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lp-diagrams (empty) → 1.0

raw patch · 11 files changed

+2029/−0 lines, 11 filesdep +basedep +containersdep +glpk-hssetup-changed

Dependencies added: base, containers, glpk-hs, graphviz, labeled-tree, lens, mtl, polynomials-bernstein, text, typography-geometry, vector

Files

+ Graphics/Diagrams.hs view
@@ -0,0 +1,6 @@+module Graphics.Diagrams (module D) where++import Graphics.Diagrams.Core as D+import Graphics.Diagrams.Path as D+import Graphics.Diagrams.Point  as D+import Graphics.Diagrams.Object as D
+ Graphics/Diagrams/Core.hs view
@@ -0,0 +1,333 @@+{-# LANGUAGE TypeSynonymInstances, FlexibleContexts, FlexibleInstances, GeneralizedNewtypeDeriving, MultiParamTypeClasses, RecursiveDo, TypeFamilies, OverloadedStrings, RecordWildCards,UndecidableInstances, PackageImports, TemplateHaskell, RankNTypes, GADTs, ImpredicativeTypes #-}++module Graphics.Diagrams.Core (module Graphics.Diagrams.Core) where+import Control.Monad.LPMonad+import Prelude hiding (sum,mapM_,mapM,concatMap)+import Control.Monad.RWS hiding (forM,forM_,mapM_,mapM)+import Data.LinearProgram+import Data.LinearProgram.Common as Graphics.Diagrams.Core (VarKind(..))+import Data.LinearProgram.LinExpr+import Data.Map (Map)+import qualified Data.Map as M+import Control.Lens hiding (element)+import Data.Traversable+import Data.Foldable+-- import MarXup.MultiRef (BoxSpec)+-- import MarXup.Tex+import System.IO.Unsafe++type LPState = LP Var Constant++-- | Solution of the linear programming problem+type Solution = Map Var Double+++type Constant = Double++-- | Expressions are linear functions of the variables+type Expr = LinExpr Var Constant++data Point' a = Point {xpart :: a, ypart :: a}+  deriving (Eq,Show)++instance Traversable Point' where+  traverse f (Point x y) = Point <$> f x <*> f y++instance Foldable Point' where+  foldMap = foldMapDefault++instance Functor Point' where+  fmap = fmapDefault++instance Applicative Point' where+  pure x = Point x x+  Point f g <*> Point x y = Point (f x) (g y)++instance Group a => Num (Point' a) where+  negate = neg+  (+) = (^+^)+  (-) = (^-^)++instance Group v => Group (Point' v) where+  zero = Point zero zero+  Point x1 y1 ^+^ Point x2 y2 = Point (x1 ^+^ x2) (y1 ^+^ y2)+  neg (Point x y) = Point (neg x) (neg y)++instance Module Constant v => Module Constant (Point' v) where+  k *^ Point x y = Point (k *^ x) (k *^ y)++type Frozen x = x Constant+type FrozenPoint = Frozen Point'+type FrozenPath = Frozen Path'+++data Segment v = CurveTo (Point' v) (Point' v) (Point' v)+                   | StraightTo (Point' v)+                   | Cycle+                     -- Other things also supported by tikz:+                   --  Rounded (Maybe Constant)+                   --  HV point | VH point+  deriving (Show,Eq)+instance Functor Segment where+  fmap = fmapDefault++instance Foldable Segment where+  foldMap = foldMapDefault+instance Traversable Segment where+  traverse _ Cycle = pure Cycle+  traverse f (StraightTo p) = StraightTo <$> traverse f p+  traverse f (CurveTo c d q) = CurveTo <$> traverse f c <*> traverse f d <*> traverse f q+++data Path' a+  = EmptyPath+  | Path {startingPoint :: Point' a+         ,segments :: [Segment a]}+  deriving Show+-- mapPoints :: (Point' a -> Point' b) -> Path' a -> Path' b+instance Functor Path' where+  fmap = fmapDefault++instance Foldable Path' where+  foldMap = foldMapDefault+instance Traversable Path' where+  traverse _ EmptyPath = pure EmptyPath+  traverse f (Path s ss) = Path <$> traverse f s <*> traverse (traverse f) ss+++-- | Tikz decoration+newtype Decoration = Decoration String+++-- | Tikz line tip+data LineTip = ToTip | CircleTip | NoTip | StealthTip | LatexTip | ReversedTip LineTip | BracketTip | ParensTip++-- | Tikz color+type Color = String++-- | Tikz line cap+data LineCap = ButtCap | RectCap | RoundCap++-- | Tikz line join+data LineJoin = MiterJoin | RoundJoin | BevelJoin++-- | Tikz dash pattern+type DashPattern = [(Constant,Constant)]++-- | Path drawing options+data PathOptions = PathOptions+                     {_drawColor :: Maybe Color+                     ,_fillColor :: Maybe Color+                     ,_lineWidth :: Constant+                     ,_startTip  :: LineTip+                     ,_endTip    :: LineTip+                     ,_lineCap   :: LineCap+                     ,_lineJoin  :: LineJoin+                     ,_dashPattern :: DashPattern+                     ,_decoration :: Decoration+                     }+$(makeLenses ''PathOptions)++-- | Size of a box, in points. boxDepth is how far the baseline is+-- from the bottom. boxHeight is how far the baseline is from the top.+-- (These are TeX meanings)+data BoxSpec = BoxSpec {boxWidth, boxHeight, boxDepth :: Double}+             deriving (Show)++nilBoxSpec :: BoxSpec+nilBoxSpec = BoxSpec 0 0 0++data Backend lab m =+                 Backend {_tracePath :: PathOptions -> FrozenPath -> m ()+                         ,_traceLabel :: forall location (x :: * -> *). Monad x =>+                                                 (location -> (FrozenPoint -> m ()) -> x ()) -> -- freezer+                                                 (forall a. m a -> x a) -> -- embedder+                                                 location ->+                                                 lab -> -- label specification+                                                 x BoxSpec+                         }+++-- tracePath :: Lens' (Backend m) (PathOptions -> FrozenPath -> m ())+-- tracePath f (Backend {..}) = fmap (\a -> Backend {_tracePath = a,..}) (f _tracePath)++-- renderLabel :: Lens' (Backend m) (FrozenPoint -> m () -> m ())+-- renderLabel f (Backend {..}) = fmap (\a -> Backend {_renderLabel = a,..}) (f _renderLabel)++-- declareLabel :: Lens' (Backend m) (FrozenPoint -> m () -> m ())+-- declareLabel f (Backend {..}) = fmap (\a -> Backend {_declareLabel = a,..}) (f _declareLabel)++$(makeLenses ''Backend) -- does not work due to the existential++data Env lab m = Env {_diaTightness :: Constant -- ^ Multiplicator to minimize constraints+                     ,_diaPathOptions :: PathOptions+                     ,_diaBackend :: Backend lab m}++$(makeLenses ''Env)++++defaultPathOptions :: PathOptions+defaultPathOptions = PathOptions+  {_drawColor = Nothing+  ,_fillColor = Nothing+  ,_lineWidth = 0.4+  ,_startTip  = NoTip+  ,_endTip    = NoTip+  ,_lineCap   = ButtCap+  ,_lineJoin  = MiterJoin+  ,_dashPattern = []+  ,_decoration = Decoration ""+  }++data Freeze m where+  Freeze :: forall t m. Functor t => (t Constant -> m ()) -> t Expr -> Freeze m++newtype Diagram lab m a = Dia (RWST (Env lab m) [Freeze m] (Var,LPState) m a)+  deriving (Monad, Applicative, Functor, MonadReader (Env lab m), MonadWriter [Freeze m])++freeze :: (Functor t, Monad m) => t Expr -> (t Constant -> m ()) -> Diagram lab m ()+freeze x f = tell [Freeze (\y -> (f y)) x]++instance Monad m => MonadState LPState (Diagram lab m) where+  get = Dia $ snd <$> get+  put y = Dia $ do+    (x,_) <- get+    put (x,y)++-------------+-- Diagrams+++relax :: Monad m => Constant -> Diagram lab m a -> Diagram lab m a+relax factor = tighten (1/factor)++tighten :: Monad m => Constant -> Diagram lab m a -> Diagram lab m a+tighten factor = local (over diaTightness (* factor))++-- instance Monoid (Diagram lab m ()) where+--   mempty = return ()+--   mappend = (>>)++-- instance IsString (Diagram ()) where+--   fromString = diaRawTex . tex++--------------+-- Variables++rawNewVar :: Monad m => Diagram lab m Var+rawNewVar = Dia $ do+      (Var x,y) <- get+      put $ (Var (x+1),y)+      return $ Var x++newVar :: Monad m => Diagram lab m Expr+newVar = do+  [v] <- newVars [ContVar]+  return v++newVars :: Monad m => [VarKind] -> Diagram lab m [Expr]+newVars kinds = newVars' (zip kinds (repeat Free))++newVars' :: Monad m => [(VarKind,Bounds Constant)] -> Diagram lab m [Expr]+newVars' kinds = forM kinds $ \(k,b) -> do+  v <- rawNewVar+  setVarKind v k+  setVarBounds v b+  return $ variable v++infix 4 <==,===,>==++----------------+-- Expressions+instance Fractional Expr where+  fromRational ratio = constant (fromRational ratio)++instance Num Expr where+  fromInteger x = LinExpr M.empty (fromInteger x)+  negate = neg+  (+) = (^+^)+  (-) = (^-^)++runDiagram :: Monad m => Backend lab m -> Diagram lab m a -> m a+runDiagram backend (Dia diag) = do+  (a,(_,problem),ds) <- runRWST diag (Env 1 defaultPathOptions backend)+                                        (Var 0,LP Min M.empty [] M.empty M.empty)+  let solution = case unsafePerformIO $ glpSolveVars simplexDefaults problem of+        (_retcode,Just (_objFunc,s)) -> s+        (retcode,Nothing) -> error $ "LP failed ret code = " ++ show retcode+  -- Raw Normal $ "%problem solved: " ++ show problem ++ "\n"+  forM_ ds (\(Freeze f x) -> f (fmap (valueIn solution) x))+  return a+++valueIn :: Solution -> Expr -> Double+valueIn sol (LinExpr m c) = sum (c:[scale * varValue v | (v,scale) <- M.assocs m])+ where varValue v = M.findWithDefault 0 v sol++variable :: Var -> Expr+variable v = LinExpr (var v) 0++constant :: Constant -> Expr+constant c = LinExpr M.empty c++(*-) :: Module Constant a => Constant -> a -> a+(*-) = (*^)+infixr 6 *-++avg :: Module Constant a => [a] -> a+avg xs = (1/fromIntegral (length xs)) *- gsum xs++-- | Absolute value, which can be MINIMIZED or put and upper bound on (but not+-- the other way around).+absoluteValue :: Monad m => Expr -> Diagram lab m Expr+absoluteValue x = do+  [t1,t2] <- newVars' [(ContVar,LBound 0),(ContVar,LBound 0)]+  t1 - t2 === x+  return $ t1 + t2++satAll :: Monad m => (Expr -> a -> Diagram lab m b) -> [a] -> Diagram lab m Expr+satAll p xs = do+  [m] <- newVars [ContVar]+  mapM_ (p m) xs+  return m++-- | Minimum or maximum of a list of expressions.+maximVar, minimVar :: Monad m => [Expr] -> Diagram lab m Expr+maximVar = satAll (>==)+minimVar = satAll (<==)++--------------+-- Expression constraints+(===), (>==), (<==) :: Expr -> Expr -> Monad m => Diagram lab m ()+e1 <== e2 = do+  let LinExpr f c = e1 - e2+  leqTo f (negate c)++(>==) = flip (<==)++e1 === e2 = do+  let LinExpr f c = e1 - e2+  equalTo f (negate c)++-- | minimize the distance between expressions+(=~=) :: Monad m => Expr -> Expr -> Diagram lab m ()+x =~= y = minimize =<< absoluteValue (x-y)++-------------------------+-- Expression objectives++minimize,maximize :: Monad m => Expr -> Diagram lab m ()+minimize (LinExpr x _) = do+  tightness <- view diaTightness+  addObjective (tightness *- x)+maximize = minimize . negate+++drawText :: Monad m => Point' Expr -> lab -> Diagram lab m BoxSpec+drawText point lab = do+  tl <- view (diaBackend . traceLabel)+  tl freeze diaRaw point lab++diaRaw :: Monad m => m a -> Diagram lab m a+diaRaw = Dia . lift
+ Graphics/Diagrams/DerivationTrees.hs view
@@ -0,0 +1,199 @@+{-# LANGUAGE DisambiguateRecordFields, NamedFieldPuns, RecordWildCards, PostfixOperators, LiberalTypeSynonyms, TypeOperators, OverloadedStrings, PackageImports, ScopedTypeVariables #-}++module Graphics.Diagrams.DerivationTrees (+-- * Basics+module Data.Monoid,+module Data.LabeledTree,++-- * Derivation' building+-- axiom, rule, etc, aborted,+emptyDrv, haltDrv', delayPre,+dummy, rule, Derivation, Premise, Rule(..),++-- * Links+LineStyle,defaultLink,Link(..),++-- * Engine+derivationTreeDiag, delayD++) where++-- import DerivationTrees.Basics+import Control.Monad.Writer+import Data.LabeledTree+import Data.Monoid+import Graphics.Diagrams as D+import qualified Data.Tree as T+------------------+--- Basics++type LineStyle = PathOptions -> PathOptions++data Link lab = Link {label :: lab, linkStyle :: LineStyle, steps :: Int}  -- ^ Regular link+              | Delayed -- ^ automatic delaying++defaultLink :: Monoid lab => Link lab+defaultLink = Link mempty (denselyDotted . outline "black")  0+++-------------------++data Rule lab = Rule {ruleStyle :: LineStyle, delimiter :: lab, ruleLabel :: lab, conclusion :: lab}+--  deriving Show++type Premise lab = Link lab ::> Derivation lab+type Derivation lab = Tree (Link lab) (Rule lab)++--------------------------------------------------+-- Delay++depth :: forall lab t. Link lab ::> Tree (Link lab) t -> Int+depth (Link{steps} ::> Node _ ps) = 1 + steps + maximum (0 : map depth ps)++isDelayed :: Premise lab -> Bool+isDelayed (Delayed{} ::> _) = True+isDelayed _ = False++delayPre :: forall lab a. Int -> Link lab ::> a -> Link lab ::> a+delayPre s (Link {..} ::> j) = Link {steps = s, ..} ::> j++delayD :: Monoid lab => Derivation lab -> Derivation lab+delayD (Node r ps0) = Node r (map delayP ps)+    where ps = fmap (fmap delayD) ps0+          ps' = filter (not . isDelayed) ps+          delayP (Delayed ::> d) = defaultLink {steps = 1 + maximum (0 : map depth ps')} ::> d+          delayP p = p++----------------------------------------------------------+-- Diagramify++derivationTreeDiag :: Monad m => Derivation lab -> Diagram lab m ()+derivationTreeDiag d = do+  [h] <- newVars [ContVar] -- the height of a layer in the tree.+  minimize h+  h >== 1+  tree@(T.Node (_,n,_) _) <- toDiagram h d+  forM_ (T.levels tree) $ \ls ->+    case ls of+      [] -> return ()+      (_:ls') -> forM_ (zip ls ls') $ \((_,_,l),(r,_,_)) ->+        (l + Point 10 0) `westOf` r+  let leftFringe = map head nonNilLevs+      rightFringe = map last nonNilLevs+      nonNilLevs = filter (not . null) $ T.levels tree+  [leftMost,rightMost] <- newVars [ContVar,ContVar]+  forM_ leftFringe $ \(p,_,_) ->+    leftMost <== xpart p+  forM_ rightFringe $ \(_,_,p) ->+    xpart p <== rightMost+  minimize $ 10 *- (rightMost - leftMost)+  n # Center .=. Point 0 0++toDiagPart :: Monad m => Expr -> Premise lab -> Diagram lab m (T.Tree (Point,Anchorage,Point))+toDiagPart layerHeight (Link{..} ::> rul)+  | steps == 0 = toDiagram layerHeight rul+  | otherwise = do+    above@(T.Node (_,concl,_) _) <- toDiagram layerHeight rul+    ptObj <- vrule+    let pt = ptObj # S+    pt `eastOf` (concl # W)+    pt `westOf` (concl # E)+    xpart pt =~= xpart (concl # Center)+    let top = ypart (concl # S)+    ypart pt + (fromIntegral steps *- layerHeight) === top+    using linkStyle $ path $ polyline [ptObj # Base,Point (xpart pt) top]+    let embedPt 1 x = T.Node (concl # W,ptObj,concl # E) [x]+        embedPt n x = T.Node (pt,ptObj,pt) [embedPt (n-1) x]+    return $ embedPt steps above++-- | @chainBases distance objects@+-- - Ensures that all the objects have the same baseline.+-- - Separates the objects by the given distance+-- - Returns an object encompassing the group, with a the baseline set correctly.+-- - Returns the average distance between the objects++chainBases :: Monad m => Expr -> [Anchorage] -> Diagram lab m (Anchorage,Expr)+chainBases _ [] = do+  o <- box+  return (o,0)+chainBases spacing ls = do+  grp <- box+  forM_ [Base,N,S] $ \ anch -> do+    D.align ypart $ map (# anch) (grp:ls)+  dxs <- forM (zip ls (tail ls)) $ \(x,y) -> do+    let dx = xdiff (x # E) (y # W)+    dx >== spacing+    return dx+  D.align xpart [grp # W,head ls # W]+  D.align xpart [grp # E,last ls # E]+  return (grp,avg dxs)++-- | Put object in a box of the same vertical extent, and baseline,+-- but whose height can be bigger.+relaxHeight :: (Monad m, Anchored a) => a -> Diagram lab m Anchorage+relaxHeight o = do+  b <- box+  -- using (outline "green")$ traceBounds o+  D.align xpart [b#W,o#W]+  D.align xpart [b#E,o#E]+  D.align ypart [b#Base,o#Base]+  o `fitsVerticallyIn` b+  return b++toDiagram :: Monad m => Expr -> Derivation lab -> Diagram lab m (T.Tree (Point,Anchorage,Point))+toDiagram layerHeight (Node Rule{..} premises) = do+  ps <- mapM (toDiagPart layerHeight) premises+  concl <- relaxHeight =<< extend 1.5 <$> labelBox conclusion+  -- using (outline "red")$ traceBounds concl+  lab <- labelBox ruleLabel++  -- Grouping+  (psGrp,premisesDist) <- chainBases 10 [p | T.Node (_,p,_) _ <- ps]+  -- using (outline "blue" . denselyDotted) $ traceBounds psGrp+  height psGrp === layerHeight++  -- Sepaartion rule+  separ <- hrule+  separ # N .=. psGrp # S+  align ypart [concl # N,separ # S]+  minimize $ width separ+  psGrp `fitsHorizontallyIn` separ+  concl `fitsHorizontallyIn` separ++  -- rule label+  lab # BaseW .=. separ # E + Point 3 (negate 1)+++  -- layout hints (not necessary for "correctness")+  let xd = xdiff (separ # W) (psGrp # W)+  xd   === xdiff (psGrp # E) (separ # E) +  relax 2 $ (2 *- xd) =~= premisesDist+  -- centering of conclusion+  xd' <- absoluteValue $ xdiff (separ # Center) (concl # Center)+  relax 3 $ minimize xd'++  -- draw the rule.+  using ruleStyle $ path $ polyline [separ # W,separ # E]+  return $ T.Node (separ # W, concl, lab # E) ps++-----------------------+++rule :: Monoid lab => lab -> lab -> Rule lab+rule ruleLabel conclusion = Rule {delimiter = mempty, ruleStyle = outline "black", ..}++dummy :: Monoid lab => Rule lab+dummy = (rule mempty mempty) {ruleStyle = const defaultPathOptions}++emptyDrv :: forall k lab. Monoid lab => Tree k (Rule lab)+emptyDrv = Node dummy []++-- abortDrv (Node Rule {..} _) = Node Rule {ruleStyle = Waved, ..} []++-- | Used when the rest of the derivation is known.+haltDrv' :: forall lab. Monoid lab => lab -> Derivation lab -> Derivation lab+haltDrv' tex (Node r _) = Node r {ruleStyle = noOutline}+     [lnk {steps = 1, label = tex} ::> emptyDrv]+  where lnk :: Link lab+        lnk = defaultLink+
+ Graphics/Diagrams/Graphviz.hs view
@@ -0,0 +1,110 @@+{-# LANGUAGE RecordWildCards, ScopedTypeVariables #-}+module Graphics.Diagrams.Graphviz (graph) where++import Graphics.Diagrams.Point as D+import Graphics.Diagrams.Object as D+import Graphics.Diagrams.Core as D+import Graphics.Diagrams.Path+import Data.GraphViz as G+import Data.GraphViz.Attributes.Complete as G+import Data.GraphViz.Parsing as G+import qualified Data.GraphViz.Types.Generalised as Gen+import Data.GraphViz.Commands.IO as G+import qualified Data.Text.Lazy as T+import System.IO.Unsafe (unsafePerformIO)+import Data.Foldable+import Control.Lens (set)+import Graphics.Typography.Geometry.Bezier (Curve)++graph :: (Monad m,PrintDotRepr g n, ParseDot n, PrintDot n) => (String -> lab) -> GraphvizCommand -> g n -> Diagram lab m ()+graph labFct cmd gr = graphToDiagram labFct $ layout cmd gr++layout :: (PrintDotRepr g n, ParseDot n, PrintDot n) => GraphvizCommand -> g n -> Gen.DotGraph n+layout command input = parseIt' $ unsafePerformIO $ graphvizWithHandle command input DotOutput hGetStrict ++pos (Pos p) = Just p+pos _= Nothing++lpos (LPos p) = Just p+lpos _= Nothing++shapeA (Shape s) = Just s+shapeA _ = Nothing++widthA (Width s) = Just s+widthA _ = Nothing++labelA (Label l) = Just l+labelA _ = Nothing++arrowHeadA (ArrowHead a) = Just a+arrowHeadA _ = Nothing++readAttr :: Monad m => (Attribute -> Maybe a) -> [Attribute] -> (a -> m ()) -> m ()+readAttr f as k = readAttr' f as k (return ())++readAttr' :: (Attribute -> Maybe a) -> [Attribute] -> (a -> k) -> k -> k+readAttr' f as k1 k2 = case [x | Just x <- map f as] of+  (x:_) -> k1 x+  _ -> k2+++pt' (G.Point x y _z _forced) = D.Point x y+pt = unfreeze . pt'++diaSpline :: [FrozenPoint] -> [Graphics.Typography.Geometry.Bezier.Curve]+diaSpline (w:x:y:z:rest) = curveSegment w x y z:diaSpline (z:rest)+diaSpline _ = []++-- ToTip | CircleTip | NoTip | StealthTip | LatexTip | ReversedTip LineTip | BracketTip | ParensTip+tipTop :: LineTip -> ArrowType -> LineTip+tipTop def (AType [(_,NoArrow)]) = NoTip+tipTop def (AType [(_,Normal)]) = LatexTip+tipTop def (AType [(_,DotArrow)]) = CircleTip+tipTop def (AType [(_,Vee)]) = StealthTip+tipTop def _ = def++graphToDiagram :: forall l m n. Monad m => (String -> l) -> Gen.DotGraph n -> Diagram l m ()+graphToDiagram labFct (Gen.DotGraph _strict _directed _grIdent stmts) = do+  forM_ stmts $ \ stmt -> case stmt of+    (Gen.DE (DotEdge _from _to attrs)) -> do+      -- diaRaw $ tex $ "%Edge: " ++ show attrs ++ "\n"+      let toTip = readAttr' arrowHeadA attrs (tipTop ToTip) ToTip+      readAttr labelA attrs $ \(StrLabel l) ->+        readAttr lpos attrs $ \p -> +        renderLab l p+      readAttr pos attrs $ \(SplinePos splines) ->+        forM_ splines $ \Spline{..} -> do+          let mid = diaSpline $ map pt' splinePoints+          let beg = case (startPoint,splinePoints) of+                (Just p,q:_) -> [lineSegment (pt' p) (pt' q)]+                _ -> []+          let end = case (endPoint,reverse splinePoints) of+                (Just p,q:_) -> [lineSegment (pt' q) (pt' p)]+                _ -> []+          using (set endTip toTip) $+            draw $ frozenPath' $ fromBeziers (beg ++ mid ++ end)++    (Gen.DN (DotNode _nodeIdent attrs)) -> do+      -- diaRaw $ tex $ "%Node: " ++ show attrs ++ "\n"+      readAttr pos   attrs $ \(PointPos p) -> do+        readAttr labelA attrs $ \l -> do+          case l of+            StrLabel l -> renderLab l p+        readAttr widthA attrs $ \w ->+         readAttr shapeA attrs $ \s ->+          case s of+            Circle -> do+              draw $ path $ circle (pt p) (constant $ inch (w/2))+            _ -> return ()+    _ -> return ()+  where+  renderLab :: T.Text -> G.Point -> Diagram l m ()+  renderLab l p = do+    l' <- labelObj $ labFct $ T.unpack $ l+    l' # D.Center .=. pt p+++inch x = 72 * x++
+ Graphics/Diagrams/Object.hs view
@@ -0,0 +1,305 @@+{-# LANGUAGE DataKinds, KindSignatures, OverloadedStrings, EmptyDataDecls, MultiParamTypeClasses, FlexibleContexts, TypeSynonymInstances, FlexibleInstances, GADTs, LambdaCase   #-}++module Graphics.Diagrams.Object where++-- import MarXup+-- import MarXup.Tex+import Graphics.Diagrams.Path+import Graphics.Diagrams.Point+import Graphics.Diagrams.Core+import Control.Monad+-- import Control.Applicative+-- import Data.Algebra+-- import Data.List (intersperse)+import Control.Lens (set,view)++data Anchor = Center | N | NW | W | SW | S | SE | E | NE | BaseW | Base | BaseE+  deriving Show++-- | Box-shaped object. (a subtype)+type Box = Object++newtype Anchorage = Anchorage {fromAnchorage :: Anchor -> Point}+data Object = Object {objectOutline :: Path, objectAnchorage :: Anchorage}++class Anchored a where+  anchors :: a -> Anchorage+  +infix 8 #++(#) :: Anchored a => a -> Anchor -> Point+(#) = fromAnchorage . anchors++instance Anchored Anchorage where+  anchors = id++instance Anchored Object where+  anchors = objectAnchorage++instance Anchored Point where+  anchors p = Anchorage $ \_ -> p++-- | Horizontal distance between objects+hdist :: Anchored a => a -> a -> Expr+hdist x y = xpart (y # W - x # E)++-- | Vertical distance between objects+vdist :: Anchored a => a -> a -> Expr+vdist x y = ypart (y # S - x # N)++-- | Extend the box boundaries by the given delta+extend :: Expr -> Anchorage -> Anchorage+extend e o = Anchorage $ \a -> o # a + shiftInDir a e++-- | Makes a shift of size 'd' in the given direction.+shiftInDir :: Anchor -> Expr -> Point+shiftInDir N d = 0 `Point` d+shiftInDir S d = 0 `Point` negate d+shiftInDir W d = negate d `Point` 0+shiftInDir BaseW d = negate d `Point` 0+shiftInDir E d  = d `Point` 0+shiftInDir BaseE d  = d `Point` 0+shiftInDir NW d = negate d `Point` d+shiftInDir SE d = d `Point` negate d+shiftInDir SW d = negate d `Point` negate d+shiftInDir NE d = d `Point` d+shiftInDir _ _  = 0 `Point` 0++-- | Make a label object. This is just some text surrounded by 4+-- points of blank.+mkLabel :: Monad m => lab -> Diagram lab m Anchorage+mkLabel texCode = extend 4 <$> labelBox texCode++labelObj :: Monad m => lab -> Diagram lab m Box+labelObj = rectangleShape <=< mkLabel++-- | Label a point by a given TeX expression, at the given anchor.+labelPt :: Monad m => lab -> Anchor -> Point -> Diagram lab m Box+labelPt labell anchor labeled  = do+  t <- labelObj labell+  t # anchor .=. labeled+  return t++-- | A free point+point :: Monad m => Diagram lab m Point+point = do+  [x,y] <- newVars (replicate 2 ContVar)+  return $ Point x y++-- | A point anchorage (similar to a box of zero width and height)+pointBox :: Monad m => Diagram lab m Anchorage+pointBox = anchors <$> point++-- | A box. Anchors are aligned along a grid.+box :: Monad m => Diagram lab m Anchorage+box = do+  [n,s,e,w,base,midx,midy] <- newVars (replicate 7 ContVar)+  n >== base+  base >== s+  w <== e+  +  midx === avg [w,e]+  midy === avg [n,s]+  let pt = flip Point+  return $ Anchorage $ \anch -> case anch of+    NW     -> pt n    w+    N      -> pt n    midx+    NE     -> pt n    e  +    E      -> pt midy e+    SE     -> pt s    e+    S      -> pt s    midx+    SW     -> pt s    w+    W      -> pt midy w+    Center -> pt midy midx+    Base   -> pt base midx+    BaseE  -> pt base e+    BaseW  -> pt base w++-- | A box of zero width+vrule :: Monad m => Diagram lab m Anchorage+vrule = do+  o <- box+  align xpart [o # W, o #Center, o#E]+  return o++-- | A box of zero height+hrule :: Monad m => Diagram lab m Anchorage+hrule = do+  o <- box+  height o === 0+  return o++height, width, ascent, descent :: Anchored a => a -> Expr+height o = ypart (o # N - o # S)+width o = xpart (o # E - o # W)+ascent o = ypart (o # N - o # Base)+descent o = ypart (o # Base - o # S)++-- | Make one object fit (snugly) in the other.+fitsIn, fitsHorizontallyIn, fitsVerticallyIn :: (Monad m, Anchored a, Anchored b) => a -> b -> Diagram lab m ()+o `fitsVerticallyIn` o' = do+  let dyN = ypart $ o' # N - o # N+      dyS = ypart $ o # S - o' # S+  minimize dyN+  dyN >== 0+  minimize dyS+  dyS >== 0++o `fitsHorizontallyIn` o' = do+  let dyW = xpart $ o # W - o' # W+      dyE = xpart $ o' # E - o # E+  minimize dyW+  dyW >== 0+  minimize dyE+  dyE >== 0++a `fitsIn` b = do+  a `fitsHorizontallyIn` b+  a `fitsVerticallyIn` b++-- | A circle+circleShape :: Monad m => Diagram lab m Object+circleShape = do+  anch <- box+  width anch === height anch+  let radius = 0.5 *- width anch+  let p = circle (anch # Center) radius+  path p+  return $ Object p anch+--   let k1 :: Constant+--       k1 = sqrt 2 / 2+--       k = k1 *^ r+--       p = circle center r+--   return $ Object p $ Anchorage $ \a -> center + case a of+--     N -> Point 0 r+--     S -> Point 0 (-r)+--     E -> Point r 0+--     W -> Point (-r) 0+--     Center -> Point 0 0+--     NE -> Point k k++rectangleShape :: Monad m => Anchorage -> Diagram lab m Object+rectangleShape l = do+  let p = polygon (map (l #) [NW,NE,SE,SW])+  path p+  return $ Object p l++traceAnchorage :: (Anchored a, Monad m) => Color -> a -> Diagram lab m ()+traceAnchorage c l = do+  stroke c $ path $ polygon (map (l #) [NW,NE,SE,SW])+  -- TODO: draw the baseline, etc.++-- | Typeset a piece of text and return its bounding box.+labelBox :: Monad m => lab -> Diagram lab m Anchorage+labelBox t = do+  l <- box+  -- traceAnchorage "red" l+  BoxSpec wid h desc <- drawText (l # NW) t++  width   l === constant wid+  descent l === constant desc+  height  l === constant (h + desc)+  return l++-- | A vector with an origin+data OVector = OVector { vectorOrigin, vectorMagnitude :: Point }++-- | Turn the orientation by 180 degrees+turn180 :: OVector -> OVector+turn180 (OVector p v) = OVector p (negate v)++data FList xs a where+  NIL :: FList '[] a+  (:%>) :: Functor t => t a -> FList fs a -> FList ('(:) t fs) a++infixr :%>++instance Functor (FList xs) where+  fmap _ NIL = NIL+  fmap f (x :%> xs) = fmap f x :%> fmap f xs+  +-- | Traces a straight edge between two objects.+-- A vector originated at the midpoint and pointing perpendicular to+-- the edge is returned.+edge :: Monad m => Object -> Object -> Diagram lab m OVector+edge source target = do+  let points@[a,b] = [source # Center,target # Center]+      link = polyline points+      targetArea = objectOutline target+      sourceArea = objectOutline source+  options <- view diaPathOptions+  tracePath' <- view (diaBackend . tracePath)+  freeze (link :%> sourceArea :%> targetArea :%> NIL) $ \(l' :%> sa' :%> ta' :%> NIL) -> do+       tracePath' options $ (l' `cutAfter` ta') `cutBefore` sa'+  return $ OVector (avg points) (rotate90 (b-a))++(.<.) :: Monad m => Point -> Point -> Diagram lab m ()+Point x1 y1 .<. Point x2 y2 = do+  x1 <== x2+  y1 <== y2++-- | Forces the point to be inside the (bounding box) of the object.+insideBox :: Monad m => Anchored a => Point -> a -> Diagram lab m ()+insideBox p o = do+  (o # SW) .<. p+  p .<. (o # NE)++-- | @autoLabel o i@ Layouts the label object @o@ at the given incidence+-- vector.+autoLabelObj :: Monad m => Box -> OVector -> Diagram lab m ()+autoLabelObj lab (OVector pt norm) = do+  pt `insideBox` lab+  minimize =<< orthoDist (lab#Center) (pt + norm)++-- | @autoLabel o i@ Layouts the label object @o@ at the given incidence+-- vector.+autoLabel :: Monad m => lab -> OVector -> Diagram lab m ()+autoLabel lab i = do+  o <- labelObj lab+  autoLabelObj o i++-- | @labeledEdge label source target@+labeledEdge :: Monad m => Object -> Object -> Box -> Diagram lab m ()+labeledEdge source target lab = autoLabelObj lab =<< edge source target++-------------------+-- Even higher-level primitives:++nodeDistance :: Expr+nodeDistance = 5++leftOf :: Monad m => Object -> Object -> Diagram lab m ()+a `leftOf` b = spread hdist nodeDistance [a,b]++topOf :: Monad m => Object -> Object -> Diagram lab m ()+a `topOf` b =  spread vdist nodeDistance [b,a]++-- | Spread a number of objects by *minimum* a given distance. example: @spread+-- hdist 30 ps@+spread :: Monad m => (t -> t -> Expr) -> Expr -> [t] -> Diagram lab m ()+spread f d (x:y:xs) = do+  f x y >== d+  minimize $ f x y+  spread f d (y:xs)+spread _ _ _ = return ()++-- | A node: a labeled circle+node :: Monad m => lab -> Diagram lab m Object+node lab = do+  l <- extend 4 <$> labelBox lab+  c <- draw $ circleShape+  l `fitsIn` c+  l # Center .=. c # Center+  return c++-- | Draw an arrow between two objects+arrow :: Monad m => Object -> Object -> Diagram lab m OVector+arrow src trg = using (outline "black" . set endTip LatexTip) $ do+  edge src trg++-- | Bounding box of a number of anchored values+boundingBox :: (Monad m, Anchored a) => [a] -> Diagram lab m Object+boundingBox os = do+  bx <- box+  mapM_ (`fitsIn` bx) os+  rectangleShape bx
+ Graphics/Diagrams/Path.hs view
@@ -0,0 +1,174 @@+{-# LANGUAGE TypeSynonymInstances, FlexibleContexts, FlexibleInstances, GeneralizedNewtypeDeriving, MultiParamTypeClasses, RecursiveDo, TypeFamilies, OverloadedStrings, RecordWildCards,UndecidableInstances, PackageImports, TemplateHaskell #-}++module Graphics.Diagrams.Path where++import Graphics.Diagrams.Core+import Graphics.Diagrams.Point+import Data.Traversable+import Data.Foldable+import Data.Algebra+-- import Data.Traversable+-- import Data.Foldable+import Graphics.Typography.Geometry.Bezier+import Graphics.Typography.Geometry.Bezier as Graphics.Diagrams.Point (Curve) +import Control.Applicative+import Data.List (sort,transpose)+import Data.Maybe (listToMaybe)+import Prelude hiding (sum,mapM_,mapM,concatMap,maximum,minimum)+import qualified Data.Vector.Unboxed as V+import Algebra.Polynomials.Bernstein (restriction,Bernsteinp(..))+import Control.Lens (over, set, view)+import Control.Monad.Reader (local)++unfreeze :: Functor t => t Constant -> t Expr+unfreeze = fmap constant++toBeziers :: FrozenPath -> [Curve]+toBeziers EmptyPath = []+toBeziers (Path start ss) | not (null ss) &&+                            isCycle (last ss) = toBeziers' start (init ss ++ [StraightTo start])+                          | otherwise = toBeziers' start ss++curveSegment (Point xa ya) (Point xb yb) (Point xc yc) (Point xd yd) = bezier3 xa ya xb yb xc yc xd yd+lineSegment (Point xa ya) (Point xb yb) = line xa ya xb yb++toBeziers' :: FrozenPoint -> [Frozen Segment] -> [Curve]+toBeziers' _ [] = []+toBeziers' start (StraightTo next:ss) = curveSegment start mid mid next : toBeziers' next ss+  where mid = avg [start, next]+toBeziers' p (CurveTo c d q:ss) = curveSegment p c d q : toBeziers' q ss++fromBeziers :: [Curve] -> FrozenPath+fromBeziers [] = EmptyPath+fromBeziers (Bezier cx cy t0 t1:bs) = case map toPt $ V.foldr (:) [] cxy of+      [p,c,d,q] -> Path p (CurveTo c d q:rest)+      [p,q] -> Path p (StraightTo q:rest)+  where [cx',cy'] = map (\c -> coefs $ restriction c t0 t1) [cx,cy]+        cxy = V.zip cx' cy'+        toPt (x,y) = Point x y+        rest = pathSegments (fromBeziers bs)++pathSegments :: Path' t -> [Segment t]+pathSegments EmptyPath = []+pathSegments (Path _ ss) = ss++isCycle Cycle = True+isCycle _  = False++frozenPointElim (Point x y) f = f x y++splitBezier (Bezier cx cy t0 t1) (u,v,_,_) = (Bezier cx cy t0 u, Bezier cx cy v t1)++clipOne :: Curve -> [Curve] -> Maybe Curve+clipOne b cutter = fmap firstPart $ listToMaybe $ sort $ concatMap (inter b) cutter+  where firstPart t = fst $ splitBezier b t++-- | @cutAfter path area@ cuts the path after its first intersection with the @area@.+cutAfter', cutBefore' :: [Curve] -> [Curve] -> [Curve]+cutAfter' [] _cutter = []+cutAfter' (b:bs) cutter = case clipOne b cutter of+  Nothing -> b:cutAfter' bs cutter+  Just b' -> [b']+ +revBernstein (Bernsteinp n c) = Bernsteinp n (V.reverse c)+revBeziers :: [Curve] -> [Curve]+revBeziers = reverse . map rev+  where rev (Bezier cx cy t0 t1) = (Bezier (revBernstein cx) (revBernstein cy) (1-t1) (1-t0))++cutBefore' path area = revBeziers $ cutAfter' (revBeziers path) area++onBeziers :: ([Curve] -> [Curve] -> [Curve])+             -> FrozenPath -> FrozenPath -> FrozenPath+onBeziers op p' q' = fromBeziers $ op (toBeziers p') (toBeziers q')+++cutAfter :: FrozenPath -> FrozenPath -> FrozenPath+cutAfter = onBeziers cutAfter'++cutBefore :: FrozenPath -> FrozenPath -> FrozenPath+cutBefore = onBeziers cutBefore'++-----------------+-- Paths+++type Path = Path' Expr++polyline :: [Point] -> Path+polyline [] = EmptyPath+polyline (x:xs) = Path x (map StraightTo xs)++polygon :: [Point] -> Path+polygon [] = EmptyPath+polygon (x:xs) = Path x (map StraightTo xs ++ [Cycle])+++-- | Circle approximated with 4 cubic bezier curves+circle :: Point -> Expr -> Path+circle center r =      Path (pt r 0)+                         [CurveTo (pt r k) (pt k r) (pt 0 r),+                          CurveTo (pt (-k) r) (pt (-r) k) (pt (-r) 0),+                          CurveTo (pt (-r) (-k)) (pt (-k) (-r)) (pt 0 (-r)),+                          CurveTo (pt k (-r)) (pt r (-k)) (pt r 0),+                          Cycle]+ where k1 :: Constant+       k1 = 4 * (sqrt 2 - 1) / 3+       k = k1 *^ r+       pt x y = center ^+^ (Point x y)+++path :: Monad m => Path -> Diagram lab m ()+path p = do+  options <- view diaPathOptions+  tracePath' <- view (diaBackend . tracePath)+  freeze p (tracePath' options)++frozenPath' :: Monad m => FrozenPath -> Diagram lab m ()+frozenPath' p = do+  options <- view diaPathOptions+  tracePath' <- view (diaBackend . tracePath)+  freeze [] $ \_ -> tracePath' options p++stroke :: Monad m => Color -> Diagram lab m a -> Diagram lab m a+stroke color = using (outline color)++draw :: Monad m => Diagram lab m a -> Diagram lab m a+draw = stroke "black"++noOutline :: PathOptions -> PathOptions+noOutline = set drawColor Nothing++outline :: Color -> PathOptions -> PathOptions+outline color = set drawColor (Just color)++fill :: Color -> PathOptions -> PathOptions+fill color = set fillColor (Just color)++zigzagDecoration :: PathOptions -> PathOptions+zigzagDecoration = set decoration (Decoration "zigzag")++using :: Monad m => (PathOptions -> PathOptions) -> Diagram lab m a -> Diagram lab m a+using f = local (over diaPathOptions f)++ultraThin, veryThin, thin, semiThick, thick, veryThick, ultraThick :: Constant+ultraThin = 0.1+veryThin = 0.2+thin = 0.4+semiThick = 0.6+thick = 0.8+veryThick = 1.2+ultraThick = 1.6++solid, dotted, denselyDotted, looselyDotted, dashed, denselyDashed,+  looselyDashed, dashDotted, denselyDashdotted, looselyDashdotted :: PathOptions -> PathOptions+solid             o@PathOptions{..} = o { _dashPattern = [] }+dotted            o@PathOptions{..} = o { _dashPattern = [(_lineWidth,2)] }+denselyDotted     o@PathOptions{..} = o { _dashPattern = [(_lineWidth, 1)] }+looselyDotted     o@PathOptions{..} = o { _dashPattern = [(_lineWidth, 4)] }+dashed            o@PathOptions{..} = o { _dashPattern = [(3, 3)] }+denselyDashed     o@PathOptions{..} = o { _dashPattern = [(3, 2)] }+looselyDashed     o@PathOptions{..} = o { _dashPattern = [(3, 6)] }+dashDotted        o@PathOptions{..} = o { _dashPattern = [(3, 2), (_lineWidth, 2)] }+denselyDashdotted o@PathOptions{..} = o { _dashPattern = [(3, 1), (_lineWidth, 1)] }+looselyDashdotted o@PathOptions{..} = o { _dashPattern = [(3, 4), (_lineWidth, 4)] }+
+ Graphics/Diagrams/Plot.hs view
@@ -0,0 +1,128 @@+{-# LANGUAGE FlexibleContexts, RankNTypes, DeriveFunctor #-}+module Graphics.Diagrams.Plot where++import Graphics.Diagrams.Core+import Graphics.Diagrams.Path+import Graphics.Diagrams.Object+import Graphics.Diagrams.Point+import Control.Monad (forM_,when)++type Vec2 = Point'+type Transform a = Iso a Constant++-- | Generic axis rendering. @axisGen origin target anchor labels@+-- traces an axis from origin to target, attaching the labels at+-- anchor.+axisGen :: Monad m => Point -> Point -> Anchor -> [(Constant,lab)] -> Diagram lab m ()+axisGen origin target anch labels = do+  draw {- using (set endTip ToTip) -} $ path $ polyline [origin,target]+  when (not $ null $ labels) $ do+    forM_ labels $ \(p,txt) -> do+      l0 <- labelObj txt+      let l = extend 3 (anchors l0)+      draw $ path $ polyline [l0 # anch, l # anch]+      l # anch .=. Point (lint p (xpart origin) (xpart target))+                         (lint p (ypart origin) (ypart target))++-- | @scale minx maxx@ maps the interval [minx,maxx] to [0,1]+scale :: forall b. Fractional b => b -> b -> Iso b b+scale minx maxx = Iso (\x -> (x - minx) / (maxx - minx))+                      (\x -> x * (maxx - minx) + minx)++-- | Make a number of steps+mkSteps :: Transform a -> ShowFct lab a -> [a] -> [(Constant,lab)]+mkSteps tx showFct xs = zip (map (forward tx) xs) (map showFct xs)++-- | render an horizontal axis on the given box+hAxis :: Monad m => Box -> [(Constant, lab)] -> Diagram lab m ()+hAxis bx = axisGen (bx # SW) (bx # SE) N++-- | render a vertical axis on the given box+vAxis :: Monad m => Box -> [(Constant, lab)] -> Diagram lab m ()+vAxis bx = axisGen (bx # SW) (bx # NW) E++-- | Draw axes. Coordinates in the [0,1] fit the box.+axes :: Monad m => Box -> Vec2 [(Constant, lab)] -> Diagram lab m ()+axes bx zs = d1 >> d2+  where Point d1 d2 = (Point hAxis vAxis) <*> pure bx <*> zs++-- | Multiply the vector (origin --> target) by p.+lint :: Constant -> Expr -> Expr -> Expr+lint p origin target = (p*-(target-origin)) + origin++-- | Draw a scatterplot in the given box.+-- Input data in the [0,1] interval fits the box.+scatterPlot :: Monad m => PlotCanvas a -> [Vec2 a] -> Diagram lab m ()+scatterPlot (bx,xform) input = forM_ (map (forward <$> xform <*>) input) $ \z -> do+  pt <- using (fill "black") $ circleShape+  width pt === constant 3+  pt # Center .=. interpBox bx z++interpBox :: forall a. Anchored a => a -> Point' Constant -> Point' Expr+interpBox bx z = lint <$> z <*> bx#SW <*> bx#NE++-- | @functionPlot c n f@.+-- Plot the function @f@ on the canvas @c@, using @n@ steps (precision).++functionPlot :: Monad m => Show a => PlotCanvas a -> Int -> (a -> a) -> Diagram lab m ()+functionPlot (bx,Point tx ty) nsteps f = draw $ path $ polyline points+  where points = do+           step <- [0..nsteps]+           let xi :: Double+               xi = fromIntegral step / fromIntegral nsteps+               x = backward tx xi+               y = f x+               yi = forward ty y+           return $ interpBox bx (Point xi yi)++data Iso a b = Iso {forward :: a -> b, backward :: b -> a}++after :: Iso b c -> Iso a b -> Iso a c+(Iso f g) `after` (Iso h i) = Iso (f . h) (i . g)++axisMarks :: a -> a -> Iso a Constant -> (a,[a],a)+axisMarks lo hi trans = (u lo',(map u [lo'..hi']),u hi')+  where u = backward trans+        t = forward trans+        lo' = fromIntegral $ (floor (t lo) :: Integer)+        hi' = fromIntegral $ (ceiling (t hi) :: Integer)++logAxis :: Constant -> Transform Constant+logAxis base = Iso t u+     where t x = log x / log base+           u x = base ** x++simplLinAxis :: Constant -> Transform Constant+simplLinAxis step = Iso (/step) (*step)++type ShowFct lab a = a -> lab++mkAxes :: Vec2 (Transform a) -> Vec2 a -> Vec2 a -> (Vec2 [a], Vec2 (Transform a))+mkAxes axesXform lows highs = (mrks <$> axisInfo,+                               after <$> (scale <$> minz <*> maxz) <*> axesXform)+  where axisInfo = axisMarks <$> lows <*> highs <*> axesXform+        minz = t <*> (lo <$> axisInfo)+        maxz = t <*> (hi <$> axisInfo)+        t = forward <$> axesXform+        lo (x,_,_) = x+        mrks (_,x,_) = x+        hi (_,_,x) = x++type PlotCanvas a = (Box, Vec2 (Transform a))++preparePlot :: Monad m => Vec2 (ShowFct lab a) -> Vec2 (Transform a) -> Vec2 a -> Vec2 a -> Diagram lab m (PlotCanvas a)+preparePlot showFct axesXform lo hi = do+  bx <- rectangleShape =<< box+  axes bx marks+  return (bx,xform)+  where marks = mkSteps <$> xform <*> showFct <*> marks0+        (marks0,xform) = mkAxes axesXform lo hi++-- | Draw a 2D scatter plot, given an axis specification and a data+-- set+simplePlot :: (Ord a, Monad m) => Vec2 (ShowFct lab a) -> Vec2 (Transform a) -> [Vec2 a] -> Diagram lab m (PlotCanvas a)+simplePlot showFct axesXform input = do+  canvas <- preparePlot showFct axesXform (minimum <$> input') (maximum <$> input')+  scatterPlot canvas input+  return canvas+  where input' = sequenceA input
+ Graphics/Diagrams/Point.hs view
@@ -0,0 +1,71 @@+{-# LANGUAGE TypeSynonymInstances, FlexibleContexts, FlexibleInstances, GeneralizedNewtypeDeriving, MultiParamTypeClasses, RecursiveDo, TypeFamilies, OverloadedStrings, RecordWildCards,UndecidableInstances, PackageImports, TemplateHaskell #-}++module Graphics.Diagrams.Point where++import Graphics.Diagrams.Core+import Data.Foldable+import Control.Applicative+import Data.List (transpose)+import Prelude hiding (sum,mapM_,mapM,concatMap,maximum,minimum)++infix 4 .=.+----------------+-- Points +-- | A point in 2d space+++type Point = Point' Expr++-- | Orthogonal norm of a vector+orthonorm :: Monad m => Point -> Diagram lab m Expr+orthonorm (Point x y) =+  (+) <$> absoluteValue x <*> absoluteValue y++-- | Orthogonal distance between points.+orthoDist :: Monad m => Point -> Point -> Diagram lab m Expr+orthoDist p q = orthonorm (q-p)++-- | Rotate a vector 90 degres in the trigonometric direction.+rotate90, rotate180 :: Point -> Point+rotate90 (Point x y) = Point (negate y) x++rotate180 = rotate90 . rotate90++xdiff,ydiff :: Point -> Point -> Expr+xdiff p q = xpart (q - p)+ydiff p q = ypart (q - p)++-----------------+-- Point constraints++(.=.),northOf,southOf,westOf,eastOf :: Monad m => Point -> Point -> Diagram lab m ()+Point x1 y1 .=. Point x2 y2 = do+  x1 === x2+  y1 === y2++northOf (Point _ y1) (Point _ y2) = y2 <== y1+southOf = flip northOf+westOf (Point x1 _) (Point x2 _) = x1 <== x2+eastOf = flip westOf++alignHoriz,alignVert :: Monad m => [Point] -> Diagram lab m ()+alignHoriz = align ypart+alignVert = align xpart++align :: Monad m => (a -> Expr) -> [a] -> Diagram lab m ()+align _ [] = return ()+align f (p:ps) = forM_ ps $ \p' -> f p === f p'++alignMatrix :: Monad m => [[Point]] -> Diagram lab m ()+alignMatrix ls = do+  forM_ ls alignHoriz+  forM_ (transpose ls) alignVert++---------------------+-- Point objectives++southwards, northwards, westwards, eastwards :: Monad m => Point -> Diagram lab m ()+southwards (Point _ y) = minimize y+westwards (Point x _) = minimize x+northwards = southwards . negate+eastwards = westwards . negate
+ LICENSE view
@@ -0,0 +1,661 @@+                    GNU AFFERO GENERAL PUBLIC LICENSE+                       Version 3, 19 November 2007++ Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/>+ Everyone is permitted to copy and distribute verbatim copies+ of this license document, but changing it is not allowed.++                            Preamble++  The GNU Affero General Public License is a free, copyleft license for+software and other kinds of works, specifically designed to ensure+cooperation with the community in the case of network server software.++  The licenses for most software and other practical works are designed+to take away your freedom to share and change the works.  By contrast,+our General Public Licenses are intended to guarantee your freedom to+share and change all versions of a program--to make sure it remains free+software for all its users.++  When we speak of free software, we are referring to freedom, not+price.  Our General Public Licenses are designed to make sure that you+have the freedom to distribute copies of free software (and charge for+them if you wish), that you receive source code or can get it if you+want it, that you can change the software or use pieces of it in new+free programs, and that you know you can do these things.++  Developers that use our General Public Licenses protect your rights+with two steps: (1) assert copyright on the software, and (2) offer+you this License which gives you legal permission to copy, distribute+and/or modify the software.++  A secondary benefit of defending all users' freedom is that+improvements made in alternate versions of the program, if they+receive widespread use, become available for other developers to+incorporate.  Many developers of free software are heartened and+encouraged by the resulting cooperation.  However, in the case of+software used on network servers, this result may fail to come about.+The GNU General Public License permits making a modified version and+letting the public access it on a server without ever releasing its+source code to the public.++  The GNU Affero General Public License is designed specifically to+ensure that, in such cases, the modified source code becomes available+to the community.  It requires the operator of a network server to+provide the source code of the modified version running there to the+users of that server.  Therefore, public use of a modified version, on+a publicly accessible server, gives the public access to the source+code of the modified version.++  An older license, called the Affero General Public License and+published by Affero, was designed to accomplish similar goals.  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+ Setup.hs view
@@ -0,0 +1,2 @@+import Distribution.Simple+main = defaultMain
+ lp-diagrams.cabal view
@@ -0,0 +1,40 @@+name:                lp-diagrams+version:             1.0+synopsis:            An EDSL for diagrams based based on linear constraints+license:             AGPL-3+license-file:        LICENSE+author:              Jean-Philippe Bernardy+maintainer:          jeanphilippe.bernardy@gmail.com+copyright:           Jean-Philippe Bernardy+category:            Graphics+build-type:          Simple+-- extra-source-files:  +cabal-version:       >=1.18++Flag graphviz+  Description: Enable graphviz support+  Default:     True++library+  if flag(graphviz)+    build-depends: graphviz+    exposed-modules: Graphics.Diagrams.Graphviz++  exposed-modules:     Graphics.Diagrams.Object,+                       Graphics.Diagrams.Path,+                       Graphics.Diagrams.Plot,+                       Graphics.Diagrams.Point,+                       Graphics.Diagrams.Core,+                       Graphics.Diagrams.DerivationTrees,+                       Graphics.Diagrams+  build-depends:       base >=4.8 && < 666,+                       lens >=4.12,+                       text >=1.2 ,+                       typography-geometry >=1.0 ,+                       glpk-hs >=0.3 ,+                       vector,+                       polynomials-bernstein,+                       mtl >=2.2 ,+                       containers >=0.5,+                       labeled-tree+  default-language:    Haskell2010