vector: Add QuadraticCurve

Updates #741

examples/vector/main.go

@@ -46,7 +46,14 @@ func drawEbitenText(screen *ebiten.Image) {
 	path.LineTo(70, 30)
 	path.LineTo(70, 20)
 
-	// TODO: Draw other letters like B, I, T, E, N
+	// B
+	path.MoveTo(80, 20)
+	path.LineTo(80, 70)
+	path.LineTo(100, 70)
+	path.QuadraticCurveTo(130, 57.5, 100, 45)
+	path.QuadraticCurveTo(130, 32.5, 100, 20)
+
+	// TODO: Draw other letters like I, T, E, N
 
 	path.Fill(screen, color.White)
 }

vector/internal/math/triangulate.go

@@ -34,7 +34,7 @@ func InTriangle(pt, pt0, pt1, pt2 Point) bool {
 	c0 := cross(Vector{pt.X - pt0.X, pt.Y - pt0.Y}, Vector{pt1.X - pt0.X, pt1.Y - pt0.Y})
 	c1 := cross(Vector{pt.X - pt1.X, pt.Y - pt1.Y}, Vector{pt2.X - pt1.X, pt2.Y - pt1.Y})
 	c2 := cross(Vector{pt.X - pt2.X, pt.Y - pt2.Y}, Vector{pt0.X - pt2.X, pt0.Y - pt2.Y})
-	return (c0 < 0 && c1 < 0 && c2 < 0) || (c0 > 0 && c1 > 0 && c2 > 0)
+	return (c0 <= 0 && c1 <= 0 && c2 <= 0) || (c0 >= 0 && c1 >= 0 && c2 >= 0)
 }
 
 func Triangulate(pts []Point) []uint16 {
@@ -60,12 +60,12 @@ dup:
 
 	// Determine the direction of the polygon from the upper-left point.
 	var upperLeft int
-	for _, i := range currentIndices {
+	for ci, i := range currentIndices {
 		if pts[upperLeft].X < pts[i].X {
-			upperLeft = int(i)
+			upperLeft = int(ci)
 		}
 		if pts[upperLeft].X == pts[i].X && pts[upperLeft].Y < pts[i].Y {
-			upperLeft = int(i)
+			upperLeft = int(ci)
 		}
 	}
 	i0, i1, i2 := adjacentIndices(currentIndices, upperLeft)

vector/internal/math/triangulate_test.go

@@ -145,6 +145,15 @@ func TestTriangulate(t *testing.T) {
 			},
 			Out: []uint16{2, 0, 1},
 		},
+		{
+			In: []Point{
+				{0, 0},
+				{1, 1},
+				{0, 1},
+				{0, 0.5},
+			},
+			Out: []uint16{2, 0, 1},
+		},
 		{
 			In: []Point{
 				{0, 0},
@@ -178,7 +187,33 @@ func TestTriangulate(t *testing.T) {
 				{3, 4},
 				{3, 3},
 			},
-			Out: []uint16{9, 0, 1, 1, 2, 3, 1, 3, 4, 9, 1, 4, 8, 5, 6, 8, 6, 7},
+			Out: []uint16{9, 0, 1, 1, 2, 3, 1, 3, 4, 1, 4, 5, 5, 6, 7, 5, 7, 8, 9, 1, 5},
+		},
+		{
+			In: []Point{
+				{0, 0},
+				{0, 5},
+				{2, 5},
+				{3, 3},
+				{2, 2},
+				{3, 1},
+				{2, 0},
+			},
+			Out: []uint16{6, 0, 1, 1, 2, 3, 1, 3, 4, 6, 1, 4, 6, 4, 5},
+		},
+		{
+			In: []Point{
+				{0, 0},
+				{0, 5},
+				{2, 5},
+				{2, 5},
+				{3, 3},
+				{2, 2},
+				{2, 2},
+				{3, 1},
+				{2, 0},
+			},
+			Out: []uint16{8, 0, 1, 1, 2, 4, 1, 4, 5, 8, 1, 5, 8, 5, 7},
 		},
 	}
 	for _, tc := range tests {

vector/path.go

@@ -48,12 +48,26 @@ func (p *Path) MoveTo(x, y float32) {
 // LineTo updates the current position to (x, y).
 func (p *Path) LineTo(x, y float32) {
 	if len(p.segs) == 0 {
-		p.segs = append(p.segs, []math.Point{{X: 0, Y: 0}})
+		p.segs = append(p.segs, []math.Point{p.cur})
 	}
 	p.segs[len(p.segs)-1] = append(p.segs[len(p.segs)-1], math.Point{X: x, Y: y})
 	p.cur = math.Point{X: x, Y: y}
 }
 
+func (p *Path) QuadraticCurveTo(cpx, cpy, x, y float32) {
+	c := p.cur
+	dist := float64((x-c.X)*(x-c.X) + (y-c.Y)*(y-c.Y))
+	num := 1.0
+	for num*num < dist {
+		num *= 2
+	}
+	for t := float32(0.0); t <= 1; t += 1.0 / 128.0 {
+		xf := t*t*x + 2*t*(1-t)*cpx + (1-t)*(1-t)*c.X
+		yf := t*t*y + 2*t*(1-t)*cpy + (1-t)*(1-t)*c.Y
+		p.LineTo(xf, yf)
+	}
+}
+
 func (p *Path) Fill(dst *ebiten.Image, clr color.Color) {
 	var vertices []ebiten.Vertex
 	var indices []uint16