Render bezier curves using distance fields

src/Picture.hs

@@ -71,23 +71,49 @@ polygonCol = PolygonCol 0
 
 -- note that much of work computing the width of the bezier curve is done here
 bezierQuad :: Color -> Color -> Float -> Float -> Point2 -> Point2 -> Point2 -> Picture
-bezierQuad cola colc ra rc a b c = BezierQuad 0 [(aX, cola, aX +.+ aRadVec , fracRadA  )
-                                                ,(bX, colb, (0,0)          , 0 )
-                                                ,(cX, colc, cX +.+ cRadVec , fracRadC )
+bezierQuad cola colc ra rc a b c = BezierQuad 0 [-- ( (0,0) , cola, (0,0), (0,0) )
+                                                 (aIn, cola, (fa aIn,fc aIn) , (1,0) )
+                                                ,(aIn, cola, (fa aIn,fc aIn) , (1,0) )
+                                                ,(cIn, colc, (fa cIn,fc cIn) , (0,1) )
+                                                ,( aX, cola, (1,0) , (fa' aX,fc' aX)  )
+                                                ,( cX, colc, (0,1) , (fa' cX,fc' cX)  )
+                                                ,( bX, colb, (0,0) , (fa' bX,fc' bX)  )
+                                                ,( bX, colb, (0,0) , (fa' bX,fc' bX)  )
                                                 ]
     where colb = mixColors 0.5 0.5 cola colc
           b2a | isLHS a b c = a -.- b
               | otherwise   = b -.- a
           aRadVec = ra *.* (normalizeV $ vNormal b2a)
-          aX = a -.- 0.5 *.* aRadVec
+          aX  = a -.- 0.5 *.* aRadVec
+          aIn = a +.+ 0.5 *.* aRadVec
           b2c | isLHS a b c = b -.- c
               | otherwise   = c -.- b
           cRadVec = rc *.* (normalizeV $ vNormal b2c)
-          cX = c -.- 0.5 *.* cRadVec
+          cX  = c -.- 0.5 *.* cRadVec
+          cIn = c +.+ 0.5 *.* cRadVec
           bX = (b -.- (0.5 *.* aRadVec) )
                   -.- (0.5 *.* cRadVec)
-          fracRadA = ra / magV (aX -.- cX)
-          fracRadC = rc / magV (aX -.- cX)
+          bIn = b +.+ (0.5 *.* aRadVec) 
+                  +.+ (0.5 *.* cRadVec)
+          fa = extrapolate aX cX bX 
+          fc = extrapolate cX aX bX
+          fa' = extrapolate aIn cIn bIn
+          fc' = extrapolate cIn aIn bIn
+
+-- given a one and two zeros of a linear function over x and y,
+-- determine the function
+-- so if f(ox,oy) = 1 and f(ax,ay) = f(bx,by) = 0, determines f
+extrapolate :: Point2 -> Point2 -> Point2 -> Point2 -> Float
+extrapolate (ox,oy) (ax,ay) (bx,by) (x,y) = 
+    (       x * ( ay - by )
+        +   y * ( bx - ax )
+        +   (ax * by - bx * ay)
+    ) 
+    / 
+    (       ox * ( ay - by )
+        +   ax * ( by - oy )
+        +   bx * ( oy - ay )
+    )
 
 color :: RGBA -> Picture -> Picture
 {-# INLINE color #-}

src/Picture/Data.hs

@@ -22,7 +22,7 @@ import Data.Traversable
 
 data RenderType
     = RenderPoly [(Point3,Point4)]
-    | RenderBezQ [(Point3,Point4,Point3)]
+    | RenderBezQ [(Point3,Point4,Point4)]
     | RenderText [(Point3,Point4,Point3)]
     | RenderArc  (Point3,Point4,Point4)
     | RenderLine [(Point3,Point4)]
@@ -75,7 +75,7 @@ data Picture
     = Blank
     | Text Int String
     | Polygon Int [Point2]
-    | BezierQuad Int [(Point2,RGBA,Point2,Float)]
+    | BezierQuad Int [(Point2,RGBA,Point2,Point2)]
     | PolygonCol Int [(Point2,RGBA)]
     | Circle Int RGBA RGBA Float
     | ThickArc Int Float Float Float Float

src/Picture/Preload.hs

@@ -50,7 +50,7 @@ preloadRender = do
                                 "data/texture/charMap.png"
 
     bezierQuadShader
-           <- makeShader "bezierQuad" [vert,geom,frag] [(0,3),(1,4),(2,3)]    Triangles pokeBezQStrat
+           <- makeShader "bezierQuad" [vert,frag] [(0,3),(1,4),(2,4)]    TriangleStrip pokeBezQStrat
 
 --the following vbo is set up to contain one fixed vertex
     dummyvbo <- genObjectName
@@ -84,7 +84,9 @@ cleanUpRenderPreload pd = do
 
 {-# INLINE pokeBezQStrat #-}
 pokeBezQStrat :: RenderType -> [[[Float]]]
-pokeBezQStrat (RenderBezQ vs) = fmap (\((x,y,z),(r,g,b,a),(s,t,v)) -> [[x,y,z],[r,g,b,a],[s,t,v]]) vs
+pokeBezQStrat (RenderBezQ vs) = fmap (\((x,y,z),(r,g,b,a),(s,t,u,v)) -> [[x,y,z],[r,g,b,a],[s,t,u,v]]
+                                     ) 
+                                     vs
 pokeBezQStrat _ = []
 
 {-# INLINE pokeTriStrat #-}

src/Picture/Tree.hs

@@ -20,7 +20,7 @@ picToLTree mx (PolygonCol i vs)
 picToLTree mx (BezierQuad i vs) 
     = filtB mx i $ LLeaf $ RenderBezQ $ zip3 (map zeroZ ps) cols rs
         where (ps,cols,offps,rads) = unzip4 vs
-              rs = zipWith (\(x,y) z -> (x,y,z)) offps rads
+              rs = zipWith (\(x,y) (z,w) -> (x,y,z,w)) offps rads
                                       
 picToLTree mx (Circle i colC colE r)
     = filtB mx i $ LLeaf $ RenderEllipse [( (-r, r,0), colC)