{-|
Module : Tgraphs
Description : Collects and exports the various Tgraph modules plus extra operations.
Copyright : (c) Chris Reade, 2021
License : BSD-style
Maintainer : chrisreade@mac.com
Stability : experimental
This is the main module for Tgraph operations which collects and exports the other Tgraph modules.
The module also defines several functions for producing overlaid diagrams for Tgraphs (including smart drawing) and
experimental combinations such as boundaryECovering, boundaryVCovering, empire1, empire2, superForce, boundaryLoopsG.
It also defines experimental TrackedTgraphs (used for tracking subsets of faces of a Tgraph).
-}
-- {-# OPTIONS_HADDOCK ignore-exports #-}
{-# LANGUAGE NoMonomorphismRestriction #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE FlexibleInstances #-} -- needed for Drawable Patch
{-# LANGUAGE TupleSections #-}
module Tgraphs
( module Tgraph.Prelude
, module Tgraph.Decompose
, module Tgraph.Compose
, module Tgraph.Force
, module Tgraph.Relabelling
-- * Smart drawing of Tgraphs
, smart
, boundaryJoinFaces
, drawJoinsFor
, smartdraw
, restrictSmart
, smartRotateBefore
, smartAlignBefore
-- * Overlaid drawing tools for Tgraphs
, drawPCompose
, drawForce
, drawSuperForce
, drawWithMax
, addBoundaryAfter
, drawCommonFaces
, emphasizeFaces
-- * Combining force, compose, decompose
, composeK
, compForce
, allCompForce
, maxCompForce
-- , forceDecomp
, allForceDecomps
-- * Boundary Covering and Empires
, forcedBoundaryECovering
, forcedBoundaryVCovering
, boundaryECovering
, boundaryEdgeSet
, commonBdry
, boundaryVCovering
, boundaryVertexSet
, internalVertexSet
, tryDartAndKiteForced
, tryDartAndKite
, drawFBCovering
, empire1
, empire2
, empire2Plus
, drawEmpire
, showEmpire1
, showEmpire2
-- * Super Force with boundary edge covers
, superForce
, trySuperForce
, singleChoiceEdges
-- * Boundary face graph
, tryBoundaryFaceGraph
-- * Boundary loops
, boundaryLoopsG
, boundaryLoops
, findLoops
, pathFromBoundaryLoops
-- * TrackedTgraphs
, TrackedTgraph(..)
, newTrackedTgraph
, makeTrackedTgraph
, trackFaces
, unionTwoTracked
-- * Forcing and Decomposing TrackedTgraphs
, addHalfDartTracked
, addHalfKiteTracked
, decomposeTracked
-- * Drawing TrackedTgraphs
, drawTrackedTgraph
, drawTrackedTgraphRotated
, drawTrackedTgraphAligned
) where
import Tgraph.Prelude
import Tgraph.Decompose
import Tgraph.Compose
import Tgraph.Force
import Tgraph.Relabelling
import Diagrams.Prelude hiding (union)
import TileLib
import Data.List (intersect, union, (\\), find, foldl', transpose)
import qualified Data.Set as Set (Set,fromList,null,intersection,deleteFindMin)-- used for boundary covers
import qualified Data.IntSet as IntSet (fromList,member,(\\)) -- for boundary vertex set
import qualified Data.IntMap.Strict as VMap (delete, fromList, findMin, null, lookup, (!)) -- used for boundary loops, boundaryLoops
import qualified Data.Maybe (fromMaybe)
-- |smart dr g - uses VPatch drawing function dr after converting g to a VPatch
-- It will add boundary joins regardless of the drawing function.
-- Examples:
--
-- smart draw g
--
-- smart (labelled draw) g
--
-- smart (labelSize normal draw) g
smart :: OKBackend b =>
(VPatch -> Diagram b) -> Tgraph -> Diagram b
smart dr g = drawJoinsFor (boundaryJoinFaces g) vp <> dr vp
where vp = makeVP g
-- |select the halftile faces of a Tgraph with a join edge on the boundary.
-- Useful for drawing join edges only on the boundary.
boundaryJoinFaces :: Tgraph -> [TileFace]
boundaryJoinFaces g = fmap snd $ incompleteHalves bdry $ boundary bdry where
bdry = makeBoundaryState g
-- |given a list of faces and a VPatch with suitable locations, draw just the dashed joins for those faces.
drawJoinsFor:: OKBackend b =>
[TileFace] -> VPatch -> Diagram b
drawJoinsFor fcs vp = drawWith dashjOnly (subVP vp fcs)
-- |same as draw except adding dashed lines on boundary join edges.
smartdraw :: OKBackend b => Tgraph -> Diagram b
smartdraw = smart draw
-- |restrictSmart g dr vp - assumes vp has locations for vertices in g.
-- It uses the VPatch drawing function dr to draw g and adds dashed boundary joins.
-- This can be used instead of smart when an appropriate vp is already available.
restrictSmart :: OKBackend b =>
Tgraph -> (VPatch -> Diagram b) -> VPatch -> Diagram b
restrictSmart g dr vp = drawJoinsFor (boundaryJoinFaces g) rvp <> dr rvp
where rvp = restrictVP vp $ faces g
-- |smartRotateBefore vfun a g - a tricky combination of smart with rotateBefore.
-- Uses vfun to produce a Diagram after converting g to a rotated VPatch but also adds the dashed boundary join edges of g.
--
-- Example: smartRotateBefore (labelled draw) angle g
smartRotateBefore :: OKBackend b =>
(VPatch -> Diagram b) -> Angle Double -> Tgraph -> Diagram b
smartRotateBefore vfun angle g = rotateBefore (restrictSmart g vfun) angle g
-- |smartAlignBefore vfun (a,b) g - a tricky combination of smart with alignBefore.
-- Uses vfun to produce a Diagram after converting g to n aligned VPatch but also adds the dashed boundary join edges of g.
--
-- Example: smartAlignBefore (labelled draw) (a,b) g
smartAlignBefore :: OKBackend b =>
(VPatch -> Diagram b) -> (Vertex,Vertex) -> Tgraph -> Diagram b
smartAlignBefore vfun (a,b) g = alignBefore (restrictSmart g vfun) (a,b) g
-- |applies partCompose to a Tgraph g, then draws the composed graph with the remainder faces (in lime).
-- (Relies on the vertices of the composition and remainder being subsets of the vertices of g.)
drawPCompose :: OKBackend b =>
Tgraph -> Diagram b
drawPCompose g =
restrictSmart g' draw vp
<> drawj (subVP vp remainder) # lw medium # lc lime
where (remainder,g') = partCompose g
vp = makeVP g
-- |drawForce g is a diagram showing the argument g in red overlayed on force g
-- It adds dashed join edges on the boundary of g
drawForce :: OKBackend b =>
Tgraph -> Diagram b
drawForce g =
restrictSmart g draw vp # lc red # lw medium
<> draw vp
where vp = makeVP $ force g
-- |drawSuperForce g is a diagram showing the argument g in red overlayed on force g in black
-- overlaid on superForce g in blue.
-- It adds dashed join edges on the boundary of g.
drawSuperForce :: OKBackend b =>
Tgraph -> Diagram b
drawSuperForce g = (dg # lc red) <> dfg <> (dsfg # lc blue) where
fg = force g
sfg = superForce fg
vp = makeVP sfg
dfg = draw $ selectFacesVP vp (faces fg \\ faces g) -- restrictSmart (force g) draw vp
dg = restrictSmart g draw vp
dsfg = draw $ selectFacesVP vp (faces sfg \\ faces fg)
-- | drawWithMax g - draws g and overlays the maximal composition of force g in red.
-- This relies on g and all compositions of force g having vertices in force g.
drawWithMax :: OKBackend b =>
Tgraph -> Diagram b
drawWithMax g = (dmax # lc red # lw medium) <> dg where
vp = makeVP $ force g -- duplicates force to get the locations of vertices in the forced Tgraph
dg = restrictSmart g draw vp
maxg = maxCompForce g
dmax = draw $ subVP vp (faces maxg)
-- |displaying the boundary of a Tgraph in lime (overlaid on the Tgraph drawn with f).
addBoundaryAfter :: OKBackend b =>
(VPatch -> Diagram b) -> Tgraph -> Diagram b
addBoundaryAfter f g = (drawEdgesVP vp edges # lc lime) <> f vp where
vp = makeVP g
edges = graphBoundary g
-- |drawCommonFaces (g1,e1) (g2,e2) uses commonFaces (g1,e1) (g2,e2) to find the common faces
-- and emphasizes them on the background g1.
drawCommonFaces :: OKBackend b =>
(Tgraph,Dedge) -> (Tgraph,Dedge) -> Diagram b
drawCommonFaces (g1,e1) (g2,e2) = emphasizeFaces (commonFaces (g1,e1) (g2,e2)) g1
-- |emphasizeFaces fcs g emphasizes the given faces (that are in g) overlaid on the background g.
emphasizeFaces :: OKBackend b =>
[TileFace] -> Tgraph -> Diagram b
emphasizeFaces fcs g = (drawj emphvp # lw thin) <> (draw vp # lw ultraThin) where
vp = makeVP g
emphvp = subVP vp (fcs `intersect` faces g)
-- | An unsound version of composition which defaults to kites when there are choices (unknowns).
-- This is unsound in that it can create an incorrect Tgraph from a correct Tgraph.
composeK :: Tgraph -> Tgraph
composeK g = runTry $ tryConnectedNoCross newfaces where
dwInfo = getDartWingInfo g
changedInfo = dwInfo{ largeKiteCentres = largeKiteCentres dwInfo ++ unknowns dwInfo
, unknowns = []
}
compositions = composedFaceGroups changedInfo
newfaces = map fst compositions
-- |compForce is semantically equivalent to (compose . force), i.e it does a force then compose (raising an error if the force fails with an incorrect Tgraph).
-- However it is more efficient because it omits the check for connected, and no crossing boundaries
-- (and uses getDartWingInfoForced instead of getDartWingInfo)
-- This relies on a proof that composition does not need to be checked for a forced Tgraph.
-- (We also have a proof that the result must be a forced Tgraph when the initial force succeeds.)
compForce:: Tgraph -> Tgraph
compForce = uncheckedCompose . force
-- |allCompForce g produces a list of the non-null iterated (forced) compositions of force g.
-- It will raise an error if the initial force fails with an incorrect Tgraph.
-- The list will be [] if g is the emptyTgraph, otherwise the list begins with force g (when the force succeeds).
-- The definition relies on (1) a proof that the composition of a forced Tgraph is forced and
-- (2) a proof that composition does not need to be checked for a forced Tgraph.
allCompForce:: Tgraph -> [Tgraph]
allCompForce = takeWhile (not . nullGraph) . iterate uncheckedCompose . force
-- |maxCompForce g produces the maximally composed (non-null) Tgraph starting from force g, provided g is not the emptyTgraph
-- and just the emptyTgraph otherwise.
-- It will raise an error if the initial force fails with an incorrect Tgraph.
maxCompForce:: Tgraph -> Tgraph
maxCompForce g | nullGraph g = g
| otherwise = last $ allCompForce g
{-
-- |force after a decomposition (raising an error if the force fails with an incorrect Tgraph)
forceDecomp:: Tgraph -> Tgraph
forceDecomp = force . decompose
-}
-- | allForceDecomps g - produces an infinite list (starting with g)
-- of forced decompositions of g (raising an error if a force fails with an incorrect Tgraph).
allForceDecomps:: Tgraph -> [Tgraph]
allForceDecomps = iterate (force . decompose)
{-| forcedBoundaryECovering g - produces a list of all boundary covers of force g, each of which
extends force g to cover the entire boundary directed edges in (force g).
(So the boundary of force g is entirely internal edges in each cover).
The covers include all possible ways faces can be added on the boundary that are correct.
The common faces of the covers constitute the empire (level 1) of g.
This will raise an error if the initial force fails with a stuck graph.
-}
forcedBoundaryECovering:: Tgraph -> [Tgraph]
forcedBoundaryECovering g = recoverGraph <$> boundaryECovering gforcedBdry where
gforcedBdry = runTry $ onFail "forcedBoundaryECovering:Initial force failed (incorrect Tgraph)\n" $
tryForce $ makeBoundaryState g
{-| forcedBoundaryVCovering g - produces a list of all boundary covers of force g as with
forcedBoundaryECovering g but covering all boundary vertices rather than just boundary edges.
-}
forcedBoundaryVCovering:: Tgraph -> [Tgraph]
forcedBoundaryVCovering g = recoverGraph <$> boundaryVCovering gforcedBdry where
gforcedBdry = runTry $ onFail "forcedBoundaryVCovering:Initial force failed (incorrect Tgraph)\n" $
tryForce $ makeBoundaryState g
{-| boundaryECovering bd - produces a list of all possible covers of the boundary directed edges in bd.
[bd should be a boundary state resulting from forcing].
A cover is a forced extension (of bd) such that the original boundary directed edges of bd are all internal edges.
Extensions are made by repeatedly adding a face to any edge on the original boundary that is still on the boundary
and forcing, repeating this until the orignal boundary is all internal edges.
The resulting covers account for all possible ways the boundary can be extended.
This can raise an error if bd is a boundary state of an unforced Tgraph.
It will raise an error if both choices on a boundary edge fail when forced (using atLeastOne).
-}
boundaryECovering:: BoundaryState -> [BoundaryState]
boundaryECovering bstate = covers [(bstate, boundaryEdgeSet bstate)] where
covers:: [(BoundaryState, Set.Set Dedge)] -> [BoundaryState]
covers [] = []
covers ((bs,es):opens)
| Set.null es = bs:covers opens -- bs is a completed cover
| otherwise = covers (newcases ++ opens)
where (de,des) = Set.deleteFindMin es
newcases = fmap (\b -> (b, commonBdry des b))
(atLeastOne $ tryDartAndKiteForced de bs)
-- |Make a set of the directed boundary edges of a BoundaryState
boundaryEdgeSet:: BoundaryState -> Set.Set Dedge
boundaryEdgeSet = Set.fromList . boundary
-- | commonBdry des b - returns those directed edges in des that are boundary directed edges of bd
commonBdry:: Set.Set Dedge -> BoundaryState -> Set.Set Dedge
commonBdry des b = des `Set.intersection` boundaryEdgeSet b
{-| boundaryVCovering bd - similar to boundaryECovering, but produces a list of all possible covers of
the boundary vertices in bd (rather than just boundary edges).
[bd should be a boundary state resulting from forcing].
This can raise an error if bd is a boundary state of an unforced Tgraph.
-}
boundaryVCovering:: BoundaryState -> [BoundaryState]
boundaryVCovering bd = covers [(bd, startbds)] where
startbds = boundaryEdgeSet bd
startbvs = boundaryVertexSet bd
--covers:: [(BoundaryState,Set.Set Dedge)] -> [BoundaryState]
covers [] = []
covers ((open,es):opens)
| Set.null es = case find (\(a,_) -> IntSet.member a startbvs) (boundary open) of
Nothing -> open:covers opens
Just dedge -> covers $ fmap (,es) (atLeastOne $ tryDartAndKiteForced dedge open) ++opens
| otherwise = covers $ fmap (\b -> (b, commonBdry des b)) (atLeastOne $ tryDartAndKiteForced de open) ++opens
where (de,des) = Set.deleteFindMin es
-- | returns the set of boundary vertices of a BoundaryState
boundaryVertexSet :: BoundaryState -> VertexSet
boundaryVertexSet bd = IntSet.fromList $ fmap fst (boundary bd)
-- | returns the set of internal vertices of a BoundaryState
internalVertexSet :: BoundaryState -> VertexSet
internalVertexSet bd = vertexSet (recoverGraph bd) IntSet.\\ boundaryVertexSet bd
-- | tryDartAndKiteForced de b - returns the list of (2) results after adding a dart (respectively kite)
-- to edge de of a Forcible b and then tries forcing. Each of the results is a Try.
tryDartAndKiteForced:: Forcible a => Dedge -> a -> [Try a]
tryDartAndKiteForced de b =
[ onFail ("tryDartAndKiteForced: Dart on edge: " ++ show de ++ "\n") $
tryAddHalfDart de b >>= tryForce
, onFail ("tryDartAndKiteForced: Kite on edge: " ++ show de ++ "\n") $
tryAddHalfKite de b >>= tryForce
]
-- | tryDartAndKite de b - returns the list of (2) results after adding a dart (respectively kite)
-- to edge de of a Forcible b. Each of the results is a Try.
tryDartAndKite:: Forcible a => Dedge -> a -> [Try a]
tryDartAndKite de b =
[ onFail ("tryDartAndKite: Dart on edge: " ++ show de ++ "\n") $
tryAddHalfDart de b
, onFail ("tryDartAndKite: Kite on edge: " ++ show de ++ "\n") $
tryAddHalfKite de b
]
-- | test function to draw a column of the list of graphs resulting from forcedBoundaryVCovering g.
drawFBCovering :: OKBackend b =>
Tgraph -> Diagram b
drawFBCovering g = lw ultraThin $ vsep 1 (draw <$> forcedBoundaryVCovering g)
-- | empire1 g - produces a TrackedTgraph representing the level 1 empire of g.
-- The tgraph of the result is the first boundary vertex cover of force g,
-- and the tracked list of the result has the common faces of all the boundary vertex covers (of force g)
-- at the head, followed by the original faces of g.
empire1:: Tgraph -> TrackedTgraph
empire1 g = makeTrackedTgraph g0 [fcs,faces g] where
covers = forcedBoundaryVCovering g
g0 = head covers
others = tail covers
fcs = foldl' intersect (faces g0) $ fmap g0Intersect others
de = defaultAlignment g
g0Intersect g1 = commonFaces (g0,de) (g1,de)
-- | empire2 g - produces a TrackedTgraph representing the level 2 empire of g.
-- NB since very large graphs can be generated with boundary vertex covers, we use boundary edge covers only.
-- That is, after finding all boundary edge covers of force g,
-- boundary edge covers are then found for each boundary edge cover to form a list of doubly-extended
-- boundary edge covers.
-- The tgraph of the result is the first (doubly-extended) boundary edge cover (of force g),
-- and the tracked list of the result has the common faces of all the (doubly-extended) boundary edge covers
-- at the head, followed by the original faces of g.
empire2:: Tgraph -> TrackedTgraph
empire2 g = makeTrackedTgraph g0 [fcs, faces g] where
covers1 = boundaryECovering $ runTry $ onFail "empire2:Initial force failed (incorrect Tgraph)\n"
$ tryForce $ makeBoundaryState g
covers2 = concatMap boundaryECovering covers1
-- (g0:others) = fmap recoverGraph covers2
gcovers = fmap recoverGraph covers2
g0 = head gcovers
others = tail gcovers
fcs = foldl' intersect (faces g0) $ fmap g0Intersect others
de = defaultAlignment g
g0Intersect g1 = commonFaces (g0,de) (g1,de)
-- | empire2Plus g - produces a TrackedTgraph representing an extended level 2 empire of g
-- similar to empire2, but using boundaryVCovering insrtead of boundaryECovering.
empire2Plus:: Tgraph -> TrackedTgraph
empire2Plus g = makeTrackedTgraph g0 [fcs, faces g] where
covers1 = boundaryVCovering $ runTry $ onFail "empire2:Initial force failed (incorrect Tgraph)\n"
$ tryForce $ makeBoundaryState g
covers2 = concatMap boundaryVCovering covers1
-- (g0:others) = fmap recoverGraph covers2
gcovers = fmap recoverGraph covers2
g0 = head gcovers
others = tail gcovers
fcs = foldl' intersect (faces g0) $ fmap g0Intersect others
de = defaultAlignment g
g0Intersect g1 = commonFaces (g0,de) (g1,de)
-- | drawEmpire e - produces a diagram for an empire e represented as a TrackedTgraph
-- as calcultaed by e.g. empire1 or empire2 or empire2Plus.
-- The diagram draws the underlying Tgraph, with the first tracked faces - the starting Tgraph shown red, and emphasising the second tracked faces
-- - the common faces.
drawEmpire :: OKBackend b =>
TrackedTgraph -> Diagram b
drawEmpire =
drawTrackedTgraph [ lw ultraThin . draw
, lw thin . fillDK lightgrey lightgrey
, lw thin . lc red . draw
]
-- | showEmpire1 g - produces a diagram emphasising the common faces of all boundary covers of force g.
-- This is drawn over one of the possible boundary covers and the faces of g are shown in red.
showEmpire1 :: OKBackend b =>
Tgraph -> Diagram b
showEmpire1 = drawEmpire . empire1
-- | showEmpire2 g - produces a diagram emphasising the common faces of a doubly-extended boundary cover of force g.
-- This is drawn over one of the possible doubly-extended boundary covers and the faces of g are shown in red.
showEmpire2 :: OKBackend b =>
Tgraph -> Diagram b
showEmpire2 = drawEmpire . empire2
-- |superForce g - after forcing g this looks for single choice boundary edges.
-- That is a boundary edge for which only a dart or only a kite addition occurs in all boundary edge covers.
-- If there is at least one such edge, it makes the choice for the first such edge and recurses,
-- otherwise it returns the forced result.
-- This will raise an error if force encounters a stuck (incorrect) tiling or if
-- both forced extensions fail for some boundary edge.
-- Otherwise, the result has exactly two correct possible extensions for each boundary edge.
superForce:: Forcible a => a -> a
superForce g = runTry $ trySuperForce g
-- |trySuperForce g - this looks for single choice edges after trying to force g.
-- If there is at least one, it makes that choice and recurses.
-- It returns a Left s if force fails or if both choices fail for some edge (where s is a failure report).
-- Otherwise Right g' is returned where g' is the super forced g.
trySuperForce:: Forcible a => a -> Try a
trySuperForce = tryFSOp trySuperForceFS where
-- |trySuperForceFS - implementation of trySuperForce for force states only
trySuperForceFS :: ForceState -> Try ForceState
trySuperForceFS fs =
do forcedFS <- onFail "trySuperForceFS: force failed (incorrect Tgraph)\n" $
tryForce fs
case singleChoiceEdges $ boundaryState forcedFS of
[] -> return forcedFS
(elpr:_) -> do extended <- addSingle elpr forcedFS
trySuperForceFS extended
addSingle (e,l) fs = if isDart l then tryAddHalfDart e fs else tryAddHalfKite e fs
-- |singleChoiceEdges bd - if bd is a boundary state of a forced Tgraph this finds those boundary edges of bd
-- which have a single choice (i.e. the other choice is incorrect), by inspecting boundary edge covers of bd.
-- The result is a list of pairs of (edge,label) where edge is a boundary edge with a single choice
-- and label indicates the choice as the common face label.
singleChoiceEdges :: BoundaryState -> [(Dedge,HalfTileLabel)]
singleChoiceEdges bstate = commonToCovering (boundaryECovering bstate) (boundary bstate)
where
-- |commonToCovering bds edgeList - when bds are all the boundary edge covers of some forced Tgraph
-- whose boundary edges were edgeList, this looks for edges in edgeList that have the same tile label added in all covers.
-- This indicates there is a single choice for such an edge (the other choice is incorrect).
-- The result is a list of pairs: edge and a common tile label.
-- commonToCovering :: [BoundaryState] -> [Dedge] -> [(Dedge,HalfTileLabel)]
commonToCovering bds edgeList = common edgeList (transpose labellists) where
labellists = fmap (`reportCover` edgeList) bds
common [] [] = []
common [] (_:_) = error "singleChoiceEdges:commonToCovering: label list is longer than edge list"
common (_:_) [] = error "singleChoiceEdges:commonToCovering: label list is shorter than edge list"
common (e:more) (ls:lls) = if matchingLabels ls
then (e,head ls):common more lls
else common more lls
matchingLabels [] = error "singleChoiceEdges:commonToCovering: empty list of labels"
matchingLabels (l:ls) = all (==l) ls
-- |reportCover bd edgelist - when bd is a boundary edge cover of some forced Tgraph whose boundary edges are edgelist,
-- this returns the tile label for the face covering each edge in edgelist (in corresponding order).
-- reportCover :: BoundaryState -> [Dedge] -> [HalfTileLabel]
reportCover bd des = fmap (tileLabel . getf) des where
efmap = dedgesFacesMap des (allFaces bd) -- more efficient than using graphEFMap?
-- efmap = graphEFMap (recoverGraph bd)
getf e = Data.Maybe.fromMaybe (error $ "singleChoiceEdges:reportCover: no face found with directed edge " ++ show e)
(faceForEdge e efmap)
-- |Tries to create a new Tgraph from all faces with a boundary vertex in a Tgraph.
-- The resulting faces could have a crossing boundary and also could be disconnected if there is a hole in the starting Tgraph
-- so these conditions are checked for, producing a Try result.
tryBoundaryFaceGraph :: Tgraph -> Try Tgraph
tryBoundaryFaceGraph = tryConnectedNoCross . boundaryFaces . makeBoundaryState
-- | Returns a list of (looping) vertex trails for the boundary of a Tgraph.
-- There will usually be a single trail, but more than one indicates the presence of boundaries round holes.
-- Each trail starts with the lowest numbered vertex in that trail, and ends with the same vertex.
-- The trails will have disjoint sets of vertices because of the no-crossing-boundaries condition of Tgraphs.
boundaryLoopsG:: Tgraph -> [[Vertex]]
boundaryLoopsG = findLoops . graphBoundary
-- | Returns a list of (looping) vertex trails for a BoundaryState.
-- There will usually be a single trail, but more than one indicates the presence of boundaries round holes.
-- Each trail starts with the lowest numbered vertex in that trail, and ends with the same vertex.
-- The trails will have disjoint sets of vertices because of the no-crossing-boundaries condition of Tgraphs (and hence BoundaryStates).
boundaryLoops:: BoundaryState -> [[Vertex]]
boundaryLoops = findLoops . boundary
-- | When applied to a boundary edge list this returns a list of (looping) vertex trails.
-- I.e. if we follow the boundary edges of a Tgraph recording vertices visited as a list returning to the starting vertex
-- we get a looping trail.
-- There will usually be a single trail, but more than one indicates the presence of boundaries round holes.
-- Each trail starts with the lowest numbered vertex in that trail, and ends with the same vertex.
findLoops:: [Dedge] -> [[Vertex]]
findLoops = collectLoops . VMap.fromList where
-- Make a vertex to vertex map from the directed edges then delete items from the map as a trail is followed
-- from the lowest numbered vertex.
-- Vertices are collected in reverse order, then the list is reversed when a loop is complete.
-- This is repeated until the map is empty, to collect all boundary trials.
collectLoops vmap --
| VMap.null vmap = []
| otherwise = chase startV vmap [startV]
where
(startV,_) = VMap.findMin vmap
chase a vm sofar -- sofar is the collected trail in reverse order.
= case VMap.lookup a vm of
Just b -> chase b (VMap.delete a vm) (b:sofar)
Nothing -> if a == startV
then reverse sofar: collectLoops vm -- look for more loops
else error $ "findLoops (collectLoops): non looping boundary component, starting at "
++show startV++
" and finishing at "
++ show a ++
"\nwith loop vertices "++ show (reverse sofar) ++"\n"
-- | Given a suitable vertex to location map and boundary loops (represented as a list of lists of vertices),
-- this will return a (Diagrams) Path for the boundary. It will raise an error if any vertex listed is not a map key.
-- (The resulting path can be filled when converted to a diagram.)
pathFromBoundaryLoops:: VertexLocMap -> [[Vertex]] -> Path V2 Double
pathFromBoundaryLoops vlocs loops = toPath $ map (locateLoop . map (vlocs VMap.!)) loops where
locateLoop pts = (`at` head pts) $ glueTrail $ trailFromVertices pts
-- * TrackedTgraphs
{-|
TrackedTgraph - introduced to allow tracking of subsets of faces
in both force and decompose operations.
Mainly used for drawing purposes but also for empires.
A TrackedTgraph has a main Tgraph (tgraph) and a list of subsets (sublists) of faces (tracked).
The list allows for tracking different subsets of faces at the same time.
-}
data TrackedTgraph = TrackedTgraph{ tgraph:: Tgraph, tracked::[[TileFace]]} deriving Show
-- |newTrackedTgraph g creates a TrackedTgraph from a Tgraph g with an empty tracked list
newTrackedTgraph :: Tgraph -> TrackedTgraph
newTrackedTgraph g = makeTrackedTgraph g []
-- |makeTrackedTgraph g trackedlist creates a TrackedTgraph from a Tgraph g
-- from trackedlist where each list in trackedlist is a subset of the faces of g.
-- Any faces not in g are ignored.
makeTrackedTgraph :: Tgraph -> [[TileFace]] -> TrackedTgraph
makeTrackedTgraph g trackedlist = TrackedTgraph{ tgraph = g, tracked = fmap (`intersect` faces g) trackedlist}
-- |trackFaces ttg - pushes the maingraph tilefaces onto the stack of tracked subsets of ttg
trackFaces:: TrackedTgraph -> TrackedTgraph
trackFaces ttg = ttg{ tracked = faces (tgraph ttg):tracked ttg }
-- |unionTwoTracked ttg - combines the top two lists of tracked tilefaces replacing them with the list union.
unionTwoTracked:: TrackedTgraph -> TrackedTgraph
unionTwoTracked ttg = ttg{ tracked = newTracked } where
newTracked = case tracked ttg of
(a:b:more) -> a `union` b:more
_ -> error $ "unionTwoTracked: Two tracked lists of faces not found: " ++ show ttg ++"\n"
{-*
Forcing and Decomposing TrackedTgraphs
-}
-- | TrackedTgraphs are Forcible
instance Forcible TrackedTgraph where
tryFSOpWith ugen f ttg = do
g' <- tryFSOpWith ugen f $ tgraph ttg
return ttg{ tgraph = g' }
tryInitFSWith ugen ttg = tryInitFSWith ugen (tgraph ttg)
tryChangeBoundaryWith ugen f ttg = do
g' <- tryChangeBoundaryWith ugen f $ tgraph ttg
return ttg{ tgraph = g' }
-- getBoundaryState = getBoundaryState . tgraph
-- |addHalfDartTracked ttg e - add a half dart to the tgraph of ttg on the given edge e,
-- and push the new singleton face list onto the tracked list.
addHalfDartTracked:: Dedge -> TrackedTgraph -> TrackedTgraph
addHalfDartTracked e ttg =
TrackedTgraph{ tgraph = g' , tracked = fcs:tracked ttg}
where
g = tgraph ttg
g' = addHalfDart e g
fcs = faces g' \\ faces g
-- |addHalfKiteTracked ttg e - add a half kite to the tgraph of ttg on the given edge e,
-- and push the new singleton face list onto the tracked list.
addHalfKiteTracked:: Dedge -> TrackedTgraph -> TrackedTgraph
addHalfKiteTracked e ttg =
TrackedTgraph{ tgraph = g' , tracked = fcs:tracked ttg}
where
g = tgraph ttg
g' = addHalfKite e g
fcs = faces g' \\ faces g
-- |decompose a TrackedTgraph - applies decomposition to all tracked subsets as well as the full Tgraph.
-- Tracked subsets get the same numbering of new vertices as the main Tgraph.
decomposeTracked :: TrackedTgraph -> TrackedTgraph
decomposeTracked ttg =
TrackedTgraph{ tgraph = g' , tracked = tlist}
where
-- makeTrackedTgraph g' tlist where
g = tgraph ttg
g' = makeUncheckedTgraph newFaces
newVFor = phiVMap g
newFaces = concatMap (decompFace newVFor) (faces g)
tlist = fmap (concatMap (decompFace newVFor)) (tracked ttg)
{-* Drawing TrackedTgraphs
-}
{-|
To draw a TrackedTgraph, we use a list of functions each turning a VPatch into a diagram.
The first function is applied to a VPatch for untracked faces.
Subsequent functions are applied to VPatches for the respective tracked subsets.
Each diagram is beneath later ones in the list, with the diagram for the untracked VPatch at the bottom.
The VPatches are all restrictions of a single VPatch for the Tgraph, so consistent.
(Any extra draw functions are applied to the VPatch for the main tgraph and the results placed atop.)
-}
drawTrackedTgraph :: OKBackend b => [VPatch -> Diagram b] -> TrackedTgraph -> Diagram b
drawTrackedTgraph drawList ttg = mconcat $ reverse $ zipWith ($) drawList vpList where
vp = makeVP (tgraph ttg)
untracked = vpFaces vp \\ concat (tracked ttg)
vpList = fmap (restrictVP vp) (untracked:tracked ttg) ++ repeat vp
{-|
To draw a TrackedTgraph rotated.
Same as drawTrackedTgraph but with additional angle argument for the rotation.
This is useful when labels are being drawn.
The angle argument is used to rotate the common vertex location map (anticlockwise) before drawing
to ensure labels are not rotated.
-}
drawTrackedTgraphRotated :: OKBackend b => [VPatch -> Diagram b] -> Angle Double -> TrackedTgraph -> Diagram b
drawTrackedTgraphRotated drawList a ttg = mconcat $ reverse $ zipWith ($) drawList vpList where
vp = rotate a $ makeVP (tgraph ttg)
untracked = vpFaces vp \\ concat (tracked ttg)
vpList = fmap (restrictVP vp) (untracked:tracked ttg) ++ repeat vp
{-|
To draw a TrackedTgraph aligned.
Same as drawTrackedTgraph but with additional vertex pair argument for the (x-axis) alignment.
This is useful when labels are being drawn.
The vertex pair argument is used to align the common vertex location map before drawing
(to ensure labels are not rotated).
This will raise an error if either of the pair of vertices is not a vertex of (the tgraph of) the TrackedTgraph
-}
drawTrackedTgraphAligned :: OKBackend b => [VPatch -> Diagram b] -> (Vertex,Vertex) -> TrackedTgraph -> Diagram b
drawTrackedTgraphAligned drawList (a,b) ttg = mconcat $ reverse $ zipWith ($) drawList vpList where
vp = makeAlignedVP (a,b) (tgraph ttg)
untracked = vpFaces vp \\ concat (tracked ttg)
vpList = fmap (restrictVP vp) (untracked:tracked ttg) ++ repeat vp