   tolerance.
+closestDistance' :: OrderedField n => n -> FixedSegment V2 n -> P2 n -> [n]
+closestDistance' eps seg p = map (distanceA p) $ closestPoint' eps seg p
 
-   and rearranging to get the matrix equation
+-- | Get the closest point(s) on a 'FixedSegment' from a point.
+closestPoint :: OrderedField n => FixedSegment V2 n -> P2 n -> [P2 n]
+closestPoint = closestPoint' defEps
 
-     [v0 -v1] [ t0 ]  =  (p1 - p0)
-              [ t1 ]
+-- | Get the closest point(s) on a 'FixedSegment' from a point within given
+--   tolerance.
+closestPoint' :: OrderedField n => n -> FixedSegment V2 n -> P2 n -> [P2 n]
+closestPoint' eps seg = map (seg `atParam`) . closestParam' eps seg
 
-   Working out the product of the inverse of [v0 -v1] with (p1 - p0)
-   results in the above formulas for t_i.
--}
+-- | Find the closest value(s) on the Bêzier to the given point.
+closestParam :: OrderedField n => FixedSegment V2 n -> P2 n -> [n]
+closestParam = closestParam' defEps
 
-  getTrace (FLinear p0 p0') = mkTrace $ \p1 v1 ->
-    let
-      v0     = p0' .-. p0
-      det    = perp v1 <.> v0
-      p      = p1 .-. p0
-      t0     = (perp v1 <.> p) / det
-      t1     = (perp v0 <.> p) / det
-    in
-      if det == 0 || t0 < 0 || t0 > 1
-        then mkSortedList []
-        else mkSortedList [t1]
+-- | Find the closest value(s) on the Bêzier to the given point within given
+--   tolerance.
+closestParam' :: OrderedField n => n -> FixedSegment V2 n -> P2 n -> [n]
+closestParam' _ (FLinear p0 p1) p
+  | t < 0     = [0]
+  | t > 1     = [1]
+  | otherwise = [t]
+  where
+    vp = p  .-. p0
+    v  = p1 .-. p0
+    dp = vp `dot` v
+    t  = dp / quadrance v
+closestParam' eps cb (P (V2 px py)) = bezierFindRoot eps poly 0 1
+  where
+    (bx, by) = bezierToBernstein cb
+    bx'  = bernsteinDeriv bx
+    by'  = bernsteinDeriv by
+    poly = (bx - listToBernstein [px, px, px, px]) * bx'
+         + (by - listToBernstein [py, py, py, py]) * by'
 
-{- To do intersection of a line with a cubic Bezier, we first rotate
-   and scale everything so that the line has parameters (origin, unitX);
-   then we find the intersection(s) of the Bezier with the x-axis.
+------------------------------------------------------------------------
+-- Low level
+------------------------------------------------------------------------
 
-   XXX could we speed this up by first checking whether all the
-   control point y-coordinates lie on the same side of the x-axis (if so,
-   there can't possibly be any intersections)?  Need to set up some
-   benchmarks.
--}
+-- | Return the intersection points with the parameters at which each segment
+--   intersects.
+segmentSegment :: OrderedField n => n -> FixedSegment V2 n -> FixedSegment V2 n -> [(n, n, P2 n)]
+segmentSegment eps s1 s2 =
+  case (s1,s2) of
+    (FCubic{}, FCubic{})  -> map (\(t1,t2) -> (t1,t2, s1 `atParam` t1))
+                           $ bezierClip eps s1 s2
+    (FCubic{}, FLinear{}) -> map flip12 $ linearSeg (segLine s2) s1
+    _                     -> linearSeg (segLine s1) s2 -- s1 is linear
+  where
+    linearSeg l s  = filter (inRange . view _1) $ lineSegment eps l s
+    flip12 (a,b,c) = (b,a,c)
 
-  getTrace bez@(FCubic {}) = mkTrace $ \p1 v1 ->
-    let
-      bez'@(FCubic x1 c1 c2 x2) =
-        bez # moveOriginTo p1
-            # rotate (negateV (direction v1))
-            # scale (1/magnitude v1)
-      [y0,y1,y2,y3] = map (snd . unp2) [x1,c1,c2,x2]
-      a  = -y0 + 3*y1 - 3*y2 + y3
-      b  = 3*y0 - 6*y1 + 3*y2
-      c  = -3*y0 + 3*y1
-      d  = y0
-      ts = filter (liftA2 (&&) (>= 0) (<= 1)) (cubForm a b c d)
-      xs = map (fst . unp2 . atParam bez') ts
-    in
-      mkSortedList xs
+-- | Return the intersection points with the parameters at which the line and segment
+--   intersect.
+lineSegment :: OrderedField n => n -> Located (V2 n) -> FixedSegment V2 n -> [(n, n, P2 n)]
+lineSegment _ l1 p@(FLinear p0 p1)
+  = map (\(tl,tp) -> (tl, tp, p `atParam` tp))
+  . filter (inRange . snd) . maybeToList $ lineLine l1 (mkLine p0 p1)
+lineSegment eps (viewLoc -> (p,r)) cb = map addPoint params
+  where
+    params = bezierFindRoot eps (listToBernstein $ cb' ^.. each . _y) 0 1
+    cb'    = transform (inv (rotationTo $ dir r)) . moveOriginTo p $ cb
+    --
+    addPoint bt = (lt, bt, intersect)
+      where
+        intersect = cb `atParam` bt
+        lt        = (cb' `atParam` bt) ^. _x / norm r
+
+-- Adapted from from kuribas's cubicbezier package https://github.com/kuribas/cubicbezier
+
+-- | Use the Bêzier clipping algorithm to return the parameters at which the
+--   Bêzier curves intersect.
+bezierClip :: OrderedField n => n -> FixedSegment V2 n -> FixedSegment V2 n -> [(n, n)]
+bezierClip eps p_ q_ = filter (allOf both inRange) -- sometimes this returns NaN
+                     $ go p_ q_ 0 1 0 1 0 False
+  where
+  go p q tmin tmax umin umax clip revCurves
+    | isNothing chopInterval = []
+
+    -- This check happens before the subdivision
+    -- test to avoid non-termination as values
+    -- transition to within epsilon.
+    | max (umax - umin) (tmax' - tmin') < eps =
+      if revCurves -- return parameters in correct order
+      then [ (avg umin  umax,  avg tmin' tmax') ]
+      else [ (avg tmin' tmax', avg umin  umax ) ]
+
+    -- split the curve if there isn't enough reduction
+    | clip > 0.8 && clip' > 0.8 =
+      if tmax' - tmin' > umax - umin -- split the longest segment
+      then let (pl, pr) = p' `splitAtParam` 0.5
+               tmid = avg tmin' tmax'
+           in  go q pl umin umax tmin' tmid  clip' (not revCurves) ++
+               go q pr umin umax tmid  tmax' clip' (not revCurves)
+      else let (ql, qr) = q `splitAtParam` 0.5
+               umid = avg umin umax
+           in  go ql p' umin umid tmin' tmax' clip' (not revCurves) ++
+               go qr p' umid umax tmin' tmax' clip' (not revCurves)
+
+    -- iterate with the curves reversed.
+    | otherwise = go q p' umin umax tmin' tmax' clip' (not revCurves)
+    where
+      chopInterval              = chopCubics p q
+      Just (tminChop, tmaxChop) = chopInterval
+      p'    = section p tminChop tmaxChop
+      clip' = tmaxChop - tminChop
+      tmin' = tmax * tminChop + tmin * (1 - tminChop)
+      tmax' = tmax * tmaxChop + tmin * (1 - tmaxChop)
+
+-- | Find the zero of a 1D Bêzier curve of any degree.  Note that this
+--   can be used as a Bernstein polynomial root solver by converting from
+--   the power basis to the Bernstein basis.
+bezierFindRoot :: OrderedField n
+               => n   -- ^ The accuracy
+               -> BernsteinPoly n -- ^ the Bernstein coefficients of the polynomial
+               -> n   -- ^ The lower bound of the interval
+               -> n   -- ^ The upper bound of the interval
+               -> [n] -- ^ The roots found
+bezierFindRoot eps p tmin tmax
+  -- If we generated the max number of roots and tmax is also a root
+  -- (which is not among the generated ones), there must in fact be an
+  -- infinite number of roots, so just include tmax.
+  | length roots == bernsteinDegree p && last roots /= tmax && abs (evaluateBernstein p tmax) <= eps
+  = roots ++ [tmax]
+  | otherwise = roots
+ where
+  -- Lazily take a number of roots at most the degree of the bernstein
+  -- polynomial, to avoid generating a ton of roots in the case of a
+  -- straight Bezier segment along the x-axis. See https://github.com/diagrams/diagrams-contrib/issues/91 .
+  roots = take (bernsteinDegree p) $ go p tmin tmax
+  go p tmin tmax
+    | isNothing chopInterval = []
+    | tmax' - tmin' < eps = [avg tmin' tmax']
+    | clip > 0.8 = let (p1, p2) = splitAtParam newP 0.5
+                       tmid     = tmin' + (tmax' - tmin') / 2
+                   in  go p1 tmin' tmid  ++
+                       go p2 tmid  tmax'
+    | otherwise = bezierFindRoot eps newP tmin' tmax'
+    where
+      chopInterval              = chopYs (bernsteinCoeffs p)
+      Just (tminChop, tmaxChop) = chopInterval
+      newP  = section p tminChop tmaxChop
+      clip  = tmaxChop - tminChop
+      tmin' = tmax * tminChop + tmin * (1 - tminChop)
+      tmax' = tmax * tmaxChop + tmin * (1 - tmaxChop)
+
+------------------------------------------------------------------------
+-- Internal
+------------------------------------------------------------------------
+
+-- | An approximation of the fat line for a cubic Bêzier segment. Returns
+--   @(0,0)@ for a linear segment.
+fatLine :: OrderedField n => FixedSegment V2 n -> (n,n)
+fatLine (FCubic p0 p1 p2 p3)
+  = case (d1 > 0, d2 > 0) of
+      (True,  True)  -> (0,                0.75 * max d1 d2)
+      (False, False) -> (0.75 * min d1 d2, 0               )
+      (True,  False) -> (4/9 * d2,         4/9 * d1        )
+      (False, True)  -> (4/9 * d1,         4/9 * d2        )
+  where
+    d = lineDistance p0 p3
+    d1 = d p1; d2 = d p2
+fatLine _ = (0,0)
+
+chopYs :: OrderedField n => [n] -> Maybe (n, n)
+chopYs ds = chopHull 0 0 points
+  where
+    points = zipWith mkP2 [fromIntegral i / fromIntegral n | i <- [0..n]] ds
+    n      = length ds - 1
+
+chopCubics :: OrderedField n => FixedSegment V2 n -> FixedSegment V2 n -> Maybe (n,n)
+chopCubics p q@(FCubic q0 _ _ q3)
+  = chopHull dmin dmax dps
+  where
+    dps = zipWith mkP2 [0, 1/3, 2/3, 1] ds
+    ds  = p ^.. each . to d
+    d   = lineDistance q0 q3
+    --
+    (dmin,dmax) = fatLine q
+chopCubics _ _ = Nothing
+
+-- Reduce the interval which the intersection is known to lie in using the fat
+-- line of one curve and convex hull of the points formed from the distance to
+-- the thin line of the other
+chopHull :: OrderedField n => n -> n -> [P2 n] -> Maybe (n, n)
+chopHull dmin dmax dps = do
+  tL <- testBelow upper           $ testBetween (head upper) $ testAbove lower
+  tR <- testBelow (reverse upper) $ testBetween (last upper) $ testAbove (reverse lower)
+  Just (tL, tR)
+    where
+      (upper, lower) = sortedConvexHull dps
+
+      testBelow (p1@(P (V2 _ y1)) : p2@(P (V2 _ y2)) : ps) continue
+        | y1 >= dmin = continue
+        | y1 >  y2   = Nothing
+        | y2 <  dmin = testBelow (p2:ps) continue
+        | otherwise  = Just $ intersectPt dmin p1 p2
+      testBelow _ _  = Nothing
+
+      testBetween (P (V2 x y)) continue
+        | y <= dmax = Just x
+        | otherwise = continue
+
+      testAbove (p1@(P (V2 _ y1)) : p2@(P (V2 _ y2)) : ps)
+        | y1 < y2      = Nothing
+        | y2 > dmax    = testAbove (p2:ps)
+        | y2 - y1 == 0 = Nothing  -- Check this condition to prevent
+                                  -- division by zero in `intersectPt`.
+        | otherwise    = Just $ intersectPt dmax p1 p2
+      testAbove _      = Nothing
+
+      -- find the x value where the line through the two points
+      -- intersect the line y=d.  Note that `y2 - y1 != 0` due
+      -- to checks above.
+      intersectPt d (P (V2 x1 y1)) (P (V2 x2 y2)) =
+          x1 + (d - y1) * (x2 - x1) / (y2 - y1)
+
+
+
+bezierToBernstein :: Fractional n => FixedSegment V2 n -> (BernsteinPoly n, BernsteinPoly n)
+bezierToBernstein seg =
+    (listToBernstein $ map (view _x) coeffs, listToBernstein $ map (view _y) coeffs)
+  where coeffs = toListOf each seg
+
+------------------------------------------------------------------------
+-- Lines
+------------------------------------------------------------------------
+
+-- Could split this into a separate module.
+
+-- | Returns @(a, b, c, d)@ such that @ax + by + c = 0@ is the line going through
+--   @p1@ and @p2@ with @(a^2)/d + (b^2)/d = 1@.  We delay the division by
+--   @d@ as it may not be needed in all cases and @d@ may be zero.
+lineEquation :: Floating n => P2 n -> P2 n -> (n, n, n, n)
+lineEquation (P (V2 x1 y1)) (P (V2 x2 y2)) = (a, b, c, d)
+  where
+    c  = -(x1*a + y1*b)
+    a = y1 - y2
+    b = x2 - x1
+    d  = a*a + b*b
+
+-- | Return the distance from a point to the line.
+lineDistance :: (Ord n, Floating n) => P2 n -> P2 n -> P2 n -> n
+lineDistance p1 p2 p3@(P (V2 x y))
+    -- I have included the check that d' <= 0 in case
+    -- there exists some d > 0 where sqrt d == 0.  I don't
+    -- think this can happen as sqrt is at least recommended
+    -- to be within one value of correct for sqrt and near
+    -- zero values get bigger.
+    | d <= 0 || d' <= 0 = norm (p1 .-. p3)
+    | otherwise = (a*x + b*y + c) / d'
+  where
+    (a, b, c, d) = lineEquation p1 p2
+    d' = sqrt d
+
+-- clockwise :: (Num n, Ord n) => V2 n -> V2 n -> Bool
+-- clockwise a b = a `cross2` b <= 0
+
+avg :: Fractional n => n -> n -> n
+avg a b = (a + b)/2
+
+lineLine :: (Fractional n, Eq n) => Located (V2 n) -> Located (V2 n) -> Maybe (n,n)
+lineLine (viewLoc -> (p,r)) (viewLoc -> (q,s))
+  | x1 == 0 && x2 /= 0 = Nothing                 -- parallel
+  | otherwise          = Just (x3 / x1, x2 / x1) -- intersecting or collinear
+  where
+    x1 = r × s
+    x2 = v × r
+    x3 = v × s
+    v  = q .-. p
+
+(×) :: Num n => V2 n -> V2 n -> n
+(×) = cross2
+
+mkLine :: InSpace v n (v n) => Point v n -> Point v n -> Located (v n)
+mkLine p0 p1 = (p1 .-. p0) `at` p0
+
+segLine :: InSpace v n (v n) => FixedSegment v n -> Located (v n)
+segLine (FLinear p0 p1)    = mkLine p0 p1
+segLine (FCubic p0 _ _ p3) = mkLine p0 p3
+
+-- This function uses `defEps`, but is used in functions
+-- above that take an epsilon parameter.  It would be nice
+-- to clearify the meaning of each of these epsilons.
+inRange :: (Fractional n, Ord n) => n -> Bool
+inRange x = x < (1+defEps) && x > (-defEps)
 
diff --git a/src/Diagrams/TwoD/Segment/Bernstein.hs b/src/Diagrams/TwoD/Segment/Bernstein.hs
new file mode 100644
--- /dev/null
+++ b/src/Diagrams/TwoD/Segment/Bernstein.hs
@@ -0,0 +1,138 @@
+{-# LANGUAGE DeriveFunctor #-}
+{-# LANGUAGE TypeFamilies  #-}
+-----------------------------------------------------------------------------
+-- |
+-- Module      :  Diagrams.TwoD.Segment.Bernstein
+-- Copyright   :  (c) 2014-2015 diagrams-lib team (see LICENSE)
+-- License     :  BSD-style (see LICENSE)
+-- Maintainer  :  diagrams-discuss@googlegroups.com
+--
+-- Bernstein polynomials, used internally by code to find
+-- intersections of paths.  This module is probably not of any
+-- relevance to most users of diagrams.
+-----------------------------------------------------------------------------
+module Diagrams.TwoD.Segment.Bernstein
+  ( BernsteinPoly (..)
+  , listToBernstein
+  , evaluateBernstein
+
+  , degreeElevate
+  , bernsteinDeriv
+  , evaluateBernsteinDerivs
+  ) where
+
+import           Data.List           (tails)
+import           Diagrams.Core.V
+import           Diagrams.Parametric
+import           Linear.V1
+
+-- | Compute the binomial coefficients of degree n.
+binomials :: Num n => Int -> [n]
+binomials n = map fromIntegral $ scanl (\x m -> x * (n - m+1) `quot` m) 1 [1..n]
+
+data BernsteinPoly n = BernsteinPoly
+  { bernsteinDegree :: Int
+  , bernsteinCoeffs :: [n]
+  } deriving (Show, Functor)
+
+type instance V        (BernsteinPoly n) = V1
+type instance N        (BernsteinPoly n) = n
+type instance Codomain (BernsteinPoly n) = V1
+
+-- | Create a bernstein polynomial from a list of coëfficients.
+listToBernstein :: Fractional n => [n] -> BernsteinPoly n
+listToBernstein [] = 0
+listToBernstein l  = BernsteinPoly (length l - 1) l
+
+-- | Degree elevate a bernstein polynomial a number of times.
+degreeElevate :: Fractional n => BernsteinPoly n -> Int -> BernsteinPoly n
+degreeElevate b                    0     = b
+degreeElevate (BernsteinPoly lp p) times =
+  degreeElevate (BernsteinPoly (lp+1) (head p:inner p 1)) (times-1)
+  where
+    n = fromIntegral lp
+
+    inner []         _ = [0]
+    inner [a]        _ = [a]
+    inner (a:b:rest) i = (i*a/(n+1) + b*(1 - i/(n+1))) : inner (b:rest) (i+1)
+
+-- | Evaluate the bernstein polynomial.
+evaluateBernstein :: Fractional n => BernsteinPoly n -> n -> n
+evaluateBernstein (BernsteinPoly _ [])       _ = 0
+evaluateBernstein (BernsteinPoly _ [b])      _ = b
+evaluateBernstein (BernsteinPoly lp (b':bs)) t = go t n (b'*u) 2 bs
+  where
+    u = 1-t
+    n = fromIntegral lp
+
+    go tn bc tmp _ [b]      = tmp + tn*bc*b
+    go tn bc tmp i (b:rest) =
+      go (tn*t)              -- tn
+         (bc*(n - i+1)/i)    -- bc
+         ((tmp + tn*bc*b)*u) -- tmp
+         (i+1)               -- i
+         rest
+    go _ _ _ _ []           = error "evaluateBernstein: impossible"
+
+-- | Evaluate the bernstein polynomial and its derivatives.
+evaluateBernsteinDerivs :: Fractional n => BernsteinPoly n -> n -> [n]
+evaluateBernsteinDerivs b t
+  | bernsteinDegree b == 0 = [evaluateBernstein b t]
+  | otherwise              = evaluateBernstein b t : evaluateBernsteinDerivs (bernsteinDeriv b) t
+
+-- | Find the derivative of a bernstein polynomial.
+bernsteinDeriv :: Fractional n => BernsteinPoly n -> BernsteinPoly n
+bernsteinDeriv (BernsteinPoly 0 _)  = 0
+bernsteinDeriv (BernsteinPoly lp p) =
+  -- BernsteinPoly (lp-1) $ map (* fromIntegral lp) $ zipWith (-) (tail p) p
+  BernsteinPoly (lp-1) $ zipWith (\a b -> (a - b) * fromIntegral lp) (tail p) p
+
+instance Fractional n => Parametric (BernsteinPoly n) where
+  atParam b = V1 . evaluateBernstein b
+instance Num n        => DomainBounds (BernsteinPoly n)
+instance Fractional n => EndValues    (BernsteinPoly n)
+instance Fractional n => Sectionable  (BernsteinPoly n) where
+  splitAtParam  = bernsteinSplit
+  reverseDomain (BernsteinPoly i xs) = BernsteinPoly i (reverse xs)
+
+-- | Split a bernstein polynomial.
+bernsteinSplit :: Num n => BernsteinPoly n -> n -> (BernsteinPoly n, BernsteinPoly n)
+bernsteinSplit (BernsteinPoly lp p) t =
+  (BernsteinPoly lp $ map head controls,
+   BernsteinPoly lp $ reverse $ map last controls)
+  where
+    interp a b = (1-t)*a + t*b
+
+    terp [_] = []
+    terp l   = let ctrs = zipWith interp l (tail l)
+               in  ctrs : terp ctrs
+    controls = p : terp p
+
+instance Fractional n => Num (BernsteinPoly n) where
+  ba@(BernsteinPoly la a) + bb@(BernsteinPoly lb b)
+    | la < lb   = BernsteinPoly lb $ zipWith (+) (bernsteinCoeffs $ degreeElevate ba $ lb - la) b
+    | la > lb   = BernsteinPoly la $ zipWith (+) a (bernsteinCoeffs $ degreeElevate bb $ la - lb)
+    | otherwise = BernsteinPoly la $ zipWith (+) a b
+
+  ba@(BernsteinPoly la a) - bb@(BernsteinPoly lb b)
+    | la < lb   = BernsteinPoly lb $ zipWith (-) (bernsteinCoeffs $ degreeElevate ba (lb - la)) b
+    | la > lb   = BernsteinPoly la $ zipWith (-) a (bernsteinCoeffs $ degreeElevate bb (la - lb))
+    | otherwise = BernsteinPoly la $ zipWith (-) a b
+
+  (BernsteinPoly la a) * (BernsteinPoly lb b) =
+    BernsteinPoly (la+lb) $
+    zipWith (flip (/)) (binomials (la + lb)) $
+                   init $ map sum $
+                   map (zipWith (*) a') (down b') ++
+                   map (zipWith (*) (reverse b')) (tail $ tails a')
+                   -- zipWith (zipWith (*)) (tail $ tails a') (repeat $ reverse b')
+    where down l = tail $ scanl (flip (:)) [] l -- [[1], [2, 1], [3, 2, 1], ...
+          a' = zipWith (*) a (binomials la)
+          b' = zipWith (*) b (binomials lb)
+
+  fromInteger a = BernsteinPoly 0 [fromInteger a]
+
+  signum (BernsteinPoly _ [])    = 0
+  signum (BernsteinPoly _ (a:_)) = BernsteinPoly 0 [signum a]
+
+  abs = fmap abs
diff --git a/src/Diagrams/TwoD/Shapes.hs b/src/Diagrams/TwoD/Shapes.hs
--- a/src/Diagrams/TwoD/Shapes.hs
+++ b/src/Diagrams/TwoD/Shapes.hs
@@ -1,7 +1,11 @@
+{-# LANGUAGE ConstraintKinds #-}
 {-# LANGUAGE FlexibleContexts #-}
 {-# LANGUAGE TemplateHaskell  #-}
 {-# LANGUAGE TypeFamilies     #-}
 
+{-# OPTIONS_GHC -fno-warn-unused-imports #-}
+  -- for Data.Semigroup
+
 -----------------------------------------------------------------------------
 -- |
 -- Module      :  Diagrams.TwoD.Shapes
@@ -45,6 +49,10 @@
        , roundedRect'
        ) where
 
+import           Control.Lens            (makeLenses, op, (&), (.~), (<>~), (^.))
+import           Data.Default
+import           Data.Semigroup
+
 import           Diagrams.Core
 
 import           Diagrams.Angle
@@ -57,12 +65,9 @@
 import           Diagrams.TwoD.Polygons
 import           Diagrams.TwoD.Transform
 import           Diagrams.TwoD.Types
-
+import           Diagrams.TwoD.Vector
 import           Diagrams.Util
 
-import           Control.Lens            (makeLenses, op, (&), (.~), (^.))
-import           Data.Default.Class
-import           Data.Semigroup
 
 -- | Create a centered horizontal (L-R) line of the given length.
 --
@@ -70,8 +75,8 @@
 --
 --   > hruleEx = vcat' (with & sep .~ 0.2) (map hrule [1..5])
 --   >         # centerXY # pad 1.1
-hrule :: (TrailLike t, V t ~ R2) => Double -> t
-hrule d = trailLike $ trailFromSegments [straight $ r2 (d, 0)] `at` (p2 (-d/2,0))
+hrule :: (InSpace V2 n t, TrailLike t) => n -> t
+hrule d = trailLike $ trailFromSegments [straight $ r2 (d, 0)] `at` p2 (-d/2,0)
 
 -- | Create a centered vertical (T-B) line of the given length.
 --
@@ -79,14 +84,14 @@
 --
 --   > vruleEx = hcat' (with & sep .~ 0.2) (map vrule [1, 1.2 .. 2])
 --   >         # centerXY # pad 1.1
-vrule :: (TrailLike t, V t ~ R2) => Double -> t
-vrule d = trailLike $ trailFromSegments [straight $ r2 (0, (-d))] `at` (p2 (0,d/2))
+vrule :: (InSpace V2 n t, TrailLike t) => n -> t
+vrule d = trailLike $ trailFromSegments [straight $ r2 (0, -d)] `at` p2 (0,d/2)
 
 -- | A square with its center at the origin and sides of length 1,
 --   oriented parallel to the axes.
 --
 --   <<diagrams/src_Diagrams_TwoD_Shapes_unitSquareEx.svg#diagram=unitSquareEx&width=100>>
-unitSquare :: (TrailLike t, V t ~ R2) => t
+unitSquare :: (InSpace V2 n t, TrailLike t) => t
 unitSquare = polygon (def & polyType   .~ PolyRegular 4 (sqrt 2 / 2)
                           & polyOrient .~ OrientH)
 
@@ -96,7 +101,7 @@
 --   length, oriented parallel to the axes.
 --
 --   <<diagrams/src_Diagrams_TwoD_Shapes_squareEx.svg#diagram=squareEx&width=200>>
-square :: (TrailLike t, Transformable t, V t ~ R2) => Double -> t
+square :: (InSpace V2 n t, TrailLike t) => n -> t
 square d = rect d d
 
 -- > squareEx = hcat' (with & sep .~ 0.5) [square 1, square 2, square 3]
@@ -106,7 +111,7 @@
 --   @h@, centered at the origin.
 --
 --   <<diagrams/src_Diagrams_TwoD_Shapes_rectEx.svg#diagram=rectEx&width=150>>
-rect :: (TrailLike t, Transformable t, V t ~ R2) => Double -> Double -> t
+rect :: (InSpace V2 n t, TrailLike t) => n -> n -> t
 rect w h = trailLike . head . op Path $ unitSquare # scaleX w # scaleY h
 
 -- > rectEx = rect 1 0.7 # pad 1.1
@@ -138,7 +143,7 @@
 --   polygons of a given /radius/).
 --
 --   The polygon will be oriented with one edge parallel to the x-axis.
-regPoly :: (TrailLike t, V t ~ R2) => Int -> Double -> t
+regPoly :: (InSpace V2 n t, TrailLike t) => Int -> n -> t
 regPoly n l = polygon (def & polyType .~
                                PolySides
                                  (repeat (1/fromIntegral n @@ turn))
@@ -158,90 +163,90 @@
 -- > dodecagonEx  = shapeEx dodecagon
 
 -- | A synonym for 'triangle', provided for backwards compatibility.
-eqTriangle :: (TrailLike t, V t ~ R2) => Double -> t
+eqTriangle :: (InSpace V2 n t, TrailLike t) => n -> t
 eqTriangle = triangle
 
 -- | An equilateral triangle, with sides of the given length and base
 --   parallel to the x-axis.
 --
 --   <<diagrams/src_Diagrams_TwoD_Shapes_triangleEx.svg#diagram=triangleEx&width=100>>
-triangle :: (TrailLike t, V t ~ R2) => Double -> t
+triangle :: (InSpace V2 n t, TrailLike t) => n -> t
 triangle = regPoly 3
 
 -- | A regular pentagon, with sides of the given length and base
 --   parallel to the x-axis.
 --
 --   <<diagrams/src_Diagrams_TwoD_Shapes_pentagonEx.svg#diagram=pentagonEx&width=100>>
-pentagon :: (TrailLike t, V t ~ R2) => Double -> t
+pentagon :: (InSpace V2 n t, TrailLike t) => n -> t
 pentagon = regPoly 5
 
 -- | A regular hexagon, with sides of the given length and base
 --   parallel to the x-axis.
 --
 --   <<diagrams/src_Diagrams_TwoD_Shapes_hexagonEx.svg#diagram=hexagonEx&width=100>>
-hexagon :: (TrailLike t, V t ~ R2) => Double -> t
+hexagon :: (InSpace V2 n t, TrailLike t) => n -> t
 hexagon = regPoly 6
 
 -- | A regular heptagon, with sides of the given length and base
 --   parallel to the x-axis.
 --
 --   <<diagrams/src_Diagrams_TwoD_Shapes_heptagonEx.svg#diagram=heptagonEx&width=100>>
-heptagon :: (TrailLike t, V t ~ R2) => Double -> t
+heptagon :: (InSpace V2 n t, TrailLike t) => n -> t
 heptagon = regPoly 7
 
 -- | A synonym for 'heptagon'.  It is, however, completely inferior,
 --   being a base admixture of the Latin /septum/ (seven) and the
 --   Greek γωνία (angle).
-septagon :: (TrailLike t, V t ~ R2) => Double -> t
+septagon :: (InSpace V2 n t, TrailLike t) => n -> t
 septagon = heptagon
 
 -- | A regular octagon, with sides of the given length and base
 --   parallel to the x-axis.
 --
 --   <<diagrams/src_Diagrams_TwoD_Shapes_octagonEx.svg#diagram=octagonEx&width=100>>
-octagon :: (TrailLike t, V t ~ R2) => Double -> t
+octagon :: (InSpace V2 n t, TrailLike t) => n -> t
 octagon = regPoly 8
 
 -- | A regular nonagon, with sides of the given length and base
 --   parallel to the x-axis.
 --
 --   <<diagrams/src_Diagrams_TwoD_Shapes_nonagonEx.svg#diagram=nonagonEx&width=100>>
-nonagon :: (TrailLike t, V t ~ R2) => Double -> t
+nonagon :: (InSpace V2 n t, TrailLike t) => n -> t
 nonagon = regPoly 9
 
 -- | A regular decagon, with sides of the given length and base
 --   parallel to the x-axis.
 --
 --   <<diagrams/src_Diagrams_TwoD_Shapes_decagonEx.svg#diagram=decagonEx&width=100>>
-decagon :: (TrailLike t, V t ~ R2) => Double -> t
+decagon :: (InSpace V2 n t, TrailLike t) => n -> t
 decagon = regPoly 10
 
 -- | A regular hendecagon, with sides of the given length and base
 --   parallel to the x-axis.
 --
 --   <<diagrams/src_Diagrams_TwoD_Shapes_hendecagonEx.svg#diagram=hendecagonEx&width=100>>
-hendecagon :: (TrailLike t, V t ~ R2) => Double -> t
+hendecagon :: (InSpace V2 n t, TrailLike t) => n -> t
 hendecagon = regPoly 11
 
 -- | A regular dodecagon, with sides of the given length and base
 --   parallel to the x-axis.
 --
 --   <<diagrams/src_Diagrams_TwoD_Shapes_dodecagonEx.svg#diagram=dodecagonEx&width=100>>
-dodecagon :: (TrailLike t, V t ~ R2) => Double -> t
+dodecagon :: (InSpace V2 n t, TrailLike t) => n -> t
 dodecagon = regPoly 12
 
 ------------------------------------------------------------
 --  Other shapes  ------------------------------------------
 ------------------------------------------------------------
-data RoundedRectOpts = RoundedRectOpts { _radiusTL :: Double
-                                       , _radiusTR :: Double
-                                       , _radiusBL :: Double
-                                       , _radiusBR :: Double
-                                       }
+data RoundedRectOpts d = RoundedRectOpts { _radiusTL :: d
+                                         , _radiusTR :: d
+                                         , _radiusBL :: d
+                                         , _radiusBR :: d
+                                         }
 
 makeLenses ''RoundedRectOpts
 
-instance Default RoundedRectOpts where
+instance (Num d) => Default (RoundedRectOpts d) where
   def = RoundedRectOpts 0 0 0 0
 
 -- | @roundedRect w h r@ generates a closed trail, or closed path
@@ -265,7 +270,7 @@
 --   >                                & radiusBR .~ 0.1)
 --   >   ]
 
-roundedRect :: (TrailLike t, V t ~ R2) => Double -> Double -> Double -> t
+roundedRect :: (InSpace V2 n t, TrailLike t, RealFloat n) => n -> n -> n -> t
 roundedRect w h r = roundedRect' w h (def & radiusTL .~ r
                                           & radiusBR .~ r
                                           & radiusTR .~ r
@@ -275,10 +280,10 @@
 --   each corner indivually, using @RoundedRectOpts@. The default corner radius is 0.
 --   Each radius can also be negative, which results in the curves being reversed
 --   to be inward instead of outward.
-roundedRect' :: (TrailLike t, V t ~ R2) => Double -> Double -> RoundedRectOpts -> t
+roundedRect' :: (InSpace V2 n t, TrailLike t, RealFloat n) => n -> n -> RoundedRectOpts n -> t
 roundedRect' w h opts
    = trailLike
-   . (`at` (p2 (w/2, abs rBR - h/2)))
+   . (`at` p2 (w/2, abs rBR - h/2))
    . wrapTrail
    . glueLine
    $ seg (0, h - abs rTR - abs rBR)
@@ -310,6 +315,8 @@
                                 else r
         sign n = if n < 0 then -1 else 1
         mkCorner k r | r == 0    = mempty
-                     | r < 0     = doArc 3 2
+                     | r < 0     = doArc 3 (-1)
                      | otherwise = doArc 0 1
-                     where doArc d d' = arc' r ((k+d)/4 @@ turn) ((k+d')/4 @@ turn)
+                     where
+                       doArc d s =
+                           arc' r (xDir & _theta <>~ ((k+d)/4 @@ turn)) (s/4 @@ turn)
diff --git a/src/Diagrams/TwoD/Size.hs b/src/Diagrams/TwoD/Size.hs
--- a/src/Diagrams/TwoD/Size.hs
+++ b/src/Diagrams/TwoD/Size.hs
@@ -1,8 +1,7 @@
-{-# LANGUAGE DeriveGeneric    #-}
+{-# LANGUAGE ConstraintKinds #-}
 {-# LANGUAGE FlexibleContexts #-}
 {-# LANGUAGE TypeFamilies     #-}
 
-{-# OPTIONS_GHC -funbox-strict-fields #-}
 -----------------------------------------------------------------------------
 -- |
 -- Module      :  Diagrams.TwoD.Size
@@ -15,143 +14,65 @@
 -----------------------------------------------------------------------------
 module Diagrams.TwoD.Size
        (
-         -- * Size and extent of diagrams in R2
          -- ** Computing sizes
-         width, height, size2D, sizeSpec2D
-       , extentX, extentY, center2D
+         width, height
+       , extentX, extentY
 
          -- ** Specifying sizes
-       , SizeSpec2D(..)
-       , mkSizeSpec
-
-       , requiredScaleT, requiredScale
+       , mkSizeSpec2D
+       , mkWidth
+       , mkHeight
+       , dims2D
 
-         -- ** Changing the size of things
-       , sized, sizedAs, sizePair
        ) where
 
 import           Diagrams.Core
+import           Diagrams.Core.Envelope
+import           Diagrams.Size
 import           Diagrams.TwoD.Types
 import           Diagrams.TwoD.Vector
 
-import           Control.Applicative  (liftA2, (<$>))
-import           Control.Arrow        ((&&&), (***))
-import           Data.Hashable        (Hashable)
-import           GHC.Generics         (Generic)
-
 ------------------------------------------------------------
 -- Computing diagram sizes
 ------------------------------------------------------------
 
 -- | Compute the width of an enveloped object.
-width :: (Enveloped a, V a ~ R2) => a -> Double
-width = maybe 0 (negate . uncurry (-)) . extentX
+--
+--   Note this is just @diameter unitX@.
+width :: (InSpace V2 n a, Enveloped a) => a -> n
+width = diameter unitX
 
 -- | Compute the height of an enveloped object.
-height :: (Enveloped a, V a ~ R2) => a -> Double
-height = maybe 0 (negate . uncurry (-)) . extentY
-
--- | Compute the width and height of an enveloped object.
-size2D :: (Enveloped a, V a ~ R2) => a -> (Double, Double)
-size2D = width &&& height
-
--- | Compute the size of an enveloped object as a 'SizeSpec2D' value.
-sizeSpec2D :: (Enveloped a, V a ~ R2) => a -> SizeSpec2D
-sizeSpec2D = uncurry Dims . size2D
+height :: (InSpace V2 n a, Enveloped a) => a -> n
+height = diameter unitY
 
--- | Compute the absolute  x-coordinate range of an enveloped object in
---   R2, in  the form (lo,hi).   Return @Nothing@ for objects  with an
---   empty envelope.
-extentX :: (Enveloped a, V a ~ R2) => a -> Maybe (Double, Double)
-extentX d = (\f -> (-f unit_X, f unitX)) <$> (appEnvelope . getEnvelope $ d)
+-- | Compute the absolute x-coordinate range of an enveloped object in
+--   the form @(lo,hi)@. Return @Nothing@ for objects with an empty
+--   envelope.
+--
+--   Note this is just @extent unitX@.
+extentX :: (InSpace v n a, R1 v, Enveloped a) => a -> Maybe (n, n)
+extentX = extent unitX
 
 -- | Compute the absolute y-coordinate range of an enveloped object in
---   R2, in the form (lo,hi).
-extentY :: (Enveloped a, V a ~ R2) => a -> Maybe (Double, Double)
-extentY d = (\f -> (-f unit_Y, f unitY)) <$> (appEnvelope . getEnvelope $ d)
-
--- | Compute the point at the center (in the x- and y-directions) of a
---   enveloped object.  Return the origin for objects with an empty
+--   the form @(lo,hi)@. Return @Nothing@ for objects with an empty
 --   envelope.
-center2D :: (Enveloped a, V a ~ R2) => a -> P2
-center2D = maybe origin (p2 . (mid *** mid)) . mm . (extentX &&& extentY)
-  where mm = uncurry (liftA2 (,))
-        mid = (/2) . uncurry (+)
-
-------------------------------------------------------------
--- Size specifications
-------------------------------------------------------------
-
--- | A specification of a (requested) rectangular size.
-data SizeSpec2D = Width  !Double       -- ^ Specify an explicit
-                                      -- width. The height should be
-                                      -- determined automatically (so
-                                      -- as to preserve aspect ratio).
-                | Height !Double       -- ^ Specify an explicit
-                                      -- height. The width should be
-                                      -- determined automatically (so
-                                      -- as to preserve aspect ratio).
-                | Dims !Double !Double  -- ^ An explicit specification
-                                      -- of a width and height.
-                | Absolute            -- ^ Absolute size: use whatever
-                                      -- size an object already has;
-                                      -- do not rescale.
-  deriving (Eq, Ord, Show, Generic)
-
-instance Hashable SizeSpec2D
-
--- | Create a size specification from a possibly-specified width and
---   height.
-mkSizeSpec :: Maybe Double -> Maybe Double -> SizeSpec2D
-mkSizeSpec Nothing  Nothing  = Absolute
-mkSizeSpec (Just w) Nothing  = Width w
-mkSizeSpec Nothing  (Just h) = Height h
-mkSizeSpec (Just w) (Just h) = Dims w h
+extentY :: (InSpace v n a, R2 v, Enveloped a) => a -> Maybe (n, n)
+extentY = extent unitY
 
--- | @requiredScaleT spec sz@ returns a transformation (a uniform scale)
---   which can be applied to something of size @sz@ to make it fit the
---   requested size @spec@, without changing the aspect ratio.
-requiredScaleT :: SizeSpec2D -> (Double, Double) -> Transformation R2
-requiredScaleT spec size = scaling (requiredScale spec size)
+-- | Make a 'SizeSpec' from possibly-specified width and height.
+mkSizeSpec2D :: Num n => Maybe n -> Maybe n -> SizeSpec V2 n
+mkSizeSpec2D x y = mkSizeSpec (V2 x y)
 
--- | @requiredScale spec sz@ returns a scaling factor necessary to
---   make something of size @sz@ fit the requested size @spec@,
---   without changing the aspect ratio.  Hence an explicit
---   specification of both dimensions may not be honored if the aspect
---   ratios do not match; in that case the scaling will be as large as
---   possible so that the object still fits within the requested size.
-requiredScale :: SizeSpec2D -> (Double, Double) -> Double
-requiredScale Absolute _    = 1
-requiredScale (Width wSpec) (w,_)
-  | wSpec == 0 || w == 0 = 1
-  | otherwise            = wSpec / w
-requiredScale (Height hSpec) (_,h)
-  | hSpec == 0 || h == 0 = 1
-  | otherwise            = hSpec / h
-requiredScale (Dims wSpec hSpec) (w,h) = s
-  where xscale  = wSpec / w
-        yscale  = hSpec / h
-        s'      = min xscale yscale
-        s | isInfinite s' = 1
-          | otherwise     = s'
+-- | Make a 'SizeSpec' from a width and height.
+dims2D :: n -> n -> SizeSpec V2 n
+dims2D x y = dims (V2 x y)
 
--- | Uniformly scale any enveloped object so that it fits within the
---   given size.
-sized :: (Transformable a, Enveloped a, V a ~ R2)
-      => SizeSpec2D -> a -> a
-sized spec a = transform (requiredScaleT spec (size2D a)) a
+-- | Make a 'SizeSpec' with only width defined.
+mkWidth :: Num n => n -> SizeSpec V2 n
+mkWidth w = dims (V2 w 0)
 
--- | Uniformly scale an enveloped object so that it \"has the same
---   size as\" (fits within the width and height of) some other
---   object.
-sizedAs :: ( Transformable a, Enveloped a, V a ~ R2
-           , Enveloped b, V b ~ R2)
-        => b -> a -> a
-sizedAs other = sized (sizeSpec2D other)
+-- | Make a 'SizeSpec' with only height defined.
+mkHeight :: Num n => n -> SizeSpec V2 n
+mkHeight h = dims (V2 0 h)
 
--- | Make width and height of `SizeSpec2D` into a tuple.
-sizePair :: SizeSpec2D -> (Double, Double)
-sizePair (Width w')   = (w',w')
-sizePair (Height h')  = (h',h')
-sizePair (Dims w' h') = (w',h')
-sizePair Absolute     = (100,100)
diff --git a/src/Diagrams/TwoD/Text.hs b/src/Diagrams/TwoD/Text.hs
--- a/src/Diagrams/TwoD/Text.hs
+++ b/src/Diagrams/TwoD/Text.hs
@@ -1,12 +1,17 @@
+{-# LANGUAGE ConstraintKinds            #-}
 {-# LANGUAGE DeriveDataTypeable         #-}
 {-# LANGUAGE FlexibleContexts           #-}
+{-# LANGUAGE FlexibleInstances          #-}
 {-# LANGUAGE GeneralizedNewtypeDeriving #-}
 {-# LANGUAGE MultiParamTypeClasses      #-}
 {-# LANGUAGE TypeFamilies               #-}
+{-# LANGUAGE TypeOperators              #-}
+{-# LANGUAGE UndecidableInstances       #-}
+
 -----------------------------------------------------------------------------
 -- |
 -- Module      :  Diagrams.TwoD.Text
--- Copyright   :  (c) 2011 diagrams-lib team (see LICENSE)
+-- Copyright   :  (c) 2011-2015 diagrams-lib team (see LICENSE)
 -- License     :  BSD-style (see LICENSE)
 -- Maintainer  :  diagrams-discuss@googlegroups.com
 --
@@ -18,72 +23,99 @@
   -- * Creating text diagrams
     Text(..), TextAlignment(..)
   , text, topLeftText, alignedText, baselineText
+  , mkText, mkText'
 
   -- * Text attributes
+
   -- ** Font family
-  , Font(..), getFont, font
+  , Font(..), _Font
+  , getFont, font, _font
+
   -- ** Font size
-  , FontSize(..), getFontSize, getFontSizeIsLocal, fontSizeA, fontSize
+  , FontSize(..), _FontSize
+  , fontSize, recommendFontSize
   , fontSizeN, fontSizeO, fontSizeL, fontSizeG
+  , getFontSize, fontSizeM
+  , _fontSizeR, _fontSize, _fontSizeU
+
   -- ** Font slant
-  , FontSlant(..), FontSlantA, getFontSlant, fontSlant, italic, oblique
+  , FontSlant(..)
+  , getFontSlant, fontSlant, italic, oblique, _fontSlant
+
   -- ** Font weight
-  , FontWeight(..), FontWeightA, getFontWeight, fontWeight, bold
+  , FontWeight(..)
+  , getFontWeight, fontWeight, bold, bolder, lighter, _fontWeight
+  , thinWeight, ultraLight, light, mediumWeight, heavy, semiBold, ultraBold
+
   ) where
 
+import           Control.Lens             hiding (transform)
+import           Diagrams.Attributes      (committed)
 import           Diagrams.Core
 import           Diagrams.Core.Envelope   (pointEnvelope)
 import           Diagrams.TwoD.Attributes (recommendFillColor)
 import           Diagrams.TwoD.Types
 
-import           Data.AffineSpace         ((.-.))
-import           Data.Colour
-import           Data.Data
-import           Data.Default.Class
+import           Data.Colour              hiding (over)
+import           Data.Default
+import           Data.Monoid.Recommend
 import           Data.Semigroup
+import           Data.Typeable
 
+import           Linear.Affine
+
 ------------------------------------------------------------
 -- Text diagrams
 ------------------------------------------------------------
 
--- | A text primitive consists of the string contents and alignment
---   specification, along with two transformations: the first
---   accumulates all transformations which have been applied to the
---   text; the second accumulates normalized, "anti-scaled" versions
---   of the transformations which have had their average scaling
---   component removed.
-data Text = Text T2 T2 TextAlignment String
+-- | A 'Text' primitive consists of the string contents, text alignment
+--   and the transformation to be applied. The transformation is scale
+--   invarient, the average scale of the transform should always be 1.
+--   All text scaling is obtained from the 'FontSize' attribute.
+--
+--   This constructor should not be used directly. Use 'text',
+--   'alignedText' or 'baselineText'.
+data Text n = Text (T2 n) (TextAlignment n) String
   deriving Typeable
 
-type instance V Text = R2
+type instance V (Text n) = V2
+type instance N (Text n) = n
 
-instance Transformable Text where
-  transform t (Text tt tn a s) = Text (t <> tt) (t <> tn <> t') a s
-    where
-      t' = scaling (1 / avgScale t)
-      -- It's important that the anti-scaling is applied *first*,
-      -- followed by the old transformation tn and then the new
-      -- transformation t.  That way translation is handled properly.
+instance Floating n => Transformable (Text n) where
+  transform t (Text tt a s) = Text (t <> tt <> t') a s
+    where t' = scaling (1 / avgScale t)
 
-instance HasOrigin Text where
+instance Floating n => HasOrigin (Text n) where
   moveOriginTo p = translate (origin .-. p)
 
-instance Renderable Text NullBackend where
+instance Floating n => Renderable (Text n) NullBackend where
   render _ _ = mempty
 
 -- | @TextAlignment@ specifies the alignment of the text's origin.
-data TextAlignment = BaselineText | BoxAlignedText Double Double
+data TextAlignment n = BaselineText | BoxAlignedText n n
 
-mkText :: Renderable Text b => TextAlignment -> String -> Diagram b R2
-mkText a t = recommendFillColor (black :: Colour Double)
-             -- See Note [recommendFillColor]
+-- | Make a text from a 'TextAlignment', recommending a fill colour of
+--   'black' and 'fontSize' of @'local' 1@.
+mkText :: (TypeableFloat n, Renderable (Text n) b)
+  => TextAlignment n -> String -> QDiagram b V2 n Any
+mkText a = recommendFillColor black
+           -- See Note [recommendFillColor]
+         . recommendFontSize (local 1)
+           -- See Note [recommendFontSize]
+         . mkText' a
 
-           $ mkQD (Prim (Text mempty mempty a t))
-                       (pointEnvelope origin)
-                       mempty
-                       mempty
-                       mempty
+-- | Make a text from a 'TextAlignment' without any default size or fill
+--   colour. This is useful is you want to recommend your own using
+--   'recommendFillColor' or 'recommendFontSize'.
+mkText' :: (TypeableFloat n, Renderable (Text n) b)
+  => TextAlignment n -> String -> QDiagram b V2 n Any
+mkText' a t = mkQD (Prim $ Text mempty a t)
+                   (pointEnvelope origin)
+                   mempty
+                   mempty
+                   mempty
 
+
 -- ~~~~ Note [recommendFillColor]
 
 -- The reason we "recommend" a fill color of black instead of setting
@@ -106,12 +138,16 @@
 -- recommendation; normally, the innermost occurrence of an attribute
 -- would override all outer occurrences.
 
+-- ~~~~ Note [recommendFontSize]
+-- The reason we "recommend" a font size is so any local scales get
+-- recorded.
+
 -- | Create a primitive text diagram from the given string, with center
 --   alignment, equivalent to @'alignedText' 0.5 0.5@.
 --
 --   Note that it /takes up no space/, as text size information is not
 --   available.
-text :: Renderable Text b => String -> Diagram b R2
+text :: (TypeableFloat n, Renderable (Text n) b) => String -> QDiagram b V2 n Any
 text = alignedText 0.5 0.5
 
 -- | Create a primitive text diagram from the given string, origin at
@@ -119,19 +155,21 @@
 --   @'alignedText' 0 1@.
 --
 --   Note that it /takes up no space/.
-topLeftText :: Renderable Text b => String -> Diagram b R2
+topLeftText :: (TypeableFloat n, Renderable (Text n) b) => String -> QDiagram b V2 n Any
 topLeftText = alignedText 0 1
 
 -- | Create a primitive text diagram from the given string, with the
 --   origin set to a point interpolated within the bounding box.  The
 --   first parameter varies from 0 (left) to 1 (right), and the second
---   parameter from 0 (bottom) to 1 (top).
+--   parameter from 0 (bottom) to 1 (top). Some backends do not
+--   implement this and instead snap to closest corner or the center.
 --
 --   The height of this box is determined by the font's potential ascent
 --   and descent, rather than the height of the particular string.
 --
 --   Note that it /takes up no space/.
-alignedText :: Renderable Text b => Double -> Double -> String -> Diagram b R2
+alignedText :: (TypeableFloat n, Renderable (Text n) b)
+  => n -> n -> String -> QDiagram b V2 n Any
 alignedText w h = mkText (BoxAlignedText w h)
 
 -- | Create a primitive text diagram from the given string, with the
@@ -140,7 +178,8 @@
 --   graphics library.
 --
 --   Note that it /takes up no space/.
-baselineText :: Renderable Text b => String -> Diagram b R2
+baselineText :: (TypeableFloat n, Renderable (Text n) b)
+  => String -> QDiagram b V2 n Any
 baselineText = mkText BaselineText
 
 ------------------------------------------------------------
@@ -154,6 +193,10 @@
 --   @Font@ attributes override outer ones.
 newtype Font = Font (Last String)
   deriving (Typeable, Semigroup, Eq)
+
+_Font :: Iso' Font String
+_Font = iso getFont (Font . Last)
+
 instance AttributeClass Font
 
 -- | Extract the font family name from a @Font@ attribute.
@@ -164,94 +207,123 @@
 font :: HasStyle a => String -> a -> a
 font = applyAttr . Font . Last
 
+-- | Lens onto the font name of a style.
+_font :: Lens' (Style v n) (Maybe String)
+_font = atAttr . mapping _Font
+
 --------------------------------------------------
 -- Font size
 
 -- | The @FontSize@ attribute specifies the size of a font's
 --   em-square.  Inner @FontSize@ attributes override outer ones.
-newtype FontSize = FontSize (Last (Measure R2, Bool))
-  deriving (Typeable, Data, Semigroup)
-instance AttributeClass FontSize
+newtype FontSize n = FontSize (Recommend (Last n))
+  deriving (Typeable, Semigroup)
 
--- Note, the Bool stored in the FontSize indicates whether it started
--- life as Local.  Typically, if the Bool is True, backends should use
--- the first T2 value stored in a Text object; otherwise, the second
--- (anti-scaled) T2 value should be used.
+-- not sure why this can't be derived
+instance Functor FontSize where
+  fmap f (FontSize (Recommend (Last a))) = FontSize (Recommend (Last (f a)))
+  fmap f (FontSize (Commit (Last a)))    = FontSize (Commit (Last (f a)))
 
-type instance V FontSize = R2
+_FontSize :: Iso' (FontSize n) (Recommend n)
+_FontSize = iso getter setter
+  where getter (FontSize (Recommend (Last a))) = Recommend a
+        getter (FontSize (Commit    (Last a))) = Commit a
+        setter (Recommend a) = FontSize $ Recommend (Last a)
+        setter (Commit    a) = FontSize $ Commit (Last a)
+      -- = iso (\(FontSize a) -> a) FontSize . mapping _Wrapped
+      -- once we depend on monoid-extras-0.4
 
-instance Default FontSize where
-    def = FontSize (Last (Local 1, True))
+_FontSizeM :: Iso' (FontSizeM n) (Measured n (Recommend n))
+_FontSizeM = mapping _FontSize
 
--- FontSize has to be Transformable + also have an instance of Data,
--- so the Measure inside it will be automatically converted to Output.
--- However, we don't actually want the Transformable instance to do
--- anything.  All the scaling of text happens not by manipulating the
--- font size but by accumulating T2 values in Text objects.
-instance Transformable FontSize where
-  transform _ f = f
+type FontSizeM n = Measured n (FontSize n)
 
--- | Extract the size from a @FontSize@ attribute.
-getFontSize :: FontSize -> Measure R2
-getFontSize (FontSize (Last (s,_))) = s
+instance Typeable n => AttributeClass (FontSize n)
 
--- | Determine whether a @FontSize@ attribute began its life measured
---   in 'Local' units.
-getFontSizeIsLocal :: FontSize -> Bool
-getFontSizeIsLocal (FontSize (Last (_,b))) = b
+instance Num n => Default (FontSizeM n) where
+  def = FontSize . Recommend . Last <$> local 1
 
+-- | Extract the size from a @FontSize@ attribute.
+getFontSize :: FontSize n -> n
+getFontSize (FontSize (Recommend (Last s))) = s
+getFontSize (FontSize (Commit (Last s)))    = s
+
 -- | Set the font size, that is, the size of the font's em-square as
---   measured within the current local vector space.  The default size
---   is @1@.
-fontSize :: (HasStyle a, V a ~ R2) => Measure R2 -> a -> a
-fontSize m@(Local {}) = applyGTAttr . FontSize . Last $ (m,True)
-fontSize m            = applyGTAttr . FontSize . Last $ (m,False)
+--   measured within the current local vector space. The default size
+--   is @local 1@ (which is applied by 'recommendFontSize').
+fontSize :: (N a ~ n, Typeable n, HasStyle a) => Measure n -> a -> a
+fontSize = applyMAttr . fmap (FontSize . Commit . Last)
 
+-- | 'Recommend' a font size. Any use of 'fontSize' above this will
+--   overwrite any recommended size. This should only be used with
+--   'mkText'', other text functions already has a recommended font
+--   size so this will be ignored.
+recommendFontSize :: (N a ~ n, Typeable n, HasStyle a) => Measure n -> a -> a
+recommendFontSize = applyMAttr . fmap (FontSize . Recommend . Last)
+
 -- | A convenient synonym for 'fontSize (Global w)'.
-fontSizeG :: (HasStyle a, V a ~ R2) => Double -> a -> a
-fontSizeG w = fontSize (Global w)
+fontSizeG :: (N a ~ n, Typeable n, Num n, HasStyle a) => n -> a -> a
+fontSizeG = fontSize . global
 
 -- | A convenient synonym for 'fontSize (Normalized w)'.
-fontSizeN :: (HasStyle a, V a ~ R2) => Double -> a -> a
-fontSizeN w = fontSize (Normalized w)
+fontSizeN :: (N a ~ n, Typeable n, Num n, HasStyle a) => n -> a -> a
+fontSizeN = fontSize . normalized
 
 -- | A convenient synonym for 'fontSize (Output w)'.
-fontSizeO :: (HasStyle a, V a ~ R2) => Double -> a -> a
-fontSizeO w = fontSize (Output w)
+fontSizeO :: (N a ~ n, Typeable n, HasStyle a) => n -> a -> a
+fontSizeO = fontSize . output
 
 -- | A convenient sysnonym for 'fontSize (Local w)'.
-fontSizeL :: (HasStyle a, V a ~ R2) => Double -> a -> a
-fontSizeL w = fontSize (Local w)
+fontSizeL :: (N a ~ n, Typeable n, Num n, HasStyle a) => n -> a -> a
+fontSizeL = fontSize . local
 
 -- | Apply a 'FontSize' attribute.
-fontSizeA :: (HasStyle a, V a ~ R2) => FontSize -> a -> a
-fontSizeA = applyGTAttr
+fontSizeM :: (N a ~ n, Typeable n, HasStyle a) => FontSizeM n -> a -> a
+fontSizeM = applyMAttr
 
+_fontSizeR :: (Typeable n, OrderedField n) => Lens' (Style v n) (Measured n (Recommend n))
+_fontSizeR = atMAttr . anon def (const False) . _FontSizeM
+
+-- | Lens to commit a font size. This is *not* a valid lens (see
+--   'commited'.
+_fontSize :: (Typeable n, OrderedField n) => Lens' (Style v n) (Measure n)
+_fontSize = _fontSizeR . mapping committed
+
+_fontSizeU :: (Typeable n) => Lens' (Style v n) (Maybe n)
+_fontSizeU = atAttr . mapping (_FontSize . committed)
+
 --------------------------------------------------
 -- Font slant
 
+-- | The @FontSlantA@ attribute specifies the slant (normal, italic,
+--   or oblique) that should be used for all text within a diagram.
+--   Inner @FontSlantA@ attributes override outer ones.
 data FontSlant = FontSlantNormal
                | FontSlantItalic
                | FontSlantOblique
-    deriving (Eq)
+  deriving (Eq, Show, Typeable, Ord)
 
--- | The @FontSlantA@ attribute specifies the slant (normal, italic,
---   or oblique) that should be used for all text within a diagram.
---   Inner @FontSlantA@ attributes override outer ones.
-newtype FontSlantA = FontSlantA (Last FontSlant)
-  deriving (Typeable, Semigroup, Eq)
-instance AttributeClass FontSlantA
+instance AttributeClass FontSlant where
+instance Semigroup FontSlant where
+  _ <> b = b
 
+instance Default FontSlant where
+  def = FontSlantNormal
+
 -- | Extract the font slant from a 'FontSlantA' attribute.
-getFontSlant :: FontSlantA -> FontSlant
-getFontSlant (FontSlantA (Last s)) = s
+getFontSlant :: FontSlant -> FontSlant
+getFontSlant = id
 
 -- | Specify the slant (normal, italic, or oblique) that should be
 --   used for all text within a diagram.  See also 'italic' and
 --   'oblique' for useful special cases.
 fontSlant :: HasStyle a => FontSlant -> a -> a
-fontSlant = applyAttr . FontSlantA . Last
+fontSlant = applyAttr
 
+-- | Lens onto the font slant in a style.
+_fontSlant :: Lens' (Style v n) FontSlant
+_fontSlant = atAttr . non def
+
 -- | Set all text in italics.
 italic :: HasStyle a => a -> a
 italic = fontSlant FontSlantItalic
@@ -263,27 +335,82 @@
 --------------------------------------------------
 -- Font weight
 
-data FontWeight = FontWeightNormal
-                | FontWeightBold
-    deriving (Eq)
-
 -- | The @FontWeightA@ attribute specifies the weight (normal or bold)
 --   that should be used for all text within a diagram.  Inner
 --   @FontWeightA@ attributes override outer ones.
-newtype FontWeightA = FontWeightA (Last FontWeight)
-  deriving (Typeable, Semigroup, Eq)
-instance AttributeClass FontWeightA
+data FontWeight = FontWeightNormal
+                | FontWeightBold
+                | FontWeightBolder
+                | FontWeightLighter
+                | FontWeightThin
+                | FontWeightUltraLight
+                | FontWeightLight
+                | FontWeightMedium
+                | FontWeightSemiBold
+                | FontWeightUltraBold
+                | FontWeightHeavy
+    deriving (Eq,
+              Ord, Show, Typeable)
 
--- | Extract the font weight from a 'FontWeightA' attribute.
-getFontWeight :: FontWeightA -> FontWeight
-getFontWeight (FontWeightA (Last w)) = w
+instance AttributeClass FontWeight
 
--- | Specify the weight (normal or bold) that should be
+-- | Last semigroup structure
+instance Semigroup FontWeight where
+  _ <> b = b
+
+instance Default FontWeight where
+  def = FontWeightNormal
+
+-- | Extract the font weight.
+getFontWeight :: FontWeight -> FontWeight
+getFontWeight = id
+
+-- | Specify the weight (normal, bolder, lighter or bold) that should be
 --   used for all text within a diagram.  See also 'bold'
 --   for a useful special case.
 fontWeight :: HasStyle a => FontWeight -> a -> a
-fontWeight = applyAttr . FontWeightA . Last
+fontWeight = applyAttr
 
 -- | Set all text using a bold font weight.
 bold :: HasStyle a => a -> a
 bold = fontWeight FontWeightBold
+
+-- | Set all text using a thin font weight.
+thinWeight :: HasStyle a => a -> a
+thinWeight = fontWeight FontWeightThin
+
+-- | Set all text using a extra light font weight.
+ultraLight :: HasStyle a => a -> a
+ultraLight = fontWeight FontWeightUltraLight
+
+-- | Set all text using a light font weight.
+light :: HasStyle a => a -> a
+light = fontWeight FontWeightLight
+
+-- | Set all text using a medium font weight.
+mediumWeight :: HasStyle a => a -> a
+mediumWeight = fontWeight FontWeightMedium
+
+-- | Set all text using a semi-bold font weight.
+semiBold :: HasStyle a => a -> a
+semiBold = fontWeight FontWeightSemiBold
+
+-- | Set all text using an ultra-bold font weight.
+ultraBold :: HasStyle a => a -> a
+ultraBold = fontWeight FontWeightUltraBold
+
+-- | Set all text using a heavy/black font weight.
+heavy :: HasStyle a => a -> a
+heavy = fontWeight FontWeightHeavy
+
+-- | Set all text to be bolder than the inherited font weight.
+bolder :: HasStyle a => a -> a
+bolder = fontWeight FontWeightBolder
+
+-- | Set all text to be lighter than the inherited font weight.
+lighter :: HasStyle a => a -> a
+lighter = fontWeight FontWeightLighter
+
+-- | Lens onto the font weight in a style.
+_fontWeight :: Lens' (Style v n) FontWeight
+_fontWeight = atAttr . non def
diff --git a/src/Diagrams/TwoD/Transform.hs b/src/Diagrams/TwoD/Transform.hs
--- a/src/Diagrams/TwoD/Transform.hs
+++ b/src/Diagrams/TwoD/Transform.hs
@@ -1,12 +1,19 @@
+{-# LANGUAGE ConstraintKinds #-}
 {-# LANGUAGE FlexibleContexts      #-}
 {-# LANGUAGE FlexibleInstances     #-}
 {-# LANGUAGE MultiParamTypeClasses #-}
+{-# LANGUAGE RankNTypes            #-}
 {-# LANGUAGE TypeFamilies          #-}
+{-# LANGUAGE TypeOperators         #-}
 {-# LANGUAGE ViewPatterns          #-}
+
+{-# OPTIONS_GHC -fno-warn-unused-imports #-}
+  -- for Data.Semigroup
+
 -----------------------------------------------------------------------------
 -- |
 -- Module      :  Diagrams.TwoD.Transform
--- Copyright   :  (c) 2011 diagrams-lib team (see LICENSE)
+-- Copyright   :  (c) 2011-2015 diagrams-lib team (see LICENSE)
 -- License     :  BSD-style (see LICENSE)
 -- Maintainer  :  diagrams-discuss@googlegroups.com
 --
@@ -18,10 +25,11 @@
 
 module Diagrams.TwoD.Transform
        (
+         T2
          -- * Rotation
-         rotation, rotate, rotateBy
-
-       , rotationAbout, rotateAbout
+       , rotation, rotate, rotateBy, rotated
+       , rotationAround, rotateAround
+       , rotationTo, rotateTo
 
          -- * Scaling
        , scalingX, scaleX
@@ -36,216 +44,262 @@
        , translationY, translateY
        , translation, translate
 
+         -- * Conformal affine maps
+       , scalingRotationTo, scaleRotateTo
+
          -- * Reflection
        , reflectionX, reflectX
        , reflectionY, reflectY
+       , reflectionXY, reflectXY
        , reflectionAbout, reflectAbout
 
          -- * Shears
        , shearingX, shearX
        , shearingY, shearY
 
-         -- * Utilities
-       , onBasis
        ) where
 
-import           Diagrams.Core
-import qualified Diagrams.Core.Transform as T
-
 import           Diagrams.Angle
+import           Diagrams.Core
+import           Diagrams.Core.Transform
+import           Diagrams.Direction
 import           Diagrams.Transform
-import           Diagrams.TwoD.Size      (height, width)
+import           Diagrams.Transform.Matrix
 import           Diagrams.TwoD.Types
-import           Diagrams.TwoD.Vector    (direction)
-import           Diagrams.Coordinates
+import           Diagrams.TwoD.Vector
 
-import           Data.AdditiveGroup
-import           Data.AffineSpace
+import           Control.Lens              hiding (at, transform)
 import           Data.Semigroup
-import           Control.Lens            (review, (^.))
 
--- Rotation ------------------------------------------------
+import           Linear.Affine
+import           Linear.Metric
+import           Linear.V2
+import           Linear.Vector
 
--- | Create a transformation which performs a rotation about the local
---   origin by the given angle.  See also 'rotate'.
-rotation :: Angle -> T2
-rotation ang = fromLinear r (linv r)
-  where
-    r            = rot theta <-> rot (-theta)
-    theta    = ang^.rad
-    rot th (coords -> x :& y) = (cos th * x - sin th * y) ^& (sin th * x + cos th * y)
+-- Rotation ------------------------------------------------
 
--- | Rotate about the local origin by the given angle. Positive angles
---   correspond to counterclockwise rotation, negative to
---   clockwise. The angle can be expressed using any of the 'Iso's on
---   'Angle'.  For example, @rotate (1\/4 \@\@ 'turn')@, @rotate
---   (tau\/4 \@\@ rad)@, and @rotate (90 \@\@ deg)@ all
---   represent the same transformation, namely, a counterclockwise
---   rotation by a right angle.  To rotate about some point other than
---   the local origin, see 'rotateAbout'.
---
---   Note that writing @rotate (1\/4)@, with no 'Angle' constructor,
---   will yield an error since GHC cannot figure out which sort of
---   angle you want to use.  In this common situation you can use
---   'rotateBy', which interprets its argument as a number of turns.
-rotate :: (Transformable t, V t ~ R2) => Angle -> t -> t
-rotate = transform . rotation
+-- For the definitions of 'rotation' and 'rotate', see Diagrams.Angle.
 
 -- | A synonym for 'rotate', interpreting its argument in units of
 -- turns; it can be more convenient to write @rotateBy (1\/4)@ than
 -- @'rotate' (1\/4 \@\@ 'turn')@.
-rotateBy :: (Transformable t, V t ~ R2) => Double -> t -> t
+rotateBy :: (InSpace V2 n t, Transformable t, Floating n) => n -> t -> t
 rotateBy = transform . rotation . review turn
 
+-- | Use an 'Angle' to make an 'Iso' between an object
+--   rotated and unrotated. This us useful for performing actions
+--   'under' a rotation:
+--
+-- @
+-- under (rotated t) f = rotate (negated t) . f . rotate t
+-- rotated t ## a      = rotate t a
+-- a ^. rotated t      = rotate (-t) a
+-- over (rotated t) f  = rotate t . f . rotate (negated t)
+-- @
+rotated :: (InSpace V2 n a, Floating n, SameSpace a b, Transformable a, Transformable b)
+        => Angle n -> Iso a b a b
+rotated a = transformed $ rotation a
+
 -- | @rotationAbout p@ is a rotation about the point @p@ (instead of
 --   around the local origin).
-rotationAbout :: P2 -> Angle -> T2
-rotationAbout p angle = conjugate (translation (origin .-. p)) (rotation angle)
+rotationAround :: Floating n => P2 n -> Angle n -> T2 n
+rotationAround p theta =
+  conjugate (translation (origin .-. p)) (rotation theta)
 
 -- | @rotateAbout p@ is like 'rotate', except it rotates around the
 --   point @p@ instead of around the local origin.
-rotateAbout :: (Transformable t, V t ~ R2) => P2 -> Angle -> t -> t
-rotateAbout p angle = rotate angle `under` translation (origin .-. p)
+rotateAround :: (InSpace V2 n t, Transformable t, Floating n)
+             => P2 n -> Angle n -> t -> t
+rotateAround p theta = transform (rotationAround p theta)
 
+-- | The rotation that aligns the x-axis with the given direction.
+rotationTo :: OrderedField n => Direction V2 n -> T2 n
+rotationTo (view _Dir -> V2 x y) = rotation (atan2A' y x)
+
+-- | Rotate around the local origin such that the x axis aligns with the
+--   given direction.
+rotateTo :: (InSpace V2 n t, OrderedField n, Transformable t) => Direction V2 n -> t -> t
+rotateTo = transform . rotationTo
+
 -- Scaling -------------------------------------------------
 
 -- | Construct a transformation which scales by the given factor in
 --   the x (horizontal) direction.
-scalingX :: Double -> T2
-scalingX c = fromLinear s s
-  where s = (\(R2 x y) -> R2 (x*c) y) <-> (\(R2 x y) -> R2 (x/c) y)
+scalingX :: (Additive v, R1 v, Fractional n) => n -> Transformation v n
+scalingX c = fromSymmetric $ (_x *~ c) <-> (_x //~ c)
 
 -- | Scale a diagram by the given factor in the x (horizontal)
 --   direction.  To scale uniformly, use 'scale'.
-scaleX :: (Transformable t, V t ~ R2) => Double -> t -> t
+scaleX :: (InSpace v n t, R2 v, Fractional n, Transformable t) => n -> t -> t
 scaleX = transform . scalingX
 
 -- | Construct a transformation which scales by the given factor in
 --   the y (vertical) direction.
-scalingY :: Double -> T2
-scalingY c = fromLinear s s
-  where s = (\(R2 x y) -> R2 x (y*c)) <-> (\(R2 x y) -> R2 x (y/c))
+scalingY :: (Additive v, R2 v, Fractional n) => n -> Transformation v n
+scalingY c = fromSymmetric $ (_y *~ c) <-> (_y //~ c)
 
 -- | Scale a diagram by the given factor in the y (vertical)
 --   direction.  To scale uniformly, use 'scale'.
-scaleY :: (Transformable t, V t ~ R2) => Double -> t -> t
+scaleY :: (InSpace v n t, R2 v, Fractional n, Transformable t)
+  => n -> t -> t
 scaleY = transform . scalingY
 
 -- | @scaleToX w@ scales a diagram in the x (horizontal) direction by
 --   whatever factor required to make its width @w@.  @scaleToX@
 --   should not be applied to diagrams with a width of 0, such as
 --   'vrule'.
-scaleToX :: (Enveloped t, Transformable t, V t ~ R2) => Double -> t -> t
-scaleToX w d = scaleX (w / width d) d
+scaleToX :: (InSpace v n t, R2 v, Enveloped t, Transformable t) => n -> t -> t
+scaleToX w d = scaleX (w / diameter unitX d) d
 
 -- | @scaleToY h@ scales a diagram in the y (vertical) direction by
 --   whatever factor required to make its height @h@.  @scaleToY@
 --   should not be applied to diagrams with a height of 0, such as
 --   'hrule'.
-scaleToY :: (Enveloped t, Transformable t, V t ~ R2) => Double -> t -> t
-scaleToY h d = scaleY (h / height d) d
+scaleToY :: (InSpace v n t, R2 v, Enveloped t, Transformable t) => n -> t -> t
+scaleToY h d = scaleY (h / diameter unitY d) d
 
 -- | @scaleUToX w@ scales a diagram /uniformly/ by whatever factor
 --   required to make its width @w@.  @scaleUToX@ should not be
 --   applied to diagrams with a width of 0, such as 'vrule'.
-scaleUToX :: (Enveloped t, Transformable t, V t ~ R2) => Double -> t -> t
-scaleUToX w d = scale (w / width d) d
+scaleUToX :: (InSpace v n t, R1 v, Enveloped t, Transformable t) => n -> t -> t
+scaleUToX w d = scale (w / diameter unitX d) d
 
 -- | @scaleUToY h@ scales a diagram /uniformly/ by whatever factor
 --   required to make its height @h@.  @scaleUToY@ should not be applied
 --   to diagrams with a height of 0, such as 'hrule'.
-scaleUToY :: (Enveloped t, Transformable t, V t ~ R2) => Double -> t -> t
-scaleUToY h d = scale (h / height d) d
+scaleUToY :: (InSpace v n t, R2 v, Enveloped t, Transformable t) => n -> t -> t
+scaleUToY h d = scale (h / diameter unitY d) d
 
 -- Translation ---------------------------------------------
 
 -- | Construct a transformation which translates by the given distance
 --   in the x (horizontal) direction.
-translationX :: Double -> T2
-translationX x = translation (x ^& 0)
+translationX :: (Additive v, R1 v, Num n) => n -> Transformation v n
+translationX x = translation (zero & _x .~ x)
 
 -- | Translate a diagram by the given distance in the x (horizontal)
 --   direction.
-translateX :: (Transformable t, V t ~ R2) => Double -> t -> t
+translateX :: (InSpace v n t, R1 v, Transformable t) => n -> t -> t
 translateX = transform . translationX
 
 -- | Construct a transformation which translates by the given distance
 --   in the y (vertical) direction.
-translationY :: Double -> T2
-translationY y = translation (0 ^& y)
+translationY :: (Additive v, R2 v, Num n) => n -> Transformation v n
+translationY y = translation (zero & _y .~ y)
 
 -- | Translate a diagram by the given distance in the y (vertical)
 --   direction.
-translateY :: (Transformable t, V t ~ R2) => Double -> t -> t
+translateY :: (InSpace v n t, R2 v, Transformable t)
+  => n -> t -> t
 translateY = transform . translationY
 
+-- Conformal affine maps -----------------------------------
+
+-- | The angle-preserving linear map that aligns the x-axis unit vector
+--   with the given vector.  See also 'scaleRotateTo'.
+scalingRotationTo :: (Floating n) => V2 n -> T2 n
+scalingRotationTo v = fromMatWithInv (conf v) (conf w) zero
+  where
+    w = reflectY (v ^/ quadrance v)
+    conf (V2 a b) = (V2 (V2 a (-b)) (V2 b a))
+
+-- | Rotate and uniformly scale around the local origin such that the
+--   x-axis aligns with the given vector.  This satisfies the equation
+--
+-- @
+-- scaleRotateTo v = rotateTo (dir v) . scale (norm v)
+-- @
+--
+-- up to floating point rounding errors, but is more accurate and
+-- performant since it avoids cancellable uses of trigonometric functions.
+scaleRotateTo :: (InSpace V2 n t, Transformable t, Floating n)
+              => V2 n -> t -> t
+scaleRotateTo = transform . scalingRotationTo
+
 -- Reflection ----------------------------------------------
 
 -- | Construct a transformation which flips a diagram from left to
 --   right, i.e. sends the point (x,y) to (-x,y).
-reflectionX :: T2
-reflectionX = scalingX (-1)
+reflectionX :: (Additive v, R1 v, Num n) => Transformation v n
+reflectionX = fromSymmetric $ (_x *~ (-1)) <-> (_x *~ (-1))
 
 -- | Flip a diagram from left to right, i.e. send the point (x,y) to
 --   (-x,y).
-reflectX :: (Transformable t, V t ~ R2) => t -> t
+reflectX :: (InSpace v n t, R1 v, Transformable t) => t -> t
 reflectX = transform reflectionX
 
 -- | Construct a transformation which flips a diagram from top to
 --   bottom, i.e. sends the point (x,y) to (x,-y).
-reflectionY :: T2
-reflectionY = scalingY (-1)
+reflectionY :: (Additive v, R2 v, Num n) => Transformation v n
+reflectionY = fromSymmetric $ (_y *~ (-1)) <-> (_y *~ (-1))
 
 -- | Flip a diagram from top to bottom, i.e. send the point (x,y) to
 --   (x,-y).
-reflectY :: (Transformable t, V t ~ R2) => t -> t
+reflectY :: (InSpace v n t, R2 v, Transformable t) => t -> t
 reflectY = transform reflectionY
 
--- | @reflectionAbout p v@ is a reflection in the line determined by
---   the point @p@ and vector @v@.
-reflectionAbout :: P2 -> R2 -> T2
-reflectionAbout p v =
-  conjugate (rotation (negateV $ direction v) <> translation (origin .-. p))
+-- | Construct a transformation which flips the diagram about x=y, i.e.
+--   sends the point (x,y) to (y,x).
+reflectionXY :: (Additive v, R2 v, Num n) => Transformation v n
+reflectionXY = fromSymmetric $ (_xy %~ view _yx) <-> (_xy %~ view _yx)
+
+-- | Flips the diagram about x=y, i.e. send the point (x,y) to (y,x).
+reflectXY :: (InSpace v n t, R2 v, Transformable t) => t -> t
+reflectXY = transform reflectionXY
+
+-- | @reflectionAbout p d@ is a reflection in the line determined by
+--   the point @p@ and direction @d@.
+reflectionAbout :: OrderedField n => P2 n -> Direction V2 n -> T2 n
+reflectionAbout p d =
+  conjugate (rotationTo (reflectY d) <> translation (origin .-. p))
             reflectionY
 
--- | @reflectAbout p v@ reflects a diagram in the line determined by
---   the point @p@ and the vector @v@.
-reflectAbout :: (Transformable t, V t ~ R2) => P2 -> R2 -> t -> t
+
+
+
+-- | @reflectAbout p d@ reflects a diagram in the line determined by
+--   the point @p@ and direction @d@.
+reflectAbout :: (InSpace V2 n t, OrderedField n, Transformable t)
+             => P2 n -> Direction V2 n -> t -> t
 reflectAbout p v = transform (reflectionAbout p v)
 
 -- Shears --------------------------------------------------
 
+-- auxiliary functions for shearingX/shearingY
+sh :: (n -> n -> n -> n) -> (n -> n -> n -> n) -> n -> V2 n -> V2 n
+sh f g k (V2 x y) = V2 (f k x y) (g k x y)
+
+sh' :: (n -> n -> n -> n) -> (n -> n -> n -> n) -> n -> V2 n -> V2 n
+sh' f g k = swap . sh f g k . swap
+
+swap :: V2 n -> V2 n
+swap (V2 x y) = V2 y x
+{-# INLINE swap #-}
+
 -- | @shearingX d@ is the linear transformation which is the identity on
 --   y coordinates and sends @(0,1)@ to @(d,1)@.
-shearingX :: Double -> T2
-shearingX d = fromLinear (sh d  <-> sh (-d))
-                         (sh' d <-> sh' (-d))
-  where sh  k (R2 x y) = R2 (x+k*y) y
-        sh' k          = swap . sh k . swap
-        swap (R2 x y)  = R2 y x
+shearingX :: Num n => n -> T2 n
+shearingX d = fromLinear (sh f g d  <-> sh f g (-d))
+                         (sh' f g d <-> sh' f g (-d))
+  where
+    f k x y = x + k*y
+    g _ _ y = y
 
 -- | @shearX d@ performs a shear in the x-direction which sends
 --   @(0,1)@ to @(d,1)@.
-shearX :: (Transformable t, V t ~ R2) => Double -> t -> t
+shearX :: (InSpace V2 n t, Transformable t) => n -> t -> t
 shearX = transform . shearingX
 
 -- | @shearingY d@ is the linear transformation which is the identity on
 --   x coordinates and sends @(1,0)@ to @(1,d)@.
-shearingY :: Double -> T2
-shearingY d = fromLinear (sh d  <-> sh (-d))
-                         (sh' d <-> sh' (-d))
-  where sh  k (R2 x y) = R2 x (y+k*x)
-        sh' k          = swap . sh k . swap
-        swap (R2 x y)  = R2 y x
+shearingY :: Num n => n -> T2 n
+shearingY d = fromLinear (sh f g d  <-> sh f g (-d))
+                         (sh' f g d <-> sh' f g (-d))
+        where
+          f _ x _ = x
+          g k x y = y + k*x
 
 -- | @shearY d@ performs a shear in the y-direction which sends
 --   @(1,0)@ to @(1,d)@.
-shearY :: (Transformable t, V t ~ R2) => Double -> t -> t
+shearY :: (InSpace V2 n t, Transformable t) => n -> t -> t
 shearY = transform . shearingY
-
--- | Get the matrix equivalent of the linear transform,
---   (as a pair of columns) and the translation vector.  This
---   is mostly useful for implementing backends.
-onBasis :: Transformation R2 -> ((R2, R2), R2)
-onBasis t = ((x, y), v)
-  where ((x:y:[]), v) = T.onBasis t
diff --git a/src/Diagrams/TwoD/Transform/ScaleInv.hs b/src/Diagrams/TwoD/Transform/ScaleInv.hs
deleted file mode 100644
--- a/src/Diagrams/TwoD/Transform/ScaleInv.hs
+++ /dev/null
@@ -1,173 +0,0 @@
-{-# LANGUAGE DeriveDataTypeable    #-}
-{-# LANGUAGE FlexibleInstances     #-}
-{-# LANGUAGE MultiParamTypeClasses #-}
-{-# LANGUAGE TemplateHaskell       #-}
-{-# LANGUAGE TypeFamilies          #-}
------------------------------------------------------------------------------
--- |
--- Module      :  Diagrams.TwoD.Transform.ScaleInv
--- Copyright   :  (c) 2012-2013 diagrams-lib team (see LICENSE)
--- License     :  BSD-style (see LICENSE)
--- Maintainer  :  diagrams-discuss@googlegroups.com
---
--- Wrapper for creating scale-invariant objects in two dimensions.
---
------------------------------------------------------------------------------
-
-module Diagrams.TwoD.Transform.ScaleInv
-    ( ScaleInv(..)
-    , scaleInvObj, scaleInvDir, scaleInvLoc
-    , scaleInv, scaleInvPrim )
-    where
-
-import           Control.Lens            (makeLenses, view)
-import           Data.AdditiveGroup
-import           Data.AffineSpace        ((.-.))
-import           Data.Semigroup
-import           Data.Typeable
-
-import           Diagrams.Core
-import           Diagrams.TwoD.Transform
-import           Diagrams.TwoD.Types
-import           Diagrams.TwoD.Vector
-
--- | The @ScaleInv@ wrapper creates two-dimensional /scale-invariant/
---   objects.  Intuitively, a scale-invariant object is affected by
---   transformations like translations and rotations, but not by scales.
---
---   However, this is problematic when it comes to /non-uniform/
---   scales (/e.g./ @scaleX 2 . scaleY 3@) since they can introduce a
---   perceived rotational component.  The prototypical example is an
---   arrowhead on the end of a path, which should be scale-invariant.
---   However, applying a non-uniform scale to the path but not the
---   arrowhead would leave the arrowhead pointing in the wrong
---   direction.
---
---   Moreover, for objects whose local origin is not at the local
---   origin of the parent diagram, any scale can result in a
---   translational component as well.
---
---   The solution is to also store a point (indicating the location,
---   /i.e./ the local origin) and a unit vector (indicating the
---   /direction/) along with a scale-invariant object.  A
---   transformation to be applied is decomposed into rotational and
---   translational components as follows:
---
---   * The transformation is applied to the direction vector, and the
---   difference in angle between the original direction vector and its
---   image under the transformation determines the rotational
---   component.  The rotation is applied with respect to the stored
---   location, rather than the global origin.
---
---   * The vector from the location to the image of the location under
---   the transformation determines the translational component.
-
-data ScaleInv t =
-  ScaleInv
-  { _scaleInvObj :: t
-  , _scaleInvDir :: R2
-  , _scaleInvLoc :: P2
-  }
-  deriving (Show, Typeable)
-
-makeLenses ''ScaleInv
-
--- | Create a scale-invariant object pointing in the given direction,
---   located at the origin.
-scaleInv :: t -> R2 -> ScaleInv t
-scaleInv t d = ScaleInv t d origin
-
-type instance V (ScaleInv t) = R2
-
-instance (V t ~ R2, HasOrigin t) => HasOrigin (ScaleInv t) where
-  moveOriginTo p (ScaleInv t v l) = ScaleInv (moveOriginTo p t) v (moveOriginTo p l)
-
-instance (V t ~ R2, Transformable t) => Transformable (ScaleInv t) where
-  transform tr (ScaleInv t v l) = ScaleInv (trans . rot $ t) (rot v) l'
-    where
-      angle = direction (transform tr v) ^-^ direction v
-      rot :: (Transformable t, V t ~ R2) => t -> t
-      rot = rotateAbout l angle
-      l'  = transform tr l
-      trans = translate (l' .-. l)
-
-{- Proof that the above satisfies the monoid action laws.
-
-   1. transform mempty (ScaleInv t v l)
-      = ScaleInv (trans . rot $ t) (rot v) l'
-        { l'    = transform mempty l = l }
-        { trans = translate (l' .-. l)
-                = translate (l .-. l)
-                = translate zeroV
-                = id
-        }
-        { rot   = rotateAbout l angle
-                = rotateAbout l (direction (transform mempty v) - direction v)
-                = rotateAbout l (direction v - direction v)
-                = rotateAbout l 0
-                = id
-        }
-      = ScaleInv t v l
-
-  2. transform t1 (transform t2 (ScaleInv t v l))
-     = let angle = direction (transform t2 v) - direction v
-           rot   = rotateAbout l angle
-           l'    = transform t2 l
-           trans = translate (l' .-. l)
-       in
-           transform t1 (ScaleInv (trans . rot $ t) (rot v) l')
-
-     = let angle  = direction (transform t2 v) - direction v
-           rot    = rotateAbout l angle
-           l'     = transform t2 l
-           trans  = translate (l' .-. l)
-           angle2 = direction (transform t1 (rot v)) - direction (rot v)
-           rot2   = rotateAbout l' angle2
-           l'2    = transform t1 l'
-           trans2 = translate (l'2 .-. l')
-       in
-           ScaleInv (trans2 . rot2 . trans . rot $ t) (rot2 . rot $ v) l'2
-
-       { l'2 = transform t1 l'
-             = transform t1 (transform t2 l)
-             = transform (t1 <> t2) l
-       }
-       { trans2 = translate (l'2 .-. l')
-                = translate (transform (t1 <> t2) l .-. transform t2 l)
-                = translate (transform t1 l .-. l)
-       }
-       { rot v  = rotateAbout l angle v
-                = rotate angle `under` translation (origin .-. l) $ v
-                = rotate angle v
-       }
-       { angle2 = direction (transform t1 (rot v)) - direction (rot v)
-                = direction (transform t1 (rotate angle v)) - direction (rotate angle v)
-                = direction (transform t1 (rotate angle v)) - direction v - angle
-       }
-       { rot2   = rotateAbout l' angle2
-                = ???
-       }
-
--}
-
-instance (Renderable t b, V t ~ R2) => Renderable (ScaleInv t) b where
-  render b = render b . view scaleInvObj
-
--- | Create a diagram from a single scale-invariant primitive.  The
---   vector argument specifies the direction in which the primitive is
---   \"pointing\" (for the purpose of keeping it rotated correctly
---   under non-uniform scaling).  The primitive is assumed to be
---   \"located\" at the origin (for the purpose of translating it
---   correctly under scaling).
---
---   Note that the resulting diagram will have an /empty/ envelope,
---   trace, and query.  The reason is that the envelope, trace, and
---   query cannot be cached---applying a transformation would cause
---   the cached envelope, etc. to get \"out of sync\" with the
---   scale-invariant object.  The intention, at any rate, is that
---   scale-invariant things will be used only as \"decorations\" (/e.g./
---   arrowheads) which should not affect the envelope, trace, and
---   query.
-scaleInvPrim :: (Transformable t, Typeable t, Renderable t b, V t ~ R2, Monoid m)
-             => t -> R2 -> QDiagram b R2 m
-scaleInvPrim t d = mkQD (Prim $ scaleInv t d) mempty mempty mempty mempty
diff --git a/src/Diagrams/TwoD/Types.hs b/src/Diagrams/TwoD/Types.hs
--- a/src/Diagrams/TwoD/Types.hs
+++ b/src/Diagrams/TwoD/Types.hs
@@ -1,13 +1,7 @@
-{-# LANGUAGE DeriveDataTypeable         #-}
-{-# LANGUAGE FlexibleInstances          #-}
-{-# LANGUAGE GeneralizedNewtypeDeriving #-}
-{-# LANGUAGE MultiParamTypeClasses      #-}
-{-# LANGUAGE RankNTypes                 #-}
-{-# LANGUAGE TypeFamilies               #-}
-{-# LANGUAGE TypeOperators              #-}
-{-# LANGUAGE TypeSynonymInstances       #-}
+{-# LANGUAGE TypeFamilies #-}
 
 {-# OPTIONS_GHC -fno-warn-orphans #-}
+
 -----------------------------------------------------------------------------
 -- |
 -- Module      :  Diagrams.TwoD.Types
@@ -21,226 +15,80 @@
 
 module Diagrams.TwoD.Types
        ( -- * 2D Euclidean space
-         R2(..), r2, unr2, mkR2, r2Iso
-       , P2, p2, mkP2, unp2, p2Iso
-       , T2
-
+         V2 (..), R1 (..), R2 (..)
+       , P2, T2
+       , r2, unr2, mkR2, r2Iso
+       , p2, mkP2, unp2, p2Iso
+       , r2PolarIso
+       , HasR (..)
        ) where
 
-import           Control.Lens           (Iso', Rewrapped, Wrapped (..), iso,
-                                         lens, (^.), _1, _2)
+import           Control.Lens            (Iso', Lens', iso, _1, _2)
 
 import           Diagrams.Angle
-import           Diagrams.Coordinates
-import           Diagrams.Core
-
-import           Data.AffineSpace.Point
-import           Data.Basis
-import           Data.MemoTrie          (HasTrie (..))
-import           Data.VectorSpace
-
-import           Data.Data
-------------------------------------------------------------
--- 2D Euclidean space
-
--- | The two-dimensional Euclidean vector space R^2.  This type is
---   intentionally abstract.
---
---   * To construct a vector, use 'r2', or '^&' (from "Diagrams.Coordinates"):
---
--- @
--- r2 (3,4) :: R2
--- 3 ^& 4    :: R2
--- @
---
---     Note that "Diagrams.Coordinates" is not re-exported by
---     "Diagrams.Prelude" and must be explicitly imported.
---
---   * To construct the vector from the origin to a point @p@, use
---     @p 'Data.AffineSpace..-.' 'origin'@.
---
---   * To convert a vector @v@ into the point obtained by following
---     @v@ from the origin, use @'origin' 'Data.AffineSpace..+^' v@.
---
---   * To convert a vector back into a pair of components, use 'unv2'
---     or 'coords' (from "Diagrams.Coordinates").  These are typically
---     used in conjunction with the @ViewPatterns@ extension:
---
--- @
--- foo (unr2 -> (x,y)) = ...
--- foo (coords -> x :& y) = ...
--- @
-
-data R2 = R2 {-# UNPACK #-} !Double
-             {-# UNPACK #-} !Double
-  deriving (Eq, Ord, Typeable, Data)
-
-instance AdditiveGroup R2 where
-  zeroV = R2 0 0
-  R2 x1 y1 ^+^ R2 x2 y2 = R2 (x1 + x2) (y1 + y2)
-  negateV (R2 x y) = R2 (-x) (-y)
-
-instance Num R2 where
-  (+)                 = (^+^)
-  R2 x1 y1 * R2 x2 y2 = R2 (x1 * x2) (y1 * y2)  -- this is sort of bogus
-  (-)                 = (^-^)
-  negate              = negateV
-  abs (R2 x y)        = R2 (abs x) (abs y)
-  signum (R2 x y)     = R2 (signum x) (signum y)
-  fromInteger i       = R2 i' i'
-    where i' = fromInteger i
+import           Diagrams.Points
 
-instance Fractional R2 where
-  R2 x1 y1 / R2 x2 y2 = R2 (x1/x2) (y1/y2)
-  recip (R2 x y) = R2 (recip x) (recip y)
-  fromRational r = R2 r' r'
-    where r' = fromRational r
+import           Diagrams.Core.Transform
+import           Diagrams.Core.V
+import           Linear.Metric
+import           Linear.V2
 
-instance Show R2 where
-  showsPrec p (R2 x y) = showParen (p >= 7) $
-    showCoord x . showString " ^& " . showCoord y
-   where
-    showCoord c | c < 0     = showParen True (shows c)
-                | otherwise = shows c
+type P2 = Point V2
+type T2 = Transformation V2
 
-instance Read R2 where
-  readsPrec d r = readParen (d > app_prec)
-                  (\rr -> [ (R2 x y, r''')
-                          | (x,r')    <- readsPrec (amp_prec + 1) rr
-                          , ("^&",r'') <- lex r'
-                          , (y,r''')  <- readsPrec (amp_prec + 1) r''
-                          ])
-                  r
-    where
-      app_prec = 10
-      amp_prec = 7
+type instance V (V2 n) = V2
+type instance N (V2 n) = n
 
 -- | Construct a 2D vector from a pair of components.  See also '&'.
-r2 :: (Double, Double) -> R2
-r2 (x,y) = R2 x y
+r2 :: (n, n) -> V2 n
+r2 = uncurry V2
 
 -- | Convert a 2D vector back into a pair of components.  See also 'coords'.
-unr2 :: R2 -> (Double, Double)
-unr2 (R2 x y) = (x,y)
+unr2 :: V2 n -> (n, n)
+unr2 (V2 x y) = (x, y)
 
 -- | Curried form of `r2`.
-mkR2 :: Double -> Double -> R2
-mkR2 = curry r2
-
--- | Lens wrapped isomorphisms for R2.
-instance Wrapped R2 where
-    type Unwrapped R2 = (Double, Double)
-    _Wrapped' = iso unr2 r2
-    {-# INLINE _Wrapped' #-}
-
-instance Rewrapped R2 R2
-
-type instance V R2 = R2
-
-instance VectorSpace R2 where
-  type Scalar R2 = Double
-  s *^ R2 x y = R2 (s*x) (s*y)
-
-data R2Basis = XB | YB deriving (Eq, Ord, Enum)
-
-instance HasTrie R2Basis where
-    data R2Basis :->: x = R2Trie x x
-    trie f = R2Trie (f XB) (f YB)
-    untrie (R2Trie x _y) XB = x
-    untrie (R2Trie _x y) YB = y
-    enumerate (R2Trie x y)  = [(XB,x),(YB,y)]
-
-instance HasBasis R2 where
-  type Basis R2 = R2Basis
-  basisValue XB          = R2 1 0
-  basisValue YB          = R2 0 1
-
-  decompose (R2 x y)             = [(XB, x), (YB, y)]
-
-  decompose' (R2 x _) (XB)  = x
-  decompose' (R2 _ y) (YB) = y
-
-instance InnerSpace R2 where
-  (R2 x1 y1) <.> (R2 x2 y2) = x1*x2 + y1*y2
-
-instance Coordinates R2 where
-  type FinalCoord R2     = Double
-  type PrevDim R2        = Double
-  type Decomposition R2  = Double :& Double
-
-  x ^& y           = R2 x y
-  coords (R2 x y) = x :& y
+mkR2 :: n -> n -> V2 n
+mkR2 = V2
 
-r2Iso :: Iso' R2 (Double, Double)
+r2Iso :: Iso' (V2 n) (n, n)
 r2Iso = iso unr2 r2
 
-instance HasX R2 where
-    _x = r2Iso . _1
-
-instance HasY R2 where
-    _y = r2Iso . _2
-
-instance HasTheta R2 where
-    _theta = lens (\v -> atanA (v^._y / v^._x))
-      (\v θ -> let r = magnitude v in R2 (r * cosA θ) (r * sinA θ))
-
-instance HasR R2 where
-    _r = lens magnitude (\v r -> let s = r/magnitude v in s *^ v)
-
--- | Points in R^2.  This type is intentionally abstract.
---
---   * To construct a point, use 'p2', or '^&' (see
---     "Diagrams.Coordinates"):
---
--- @
--- p2 (3,4)  :: P2
--- 3 ^& 4    :: P2
--- @
---
---   * To construct a point from a vector @v@, use @'origin' 'Data.AffineSpace..+^' v@.
---
---   * To convert a point @p@ into the vector from the origin to @p@,
---   use @p 'Data.AffineSpace..-.' 'origin'@.
---
---   * To convert a point back into a pair of coordinates, use 'unp2',
---     or 'coords' (from "Diagrams.Coordinates").  It's common to use
---     these in conjunction with the @ViewPatterns@ extension:
---
--- @
--- foo (unp2 -> (x,y)) = ...
--- foo (coords -> x :& y) = ...
--- @
-type P2 = Point R2
-
 -- | Construct a 2D point from a pair of coordinates.  See also '^&'.
-p2 :: (Double, Double) -> P2
-p2 = P . r2
+p2 :: (n, n) -> P2 n
+p2 = P . uncurry V2
 
 -- | Convert a 2D point back into a pair of coordinates.  See also 'coords'.
-unp2 :: P2 -> (Double, Double)
-unp2 (P v) = unr2 v
+unp2 :: P2 n -> (n,n)
+unp2 (P (V2 x y)) = (x,y)
 
 -- | Curried form of `p2`.
-mkP2 :: Double -> Double -> P2
-mkP2 = curry p2
+mkP2 :: n -> n -> P2 n
+mkP2 x y = P (V2 x y)
 
--- | Transformations in R^2.
-type T2 = Transformation R2
+p2Iso :: Iso' (Point V2 n) (n, n)
+p2Iso = iso unp2 p2
 
-instance Transformable R2 where
+instance Transformable (V2 n) where
   transform = apply
 
-p2Iso :: Iso' P2 (Double, Double)
-p2Iso = iso unp2 p2
+r2PolarIso :: RealFloat n => Iso' (V2 n) (n, Angle n)
+r2PolarIso = iso (\v@(V2 x y) -> (norm v, atan2A y x))
+              (\(r,θ)      -> V2 (r * cosA θ) (r * sinA θ))
+{-# INLINE r2PolarIso #-}
 
-instance HasX P2 where
-    _x = p2Iso . _1
+-- | A space which has magnitude '_r' that can be calculated numerically.
+class HasR t where
+  _r :: RealFloat n => Lens' (t n) n
 
-instance HasY P2 where
-    _y = p2Iso . _2
+instance HasR v => HasR (Point v) where
+  _r = lensP . _r
+  {-# INLINE _r #-}
 
-instance HasR P2 where
-    _r = _relative origin . _r
+instance HasR V2 where
+  _r = r2PolarIso . _1
+  {-# INLINE _r #-}
 
-instance HasTheta P2 where
-    _theta = _relative origin . _theta
+instance HasTheta V2 where
+  _theta = r2PolarIso . _2
+  {-# INLINE _theta #-}
diff --git a/src/Diagrams/TwoD/Vector.hs b/src/Diagrams/TwoD/Vector.hs
--- a/src/Diagrams/TwoD/Vector.hs
+++ b/src/Diagrams/TwoD/Vector.hs
@@ -1,6 +1,3 @@
-{-# LANGUAGE FlexibleContexts #-}
-{-# LANGUAGE TypeFamilies     #-}
-{-# LANGUAGE ViewPatterns     #-}
 -----------------------------------------------------------------------------
 -- |
 -- Module      :  Diagrams.TwoD.Vector
@@ -14,59 +11,82 @@
 module Diagrams.TwoD.Vector
        ( -- * Special 2D vectors
          unitX, unitY, unit_X, unit_Y
+       , xDir, yDir
 
          -- * Converting between vectors and angles
-       , direction, angleBetween, fromDirection, e
+       , angleV, angleDir, e, signedAngleBetween, signedAngleBetweenDirs
 
          -- * 2D vector utilities
-       , perp, leftTurn
+       , perp, leftTurn, cross2
+
        ) where
 
-import           Control.Lens         ((^.))
-import           Data.VectorSpace     ((<.>))
+import           Control.Lens        (view, (&), (.~), (^.))
 
 import           Diagrams.Angle
+import           Diagrams.Direction
 import           Diagrams.TwoD.Types
-import           Diagrams.Coordinates
 
--- | The unit vector in the positive X direction.
-unitX :: R2
-unitX = 1 ^& 0
+import           Linear.Metric
+import           Linear.V2
+import           Linear.Vector
 
--- | The unit vector in the positive Y direction.
-unitY :: R2
-unitY = 0 ^& 1
+-- | The unit vector in the positive X direction.
+unitX :: (R1 v, Additive v, Num n) => v n
+unitX = zero & _x .~ 1
 
 -- | The unit vector in the negative X direction.
-unit_X :: R2
-unit_X = (-1) ^& 0
+unit_X :: (R1 v, Additive v, Num n) => v n
+unit_X = zero & _x .~ (-1)
 
+-- | The unit vector in the positive Y direction.
+unitY :: (R2 v, Additive v, Num n) => v n
+unitY = zero & _y .~ 1
+
 -- | The unit vector in the negative Y direction.
-unit_Y :: R2
-unit_Y = 0 ^& (-1)
+unit_Y :: (R2 v, Additive v, Num n) => v n
+unit_Y = zero & _y .~ (-1)
 
--- | Compute the direction of a vector, measured counterclockwise from
---   the positive x-axis as a fraction of a full turn.  The zero
---   vector is arbitrarily assigned the direction 0.
-direction :: R2 -> Angle
-direction (coords -> x :& y) = atan2 y x @@ rad
+-- | A 'Direction' pointing in the X direction.
+xDir :: (R1 v, Additive v, Num n) => Direction v n
+xDir = dir unitX
 
--- | Convert an angle into a unit vector pointing in that direction.
-fromDirection :: Angle -> R2
-fromDirection a = cos a' ^& sin a'
-  where a' = a^.rad
+-- | A 'Direction' pointing in the Y direction.
+yDir :: (R2 v, Additive v, Num n) => Direction v n
+yDir = dir unitY
 
--- | A convenient synonym for 'fromDirection'.
-e :: Angle -> R2
-e = fromDirection
+-- | A direction at a specified angle counter-clockwise from the 'xDir'.
+angleDir :: Floating n => Angle n -> Direction V2 n
+angleDir = dir . angleV
 
--- | @perp v@ is perpendicular to and has the same magnitude as @v@.
---   In particular @perp v == rotateBy (1/4) v@.
-perp :: R2 -> R2
-perp (coords -> x :& y) = (-y) ^& x
+-- | A unit vector at a specified angle counter-clockwise from the
+--   positive x-axis
+angleV :: Floating n => Angle n -> V2 n
+angleV = angle . view rad
 
+-- | A unit vector at a specified angle counter-clockwise from the
+--   positive X axis.
+e :: Floating n => Angle n -> V2 n
+e = angleV
+
 -- | @leftTurn v1 v2@ tests whether the direction of @v2@ is a left
 --   turn from @v1@ (that is, if the direction of @v2@ can be obtained
 --   from that of @v1@ by adding an angle 0 <= theta <= tau/2).
-leftTurn :: R2 -> R2 -> Bool
-leftTurn v1 v2 = (v1 <.> perp v2) < 0
+leftTurn :: (Num n, Ord n) => V2 n -> V2 n -> Bool
+leftTurn v1 v2 = (v1 `dot` perp v2) < 0
+
+-- | Cross product on vectors in R2.
+cross2 :: Num n => V2 n -> V2 n -> n
+cross2 (V2 x1 y1) (V2 x2 y2) = x1 * y2 - y1 * x2
+
+-- | Signed angle between two vectors. Currently defined as
+--
+-- @
+-- signedAngleBetween u v = (u ^. _theta) ^-^ (v ^. _theta)
+-- @
+signedAngleBetween :: RealFloat n => V2 n -> V2 n -> Angle n
+signedAngleBetween u v = (u ^. _theta) ^-^ (v ^. _theta)
+
+-- | Same as 'signedAngleBetween' but for 'Directions's.
+signedAngleBetweenDirs :: RealFloat n => Direction V2 n -> Direction V2 n -> Angle n
+signedAngleBetweenDirs u v = (u ^. _theta) ^-^ (v ^. _theta)
diff --git a/src/Diagrams/Util.hs b/src/Diagrams/Util.hs
--- a/src/Diagrams/Util.hs
+++ b/src/Diagrams/Util.hs
@@ -1,7 +1,9 @@
+{-# LANGUAGE CPP #-}
+
 -----------------------------------------------------------------------------
 -- |
 -- Module      :  Diagrams.Util
--- Copyright   :  (c) 2011 diagrams-lib team (see LICENSE)
+-- Copyright   :  (c) 2011-2015 diagrams-lib team (see LICENSE)
 -- License     :  BSD-style (see LICENSE)
 -- Maintainer  :  diagrams-discuss@googlegroups.com
 --
@@ -10,23 +12,44 @@
 -----------------------------------------------------------------------------
 
 module Diagrams.Util
-       ( -- * Utilities for users
+  ( -- * Utilities for users
 
-         with
-       , applyAll
-       , (#)
+    with
+  , applyAll
+  , (#)
+  , (##)
 
-       , iterateN
+  , iterateN
 
-       , tau
+  , tau
 
-         -- * Internal utilities
-       , foldB
+    -- * Finding files
+  , findHsFile
 
-       ) where
+    -- * Finding sandboxes
+  , findSandbox
+  , globalPackage
 
-import           Data.Default.Class
+    -- * Internal utilities
+  , foldB
+
+  ) where
+
+import           Control.Applicative
+import           Control.Lens              hiding (( # ))
+import           Control.Monad
+import           Control.Monad.Catch
+import           Control.Monad.Trans
+import           Control.Monad.Trans.Maybe
+import           Data.Default
+import           Data.List
+import           Data.Maybe
 import           Data.Monoid
+import           System.Directory
+import           System.Environment
+import           System.FilePath
+import           System.FilePath.Lens
+import           System.Process
 
 -- | Several functions exported by the diagrams library take a number
 --   of arguments giving the user control to \"tweak\" various aspects
@@ -67,6 +90,13 @@
 (#) :: a -> (a -> b) -> b
 (#) = flip ($)
 
+-- | A replacement for lenses' 'Control.Lens.Review.#' operator.
+(##) :: AReview t b -> b -> t
+(##) = review
+{-# INLINE (##) #-}
+infixr 8 ##
+
+
 -- | @iterateN n f x@ returns the list of the first @n@ iterates of
 --   @f@ starting at @x@, that is, the list @[x, f x, f (f x), ...]@
 --   of length @n@. (Note that the last element of the list will be
@@ -102,3 +132,127 @@
         go []         = []
         go [x]        = [x]
         go (x1:x2:xs) = f x1 x2 : go xs
+
+------------------------------------------------------------------------
+-- Files
+------------------------------------------------------------------------
+
+-- | Given some file (no extension or otherwise) try to find a haskell
+--   source file.
+findHsFile :: FilePath -> IO (Maybe FilePath)
+findHsFile file = runMaybeT $ hs <|> lhs
+  where
+    hs      = check (addExtension file "hs")
+    lhs     = check (addExtension file "lhs")
+    check f = do
+      lift (doesFileExist f) >>= guard
+      pure f
+
+------------------------------------------------------------------------
+-- Sandbox
+------------------------------------------------------------------------
+
+-- | Parse cabal config file to find the location of the package
+--   database.
+parseConfig :: FilePath -> MaybeT IO FilePath
+parseConfig file = do
+  config <- maybeIO $ readFile file
+  hoistMaybe $ config ^? lined . prefixed "package-db: "
+
+-- | Seach the given directory and all parent directories until a cabal
+--   config file is found. First search for \"cabal.config\", then
+--   \"cabal.sandbox.config\". Return the location of the package
+--   database in the config file.
+configSearch :: FilePath -> MaybeT IO FilePath
+configSearch p0 = do
+  p0' <- maybeIO $ canonicalizePath p0
+
+  let mkPaths p
+        | all isPathSeparator p || p == "."
+                    = []
+        | otherwise = (p </> "cabal.sandbox.config")
+                    : mkPaths (p ^. directory)
+
+  foldMaybeT parseConfig (mkPaths p0')
+
+-- | Check if the folder is a database, or if it contains a database.
+--   Returns the database location if it's found.
+isDB :: FilePath -> MaybeT IO FilePath
+isDB path =
+  if isConf path
+    then return path
+    else maybeIO (getDirectoryContents path) >>= hoistMaybe . find isConf
+    where
+      isConf = isSuffixOf ".conf.d"
+
+-- | Search for a sandbox in the following order:
+--
+--   * Test given FilePaths if they point directly to a database or
+--     contain a cabal config file (or any parent directory containing a
+--     config file).
+--
+--   * Same test for @DIAGRAMS_SANDBOX@ environment value
+--
+--   * Environment values of @GHC_PACKAGE_PATH@, @HSENV@ and
+--     @PACKAGE_DB_FOR_GHC@ that point to a database.
+--
+--   * Test for config file (cabal.sandbox.config) in the current
+--     directory and its parents.
+--
+findSandbox :: [FilePath] -> IO (Maybe FilePath)
+findSandbox paths = runMaybeT $ pathsTest <|> diaSB <|> envDB <|> wdConfig
+  where
+    -- first path in environment
+    lookEnv = MaybeT . (fmap . fmap) (head . splitSearchPath) . lookupEnv
+    envDB   = foldMaybeT lookEnv ["GHC_PACKAGE_PATH", "HSENV", "PACKAGE_DB_FOR_GHC"]
+
+    -- test if path points directly to db or contains a config file
+    test x    = isDB x <|> configSearch x
+    pathsTest = foldMaybeT test paths
+    diaSB     = lookEnv "DIAGRAMS_SANDBOX" >>= test
+    wdConfig  = maybeIO getCurrentDirectory >>= configSearch
+
+-- -- | Use the given path for the sandbox in the @GHC_PACKAGE_PATH@
+-- --   environment (appending the ghc global package database from @ghc
+-- --   --info@. @GHC_PACKAGE_PATH@ if the variable ghc and other tools use
+-- --   to find the package database. (This is what @cabal exec@ sets)
+-- ghcPackagePath :: FilePath -> IO ()
+-- ghcPackagePath db = do
+--   gdb <- globalPackage
+--   let dbs = intercalate [searchPathSeparator] [db,gdb]
+--   setEnv "GHC_PACKAGE_PATH" dbs
+-- -- setEnv is only in base > 4.7, either need to use setenv package or
+-- -- -package-db flag
+
+-- | Find ghc's global package database. Throws an error if it isn't
+--   found.
+globalPackage :: IO FilePath
+globalPackage = do
+  info <- read <$> readProcess "ghc" ["--info"] ""
+  return $ fromMaybe (error "Unable to parse ghc --info.")
+                     (lookup "Global Package DB" info)
+
+-- MaybeT utilities
+
+-- | Lift an 'IO' action. If any exceptions are raised, return Nothing.
+maybeIO :: (MonadCatch m, MonadIO m) => IO a -> MaybeT m a
+maybeIO io = liftIO io `catchAll` const mzero
+
+-- hoistMaybe is exported from transformers as of version 0.6
+#if MIN_VERSION_transformers(0,6,0)
+#else
+-- | Lift a maybe value to a MaybeT of any monad.
+hoistMaybe :: Monad m => Maybe a -> MaybeT m a
+hoistMaybe = MaybeT . return
+#endif
+
+-- | Fold a list of 'MaybeT's that short-circuits as soon as a Just value
+--   is found (instead going through the whole list).
+foldMaybeT :: Monad m => (a -> MaybeT m b) -> [a] -> MaybeT m b
+foldMaybeT _ []     = mzero
+foldMaybeT f (a:as) = MaybeT $ do
+  x <- runMaybeT (f a)
+  if isJust x
+    then return x
+    else runMaybeT (foldMaybeT f as)
+
diff --git a/src/Linear/Vector/Compat.hs b/src/Linear/Vector/Compat.hs
new file mode 100644
--- /dev/null
+++ b/src/Linear/Vector/Compat.hs
@@ -0,0 +1,24 @@
+{-# LANGUAGE CPP #-}
+
+-- |
+-- Module      :  Linear.Vector.Compat
+-- Copyright   :  (c) 2024 diagrams-lib team (see LICENSE)
+-- License     :  BSD-style (see LICENSE)
+-- Maintainer  :  diagrams-discuss@googlegroups.com
+--
+-- Compatibility layer for working with versions of linear both before
+-- (< 1.23) and after (>= 1.23) the interpolation direction of `lerp`
+-- was reversed.
+module Linear.Vector.Compat (lerp) where
+
+import qualified Linear.Vector as V
+
+-- | Linearly interpolate between two vectors, such that @lerp 0 x y =
+--   x@ and @lerp 1 x y = 1@.
+lerp :: (V.Additive f, Num a) => a -> f a -> f a -> f a
+lerp =
+#if MIN_VERSION_linear(1,23,0)
+  V.lerp
+#else
+  V.lerp . (1-)
+#endif
diff --git a/test/Diagrams/Test/Angle.hs b/test/Diagrams/Test/Angle.hs
new file mode 100644
--- /dev/null
+++ b/test/Diagrams/Test/Angle.hs
@@ -0,0 +1,29 @@
+-- |
+
+module Diagrams.Test.Angle where
+
+
+import           Test.Tasty
+import           Test.Tasty.QuickCheck
+import           Diagrams.Prelude
+import Instances
+
+tests :: TestTree
+tests = testGroup "Angle" [
+         testProperty "2π radians per turn" $
+           \θ -> θ^.rad =~ θ^.turn*2*(pi :: Double)
+         , testProperty "360 degrees per turn" $
+           \θ -> θ^.deg =~ θ^.turn*(360 :: Double)
+         , testProperty "Angle vector addition is commutative" $
+           \θ φ -> (θ :: Angle Double) ^+^ φ =~ φ ^+^ θ
+         , testProperty "Angle subtraction is the inverse of addition" $
+           \θ φ -> (θ :: Angle Double) ^+^ φ ^-^ φ =~ θ
+         , testProperty "Angle vector negation squared is identity" $
+           \θ -> negated (negated (θ :: Angle Double)) =~ θ
+         , testProperty "A negated angle is the additive inverse of the original" $
+           \θ -> (θ :: Angle Double) ^+^ (negated θ) =~ 0@@turn
+         , testProperty "A negated angle is the additive inverse of the original" $
+           \θ -> (θ :: Angle Double) ^+^ (negated θ) =~ 0@@turn
+
+
+      ]
diff --git a/test/Diagrams/Test/Direction.hs b/test/Diagrams/Test/Direction.hs
new file mode 100644
--- /dev/null
+++ b/test/Diagrams/Test/Direction.hs
@@ -0,0 +1,34 @@
+-- |
+
+module Diagrams.Test.Direction where
+
+
+import           Diagrams.Direction
+import           Diagrams.Prelude
+import           Instances
+import           Test.Tasty
+import           Test.Tasty.QuickCheck
+
+tests :: TestTree
+tests = testGroup "Direction" [
+         testProperty "Length does not effect from direction" $
+           \(Positive f) (NonZero v) -> fromDirection(dir ((v  :: V2 Double) ^* (f+0.001))) =~ fromDirection(dir v)
+         , testProperty "HasTheta subtraction yeilds same result as anglebetween" $
+            (anglebetsub)
+         , testProperty "anglebetweenDirs is commutative" $
+           \a b -> angleBetweenDirs (a :: Direction V2 Double) b =~ angleBetweenDirs b a
+         , testProperty "fromdirection does not effect angleBetweenDirs" $
+           \a b -> angleBetween (fromDirection (a  :: Direction V2 Double)) (fromDirection b) =~ angleBetweenDirs a b
+
+
+
+      ]
+
+if' :: Bool -> a -> a -> a
+if' True  x _ = x
+if' False _ y = y
+
+anglebetsub :: Direction V2 Double -> Direction V2 Double -> Bool
+anglebetsub a b = (if' (abs (a ^.  _theta^.rad  - b ^. _theta^.rad) < pi)
+                       (abs ((a ^.  _theta  ^-^ b ^. _theta)^.rad))
+                       (2*pi - abs (a ^.  _theta^.rad  - b ^. _theta^.rad) ) =~ angleBetweenDirs a b ^.rad)
diff --git a/test/Diagrams/Test/Trail.hs b/test/Diagrams/Test/Trail.hs
new file mode 100644
--- /dev/null
+++ b/test/Diagrams/Test/Trail.hs
@@ -0,0 +1,113 @@
+{-# LANGUAGE FlexibleContexts #-}
+{-# LANGUAGE TypeFamilies     #-}
+
+module Diagrams.Test.Trail where
+
+import           Diagrams.Prelude
+import           Instances
+import           Test.Tasty
+import           Test.Tasty.QuickCheck
+
+import           Data.Fixed
+import           Data.List
+
+tests :: TestTree
+tests = testGroup "Trail"
+  [ let wrap :: Trail' Line V2 Double -> Located (Trail V2 Double)
+        wrap = (`at` origin) . wrapLine
+    in
+    testProperty "unfixTrail . fixTrail == id for lines" $
+    \l -> (unfixTrail . fixTrail $ wrap l) =~ (wrap l)
+
+  , testProperty "glueLine . cutLoop == id" $
+    \loop -> (glueLine . cutLoop $ loop) =~ (loop :: Trail' Loop V2 Double)
+
+  , testProperty "trailOffset == sumV . trailOffsets" $
+    \t -> trailOffset t =~ (sumV . trailOffsets $ (t :: Trail V2 Double))
+
+  , testProperty "reverseTrail . reverseTrail == id" $
+    \t -> (reverseTrail . reverseTrail $ t) =~ (t :: Trail V2 Double)
+
+  , testProperty "reverseLocTrail . reverseLocTrail == id" $
+    \t -> (reverseLocTrail . reverseLocTrail $ t) =~
+          (t :: Located (Trail V2 Double))
+
+  , testProperty "reverseLine . reverseLine == id" $
+    \t -> (reverseLine . reverseLine $ t) =~
+          (t :: Trail' Line V2 Double)
+
+  , testProperty "reverseLocLine . reverseLocLine == id" $
+    \t -> (reverseLocLine . reverseLocLine $ t) =~
+          (t :: Located (Trail' Line V2 Double))
+
+  , testProperty "reverseLoop . reverseLoop == id" $
+    \t -> (reverseLoop . reverseLoop $ t) =~
+          (t :: Trail' Loop V2 Double)
+
+  , testProperty "reverseLocLoop . reverseLocLoop == id" $
+    \t -> (reverseLocLoop . reverseLocLoop $ t) =~
+          (t :: Located (Trail' Loop V2 Double))
+
+  , testProperty "section on Trail' Line endpoints match paramaters" $
+    \t (Param a) (Param b) ->
+      let s = section (t :: Located (Trail' Line V2 Double)) a b
+      in  t `atParam` a =~ s `atParam` 0 &&
+          t `atParam` b =~ s `atParam` 1
+
+  , testProperty "section on Trail' Line where a paramater is 0 or 1" $
+    \t (Param a) ->
+      let l = section (t :: Located (Trail' Line V2 Double)) 0 a
+          r = section (t :: Located (Trail' Line V2 Double)) a 1
+      in  t `atParam` 0 =~ l `atParam` 0 &&
+          t `atParam` a =~ l `atParam` 1 &&
+          t `atParam` a =~ r `atParam` 0 &&
+          t `atParam` 1 =~ r `atParam` 1
+
+  , testProperty "section on Trail' Line where a segment paramater is 0 or 1" $
+    \t (Param a) i ->
+      let st = unLoc t # \(Line st') -> st' :: SegTree V2 Double
+          b | (numSegs st :: Word) > 0 = (fromIntegral (i `mod` (numSegs st + 1) :: Word)) / numSegs st
+            | otherwise                = 0
+          s = section (t :: Located (Trail' Line V2 Double)) a b
+      in  t `atParam` a =~ s `atParam` 0 &&
+          t `atParam` b =~ s `atParam` 1
+
+  , testProperty "section on Trail' Line matches section on FixedSegment" $
+    \t (Param a) (Param b) -> sectionTrailSectionFixedSegment t a b
+
+  ]
+
+data Param = Param Double deriving Show
+
+instance Arbitrary Param where
+  arbitrary = Param <$> choose (-0.5, 1.5)
+
+sectionTrailSectionFixedSegment :: Located (Trail' Line V2 Double) -> Double -> Double -> Bool
+sectionTrailSectionFixedSegment t k1 k2
+  | null segs = t == t'
+  | otherwise = aSecT =~ aSecFS && bSecT =~ bSecFS
+  where
+    a = min k1 k2
+    b = max k1 k2
+    t' = section t a b
+
+    segs  = fixTrail $ mapLoc wrapLine t
+    segs' = fixTrail $ mapLoc wrapLine t'
+
+    aSecT = head segs'
+    bSecT = last segs'
+
+    (aSegIx, a') = splitParam a
+    (bSegIx, b') = splitParam b
+
+    aSecFS = section (segs !! floor aSegIx) a' x
+      where x = if aSegIx == bSegIx then b' else 1
+    bSecFS = section (segs !! floor bSegIx) x  b'
+      where x = if aSegIx == bSegIx then a' else 0
+
+    splitParam p | p <  0    = (0    , p           * n)
+                 | p >= 1    = (n - 1, 1 + (p - 1) * n)
+                 | otherwise = propFrac $  p       * n
+      where
+        propFrac x = let m = x `mod'` 1 in (x - m, m)
+        n = genericLength segs
diff --git a/test/Diagrams/Test/Transform.hs b/test/Diagrams/Test/Transform.hs
new file mode 100644
--- /dev/null
+++ b/test/Diagrams/Test/Transform.hs
@@ -0,0 +1,76 @@
+{-# LANGUAGE ConstraintKinds       #-}
+{-# LANGUAGE FlexibleContexts      #-}
+{-# LANGUAGE TypeFamilies          #-}
+
+
+module Diagrams.Test.Transform where
+
+import           Test.Tasty
+import           Test.Tasty.QuickCheck
+import           Diagrams.Prelude
+import           Diagrams.Direction
+import Instances
+
+tests :: TestTree
+tests = testGroup "Transform" [
+
+        testProperty "rotating a vector by a number then its additive inverse will yield the original vector" $
+          \θ a -> rotate ((θ * (-1)) @@ deg) (rotate ((θ :: Double) @@ deg) (a ::  V2 Double)) =~ a
+        , testProperty "under rotated allows scaling along an angle" $
+          \θ f a -> under (rotated ((θ :: Double) @@ deg)) (scaleX (f :: Double)) (a ::  V2 Double) =~ (rotate (negated (θ @@ deg)) . (scaleX f) . rotate (θ @@ deg)) a
+        , testProperty "a rotation of 0 does nothing" $
+          \a -> rotate (0 @@ deg) (a ::  V2 Double) =~ a
+        , testProperty "adding 360 degrees to a turn does nothing" $
+          \c a -> rotate (((c :: Double) + 360) @@ deg) (a ::  V2 Double) =~ rotate (c @@ deg) a
+        , testProperty "over rotated allows scaling along x of a rotated shape" $
+          \θ f a -> over (rotated ((θ :: Double) @@ deg)) (scaleX (f :: Double)) (a ::  V2 Double) =~ (rotate (θ @@ deg) . (scaleX f) . rotate (negated (θ @@ deg))) a
+        , testProperty "scaleX" $
+          \f a b -> (scaleX (f :: Double)) (V2 (a ::  Double) b) =~ V2 (a * f) b
+        , testProperty "scaleY" $
+          \f a b -> (scaleY (f :: Double)) (V2 (a ::  Double) b) =~ V2 a  (f * b)
+        , testProperty "reflectX" $
+          \a b -> reflectX (V2 (a ::  Double) b) =~ V2 (a * (-1))  b
+        , testProperty "reflectY" $
+          \a b -> reflectY (V2 (a ::  Double) b) =~ V2 a  ((-1) * b)
+        , testProperty "reflectXY" $
+          \a b -> reflectXY (V2 (a ::  Double) b) =~ V2 b a
+        , testProperty "translate" $
+          \a b c d -> translateX (a :: Double) (translateY b (P (V2 c d ))) =~ P (V2 (a + c) (b + d))
+        , testProperty "shear" $
+          \a b c d -> shearX (a :: Double) (shearY b (V2 c d)) =~ V2 ((c*b + d) * a + c) (c*b + d)
+        , testProperty "(1,0) rotateTo some dir will return normalised dir" $
+          \(NonZero a) b -> rotateTo  (dir (V2 (a :: Double) b)) (V2 1 0) =~ signorm (V2 a b)
+        , testProperty "rotates" $
+          \a c -> rotate ((a :: Double)@@ deg) (c :: V2 Double)   =~ rotate'' ((a :: Double)@@ deg) (c :: V2 Double) && rotate ((a :: Double)@@ deg) (c :: V2 Double)   =~ rotate' ((a :: Double)@@ deg) (c :: V2 Double)
+        , testProperty "reflectAbout works for a vector" $
+          \a b c d e f -> reflectAbout (P (V2 (a :: Double) b)) (dir (V2 c d)) (V2 e f) =~  over (rotated (atan2A' d c)) reflectY (V2 e f)
+        , testProperty "reflectAbout works for a point" $
+          \a b c d e f -> reflectAbout (P (V2 (a :: Double) b)) (dir (V2 c d)) (P (V2 e f)) =~ translate (V2 a b)  ((over (rotated (atan2A' d c)) reflectY) ((translate (V2 (-a) (-b)) )  (P (V2 e f))))
+
+
+        ]
+
+--the original " '' " and a secondary " ' " rotate function for testing
+
+rotation'' :: Floating n => Angle n -> T2 n
+rotation'' theta = fromLinear r (linv r)
+          where
+            r               = rot theta <-> rot (negated theta)
+            rot th (V2 x y) = V2 (cosA th * x - sinA th * y)
+                                 (sinA th * x + cosA th * y)
+
+rotate'' :: (InSpace V2 n t, Transformable t, Floating n) => Angle n -> t -> t
+rotate'' = transform . rotation''
+
+rotation' :: Floating n => Angle n -> T2 n
+rotation' theta = fromLinear r (linv r)
+            where
+            r               = rot theta <-> rot (negated theta)
+            rot th (V2 x y) = V2 (c * x - s * y)
+                                 (s * x + c * y)
+                                  where
+                                    c = cosA th
+                                    s = sinA th
+
+rotate' :: (InSpace V2 n t, Transformable t, Floating n) => Angle n -> t -> t
+rotate'  = transform . rotation'
diff --git a/test/Diagrams/Test/Transform/Matrix.hs b/test/Diagrams/Test/Transform/Matrix.hs
new file mode 100644
--- /dev/null
+++ b/test/Diagrams/Test/Transform/Matrix.hs
@@ -0,0 +1,26 @@
+{-# LANGUAGE ScopedTypeVariables #-}
+
+-- |
+
+module Diagrams.Test.Transform.Matrix where
+
+
+import           Test.Tasty
+import           Test.Tasty.QuickCheck
+import           Diagrams.Transform.Matrix
+import           Diagrams.Prelude
+import           Data.Distributive (distribute)
+
+import Instances
+
+tests :: TestTree
+tests = testGroup "Transform.Matrix"
+  [
+    testProperty "mkMat column vectors (2D)" $
+      \(Blind (t :: T2 Double)) -> distribute (mkMat t) =~ V2 (transform t unitX) (transform t unitY)
+  , testProperty "mkMat / fromMat22" $
+      \(m :: V2 (V2 Double)) -> mkMat (fromMat22 m zero) =~ m
+
+  , testProperty "mkMat / fromMat33" $
+      \(m :: V3 (V3 Double)) -> mkMat (fromMat33 m zero) =~ m
+  ]
diff --git a/test/Diagrams/Test/TwoD.hs b/test/Diagrams/Test/TwoD.hs
new file mode 100644
--- /dev/null
+++ b/test/Diagrams/Test/TwoD.hs
@@ -0,0 +1,65 @@
+-- |
+
+module Diagrams.Test.TwoD where
+
+import           Diagrams.Prelude
+import qualified Diagrams.Query as Query (sample)
+import           Diagrams.Trail        (linePoints)
+import           Instances
+import           Test.Tasty
+import           Test.Tasty.QuickCheck as QC
+
+newtype SmallAngle = SmallAngle (Angle Double)
+  deriving (Eq, Ord, Show)
+
+-- Generate random angles within a reasonably small range (+/- 5
+-- turns).
+instance Arbitrary SmallAngle where
+  arbitrary = SmallAngle . (@@turn) <$> choose (-5, 5)
+
+tests :: TestTree
+tests = testGroup "TwoD"
+    [ testGroup "TwoD.Arc" [
+           testProperty "arc start point is at radius 1 in the starting direction" $ \d (SmallAngle a) ->
+               pathVertices (arc d a :: Path V2 Double) ^? _head . _head =~ Just (origin .+^ fromDirection d )
+           , testProperty "arc end point is at radius 1 in the ending direction" $ \d (SmallAngle a) ->
+               pathVertices (arc d a :: Path V2 Double) ^? _head . _last =~ Just (origin .+^ fromDirection (rotate a d))
+         ]
+    , testGroup "TwoD.Types" [
+         testProperty "R2 vector addition is commutative" $
+           \u v -> (u :: V2 Double) ^+^ v =~ v ^+^ u
+         , testProperty "R2 subtraction is the inverse of addition" $
+           \u v -> u ^+^ v ^-^ v =~ (u :: V2 Double)
+         , testProperty "R2 vector negation squared is identity" $
+           \u -> negated (negated (u :: V2 Double)) =~ u
+         ]
+      , testGroup "cubicSpline" [
+         testProperty "Open cubic spline interpolates all points" $
+         \pts -> length pts > 1 ==> and (zipWith (=~) pts (cubicSpline False pts :: [P2 Double]))
+         , testProperty "Closed cubic spline interpolates all points" $
+           \pts -> length pts > 1 ==> and (zipWith (=~) pts (cubicSpline True pts :: [P2 Double]))
+    ]
+      , testGroup "Trail" [
+         testProperty "glueLine . cutLoop === id" $
+         \l -> glueLine (cutLoop l :: Trail' Line V2 Double) =~ l
+         , testProperty "cutLoop ends at starting point" $
+           \l -> let ps = linePoints (cutLoop (l :: Trail' Loop V2 Double) `at` origin) in (ps ^? _head) =~ (ps ^? _last)
+         , testProperty "cutTrail makes a Line" $
+           \t -> isLine (cutTrail (t :: Trail V2 Double))
+          , testProperty "fromSegments . lineSegments === id" $
+            \l -> fromSegments (lineSegments l) =~ (l :: Trail' Line V2 Double)
+          , testProperty "lineSegments . fromSegments === id" $
+            \segs -> lineSegments (fromSegments segs) =~ (segs :: [Segment Closed V2 Double])
+          ]
+    , testGroup "Queries and Backgrounds"
+        (let dia :: QDiagram NullBackend V2 Double [Int]
+             dia = circle 5 # scaleX 2 # rotateBy (1/14) # value [1]
+                   <>
+                   circle 2 # scaleX 5 # rotateBy (-4/14) # value [2]
+         in [
+           testProperty "sample dia pt === sample (dia # bg color) pt" $
+           \pt -> Query.sample dia pt QC.=== Query.sample (dia # bg orange) pt
+         , testProperty "sample dia pt === sample (dia # bgFrame 0.1 color) pt" $
+           \pt -> Query.sample dia pt QC.=== Query.sample (dia # bgFrame 0.1 green) pt
+         ])
+    ]
diff --git a/test/Diagrams/Test/TwoD/Offset.hs b/test/Diagrams/Test/TwoD/Offset.hs
new file mode 100644
--- /dev/null
+++ b/test/Diagrams/Test/TwoD/Offset.hs
@@ -0,0 +1,48 @@
+module Diagrams.Test.TwoD.Offset
+    (
+      tests
+    ) where
+
+import Test.Tasty (TestTree)
+import Test.Tasty.HUnit
+
+import Diagrams.Prelude
+import Diagrams.TwoD.Offset
+
+tests :: [TestTree]
+tests =
+    [ testCase "line"
+          (offsetTrailVertices
+              [p2 (0, 0), p2 (1, 0)]
+              [p2 (0, -1), p2 (1, -1)])
+    , testCase "square"
+          (offsetTrailVertices
+              [p2 (0, 0), p2 (1, 0), p2 (1, 1), p2 (0, 1), p2 (0, 0)]
+              [p2 (0, -1), p2 (2, -1), p2 (2, 2), p2 (-1, 2), p2 (-1, 0)])
+    , testCase "square loop"
+          (offsetTrailLoopVertices
+              [p2 (0, 0), p2 (1, 0), p2 (1, 1), p2 (0, 1), p2 (0, 0)]
+              [p2 (2, -1), p2 (2, 2), p2 (-1, 2), p2 (-1, -1)])
+    , testCase "redundant line"
+          (offsetTrailVertices
+              [p2 (0, 0), p2 (0.5, 0), p2 (1, 0)]
+              [p2 (0, -1), p2 (1, -1)])
+    , testCase "redundant square"
+          (offsetTrailVertices
+              [p2 (0, 0), p2 (1, 0), p2 (1, 0.5), p2 (1, 1), p2 (0, 1), p2 (0, 0)]
+              [p2 (0, -1), p2 (2, -1), p2 (2, 2), p2 (-1, 2), p2 (-1, 0)])
+    , testCase "redundant square loop"
+          (offsetTrailLoopVertices
+              [p2 (0, 0), p2 (1, 0), p2 (1, 0.5), p2 (1, 1), p2 (0, 1), p2 (0, 0)]
+              [p2 (2, -1), p2 (2, 2), p2 (-1, 2), p2 (-1, -1)])
+    ]
+
+offsetTrailVertices :: [Point V2 Double] -> [Point V2 Double] -> Assertion
+offsetTrailVertices orig off =
+    (trailVertices . offsetTrail 1 . fromVertices $ orig) @?= off
+
+offsetTrailLoopVertices :: [Point V2 Double] -> [Point V2 Double] -> Assertion
+offsetTrailLoopVertices orig off =
+    (trailVertices . offsetTrail 1 . loopTrailFromVertices $ orig) @?= off
+  where
+    loopTrailFromVertices = (`at` origin) . wrapTrail . glueLine . lineFromVertices
diff --git a/test/Diagrams/Test/TwoD/Segment.hs b/test/Diagrams/Test/TwoD/Segment.hs
new file mode 100644
--- /dev/null
+++ b/test/Diagrams/Test/TwoD/Segment.hs
@@ -0,0 +1,54 @@
+{-# LANGUAGE FlexibleContexts  #-}
+{-# LANGUAGE FlexibleInstances #-}
+
+{-# OPTIONS_GHC -fno-warn-orphans #-}
+
+module Diagrams.Test.TwoD.Segment
+    (
+      tests
+    ) where
+
+import qualified Test.QuickCheck.Property as Q
+import           Test.Tasty               (TestTree)
+import           Test.Tasty.QuickCheck
+
+import           Diagrams.Prelude
+import           Diagrams.TwoD.Segment
+
+newtype InBox = InBox { unInBox :: Double }
+
+instance Arbitrary InBox where
+  arbitrary = InBox <$> choose (-1, 1)
+
+instance Arbitrary (Point V2 Double) where
+  arbitrary = curry p2 <$> (unInBox <$> arbitrary)
+                       <*> (unInBox <$> arbitrary)
+
+instance Arbitrary (FixedSegment V2 Double) where
+   arbitrary = oneof [FLinear <$> arbitrary <*> arbitrary, FCubic <$> arbitrary <*> arbitrary <*> arbitrary <*> arbitrary]
+
+epsT, epsE :: Double
+epsT = 1.0e-9 -- parameter space epsilon
+epsE = 1.0e-8 -- Euclidean space epsilon
+
+(.=~.) :: P2 Double -> P2 Double -> Bool
+x .=~. y = norm (x .-. y) < epsE
+
+tests :: [TestTree]
+tests =
+    [ testProperty "segmentSegment" $
+        \a b -> validateIntersections a b (segmentSegment epsT a b)
+    ]
+
+validateIntersections :: FixedSegment V2 Double -> FixedSegment V2 Double -> [(Double, Double, P2 Double)] -> Q.Result
+validateIntersections _ _ [] = Q.rejected -- TODO: check for false negatives (rasterize both and look for overlap?)
+validateIntersections a b isects = go isects
+  where
+    go [] = Q.succeeded
+    go ((ta,tb,p):is)
+      | and [ 0 <= ta && ta <= 1
+            , 0 <= tb && tb <= 1
+            , a `atParam` ta .=~. p
+            , b `atParam` tb .=~. p
+            ] = go is
+      | otherwise = Q.failed
diff --git a/test/Instances.hs b/test/Instances.hs
new file mode 100644
--- /dev/null
+++ b/test/Instances.hs
@@ -0,0 +1,157 @@
+{-# LANGUAGE FlexibleContexts     #-}
+{-# LANGUAGE FlexibleInstances    #-}
+{-# LANGUAGE GADTs                #-}
+{-# LANGUAGE ScopedTypeVariables  #-}
+{-# LANGUAGE UndecidableInstances #-}
+{-# LANGUAGE ViewPatterns         #-}
+
+{-# OPTIONS_GHC -fno-warn-orphans #-}
+
+-- | instances for QuickCheck Arbitrary and approximate equality
+
+module Instances where
+
+import           Diagrams.Prelude
+import           Numeric.Extras
+import           Test.Tasty.QuickCheck (Arbitrary (..), Gen)
+import qualified Test.Tasty.QuickCheck as QC
+
+------------------------------------------------------------
+    -- Approximate Comparison for Doubles, Points
+
+epsilon :: Double
+epsilon = 0.001
+
+class Approx a where
+  (=~) :: a -> a -> Bool
+
+infix 4 =~
+
+--instance (Fractional a, Ord a) => Approx a where
+instance Approx Double where
+  (=~) a b = abs (a - b) < epsilon
+
+instance Approx Float where
+    (=~) a b = abs (a - b) < 0.001
+
+instance Approx n => Approx (V2 n) where
+    z1 =~ z2 = (z1^._x) =~ (z2^._x) && (z1^._y) =~ (z2^._y)
+
+instance Approx n => Approx (V3 n) where
+    z1 =~ z2 = (z1^._x) =~ (z2^._x) && (z1^._y) =~ (z2^._y) && (z1^._z) =~ (z2^._z)
+
+instance Approx (v n) => Approx (Point v n) where
+    p =~ q = view _Point p =~ view _Point q
+
+instance (Approx n, RealExtras n) => Approx (Angle n) where
+    a =~ b = normA (a^.rad) =~ normA (b^.rad) where
+      normA ang = let ang' = ang `fmod` pi in if ang' >= 0 then ang' else ang'+pi
+
+instance Approx n => Approx (Offset Closed V2 n) where
+    OffsetClosed v0 =~ OffsetClosed v1 = v0 =~ v1
+
+instance Approx n => Approx (Segment Closed V2 n) where
+    Linear o0 =~ Linear o1 = o0 =~ o1
+    Cubic c0 d0 o0 =~ Cubic c1 d1 o1 = c0 =~ c1 && d0 =~ d1 && o0 =~ o1
+    _ =~ _ = False
+    -- The above is conservative:
+    -- Cubic never equals Linear even if they describe the same points
+
+instance Approx n => Approx (FixedSegment V2 n) where
+    FLinear a0 b0 =~ FLinear a1 b1 = a0 =~ a1 && b0 =~ b1
+    FCubic a0 b0 c0 d0 =~ FCubic a1 b1 c1 d1 = a0 =~ a1 && b0 =~ b1 && c0 =~ c1 && d0 =~ d1
+    _ =~ _ = False
+
+instance Approx n => Approx (Trail' Line V2 n) where
+    l0 =~ l1 = and $ zipWith (=~) (lineSegments l0) (lineSegments l1)
+
+instance Approx n => Approx (Trail' Loop V2 n) where
+    l0 =~ l1 = fst (loopSegments l0) =~ fst (loopSegments l1)
+
+instance (Approx n, Floating n, Ord n) => Approx (Trail V2 n) where
+    t0 =~ t1 = and $ zipWith (=~) (trailSegments t0) (trailSegments t1)
+
+instance (Approx a, Approx (Vn a), Num (N a), Additive (V a)) =>
+         Approx (Located a) where
+           a0 =~ a1 = (loc a0 .-. origin) =~ (loc a1 .-. origin) && unLoc a0 =~ unLoc a1
+
+instance Approx a => Approx (Maybe a) where
+    Nothing =~ Nothing = True
+    Nothing =~ Just _ = False
+    Just _ =~ Nothing = False
+    Just l =~ Just r = l =~ r
+
+-- These may be too general
+instance Approx a => Approx [a] where
+    a =~ b = and $ zipWith (=~) a b
+
+instance (Approx a, Approx b) => Approx (a, b) where
+    (a0, b0) =~ (a1,b1) = (a0 =~ a1) && (b0 =~ b1)
+
+------------------------------------------------------------
+-- Arbitrary instances for Points, Paths
+
+instance Arbitrary n => Arbitrary (V2 n) where
+    arbitrary = (^&) <$> arbitrary <*> arbitrary
+    shrink (coords -> x :& y) = (^&) <$> shrink x <*> shrink y
+
+instance Arbitrary n => Arbitrary (V3 n) where
+    arbitrary = V3 <$> arbitrary <*> arbitrary <*> arbitrary
+    shrink (coords -> x :& y :& z) = V3 <$> shrink x <*> shrink y <*> shrink z
+
+instance Arbitrary (v n) => Arbitrary (Point v n) where
+    arbitrary = P <$> arbitrary
+    shrink (P v) = P <$> shrink v
+
+instance (Arbitrary n, Floating n, Ord n) => Arbitrary (Transformation V2 n) where
+    arbitrary = QC.sized arbT
+      where
+        arbT 0 = return mempty
+        arbT n = QC.oneof
+          [ rotation    <$> arbitrary
+          , scaling     <$> arbitrary
+          , translation <$> arbitrary
+          , reflectionAbout <$> arbitrary <*> arbitrary
+          , (<>) <$> arbT (n `div` 2) <*> arbT (n `div` 2)
+          ]
+
+instance Arbitrary n => Arbitrary (Angle n) where
+    arbitrary = review rad <$> arbitrary
+
+instance (Arbitrary n, Floating n) => Arbitrary (Direction V2 n) where
+    arbitrary = rotate <$> arbitrary <*> pure xDir
+
+-- -- | Not a valid Show instance because not valid Haskell input
+-- instance (Show n, RealFloat n) => Show (Direction V2 n) where
+--     show d = "Dir" <> ( show $ d ^. _theta . turn )
+
+-- NOTE on shrinks: Adding definitions of 'shrink' below seems to work
+--   in simple tests, but test case failures hang for a very long time
+--   (presumably trying lots and lots of expensive shrinks).  Not sure
+--   how to make shrinking more tractable.
+
+instance (Arbitrary a, Arbitrary (Vn a)) => Arbitrary (Located a) where
+    arbitrary = at <$> arbitrary <*> arbitrary
+--    shrink (viewLoc -> (p,a)) = uncurry at <$> shrink (a,p)
+
+instance Arbitrary n => Arbitrary (Offset Closed V2 n) where
+    arbitrary = OffsetClosed <$> arbitrary
+--    shrink (OffsetClosed x) = OffsetClosed <$> shrink x
+
+instance Arbitrary n =>  Arbitrary (Segment Closed V2 n) where
+    arbitrary = QC.oneof [Linear <$> arbitrary, Cubic <$> arbitrary <*> arbitrary <*> arbitrary]
+    -- shrink (Linear x) = Linear <$> shrink x
+    -- shrink (Cubic x y z) = Linear z
+    --                      : [Cubic x' y' z' | (x',y',z') <- shrink (x,y,z)]
+
+instance (Arbitrary n, Floating n, Ord n) => Arbitrary (Trail' Line V2 n) where
+    arbitrary = lineFromSegments <$> arbitrary
+--    shrink (lineSegments -> segs) = lineFromSegments <$> shrink segs
+
+instance (Arbitrary n, Floating n, Ord n) => Arbitrary (Trail' Loop V2 n) where
+    arbitrary = closeLine <$> arbitrary
+--    shrink (cutLoop -> l) = closeLine <$> shrink l
+
+instance (Arbitrary n, Floating n, Ord n) => Arbitrary (Trail V2 n) where
+    arbitrary = QC.oneof [Trail <$> (arbitrary :: Gen (Trail' Loop V2 n)), Trail <$> (arbitrary :: Gen (Trail' Line V2 n))]
+
diff --git a/test/Speed.hs b/test/Speed.hs
new file mode 100644
--- /dev/null
+++ b/test/Speed.hs
@@ -0,0 +1,47 @@
+{-# LANGUAGE ConstraintKinds       #-}
+{-# LANGUAGE FlexibleContexts      #-}
+{-# LANGUAGE TypeFamilies          #-}
+
+module Main where
+
+import Criterion
+import Criterion.Main (defaultMain)
+
+import Diagrams.Prelude
+
+
+main :: IO ()
+main = defaultMain
+    [ bgroup "rotates"
+        [ bench "rotate"  $ whnf (rotate (90 @@ deg :: Angle Double)) (V2 3 3)
+         ,bench "rotate1" $ whnf (rotate' (90 @@ deg :: Angle Double)) (V2 3 3)
+         ,bench "rotate2" $ whnf (rotate'' (90 @@ deg :: Angle Double)) (V2 3 3)
+        ]
+    ]
+
+--the original " '' " and a secondary " ' " rotate function for comparing speed testing
+--note: function time changes dramatically when function is in this file rather than imported
+
+
+rotation' :: Floating n => Angle n -> T2 n
+rotation' theta = fromLinear r (linv r)
+                where
+                r               = rot theta <-> rot (negated theta)
+                rot th (V2 x y) = V2 (c * x - s * y)
+                                     (s * x + c * y)
+                                      where
+                                        c = cosA th
+                                        s = sinA th
+
+rotate' :: (InSpace V2 n t, Transformable t, Floating n) => Angle n -> t -> t
+rotate'  = transform . rotation'
+
+rotation'' :: Floating n => Angle n -> T2 n
+rotation'' theta = fromLinear r (linv r)
+              where
+                r               = rot theta <-> rot (negated theta)
+                rot th (V2 x y) = V2 (cosA th * x - sinA th * y)
+                                     (sinA th * x + cosA th * y)
+
+rotate'' :: (InSpace V2 n t, Transformable t, Floating n) => Angle n -> t -> t
+rotate'' = transform . rotation''
diff --git a/test/Test.hs b/test/Test.hs
new file mode 100644
--- /dev/null
+++ b/test/Test.hs
@@ -0,0 +1,26 @@
+import           Test.Tasty                (TestTree, defaultMain, testGroup)
+
+import qualified Diagrams.Test.Angle            as Angle
+import qualified Diagrams.Test.Direction        as Direction
+import qualified Diagrams.Test.Transform        as Transform
+import qualified Diagrams.Test.Transform.Matrix as TransformMatrix
+import qualified Diagrams.Test.TwoD             as TwoD
+import qualified Diagrams.Test.TwoD.Offset      as TwoD.Offset
+import qualified Diagrams.Test.TwoD.Segment     as TwoD.Segment
+
+import qualified Diagrams.Test.Trail            as Trail
+
+tests :: TestTree
+tests = testGroup "unit tests"
+    [ testGroup "TwoD.Offset" TwoD.Offset.tests
+    , testGroup "TwoD.Segment" TwoD.Segment.tests
+    , TwoD.tests
+    , Angle.tests
+    , Direction.tests
+    , Transform.tests
+    , TransformMatrix.tests
+    , Trail.tests
+    ]
+
+main :: IO ()
+main = defaultMain tests