implemented self intersecting polygon support

README.md

@@ -120,17 +120,22 @@ These features *should* work just like their HTML5 counterparts, but there are l
 - shadowOffset(X/Y)
 - shadowBlur
 - isPointInPath
+- self intersecting polygons
 
 # Missing features
 
 - globalCompositeOperation
 - isPointInStroke
 - textBaseline hanging and ideographic (currently work just like top and bottom)
-- full self intersecting polygon support
 - image patterns with repeat and transform
 
 # Version history
 
+v0.8.0
+
+- Self intersecting polygon support
+- isPointInPath implemented
+
 v0.7.2
 
 - Fixed build tags for macOS and iOS

path2d.go

@@ -287,21 +287,21 @@ func (p *Path2D) Rect(x, y, w, h float64) {
 // func (p *Path2D) Ellipse(...) {
 // }
 
-func runSubPaths(path *Path2D, fn func(subPath []pathPoint) bool) {
+func runSubPaths(path []pathPoint, fn func(subPath []pathPoint) bool) {
 	start := 0
-	for i, p := range path.p {
+	for i, p := range path {
 		if p.flags&pathMove == 0 {
 			continue
 		}
 		if i >= start+3 {
-			if fn(path.p[start:i]) {
+			if fn(path[start:i]) {
 				return
 			}
 		}
 		start = i
 	}
-	if len(path.p) >= start+3 {
-		fn(path.p[start:])
+	if len(path) >= start+3 {
+		fn(path[start:])
 	}
 }
 
@@ -318,7 +318,7 @@ const (
 // to the given rule
 func (p *Path2D) IsPointInPath(x, y float64, rule pathRule) bool {
 	inside := false
-	runSubPaths(p, func(sp []pathPoint) bool {
+	runSubPaths(p.p, func(sp []pathPoint) bool {
 		num := 0
 		prev := sp[len(sp)-1].pos
 		for _, pt := range p.p {

paths.go

@@ -339,7 +339,7 @@ func (cv *Canvas) FillPath(path *Path2D) {
 
 	var triBuf [500][2]float64
 	tris := triBuf[:0]
-	runSubPaths(path, func(sp []pathPoint) bool {
+	runSubPaths(path.p, func(sp []pathPoint) bool {
 		tris = appendSubPathTriangles(tris, sp)
 		return false
 	})
@@ -364,8 +364,10 @@ func appendSubPathTriangles(tris [][2]float64, path []pathPoint) [][2]float64 {
 			p1 = p2
 		}
 	} else if last.flags&pathSelfIntersects != 0 {
-		path = cutIntersections(path)
-		tris = triangulatePath(path, tris)
+		selfIntersectingPathParts(path, func(sp []pathPoint) bool {
+			tris = triangulatePath(sp, tris)
+			return false
+		})
 	} else {
 		tris = triangulatePath(path, tris)
 	}
@@ -385,7 +387,7 @@ func (cv *Canvas) clip(path *Path2D) {
 
 	var triBuf [500][2]float64
 	tris := triBuf[:0]
-	runSubPaths(path, func(sp []pathPoint) bool {
+	runSubPaths(path.p, func(sp []pathPoint) bool {
 		tris = appendSubPathTriangles(tris, sp)
 		return false
 	})

triangulation.go

@@ -5,6 +5,8 @@ import (
 	"sort"
 )
 
+const samePointTolerance = 1e-20
+
 func pointIsRightOfLine(a, b, p vec) (bool, bool) {
 	if a[1] == b[1] {
 		return false, false
@@ -23,6 +25,24 @@ func pointIsRightOfLine(a, b, p vec) (bool, bool) {
 	return p[0] > x, dir
 }
 
+func pointIsBelowLine(a, b, p vec) (bool, bool) {
+	if a[0] == b[0] {
+		return false, false
+	}
+	dir := false
+	if a[0] > b[0] {
+		a, b = b, a
+		dir = !dir
+	}
+	if p[0] < a[0] || p[0] > b[0] {
+		return false, false
+	}
+	v := b.sub(a)
+	r := (p[0] - a[0]) / v[0]
+	x := a[1] + r*v[1]
+	return p[1] > x, dir
+}
+
 func triangleContainsPoint(a, b, c, p vec) bool {
 	// if point is outside triangle bounds, return false
 	if p[0] < a[0] && p[0] < b[0] && p[0] < c[0] {
@@ -104,11 +124,52 @@ func triangulatePath(path []pathPoint, target [][2]float64) [][2]float64 {
 	return target
 }
 
-func cutIntersections(path []pathPoint) []pathPoint {
+/*
+tesselation strategy:
+
+- cut the path at the intersections
+- build a network of connected vertices and edges
+- find out which side of each edge is inside the polygon
+- pick an edge with only one side in the polygon, then follow it
+  along the side on which the polygon is, always picking the edge
+  with the smallest angle, until the path goes back to the starting
+  point. set each edge as no longer having the polygon on that side
+- repeat until no more edges have a polygon on either side
+
+*/
+
+type tessNet struct {
+	verts []tessVert
+	edges []tessEdge
+}
+
+type tessVert struct {
+	pos      vec
+	attached []int
+	count    int
+}
+
+type tessEdge struct {
+	a, b        int
+	leftInside  bool
+	rightInside bool
+}
+
+func cutIntersections(path []pathPoint) tessNet {
+	// eliminate adjacent duplicate points
+	for i := 0; i < len(path); i++ {
+		a := path[i]
+		b := path[(i+1)%len(path)]
+		if isSamePoint(a.pos, b.pos, samePointTolerance) {
+			copy(path[i:], path[i+1:])
+			path = path[:len(path)-1]
+			i--
+		}
+	}
+
+	// find all the cuts
 	type cut struct {
 		from, to int
-		j        int
-		b        bool
 		ratio    float64
 		point    vec
 	}
@@ -116,8 +177,8 @@ func cutIntersections(path []pathPoint) []pathPoint {
 	var cutBuf [50]cut
 	cuts := cutBuf[:0]
 
+	ip := len(path) - 1
 	for i := 0; i < len(path); i++ {
-		ip := (i + len(path) - 1) % len(path)
 		a0 := path[ip].pos
 		a1 := path[i].pos
 		for j := i + 1; j < len(path); j++ {
@@ -136,21 +197,19 @@ func cutIntersections(path []pathPoint) []pathPoint {
 				to:    i,
 				ratio: r1,
 				point: p,
-				j:     j,
 			})
 			cuts = append(cuts, cut{
 				from:  jp,
 				to:    j,
 				ratio: r2,
 				point: p,
-				j:     i,
-				b:     true,
 			})
 		}
+		ip = i
 	}
 
 	if len(cuts) == 0 {
-		return path
+		return tessNet{}
 	}
 
 	sort.Slice(cuts, func(i, j int) bool {
@@ -158,14 +217,245 @@ func cutIntersections(path []pathPoint) []pathPoint {
 		return a.to > b.to || (a.to == b.to && a.ratio > b.ratio)
 	})
 
-	newPath := make([]pathPoint, len(path)+len(cuts))
-	copy(newPath[:len(path)], path)
-
+	// build vertex and edge lists
+	verts := make([]tessVert, len(path)+len(cuts))
+	for i, pp := range path {
+		verts[i] = tessVert{
+			pos:   pp.pos,
+			count: 2,
+		}
+	}
 	for _, cut := range cuts {
-		copy(newPath[cut.to+1:], newPath[cut.to:])
-		newPath[cut.to].next = newPath[cut.to+1].pos
-		newPath[cut.to].pos = cut.point
+		copy(verts[cut.to+1:], verts[cut.to:])
+		verts[cut.to].pos = cut.point
+	}
+	edges := make([]tessEdge, 0, len(path)+len(cuts)*2)
+	for i := range verts {
+		next := (i + 1) % len(verts)
+		edges = append(edges, tessEdge{a: i, b: next})
 	}
 
-	return newPath
+	// eliminate duplicate points
+	for i := 0; i < len(verts); i++ {
+		a := verts[i]
+		for j := i + 1; j < len(verts); j++ {
+			b := verts[j]
+			if isSamePoint(a.pos, b.pos, samePointTolerance) {
+				copy(verts[j:], verts[j+1:])
+				verts = verts[:len(verts)-1]
+				for k, e := range edges {
+					if e.a == j {
+						edges[k].a = i
+					} else if e.a > j {
+						edges[k].a--
+					}
+					if e.b == j {
+						edges[k].b = i
+					} else if e.b > j {
+						edges[k].b--
+					}
+				}
+				verts[i].count += 2
+				j--
+			}
+		}
+	}
+
+	// build the attached edge lists on all vertices
+	total := 0
+	for _, v := range verts {
+		total += v.count
+	}
+	attachedBuf := make([]int, 0, total)
+	pos := 0
+	for i := range verts {
+		for j, e := range edges {
+			if e.a == i || e.b == i {
+				attachedBuf = append(attachedBuf, j)
+			}
+		}
+		verts[i].attached = attachedBuf[pos:len(attachedBuf)]
+		pos = len(attachedBuf)
+	}
+
+	return tessNet{verts: verts, edges: edges}
+}
+
+func setPathLeftRightInside(net *tessNet) {
+	for i, e1 := range net.edges {
+		a1, b1 := net.verts[e1.a], net.verts[e1.b]
+		diff := b1.pos.sub(a1.pos)
+		mid := a1.pos.add(diff.mulf(0.5))
+		num := 0
+
+		if math.Abs(diff[1]) < math.Abs(diff[0]) {
+			edir := diff[1] > 0
+
+			for j, e2 := range net.edges {
+				if i == j {
+					continue
+				}
+				a2, b2 := net.verts[e2.a], net.verts[e2.b]
+				r, dir := pointIsRightOfLine(a2.pos, b2.pos, mid)
+				if !r {
+					continue
+				}
+				if dir {
+					num++
+				} else {
+					num--
+				}
+			}
+
+			if edir {
+				net.edges[i].leftInside = (num - 1) != 0
+				net.edges[i].rightInside = num != 0
+			} else {
+				net.edges[i].leftInside = num != 0
+				net.edges[i].rightInside = (num + 1) != 0
+			}
+		} else {
+			edir := diff[0] > 0
+
+			for j, e2 := range net.edges {
+				if i == j {
+					continue
+				}
+				a2, b2 := net.verts[e2.a], net.verts[e2.b]
+				b, dir := pointIsBelowLine(a2.pos, b2.pos, mid)
+				if !b {
+					continue
+				}
+				if dir {
+					num++
+				} else {
+					num--
+				}
+			}
+
+			if edir {
+				net.edges[i].leftInside = num != 0
+				net.edges[i].rightInside = (num - 1) != 0
+			} else {
+				net.edges[i].leftInside = (num + 1) != 0
+				net.edges[i].rightInside = num != 0
+			}
+		}
+	}
+}
+
+func selfIntersectingPathParts(p []pathPoint, partFn func(sp []pathPoint) bool) {
+	runSubPaths(p, func(sp1 []pathPoint) bool {
+		net := cutIntersections(sp1)
+		if net.verts == nil {
+			return false
+		}
+
+		setPathLeftRightInside(&net)
+
+		var sp2Buf [50]pathPoint
+		sp2 := sp2Buf[:0]
+
+		for {
+			var start, from, cur, count int
+			var left bool
+			for i, e := range net.edges {
+				if e.leftInside != e.rightInside {
+					count++
+					start = e.a
+					from = i
+					cur = e.b
+					if e.leftInside {
+						left = true
+						net.edges[i].leftInside = false
+					} else {
+						net.edges[i].rightInside = false
+					}
+					break
+				}
+			}
+			if count == 0 {
+				break
+			}
+
+			// fmt.Println("start", start, from, cur, net.verts[cur], left)
+
+			sp2 = append(sp2, pathPoint{
+				pos:   net.verts[cur].pos,
+				flags: pathMove,
+			})
+
+			for limit := 0; limit < len(net.edges); limit++ {
+				ecur := net.edges[from]
+				acur, bcur := net.verts[ecur.a], net.verts[ecur.b]
+				dir := bcur.pos.sub(acur.pos)
+				dirAngle := math.Atan2(dir[1], dir[0])
+				minAngleDiff := math.Pi * 2
+				var next, nextEdge int
+				any := false
+				for _, ei := range net.verts[cur].attached {
+					if ei == from {
+						continue
+					}
+					e := net.edges[ei]
+					if (left && !e.leftInside) || (!left && !e.rightInside) {
+						continue
+					}
+					na, nb := net.verts[e.a], net.verts[e.b]
+					if e.b == cur {
+						na, nb = nb, na
+					}
+					ndir := nb.pos.sub(na.pos)
+					nextAngle := math.Atan2(ndir[1], ndir[0]) + math.Pi
+					if nextAngle < dirAngle {
+						nextAngle += math.Pi * 2
+					} else if nextAngle > dirAngle+math.Pi*2 {
+						nextAngle -= math.Pi * 2
+					}
+					var angleDiff float64
+					if left {
+						angleDiff = nextAngle - dirAngle
+					} else {
+						angleDiff = dirAngle - nextAngle
+					}
+					if angleDiff < minAngleDiff {
+						minAngleDiff = angleDiff
+						nextEdge = ei
+						if e.a == cur {
+							next = e.b
+						} else {
+							next = e.a
+						}
+						any = true
+						// fmt.Println("-", e, nextEdge, next)
+					}
+				}
+				if !any {
+					break
+				}
+				// fmt.Println(start, from, cur, net.verts[cur], nextEdge, next, net.verts[next])
+				if left {
+					net.edges[nextEdge].leftInside = false
+				} else {
+					net.edges[nextEdge].rightInside = false
+				}
+				sp2 = append(sp2, pathPoint{
+					pos: net.verts[next].pos,
+				})
+				from = nextEdge
+				cur = next
+				if next == start {
+					break
+				}
+			}
+
+			stop := partFn(sp2)
+			if stop {
+				return true
+			}
+			sp2 = sp2[:0]
+		}
+
+		return false
+	})
 }