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Add quadratic subdivision

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This commit is contained in:
Laurent Le Goff 2011-05-19 23:24:56 +02:00
parent c20e243ba4
commit 4dd2a24c2d
6 changed files with 217 additions and 73 deletions
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6
draw2d/curve/Makefile
View file

@ -2,6 +2,8 @@ include $(GOROOT)/src/Make.inc
TARG=draw2d.googlecode.com/hg/draw2d/curve
GOFILES=\
curve_float64.go\
cubic_float64.go\
quad_float64.go\
cubic_float64_others.go\
include $(GOROOT)/src/Make.pkg

41
draw2d/curve/_testmain.go Normal file
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@ -0,0 +1,41 @@
package main
import "draw2d.googlecode.com/hg/draw2d/curve"
import "testing"
import __os__ "os"
import __regexp__ "regexp"
var tests = []testing.InternalTest{
{"curve.TestCubicCurveRec", curve.TestCubicCurveRec},
{"curve.TestCubicCurve", curve.TestCubicCurve},
{"curve.TestCubicCurveAdaptiveRec", curve.TestCubicCurveAdaptiveRec},
{"curve.TestCubicCurveAdaptive", curve.TestCubicCurveAdaptive},
{"curve.TestCubicCurveParabolic", curve.TestCubicCurveParabolic},
{"curve.TestQuadCurve", curve.TestQuadCurve},
}
var benchmarks = []testing.InternalBenchmark{{"curve.BenchmarkCubicCurveRec", curve.BenchmarkCubicCurveRec},
{"curve.BenchmarkCubicCurve", curve.BenchmarkCubicCurve},
{"curve.BenchmarkCubicCurveAdaptiveRec", curve.BenchmarkCubicCurveAdaptiveRec},
{"curve.BenchmarkCubicCurveAdaptive", curve.BenchmarkCubicCurveAdaptive},
{"curve.BenchmarkCubicCurveParabolic", curve.BenchmarkCubicCurveParabolic},
{"curve.BenchmarkQuadCurve", curve.BenchmarkQuadCurve},
}
var matchPat string
var matchRe *__regexp__.Regexp
func matchString(pat, str string) (result bool, err __os__.Error) {
if matchRe == nil || matchPat != pat {
matchPat = pat
matchRe, err = __regexp__.Compile(matchPat)
if err != nil {
return
}
}
return matchRe.MatchString(str), nil
}
func main() {
testing.Main(matchString, tests, benchmarks)
}

69
draw2d/curve/cubic_float64.go Normal file
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@ -0,0 +1,69 @@
// Copyright 2010 The draw2d Authors. All rights reserved.
// created: 17/05/2011 by Laurent Le Goff
package curve
import (
"math"
)
const (
CurveRecursionLimit = 32
)
type CubicCurveFloat64 struct {
X1, Y1, X2, Y2, X3, Y3, X4, Y4 float64
}
type LineTracer interface {
LineTo(x, y float64)
}
func (c *CubicCurveFloat64) Subdivide(c1, c2 *CubicCurveFloat64) (x23, y23 float64) {
// Calculate all the mid-points of the line segments
//----------------------
c1.X1, c1.Y1 = c.X1, c.Y1
c2.X4, c2.Y4 = c.X4, c.Y4
c1.X2 = (c.X1 + c.X2) / 2
c1.Y2 = (c.Y1 + c.Y2) / 2
x23 = (c.X2 + c.X3) / 2
y23 = (c.Y2 + c.Y3) / 2
c2.X3 = (c.X3 + c.X4) / 2
c2.Y3 = (c.Y3 + c.Y4) / 2
c1.X3 = (c1.X2 + x23) / 2
c1.Y3 = (c1.Y2 + y23) / 2
c2.X2 = (x23 + c2.X3) / 2
c2.Y2 = (y23 + c2.Y3) / 2
c1.X4 = (c1.X3 + c2.X2) / 2
c1.Y4 = (c1.Y3 + c2.Y2) / 2
c2.X1, c2.Y1 = c1.X4, c1.Y4
return
}
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
// current curve
var c *CubicCurveFloat64
var dx, dy, d2, d3 float64
for i >= 0 {
c = &curves[i]
dx = c.X4 - c.X1
dy = c.Y4 - c.Y1
d2 = math.Fabs(((c.X2-c.X4)*dy - (c.Y2-c.Y4)*dx))
d3 = math.Fabs(((c.X3-c.X4)*dy - (c.Y3-c.Y4)*dx))
if (d2+d3)*(d2+d3) < flattening_threshold*(dx*dx+dy*dy) || i == len(curves)-1 {
t.LineTo(c.X4, c.Y4)
i--
} else {
// second half of bezier go lower onto the stack
c.Subdivide(&curves[i+1], &curves[i])
i++
}
}
}

59
draw2d/curve/curve_float64.go → draw2d/curve/cubic_float64_others.go
View file

@ -7,19 +7,10 @@ import (
)
const (
CurveRecursionLimit = 32
CurveCollinearityEpsilon = 1e-30
CurveAngleToleranceEpsilon = 0.01
)
type CubicCurveFloat64 struct {
X1, Y1, X2, Y2, X3, Y3, X4, Y4 float64
}
type LineTracer interface {
LineTo(x, y float64)
}
//mu ranges from 0 to 1, start to end of curve
func (c *CubicCurveFloat64) ArbitraryPoint(mu float64) (x, y float64) {
@ -60,27 +51,6 @@ func (c *CubicCurveFloat64) SubdivideAt(c1, c2 *CubicCurveFloat64, t float64) (x
return
}
func (c *CubicCurveFloat64) Subdivide(c1, c2 *CubicCurveFloat64) (x23, y23 float64) {
// Calculate all the mid-points of the line segments
//----------------------
c1.X1, c1.Y1 = c.X1, c.Y1
c2.X4, c2.Y4 = c.X4, c.Y4
c1.X2 = (c.X1 + c.X2) / 2
c1.Y2 = (c.Y1 + c.Y2) / 2
x23 = (c.X2 + c.X3) / 2
y23 = (c.Y2 + c.Y3) / 2
c2.X3 = (c.X3 + c.X4) / 2
c2.Y3 = (c.Y3 + c.Y4) / 2
c1.X3 = (c1.X2 + x23) / 2
c1.Y3 = (c1.Y2 + y23) / 2
c2.X2 = (x23 + c2.X3) / 2
c2.Y2 = (y23 + c2.Y3) / 2
c1.X4 = (c1.X3 + c2.X2) / 2
c1.Y4 = (c1.Y3 + c2.Y2) / 2
c2.X1, c2.Y1 = c1.X4, c1.Y4
return
}
func (c *CubicCurveFloat64) EstimateDistance() float64 {
dx1 := c.X2 - c.X1
dy1 := c.Y2 - c.Y1
@ -121,35 +91,6 @@ func (c *CubicCurveFloat64) segmentRec(t LineTracer, flattening_threshold float6
c2.segmentRec(t, flattening_threshold)
}
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
// current curve
var c *CubicCurveFloat64
var dx, dy, d2, d3 float64
for i >= 0 {
c = &curves[i]
dx = c.X4 - c.X1
dy = c.Y4 - c.Y1
d2 = math.Fabs(((c.X2-c.X4)*dy - (c.Y2-c.Y4)*dx))
d3 = math.Fabs(((c.X3-c.X4)*dy - (c.Y3-c.Y4)*dx))
if (d2+d3)*(d2+d3) < flattening_threshold*(dx*dx+dy*dy) || i == len(curves)-1 {
t.LineTo(c.X4, c.Y4)
i--
} else {
// second half of bezier go lower onto the stack
c.Subdivide(&curves[i+1], &curves[i])
i++
}
}
}
/*
The function has the following parameters:
approximationScale :

59
draw2d/curve/curve_test.go
View file

@ -15,7 +15,7 @@ import (
var (
flattening_threshold float64 = 0.25
testsFloat64 = []CubicCurveFloat64{
testsCubicFloat64 = []CubicCurveFloat64{
CubicCurveFloat64{100, 100, 200, 100, 100, 200, 200, 200},
CubicCurveFloat64{100, 100, 300, 200, 200, 200, 300, 100},
CubicCurveFloat64{100, 100, 0, 300, 200, 0, 300, 300},
@ -23,6 +23,14 @@ var (
CubicCurveFloat64{10, 290, 10, 10, 290, 10, 290, 290},
CubicCurveFloat64{100, 290, 290, 10, 10, 10, 200, 290},
}
testsQuadFloat64 = []QuadCurveFloat64{
QuadCurveFloat64{100, 100, 200, 100, 200, 200},
QuadCurveFloat64{100, 100, 290, 200, 290, 100},
QuadCurveFloat64{100, 100, 0, 290, 200, 290},
QuadCurveFloat64{150, 290, 10, 10, 290, 290},
QuadCurveFloat64{10, 290, 10, 10, 290, 290},
QuadCurveFloat64{100, 290, 290, 10, 120, 290},
}
)
type Path struct {
@ -50,9 +58,12 @@ func init() {
defer f.Close()
log.Printf("Create html viewer")
f.Write([]byte("<html><body>"))
for i := 0; i < len(testsFloat64); i++ {
for i := 0; i < len(testsCubicFloat64); i++ {
f.Write([]byte(fmt.Sprintf("<div><img src='_testRec%d.png'/>\n<img src='_test%d.png'/>\n<img src='_testAdaptiveRec%d.png'/>\n<img src='_testAdaptive%d.png'/>\n<img src='_testParabolic%d.png'/>\n</div>\n", i, i, i, i, i)))
}
for i := 0; i < len(testsQuadFloat64); i++ {
f.Write([]byte(fmt.Sprintf("<div><img src='_testQuad%d.png'/>\n</div>\n", i)))
}
f.Write([]byte("</body></html>"))
}
@ -95,7 +106,7 @@ func drawPoints(img draw.Image, c image.Color, s ...float64) image.Image {
}
func TestCubicCurveRec(t *testing.T) {
for i, curve := range testsFloat64 {
for i, curve := range testsCubicFloat64 {
var p Path
curve.SegmentRec(&p, flattening_threshold)
img := image.NewNRGBA(300, 300)
@ -110,7 +121,7 @@ func TestCubicCurveRec(t *testing.T) {
}
func TestCubicCurve(t *testing.T) {
for i, curve := range testsFloat64 {
for i, curve := range testsCubicFloat64 {
var p Path
curve.Segment(&p, flattening_threshold)
img := image.NewNRGBA(300, 300)
@ -125,7 +136,7 @@ func TestCubicCurve(t *testing.T) {
}
func TestCubicCurveAdaptiveRec(t *testing.T) {
for i, curve := range testsFloat64 {
for i, curve := range testsCubicFloat64 {
var p Path
curve.AdaptiveSegmentRec(&p, 1, 0, 0)
img := image.NewNRGBA(300, 300)
@ -140,7 +151,7 @@ func TestCubicCurveAdaptiveRec(t *testing.T) {
}
func TestCubicCurveAdaptive(t *testing.T) {
for i, curve := range testsFloat64 {
for i, curve := range testsCubicFloat64 {
var p Path
curve.AdaptiveSegment(&p, 1, 0, 0)
img := image.NewNRGBA(300, 300)
@ -155,7 +166,7 @@ func TestCubicCurveAdaptive(t *testing.T) {
}
func TestCubicCurveParabolic(t *testing.T) {
for i, curve := range testsFloat64 {
for i, curve := range testsCubicFloat64 {
var p Path
curve.ParabolicSegment(&p, flattening_threshold)
img := image.NewNRGBA(300, 300)
@ -169,9 +180,24 @@ func TestCubicCurveParabolic(t *testing.T) {
fmt.Println()
}
func TestQuadCurve(t *testing.T) {
for i, curve := range testsQuadFloat64 {
var p Path
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)
raster.PolylineBresenham(img, image.Black, p.points...)
drawPoints(img, image.NRGBAColor{0, 0, 0, 0xff}, p.points...)
savepng(fmt.Sprintf("_testQuad%d.png", i), img)
log.Printf("Num of points: %d\n", len(p.points))
}
fmt.Println()
}
func BenchmarkCubicCurveRec(b *testing.B) {
for i := 0; i < b.N; i++ {
for _, curve := range testsFloat64 {
for _, curve := range testsCubicFloat64 {
p := Path{make([]float64, 0, 32)}
curve.SegmentRec(&p, flattening_threshold)
}
@ -180,7 +206,7 @@ func BenchmarkCubicCurveRec(b *testing.B) {
func BenchmarkCubicCurve(b *testing.B) {
for i := 0; i < b.N; i++ {
for _, curve := range testsFloat64 {
for _, curve := range testsCubicFloat64 {
p := Path{make([]float64, 0, 32)}
curve.Segment(&p, flattening_threshold)
}
@ -189,7 +215,7 @@ func BenchmarkCubicCurve(b *testing.B) {
func BenchmarkCubicCurveAdaptiveRec(b *testing.B) {
for i := 0; i < b.N; i++ {
for _, curve := range testsFloat64 {
for _, curve := range testsCubicFloat64 {
p := Path{make([]float64, 0, 32)}
curve.AdaptiveSegmentRec(&p, 1, 0, 0)
}
@ -198,7 +224,7 @@ func BenchmarkCubicCurveAdaptiveRec(b *testing.B) {
func BenchmarkCubicCurveAdaptive(b *testing.B) {
for i := 0; i < b.N; i++ {
for _, curve := range testsFloat64 {
for _, curve := range testsCubicFloat64 {
p := Path{make([]float64, 0, 32)}
curve.AdaptiveSegment(&p, 1, 0, 0)
}
@ -207,9 +233,18 @@ func BenchmarkCubicCurveAdaptive(b *testing.B) {
func BenchmarkCubicCurveParabolic(b *testing.B) {
for i := 0; i < b.N; i++ {
for _, curve := range testsFloat64 {
for _, curve := range testsCubicFloat64 {
p := Path{make([]float64, 0, 32)}
curve.ParabolicSegment(&p, flattening_threshold)
}
}
}
func BenchmarkQuadCurve(b *testing.B) {
for i := 0; i < b.N; i++ {
for _, curve := range testsQuadFloat64 {
p := Path{make([]float64, 0, 32)}
curve.Segment(&p, flattening_threshold)
}
}
}

56
draw2d/curve/quad_float64.go Normal file
View file

@ -0,0 +1,56 @@
// Copyright 2010 The draw2d Authors. All rights reserved.
// created: 17/05/2011 by Laurent Le Goff
package curve
import (
"math"
)
type QuadCurveFloat64 struct {
X1, Y1, X2, Y2, X3, Y3 float64
}
func (c *QuadCurveFloat64) Subdivide(c1, c2 *QuadCurveFloat64) {
// Calculate all the mid-points of the line segments
//----------------------
c1.X1, c1.Y1 = c.X1, c.Y1
c2.X3, c2.Y3 = c.X3, c.Y3
c1.X2 = (c.X1 + c.X2) / 2
c1.Y2 = (c.Y1 + c.Y2) / 2
c2.X2 = (c.X2 + c.X3) / 2
c2.Y2 = (c.Y2 + c.Y3) / 2
c1.X3 = (c1.X2 + c2.X2) / 2
c1.Y3 = (c1.Y2 + c2.Y2) / 2
c2.X1, c2.Y1 = c1.X3, c1.Y3
return
}
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
// current curve
var c *QuadCurveFloat64
var dx, dy, d float64
for i >= 0 {
c = &curves[i]
dx = c.X3 - c.X1
dy = c.Y3 - c.Y1
d = math.Fabs(((c.X2-c.X3)*dy - (c.Y2-c.Y3)*dx))
if (d*d) < flattening_threshold*(dx*dx+dy*dy) || i == len(curves)-1 {
t.LineTo(c.X3, c.Y3)
i--
} else {
// second half of bezier go lower onto the stack
c.Subdivide(&curves[i+1], &curves[i])
i++
}
}
}