Add arc segmentation

draw2d/curve/arc.go

@@ -0,0 +1,37 @@
+// Copyright 2010 The draw2d Authors. All rights reserved.
+// created: 21/11/2010 by Laurent Le Goff
+package draw2d
+
+import (
+	"freetype-go.googlecode.com/hg/freetype/raster"
+	"math"
+)
+
+func SegmentArc(t LineTracer, x, y, rx, ry, start, angle, scale float64) {
+	end := start + angle
+	clockWise := true
+	if angle < 0 {
+		clockWise = false
+	}
+	ra := (math.Fabs(rx) + math.Fabs(ry)) / 2
+	da := math.Acos(ra/(ra+0.125/scale)) * 2
+	//normalize
+	if !clockWise {
+		da = -da
+	}
+	angle = start + da
+	var curX, curY float64
+	for {
+		if (angle < end-da/4) != clockWise {
+			curX = x + math.Cos(end)*rx
+			curY = y + math.Sin(end)*ry
+			return curX, curY
+		}
+		curX = x + math.Cos(angle)*rx
+		curY = y + math.Sin(angle)*ry
+
+		angle += da
+		t.LineTo(curX, curY)
+	}
+	t.LineTo(curX, curY)
+}

draw2d/curve/cubic_float64.go

@@ -40,9 +40,6 @@ func (c *CubicCurveFloat64) Subdivide(c1, c2 *CubicCurveFloat64) (x23, y23 float
 }
 
 func (curve *CubicCurveFloat64) Segment(t LineTracer, flattening_threshold float64) {
-	// Add the first point
-	t.LineTo(curve.X1, curve.Y1)
-
 	var curves [CurveRecursionLimit]CubicCurveFloat64
 	curves[0] = *curve
 	i := 0

draw2d/curve/cubic_float64_others.go

@@ -63,8 +63,6 @@ func (c *CubicCurveFloat64) EstimateDistance() float64 {
 
 // subdivide the curve in straight lines using line approximation and Casteljau recursive subdivision 
 func (c *CubicCurveFloat64) SegmentRec(t LineTracer, flattening_threshold float64) {
-	// reinit segments
-	t.LineTo(c.X1, c.Y1)
 	c.segmentRec(t, flattening_threshold)
 	t.LineTo(c.X4, c.Y4)
 }
@@ -115,7 +113,6 @@ func (c *CubicCurveFloat64) AdaptiveSegmentRec(t LineTracer, approximationScale,
 	cuspLimit = computeCuspLimit(cuspLimit)
 	distanceToleranceSquare := 0.5 / approximationScale
 	distanceToleranceSquare = distanceToleranceSquare * distanceToleranceSquare
-	t.LineTo(c.X1, c.Y1)
 	c.adaptiveSegmentRec(t, 0, distanceToleranceSquare, angleTolerance, cuspLimit)
 	t.LineTo(c.X4, c.Y4)
 }
@@ -314,8 +311,6 @@ func (c *CubicCurveFloat64) adaptiveSegmentRec(t LineTracer, level int, distance
 }
 
 func (curve *CubicCurveFloat64) AdaptiveSegment(t LineTracer, approximationScale, angleTolerance, cuspLimit float64) {
-	// Add the first point
-	t.LineTo(curve.X1, curve.Y1)
 	cuspLimit = computeCuspLimit(cuspLimit)
 	distanceToleranceSquare := 0.5 / approximationScale
 	distanceToleranceSquare = distanceToleranceSquare * distanceToleranceSquare
@@ -529,7 +524,6 @@ func (curve *CubicCurveFloat64) AdaptiveSegment(t LineTracer, approximationScale
 
 
 func (c *CubicCurveFloat64) ParabolicSegment(t LineTracer, flattening_threshold float64) {
-	t.LineTo(c.X1, c.Y1)
 	estimatedIFP := c.numberOfInflectionPoints()
 	if estimatedIFP == 0 {
 		// If no inflection points then apply PA on the full Bezier segment.

draw2d/curve/curve_test.go

@@ -108,6 +108,7 @@ func drawPoints(img draw.Image, c image.Color, s ...float64) image.Image {
 func TestCubicCurveRec(t *testing.T) {
 	for i, curve := range testsCubicFloat64 {
 		var p Path
+		p.LineTo(curve.X1, Y1)
 		curve.SegmentRec(&p, flattening_threshold)
 		img := image.NewNRGBA(300, 300)
 		raster.PolylineBresenham(img, image.NRGBAColor{0xff, 0, 0, 0xff}, curve.X1, curve.Y1, curve.X2, curve.Y2, curve.X3, curve.Y3, curve.X4, curve.Y4)
@@ -123,6 +124,7 @@ func TestCubicCurveRec(t *testing.T) {
 func TestCubicCurve(t *testing.T) {
 	for i, curve := range testsCubicFloat64 {
 		var p Path
+		p.LineTo(curve.X1, Y1)
 		curve.Segment(&p, flattening_threshold)
 		img := image.NewNRGBA(300, 300)
 		raster.PolylineBresenham(img, image.NRGBAColor{0xff, 0, 0, 0xff}, curve.X1, curve.Y1, curve.X2, curve.Y2, curve.X3, curve.Y3, curve.X4, curve.Y4)
@@ -138,6 +140,7 @@ func TestCubicCurve(t *testing.T) {
 func TestCubicCurveAdaptiveRec(t *testing.T) {
 	for i, curve := range testsCubicFloat64 {
 		var p Path
+		p.LineTo(curve.X1, Y1)
 		curve.AdaptiveSegmentRec(&p, 1, 0, 0)
 		img := image.NewNRGBA(300, 300)
 		raster.PolylineBresenham(img, image.NRGBAColor{0xff, 0, 0, 0xff}, curve.X1, curve.Y1, curve.X2, curve.Y2, curve.X3, curve.Y3, curve.X4, curve.Y4)
@@ -153,6 +156,7 @@ func TestCubicCurveAdaptiveRec(t *testing.T) {
 func TestCubicCurveAdaptive(t *testing.T) {
 	for i, curve := range testsCubicFloat64 {
 		var p Path
+		p.LineTo(curve.X1, Y1)
 		curve.AdaptiveSegment(&p, 1, 0, 0)
 		img := image.NewNRGBA(300, 300)
 		raster.PolylineBresenham(img, image.NRGBAColor{0xff, 0, 0, 0xff}, curve.X1, curve.Y1, curve.X2, curve.Y2, curve.X3, curve.Y3, curve.X4, curve.Y4)
@@ -168,6 +172,7 @@ func TestCubicCurveAdaptive(t *testing.T) {
 func TestCubicCurveParabolic(t *testing.T) {
 	for i, curve := range testsCubicFloat64 {
 		var p Path
+		p.LineTo(curve.X1, Y1)
 		curve.ParabolicSegment(&p, flattening_threshold)
 		img := image.NewNRGBA(300, 300)
 		raster.PolylineBresenham(img, image.NRGBAColor{0xff, 0, 0, 0xff}, curve.X1, curve.Y1, curve.X2, curve.Y2, curve.X3, curve.Y3, curve.X4, curve.Y4)
@@ -184,6 +189,7 @@ func TestCubicCurveParabolic(t *testing.T) {
 func TestQuadCurve(t *testing.T) {
 	for i, curve := range testsQuadFloat64 {
 		var p Path
+		p.LineTo(curve.X1, Y1)
 		curve.Segment(&p, flattening_threshold)
 		img := image.NewNRGBA(300, 300)
 		raster.PolylineBresenham(img, image.NRGBAColor{0xff, 0, 0, 0xff}, curve.X1, curve.Y1, curve.X2, curve.Y2, curve.X3, curve.Y3)
@@ -199,6 +205,7 @@ func BenchmarkCubicCurveRec(b *testing.B) {
 	for i := 0; i < b.N; i++ {
 		for _, curve := range testsCubicFloat64 {
 			p := Path{make([]float64, 0, 32)}
+			p.LineTo(curve.X1, Y1)
 			curve.SegmentRec(&p, flattening_threshold)
 		}
 	}
@@ -208,6 +215,7 @@ func BenchmarkCubicCurve(b *testing.B) {
 	for i := 0; i < b.N; i++ {
 		for _, curve := range testsCubicFloat64 {
 			p := Path{make([]float64, 0, 32)}
+			p.LineTo(curve.X1, Y1)
 			curve.Segment(&p, flattening_threshold)
 		}
 	}
@@ -217,6 +225,7 @@ func BenchmarkCubicCurveAdaptiveRec(b *testing.B) {
 	for i := 0; i < b.N; i++ {
 		for _, curve := range testsCubicFloat64 {
 			p := Path{make([]float64, 0, 32)}
+			p.LineTo(curve.X1, Y1)
 			curve.AdaptiveSegmentRec(&p, 1, 0, 0)
 		}
 	}
@@ -226,6 +235,7 @@ func BenchmarkCubicCurveAdaptive(b *testing.B) {
 	for i := 0; i < b.N; i++ {
 		for _, curve := range testsCubicFloat64 {
 			p := Path{make([]float64, 0, 32)}
+			p.LineTo(curve.X1, Y1)
 			curve.AdaptiveSegment(&p, 1, 0, 0)
 		}
 	}
@@ -235,6 +245,7 @@ func BenchmarkCubicCurveParabolic(b *testing.B) {
 	for i := 0; i < b.N; i++ {
 		for _, curve := range testsCubicFloat64 {
 			p := Path{make([]float64, 0, 32)}
+			p.LineTo(curve.X1, Y1)
 			curve.ParabolicSegment(&p, flattening_threshold)
 		}
 	}
@@ -244,6 +255,7 @@ func BenchmarkQuadCurve(b *testing.B) {
 	for i := 0; i < b.N; i++ {
 		for _, curve := range testsQuadFloat64 {
 			p := Path{make([]float64, 0, 32)}
+			p.LineTo(curve.X1, Y1)
 			curve.Segment(&p, flattening_threshold)
 		}
 	}

draw2d/curve/quad_float64.go

@@ -28,9 +28,6 @@ func (c *QuadCurveFloat64) Subdivide(c1, c2 *QuadCurveFloat64) {
 
 
 func (curve *QuadCurveFloat64) Segment(t LineTracer, flattening_threshold float64) {
-	// Add the first point
-	t.LineTo(curve.X1, curve.Y1)
-
 	var curves [CurveRecursionLimit]QuadCurveFloat64
 	curves[0] = *curve
 	i := 0