Clean curve package
This commit is contained in:
Laurent Le Goff
parent
f8fb5a2052
commit
216d3f60dd
6 changed files with 65 additions and 864 deletions
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@ -1,12 +1,14 @@
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// Copyright 2010 The draw2d Authors. All rights reserved.
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// Copyright 2010 The draw2d Authors. All rights reserved.
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// created: 21/11/2010 by Laurent Le Goff
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// created: 21/11/2010 by Laurent Le Goff
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package curve
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package curve
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import (
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import (
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"math"
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"math"
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)
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)
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func SegmentArc(t LineTracer, x, y, rx, ry, start, angle, scale float64) {
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// TraceArc trace an arc using a LineTracer
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func TraceArc(t LineTracer, x, y, rx, ry, start, angle, scale float64) {
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end := start + angle
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end := start + angle
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clockWise := true
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clockWise := true
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if angle < 0 {
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if angle < 0 {
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@ -1,5 +1,7 @@
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// Copyright 2010 The draw2d Authors. All rights reserved.
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// Copyright 2010 The draw2d Authors. All rights reserved.
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// created: 17/05/2011 by Laurent Le Goff
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// created: 17/05/2011 by Laurent Le Goff
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// Package curve implements Bezier Curve Subdivision using De Casteljau's algorithm
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package curve
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package curve
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import (
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import (
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@ -10,38 +12,48 @@ const (
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CurveRecursionLimit = 32
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CurveRecursionLimit = 32
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)
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)
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// X1, Y1, X2, Y2, X3, Y3, X4, Y4 float64
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// x1, y1, cpx1, cpx2, cpx2, cpy2, x2, y2 float64
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type CubicCurveFloat64 [8]float64
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type CubicCurveFloat64 [8]float64
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type LineTracer interface {
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// Subdivide a Bezier cubic curve in 2 equivalents Bezier cubic curves.
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LineTo(x, y float64)
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// c1 and c2 parameters are the resulting curves
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}
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func (c *CubicCurveFloat64) Subdivide(c1, c2 *CubicCurveFloat64) {
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// First point of c is the first point of c1
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func (c *CubicCurveFloat64) Subdivide(c1, c2 *CubicCurveFloat64) (x23, y23 float64) {
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// Calculate all the mid-points of the line segments
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//----------------------
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c1[0], c1[1] = c[0], c[1]
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c1[0], c1[1] = c[0], c[1]
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// Last point of c is the last point of c2
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c2[6], c2[7] = c[6], c[7]
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c2[6], c2[7] = c[6], c[7]
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// Subdivide segment using midpoints
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c1[2] = (c[0] + c[2]) / 2
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c1[2] = (c[0] + c[2]) / 2
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c1[3] = (c[1] + c[3]) / 2
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c1[3] = (c[1] + c[3]) / 2
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x23 = (c[2] + c[4]) / 2
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y23 = (c[3] + c[5]) / 2
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midX := (c[2] + c[4]) / 2
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midY := (c[3] + c[5]) / 2
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c2[4] = (c[4] + c[6]) / 2
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c2[4] = (c[4] + c[6]) / 2
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c2[5] = (c[5] + c[7]) / 2
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c2[5] = (c[5] + c[7]) / 2
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c1[4] = (c1[2] + x23) / 2
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c1[5] = (c1[3] + y23) / 2
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c1[4] = (c1[2] + midX) / 2
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c2[2] = (x23 + c2[4]) / 2
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c1[5] = (c1[3] + midY) / 2
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c2[3] = (y23 + c2[5]) / 2
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c2[2] = (midX + c2[4]) / 2
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c2[3] = (midY + c2[5]) / 2
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c1[6] = (c1[4] + c2[2]) / 2
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c1[6] = (c1[4] + c2[2]) / 2
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c1[7] = (c1[5] + c2[3]) / 2
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c1[7] = (c1[5] + c2[3]) / 2
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// Last Point of c1 is equal to the first point of c2
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c2[0], c2[1] = c1[6], c1[7]
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c2[0], c2[1] = c1[6], c1[7]
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return
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}
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}
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func (curve *CubicCurveFloat64) Segment(t LineTracer, flattening_threshold float64) {
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// Trace generate lines subdividing the curve using a LineTracer
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// flattening_threshold helps determines the flattening expectation of the curve
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func (curve *CubicCurveFloat64) Trace(t LineTracer, flattening_threshold float64) {
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// Allocation curves
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var curves [CurveRecursionLimit]CubicCurveFloat64
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var curves [CurveRecursionLimit]CubicCurveFloat64
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curves[0] = *curve
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curves[0] = *curve
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i := 0
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i := 0
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// current curve
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// current curve
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var c *CubicCurveFloat64
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var c *CubicCurveFloat64
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@ -52,9 +64,10 @@ func (curve *CubicCurveFloat64) Segment(t LineTracer, flattening_threshold float
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dx = c[6] - c[0]
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dx = c[6] - c[0]
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dy = c[7] - c[1]
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dy = c[7] - c[1]
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d2 = math.Abs(((c[2]-c[6])*dy - (c[3]-c[7])*dx))
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d2 = math.Abs((c[2]-c[6])*dy - (c[3]-c[7])*dx)
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d3 = math.Abs(((c[4]-c[6])*dy - (c[5]-c[7])*dx))
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d3 = math.Abs((c[4]-c[6])*dy - (c[5]-c[7])*dx)
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// if it's flat then trace a line
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if (d2+d3)*(d2+d3) < flattening_threshold*(dx*dx+dy*dy) || i == len(curves)-1 {
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if (d2+d3)*(d2+d3) < flattening_threshold*(dx*dx+dy*dy) || i == len(curves)-1 {
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t.LineTo(c[6], c[7])
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t.LineTo(c[6], c[7])
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i--
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i--
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@ -1,696 +0,0 @@
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// Copyright 2010 The draw2d Authors. All rights reserved.
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// created: 17/05/2011 by Laurent Le Goff
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package curve
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import (
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"math"
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)
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const (
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CurveCollinearityEpsilon = 1e-30
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CurveAngleToleranceEpsilon = 0.01
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)
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//mu ranges from 0 to 1, start to end of curve
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func (c *CubicCurveFloat64) ArbitraryPoint(mu float64) (x, y float64) {
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mum1 := 1 - mu
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mum13 := mum1 * mum1 * mum1
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mu3 := mu * mu * mu
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x = mum13*c[0] + 3*mu*mum1*mum1*c[2] + 3*mu*mu*mum1*c[4] + mu3*c[6]
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y = mum13*c[1] + 3*mu*mum1*mum1*c[3] + 3*mu*mu*mum1*c[5] + mu3*c[7]
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return
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}
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func (c *CubicCurveFloat64) SubdivideAt(c1, c2 *CubicCurveFloat64, t float64) (x23, y23 float64) {
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inv_t := (1 - t)
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c1[0], c1[1] = c[0], c[1]
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c2[6], c2[7] = c[6], c[7]
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c1[2] = inv_t*c[0] + t*c[2]
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c1[3] = inv_t*c[1] + t*c[3]
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x23 = inv_t*c[2] + t*c[4]
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y23 = inv_t*c[3] + t*c[5]
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c2[4] = inv_t*c[4] + t*c[6]
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c2[5] = inv_t*c[5] + t*c[7]
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c1[4] = inv_t*c1[2] + t*x23
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c1[5] = inv_t*c1[3] + t*y23
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c2[2] = inv_t*x23 + t*c2[4]
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c2[3] = inv_t*y23 + t*c2[5]
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c1[6] = inv_t*c1[4] + t*c2[2]
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c1[7] = inv_t*c1[5] + t*c2[3]
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c2[0], c2[1] = c1[6], c1[7]
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return
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}
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func (c *CubicCurveFloat64) EstimateDistance() float64 {
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dx1 := c[2] - c[0]
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dy1 := c[3] - c[1]
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dx2 := c[4] - c[2]
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dy2 := c[5] - c[3]
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dx3 := c[6] - c[4]
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dy3 := c[7] - c[5]
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return math.Sqrt(dx1*dx1+dy1*dy1) + math.Sqrt(dx2*dx2+dy2*dy2) + math.Sqrt(dx3*dx3+dy3*dy3)
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}
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// subdivide the curve in straight lines using line approximation and Casteljau recursive subdivision
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func (c *CubicCurveFloat64) SegmentRec(t LineTracer, flattening_threshold float64) {
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c.segmentRec(t, flattening_threshold)
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t.LineTo(c[6], c[7])
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}
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func (c *CubicCurveFloat64) segmentRec(t LineTracer, flattening_threshold float64) {
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var c1, c2 CubicCurveFloat64
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c.Subdivide(&c1, &c2)
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// Try to approximate the full cubic curve by a single straight line
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//------------------
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dx := c[6] - c[0]
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dy := c[7] - c[1]
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d2 := math.Abs(((c[2]-c[6])*dy - (c[3]-c[7])*dx))
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d3 := math.Abs(((c[4]-c[6])*dy - (c[5]-c[7])*dx))
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if (d2+d3)*(d2+d3) < flattening_threshold*(dx*dx+dy*dy) {
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t.LineTo(c[6], c[7])
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return
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}
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// Continue subdivision
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//----------------------
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c1.segmentRec(t, flattening_threshold)
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c2.segmentRec(t, flattening_threshold)
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}
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/*
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The function has the following parameters:
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approximationScale :
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Eventually determines the approximation accuracy. In practice we need to transform points from the World coordinate system to the Screen one.
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It always has some scaling coefficient.
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The curves are usually processed in the World coordinates, while the approximation accuracy should be eventually in pixels.
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Usually it looks as follows:
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curved.approximationScale(transform.scale());
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where transform is the affine matrix that includes all the transformations, including viewport and zoom.
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angleTolerance :
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You set it in radians.
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The less this value is the more accurate will be the approximation at sharp turns.
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But 0 means that we don't consider angle conditions at all.
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cuspLimit :
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An angle in radians.
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If 0, only the real cusps will have bevel cuts.
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If more than 0, it will restrict the sharpness.
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The more this value is the less sharp turns will be cut.
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Typically it should not exceed 10-15 degrees.
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*/
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func (c *CubicCurveFloat64) AdaptiveSegmentRec(t LineTracer, approximationScale, angleTolerance, cuspLimit float64) {
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cuspLimit = computeCuspLimit(cuspLimit)
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distanceToleranceSquare := 0.5 / approximationScale
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distanceToleranceSquare = distanceToleranceSquare * distanceToleranceSquare
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c.adaptiveSegmentRec(t, 0, distanceToleranceSquare, angleTolerance, cuspLimit)
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t.LineTo(c[6], c[7])
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}
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func computeCuspLimit(v float64) (r float64) {
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if v == 0.0 {
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r = 0.0
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} else {
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r = math.Pi - v
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}
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return
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}
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func squareDistance(x1, y1, x2, y2 float64) float64 {
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dx := x2 - x1
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dy := y2 - y1
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return dx*dx + dy*dy
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}
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/**
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* http://www.antigrain.com/research/adaptive_bezier/index.html
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*/
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func (c *CubicCurveFloat64) adaptiveSegmentRec(t LineTracer, level int, distanceToleranceSquare, angleTolerance, cuspLimit float64) {
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if level > CurveRecursionLimit {
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return
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}
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var c1, c2 CubicCurveFloat64
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x23, y23 := c.Subdivide(&c1, &c2)
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// Try to approximate the full cubic curve by a single straight line
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//------------------
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dx := c[6] - c[0]
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dy := c[7] - c[1]
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d2 := math.Abs(((c[2]-c[6])*dy - (c[3]-c[7])*dx))
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d3 := math.Abs(((c[4]-c[6])*dy - (c[5]-c[7])*dx))
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switch {
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case d2 <= CurveCollinearityEpsilon && d3 <= CurveCollinearityEpsilon:
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// All collinear OR p1==p4
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//----------------------
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k := dx*dx + dy*dy
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if k == 0 {
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d2 = squareDistance(c[0], c[1], c[2], c[3])
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d3 = squareDistance(c[6], c[7], c[4], c[5])
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} else {
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k = 1 / k
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da1 := c[2] - c[0]
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da2 := c[3] - c[1]
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d2 = k * (da1*dx + da2*dy)
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da1 = c[4] - c[0]
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da2 = c[5] - c[1]
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d3 = k * (da1*dx + da2*dy)
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if d2 > 0 && d2 < 1 && d3 > 0 && d3 < 1 {
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// Simple collinear case, 1---2---3---4
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// We can leave just two endpoints
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return
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}
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if d2 <= 0 {
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d2 = squareDistance(c[2], c[3], c[0], c[1])
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} else if d2 >= 1 {
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d2 = squareDistance(c[2], c[3], c[6], c[7])
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} else {
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d2 = squareDistance(c[2], c[3], c[0]+d2*dx, c[1]+d2*dy)
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}
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if d3 <= 0 {
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d3 = squareDistance(c[4], c[5], c[0], c[1])
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} else if d3 >= 1 {
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d3 = squareDistance(c[4], c[5], c[6], c[7])
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} else {
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d3 = squareDistance(c[4], c[5], c[0]+d3*dx, c[1]+d3*dy)
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}
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}
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if d2 > d3 {
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if d2 < distanceToleranceSquare {
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t.LineTo(c[2], c[3])
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return
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}
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} else {
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if d3 < distanceToleranceSquare {
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t.LineTo(c[4], c[5])
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return
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}
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}
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case d2 <= CurveCollinearityEpsilon && d3 > CurveCollinearityEpsilon:
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// p1,p2,p4 are collinear, p3 is significant
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//----------------------
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if d3*d3 <= distanceToleranceSquare*(dx*dx+dy*dy) {
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if angleTolerance < CurveAngleToleranceEpsilon {
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t.LineTo(x23, y23)
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return
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}
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// Angle Condition
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//----------------------
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da1 := math.Abs(math.Atan2(c[7]-c[5], c[6]-c[4]) - math.Atan2(c[5]-c[3], c[4]-c[2]))
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if da1 >= math.Pi {
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da1 = 2*math.Pi - da1
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}
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if da1 < angleTolerance {
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t.LineTo(c[2], c[3])
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t.LineTo(c[4], c[5])
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return
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}
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if cuspLimit != 0.0 {
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if da1 > cuspLimit {
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t.LineTo(c[4], c[5])
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return
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}
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}
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}
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case d2 > CurveCollinearityEpsilon && d3 <= CurveCollinearityEpsilon:
|
|
||||||
// p1,p3,p4 are collinear, p2 is significant
|
|
||||||
//----------------------
|
|
||||||
if d2*d2 <= distanceToleranceSquare*(dx*dx+dy*dy) {
|
|
||||||
if angleTolerance < CurveAngleToleranceEpsilon {
|
|
||||||
t.LineTo(x23, y23)
|
|
||||||
return
|
|
||||||
}
|
|
||||||
|
|
||||||
// Angle Condition
|
|
||||||
//----------------------
|
|
||||||
da1 := math.Abs(math.Atan2(c[5]-c[3], c[4]-c[2]) - math.Atan2(c[3]-c[1], c[2]-c[0]))
|
|
||||||
if da1 >= math.Pi {
|
|
||||||
da1 = 2*math.Pi - da1
|
|
||||||
}
|
|
||||||
|
|
||||||
if da1 < angleTolerance {
|
|
||||||
t.LineTo(c[2], c[3])
|
|
||||||
t.LineTo(c[4], c[5])
|
|
||||||
return
|
|
||||||
}
|
|
||||||
|
|
||||||
if cuspLimit != 0.0 {
|
|
||||||
if da1 > cuspLimit {
|
|
||||||
t.LineTo(c[2], c[3])
|
|
||||||
return
|
|
||||||
}
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
case d2 > CurveCollinearityEpsilon && d3 > CurveCollinearityEpsilon:
|
|
||||||
// Regular case
|
|
||||||
//-----------------
|
|
||||||
if (d2+d3)*(d2+d3) <= distanceToleranceSquare*(dx*dx+dy*dy) {
|
|
||||||
// If the curvature doesn't exceed the distanceTolerance value
|
|
||||||
// we tend to finish subdivisions.
|
|
||||||
//----------------------
|
|
||||||
if angleTolerance < CurveAngleToleranceEpsilon {
|
|
||||||
t.LineTo(x23, y23)
|
|
||||||
return
|
|
||||||
}
|
|
||||||
|
|
||||||
// Angle & Cusp Condition
|
|
||||||
//----------------------
|
|
||||||
k := math.Atan2(c[5]-c[3], c[4]-c[2])
|
|
||||||
da1 := math.Abs(k - math.Atan2(c[3]-c[1], c[2]-c[0]))
|
|
||||||
da2 := math.Abs(math.Atan2(c[7]-c[5], c[6]-c[4]) - k)
|
|
||||||
if da1 >= math.Pi {
|
|
||||||
da1 = 2*math.Pi - da1
|
|
||||||
}
|
|
||||||
if da2 >= math.Pi {
|
|
||||||
da2 = 2*math.Pi - da2
|
|
||||||
}
|
|
||||||
|
|
||||||
if da1+da2 < angleTolerance {
|
|
||||||
// Finally we can stop the recursion
|
|
||||||
//----------------------
|
|
||||||
t.LineTo(x23, y23)
|
|
||||||
return
|
|
||||||
}
|
|
||||||
|
|
||||||
if cuspLimit != 0.0 {
|
|
||||||
if da1 > cuspLimit {
|
|
||||||
t.LineTo(c[2], c[3])
|
|
||||||
return
|
|
||||||
}
|
|
||||||
|
|
||||||
if da2 > cuspLimit {
|
|
||||||
t.LineTo(c[4], c[5])
|
|
||||||
return
|
|
||||||
}
|
|
||||||
}
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
// Continue subdivision
|
|
||||||
//----------------------
|
|
||||||
c1.adaptiveSegmentRec(t, level+1, distanceToleranceSquare, angleTolerance, cuspLimit)
|
|
||||||
c2.adaptiveSegmentRec(t, level+1, distanceToleranceSquare, angleTolerance, cuspLimit)
|
|
||||||
|
|
||||||
}
|
|
||||||
|
|
||||||
func (curve *CubicCurveFloat64) AdaptiveSegment(t LineTracer, approximationScale, angleTolerance, cuspLimit float64) {
|
|
||||||
cuspLimit = computeCuspLimit(cuspLimit)
|
|
||||||
distanceToleranceSquare := 0.5 / approximationScale
|
|
||||||
distanceToleranceSquare = distanceToleranceSquare * distanceToleranceSquare
|
|
||||||
|
|
||||||
var curves [CurveRecursionLimit]CubicCurveFloat64
|
|
||||||
curves[0] = *curve
|
|
||||||
i := 0
|
|
||||||
// current curve
|
|
||||||
var c *CubicCurveFloat64
|
|
||||||
var c1, c2 CubicCurveFloat64
|
|
||||||
var dx, dy, d2, d3, k, x23, y23 float64
|
|
||||||
for i >= 0 {
|
|
||||||
c = &curves[i]
|
|
||||||
x23, y23 = c.Subdivide(&c1, &c2)
|
|
||||||
|
|
||||||
// Try to approximate the full cubic curve by a single straight line
|
|
||||||
//------------------
|
|
||||||
dx = c[6] - c[0]
|
|
||||||
dy = c[7] - c[1]
|
|
||||||
|
|
||||||
d2 = math.Abs(((c[2]-c[6])*dy - (c[3]-c[7])*dx))
|
|
||||||
d3 = math.Abs(((c[4]-c[6])*dy - (c[5]-c[7])*dx))
|
|
||||||
switch {
|
|
||||||
case i == len(curves)-1:
|
|
||||||
t.LineTo(c[6], c[7])
|
|
||||||
i--
|
|
||||||
continue
|
|
||||||
case d2 <= CurveCollinearityEpsilon && d3 <= CurveCollinearityEpsilon:
|
|
||||||
// All collinear OR p1==p4
|
|
||||||
//----------------------
|
|
||||||
k = dx*dx + dy*dy
|
|
||||||
if k == 0 {
|
|
||||||
d2 = squareDistance(c[0], c[1], c[2], c[3])
|
|
||||||
d3 = squareDistance(c[6], c[7], c[4], c[5])
|
|
||||||
} else {
|
|
||||||
k = 1 / k
|
|
||||||
da1 := c[2] - c[0]
|
|
||||||
da2 := c[3] - c[1]
|
|
||||||
d2 = k * (da1*dx + da2*dy)
|
|
||||||
da1 = c[4] - c[0]
|
|
||||||
da2 = c[5] - c[1]
|
|
||||||
d3 = k * (da1*dx + da2*dy)
|
|
||||||
if d2 > 0 && d2 < 1 && d3 > 0 && d3 < 1 {
|
|
||||||
// Simple collinear case, 1---2---3---4
|
|
||||||
// We can leave just two endpoints
|
|
||||||
i--
|
|
||||||
continue
|
|
||||||
}
|
|
||||||
if d2 <= 0 {
|
|
||||||
d2 = squareDistance(c[2], c[3], c[0], c[1])
|
|
||||||
} else if d2 >= 1 {
|
|
||||||
d2 = squareDistance(c[2], c[3], c[6], c[7])
|
|
||||||
} else {
|
|
||||||
d2 = squareDistance(c[2], c[3], c[0]+d2*dx, c[1]+d2*dy)
|
|
||||||
}
|
|
||||||
|
|
||||||
if d3 <= 0 {
|
|
||||||
d3 = squareDistance(c[4], c[5], c[0], c[1])
|
|
||||||
} else if d3 >= 1 {
|
|
||||||
d3 = squareDistance(c[4], c[5], c[6], c[7])
|
|
||||||
} else {
|
|
||||||
d3 = squareDistance(c[4], c[5], c[0]+d3*dx, c[1]+d3*dy)
|
|
||||||
}
|
|
||||||
}
|
|
||||||
if d2 > d3 {
|
|
||||||
if d2 < distanceToleranceSquare {
|
|
||||||
t.LineTo(c[2], c[3])
|
|
||||||
i--
|
|
||||||
continue
|
|
||||||
}
|
|
||||||
} else {
|
|
||||||
if d3 < distanceToleranceSquare {
|
|
||||||
t.LineTo(c[4], c[5])
|
|
||||||
i--
|
|
||||||
continue
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
case d2 <= CurveCollinearityEpsilon && d3 > CurveCollinearityEpsilon:
|
|
||||||
// p1,p2,p4 are collinear, p3 is significant
|
|
||||||
//----------------------
|
|
||||||
if d3*d3 <= distanceToleranceSquare*(dx*dx+dy*dy) {
|
|
||||||
if angleTolerance < CurveAngleToleranceEpsilon {
|
|
||||||
t.LineTo(x23, y23)
|
|
||||||
i--
|
|
||||||
continue
|
|
||||||
}
|
|
||||||
|
|
||||||
// Angle Condition
|
|
||||||
//----------------------
|
|
||||||
da1 := math.Abs(math.Atan2(c[7]-c[5], c[6]-c[4]) - math.Atan2(c[5]-c[3], c[4]-c[2]))
|
|
||||||
if da1 >= math.Pi {
|
|
||||||
da1 = 2*math.Pi - da1
|
|
||||||
}
|
|
||||||
|
|
||||||
if da1 < angleTolerance {
|
|
||||||
t.LineTo(c[2], c[3])
|
|
||||||
t.LineTo(c[4], c[5])
|
|
||||||
i--
|
|
||||||
continue
|
|
||||||
}
|
|
||||||
|
|
||||||
if cuspLimit != 0.0 {
|
|
||||||
if da1 > cuspLimit {
|
|
||||||
t.LineTo(c[4], c[5])
|
|
||||||
i--
|
|
||||||
continue
|
|
||||||
}
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
case d2 > CurveCollinearityEpsilon && d3 <= CurveCollinearityEpsilon:
|
|
||||||
// p1,p3,p4 are collinear, p2 is significant
|
|
||||||
//----------------------
|
|
||||||
if d2*d2 <= distanceToleranceSquare*(dx*dx+dy*dy) {
|
|
||||||
if angleTolerance < CurveAngleToleranceEpsilon {
|
|
||||||
t.LineTo(x23, y23)
|
|
||||||
i--
|
|
||||||
continue
|
|
||||||
}
|
|
||||||
|
|
||||||
// Angle Condition
|
|
||||||
//----------------------
|
|
||||||
da1 := math.Abs(math.Atan2(c[5]-c[3], c[4]-c[2]) - math.Atan2(c[3]-c[1], c[2]-c[0]))
|
|
||||||
if da1 >= math.Pi {
|
|
||||||
da1 = 2*math.Pi - da1
|
|
||||||
}
|
|
||||||
|
|
||||||
if da1 < angleTolerance {
|
|
||||||
t.LineTo(c[2], c[3])
|
|
||||||
t.LineTo(c[4], c[5])
|
|
||||||
i--
|
|
||||||
continue
|
|
||||||
}
|
|
||||||
|
|
||||||
if cuspLimit != 0.0 {
|
|
||||||
if da1 > cuspLimit {
|
|
||||||
t.LineTo(c[2], c[3])
|
|
||||||
i--
|
|
||||||
continue
|
|
||||||
}
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
case d2 > CurveCollinearityEpsilon && d3 > CurveCollinearityEpsilon:
|
|
||||||
// Regular case
|
|
||||||
//-----------------
|
|
||||||
if (d2+d3)*(d2+d3) <= distanceToleranceSquare*(dx*dx+dy*dy) {
|
|
||||||
// If the curvature doesn't exceed the distanceTolerance value
|
|
||||||
// we tend to finish subdivisions.
|
|
||||||
//----------------------
|
|
||||||
if angleTolerance < CurveAngleToleranceEpsilon {
|
|
||||||
t.LineTo(x23, y23)
|
|
||||||
i--
|
|
||||||
continue
|
|
||||||
}
|
|
||||||
|
|
||||||
// Angle & Cusp Condition
|
|
||||||
//----------------------
|
|
||||||
k := math.Atan2(c[5]-c[3], c[4]-c[2])
|
|
||||||
da1 := math.Abs(k - math.Atan2(c[3]-c[1], c[2]-c[0]))
|
|
||||||
da2 := math.Abs(math.Atan2(c[7]-c[5], c[6]-c[4]) - k)
|
|
||||||
if da1 >= math.Pi {
|
|
||||||
da1 = 2*math.Pi - da1
|
|
||||||
}
|
|
||||||
if da2 >= math.Pi {
|
|
||||||
da2 = 2*math.Pi - da2
|
|
||||||
}
|
|
||||||
|
|
||||||
if da1+da2 < angleTolerance {
|
|
||||||
// Finally we can stop the recursion
|
|
||||||
//----------------------
|
|
||||||
t.LineTo(x23, y23)
|
|
||||||
i--
|
|
||||||
continue
|
|
||||||
}
|
|
||||||
|
|
||||||
if cuspLimit != 0.0 {
|
|
||||||
if da1 > cuspLimit {
|
|
||||||
t.LineTo(c[2], c[3])
|
|
||||||
i--
|
|
||||||
continue
|
|
||||||
}
|
|
||||||
|
|
||||||
if da2 > cuspLimit {
|
|
||||||
t.LineTo(c[4], c[5])
|
|
||||||
i--
|
|
||||||
continue
|
|
||||||
}
|
|
||||||
}
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
// Continue subdivision
|
|
||||||
//----------------------
|
|
||||||
curves[i+1], curves[i] = c1, c2
|
|
||||||
i++
|
|
||||||
}
|
|
||||||
t.LineTo(curve[6], curve[7])
|
|
||||||
}
|
|
||||||
|
|
||||||
/********************** Ahmad thesis *******************/
|
|
||||||
|
|
||||||
/**************************************************************************************
|
|
||||||
* This code is the implementation of the Parabolic Approximation (PA). Although *
|
|
||||||
* it uses recursive subdivision as a safe net for the failing cases, this is an *
|
|
||||||
* iterative routine and reduces considerably the number of vertices (point) *
|
|
||||||
* generation. *
|
|
||||||
**************************************************************************************/
|
|
||||||
|
|
||||||
func (c *CubicCurveFloat64) ParabolicSegment(t LineTracer, flattening_threshold float64) {
|
|
||||||
estimatedIFP := c.numberOfInflectionPoints()
|
|
||||||
if estimatedIFP == 0 {
|
|
||||||
// If no inflection points then apply PA on the full Bezier segment.
|
|
||||||
c.doParabolicApproximation(t, flattening_threshold)
|
|
||||||
return
|
|
||||||
}
|
|
||||||
// If one or more inflection point then we will have to subdivide the curve
|
|
||||||
numOfIfP, t1, t2 := c.findInflectionPoints()
|
|
||||||
if numOfIfP == 2 {
|
|
||||||
// Case when 2 inflection points then divide at the smallest one first
|
|
||||||
var sub1, tmp1, sub2, sub3 CubicCurveFloat64
|
|
||||||
c.SubdivideAt(&sub1, &tmp1, t1)
|
|
||||||
// Now find the second inflection point in the second curve an subdivide
|
|
||||||
numOfIfP, t1, t2 = tmp1.findInflectionPoints()
|
|
||||||
if numOfIfP == 2 {
|
|
||||||
tmp1.SubdivideAt(&sub2, &sub3, t2)
|
|
||||||
} else if numOfIfP == 1 {
|
|
||||||
tmp1.SubdivideAt(&sub2, &sub3, t1)
|
|
||||||
} else {
|
|
||||||
return
|
|
||||||
}
|
|
||||||
// Use PA for first subsegment
|
|
||||||
sub1.doParabolicApproximation(t, flattening_threshold)
|
|
||||||
// Use RS for the second (middle) subsegment
|
|
||||||
sub2.Segment(t, flattening_threshold)
|
|
||||||
// Drop the last point in the array will be added by the PA in third subsegment
|
|
||||||
//noOfPoints--;
|
|
||||||
// Use PA for the third curve
|
|
||||||
sub3.doParabolicApproximation(t, flattening_threshold)
|
|
||||||
} else if numOfIfP == 1 {
|
|
||||||
// Case where there is one inflection point, subdivide once and use PA on
|
|
||||||
// both subsegments
|
|
||||||
var sub1, sub2 CubicCurveFloat64
|
|
||||||
c.SubdivideAt(&sub1, &sub2, t1)
|
|
||||||
sub1.doParabolicApproximation(t, flattening_threshold)
|
|
||||||
//noOfPoints--;
|
|
||||||
sub2.doParabolicApproximation(t, flattening_threshold)
|
|
||||||
} else {
|
|
||||||
// Case where there is no inflection USA PA directly
|
|
||||||
c.doParabolicApproximation(t, flattening_threshold)
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
// Find the third control point deviation form the axis
|
|
||||||
func (c *CubicCurveFloat64) thirdControlPointDeviation() float64 {
|
|
||||||
dx := c[2] - c[0]
|
|
||||||
dy := c[3] - c[1]
|
|
||||||
l2 := dx*dx + dy*dy
|
|
||||||
if l2 == 0 {
|
|
||||||
return 0
|
|
||||||
}
|
|
||||||
l := math.Sqrt(l2)
|
|
||||||
r := (c[3] - c[1]) / l
|
|
||||||
s := (c[0] - c[2]) / l
|
|
||||||
u := (c[2]*c[1] - c[0]*c[3]) / l
|
|
||||||
return math.Abs(r*c[4] + s*c[5] + u)
|
|
||||||
}
|
|
||||||
|
|
||||||
// Find the number of inflection point
|
|
||||||
func (c *CubicCurveFloat64) numberOfInflectionPoints() int {
|
|
||||||
dx21 := (c[2] - c[0])
|
|
||||||
dy21 := (c[3] - c[1])
|
|
||||||
dx32 := (c[4] - c[2])
|
|
||||||
dy32 := (c[5] - c[3])
|
|
||||||
dx43 := (c[6] - c[4])
|
|
||||||
dy43 := (c[7] - c[5])
|
|
||||||
if ((dx21*dy32 - dy21*dx32) * (dx32*dy43 - dy32*dx43)) < 0 {
|
|
||||||
return 1 // One inflection point
|
|
||||||
} else if ((dx21*dy32 - dy21*dx32) * (dx21*dy43 - dy21*dx43)) > 0 {
|
|
||||||
return 0 // No inflection point
|
|
||||||
} else {
|
|
||||||
// Most cases no inflection point
|
|
||||||
b1 := (dx21*dx32 + dy21*dy32) > 0
|
|
||||||
b2 := (dx32*dx43 + dy32*dy43) > 0
|
|
||||||
if b1 || b2 && !(b1 && b2) { // xor!!
|
|
||||||
return 0
|
|
||||||
}
|
|
||||||
}
|
|
||||||
return -1 // cases where there in zero or two inflection points
|
|
||||||
}
|
|
||||||
|
|
||||||
// This is the main function where all the work is done
|
|
||||||
func (curve *CubicCurveFloat64) doParabolicApproximation(tracer LineTracer, flattening_threshold float64) {
|
|
||||||
var c *CubicCurveFloat64
|
|
||||||
c = curve
|
|
||||||
var d, t, dx, dy, d2, d3 float64
|
|
||||||
for {
|
|
||||||
dx = c[6] - c[0]
|
|
||||||
dy = c[7] - c[1]
|
|
||||||
|
|
||||||
d2 = math.Abs(((c[2]-c[6])*dy - (c[3]-c[7])*dx))
|
|
||||||
d3 = math.Abs(((c[4]-c[6])*dy - (c[5]-c[7])*dx))
|
|
||||||
|
|
||||||
if (d2+d3)*(d2+d3) < flattening_threshold*(dx*dx+dy*dy) {
|
|
||||||
// If the subsegment deviation satisfy the flatness then store the last
|
|
||||||
// point and stop
|
|
||||||
tracer.LineTo(c[6], c[7])
|
|
||||||
break
|
|
||||||
}
|
|
||||||
// Find the third control point deviation and the t values for subdivision
|
|
||||||
d = c.thirdControlPointDeviation()
|
|
||||||
t = 2 * math.Sqrt(flattening_threshold/d/3)
|
|
||||||
if t > 1 {
|
|
||||||
// Case where the t value calculated is invalid so using RS
|
|
||||||
c.Segment(tracer, flattening_threshold)
|
|
||||||
break
|
|
||||||
}
|
|
||||||
// Valid t value to subdivide at that calculated value
|
|
||||||
var b1, b2 CubicCurveFloat64
|
|
||||||
c.SubdivideAt(&b1, &b2, t)
|
|
||||||
// First subsegment should have its deviation equal to flatness
|
|
||||||
dx = b1[6] - b1[0]
|
|
||||||
dy = b1[7] - b1[1]
|
|
||||||
|
|
||||||
d2 = math.Abs(((b1[2]-b1[6])*dy - (b1[3]-b1[7])*dx))
|
|
||||||
d3 = math.Abs(((b1[4]-b1[6])*dy - (b1[5]-b1[7])*dx))
|
|
||||||
|
|
||||||
if (d2+d3)*(d2+d3) > flattening_threshold*(dx*dx+dy*dy) {
|
|
||||||
// if not then use RS to handle any mathematical errors
|
|
||||||
b1.Segment(tracer, flattening_threshold)
|
|
||||||
} else {
|
|
||||||
tracer.LineTo(b1[6], b1[7])
|
|
||||||
}
|
|
||||||
// repeat the process for the left over subsegment.
|
|
||||||
c = &b2
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
// Find the actual inflection points and return the number of inflection points found
|
|
||||||
// if 2 inflection points found, the first one returned will be with smaller t value.
|
|
||||||
func (curve *CubicCurveFloat64) findInflectionPoints() (int, firstIfp, secondIfp float64) {
|
|
||||||
// For Cubic Bezier curve with equation P=a*t^3 + b*t^2 + c*t + d
|
|
||||||
// slope of the curve dP/dt = 3*a*t^2 + 2*b*t + c
|
|
||||||
// a = (float)(-bez.p1 + 3*bez.p2 - 3*bez.p3 + bez.p4);
|
|
||||||
// b = (float)(3*bez.p1 - 6*bez.p2 + 3*bez.p3);
|
|
||||||
// c = (float)(-3*bez.p1 + 3*bez.p2);
|
|
||||||
ax := (-curve[0] + 3*curve[2] - 3*curve[4] + curve[6])
|
|
||||||
bx := (3*curve[0] - 6*curve[2] + 3*curve[4])
|
|
||||||
cx := (-3*curve[0] + 3*curve[2])
|
|
||||||
ay := (-curve[1] + 3*curve[3] - 3*curve[5] + curve[7])
|
|
||||||
by := (3*curve[1] - 6*curve[3] + 3*curve[5])
|
|
||||||
cy := (-3*curve[1] + 3*curve[3])
|
|
||||||
a := (3 * (ay*bx - ax*by))
|
|
||||||
b := (3 * (ay*cx - ax*cy))
|
|
||||||
c := (by*cx - bx*cy)
|
|
||||||
r2 := (b*b - 4*a*c)
|
|
||||||
firstIfp = 0.0
|
|
||||||
secondIfp = 0.0
|
|
||||||
if r2 >= 0.0 && a != 0.0 {
|
|
||||||
r := math.Sqrt(r2)
|
|
||||||
firstIfp = ((-b + r) / (2 * a))
|
|
||||||
secondIfp = ((-b - r) / (2 * a))
|
|
||||||
if (firstIfp > 0.0 && firstIfp < 1.0) && (secondIfp > 0.0 && secondIfp < 1.0) {
|
|
||||||
if firstIfp > secondIfp {
|
|
||||||
tmp := firstIfp
|
|
||||||
firstIfp = secondIfp
|
|
||||||
secondIfp = tmp
|
|
||||||
}
|
|
||||||
if secondIfp-firstIfp > 0.00001 {
|
|
||||||
return 2, firstIfp, secondIfp
|
|
||||||
} else {
|
|
||||||
return 1, firstIfp, secondIfp
|
|
||||||
}
|
|
||||||
} else if firstIfp > 0.0 && firstIfp < 1.0 {
|
|
||||||
return 1, firstIfp, secondIfp
|
|
||||||
} else if secondIfp > 0.0 && secondIfp < 1.0 {
|
|
||||||
firstIfp = secondIfp
|
|
||||||
return 1, firstIfp, secondIfp
|
|
||||||
}
|
|
||||||
return 0, firstIfp, secondIfp
|
|
||||||
}
|
|
||||||
return 0, firstIfp, secondIfp
|
|
||||||
}
|
|
||||||
|
|
@ -1,16 +1,15 @@
|
||||||
package curve
|
package curve
|
||||||
|
|
||||||
import (
|
import (
|
||||||
"bufio"
|
|
||||||
"fmt"
|
"fmt"
|
||||||
"image"
|
"image"
|
||||||
"image/color"
|
"image/color"
|
||||||
"image/draw"
|
"image/draw"
|
||||||
"image/png"
|
|
||||||
"log"
|
"log"
|
||||||
"os"
|
"os"
|
||||||
"testing"
|
"testing"
|
||||||
|
|
||||||
|
"github.com/llgcode/draw2d"
|
||||||
"github.com/llgcode/draw2d/raster"
|
"github.com/llgcode/draw2d/raster"
|
||||||
)
|
)
|
||||||
|
|
||||||
|
|
@ -51,7 +50,8 @@ func (p *Path) LineTo(x, y float64) {
|
||||||
}
|
}
|
||||||
|
|
||||||
func init() {
|
func init() {
|
||||||
f, err := os.Create("_test.html")
|
os.Mkdir("test_results", 0666)
|
||||||
|
f, err := os.Create("test_results/_test.html")
|
||||||
if err != nil {
|
if err != nil {
|
||||||
log.Println(err)
|
log.Println(err)
|
||||||
os.Exit(1)
|
os.Exit(1)
|
||||||
|
|
@ -60,7 +60,7 @@ func init() {
|
||||||
log.Printf("Create html viewer")
|
log.Printf("Create html viewer")
|
||||||
f.Write([]byte("<html><body>"))
|
f.Write([]byte("<html><body>"))
|
||||||
for i := 0; i < len(testsCubicFloat64); 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)))
|
f.Write([]byte(fmt.Sprintf("<div><img src='_test%d.png'/></div>\n", i)))
|
||||||
}
|
}
|
||||||
for i := 0; i < len(testsQuadFloat64); 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(fmt.Sprintf("<div><img src='_testQuad%d.png'/>\n</div>\n", i)))
|
||||||
|
|
@ -69,28 +69,8 @@ func init() {
|
||||||
|
|
||||||
}
|
}
|
||||||
|
|
||||||
func savepng(filePath string, m image.Image) {
|
|
||||||
f, err := os.Create(filePath)
|
|
||||||
if err != nil {
|
|
||||||
log.Println(err)
|
|
||||||
os.Exit(1)
|
|
||||||
}
|
|
||||||
defer f.Close()
|
|
||||||
b := bufio.NewWriter(f)
|
|
||||||
err = png.Encode(b, m)
|
|
||||||
if err != nil {
|
|
||||||
log.Println(err)
|
|
||||||
os.Exit(1)
|
|
||||||
}
|
|
||||||
err = b.Flush()
|
|
||||||
if err != nil {
|
|
||||||
log.Println(err)
|
|
||||||
os.Exit(1)
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
func drawPoints(img draw.Image, c color.Color, s ...float64) image.Image {
|
func drawPoints(img draw.Image, c color.Color, s ...float64) image.Image {
|
||||||
/*for i := 0; i < len(s); i += 2 {
|
for i := 0; i < len(s); i += 2 {
|
||||||
x, y := int(s[i]+0.5), int(s[i+1]+0.5)
|
x, y := int(s[i]+0.5), int(s[i+1]+0.5)
|
||||||
img.Set(x, y, c)
|
img.Set(x, y, c)
|
||||||
img.Set(x, y+1, c)
|
img.Set(x, y+1, c)
|
||||||
|
|
@ -102,85 +82,21 @@ func drawPoints(img draw.Image, c color.Color, s ...float64) image.Image {
|
||||||
img.Set(x-1, y+1, c)
|
img.Set(x-1, y+1, c)
|
||||||
img.Set(x-1, y-1, c)
|
img.Set(x-1, y-1, c)
|
||||||
|
|
||||||
}*/
|
}
|
||||||
return img
|
return img
|
||||||
}
|
}
|
||||||
|
|
||||||
func TestCubicCurveRec(t *testing.T) {
|
|
||||||
for i, curve := range testsCubicFloat64 {
|
|
||||||
var p Path
|
|
||||||
p.LineTo(curve[0], curve[1])
|
|
||||||
curve.SegmentRec(&p, flattening_threshold)
|
|
||||||
img := image.NewNRGBA(image.Rect(0, 0, 300, 300))
|
|
||||||
raster.PolylineBresenham(img, color.NRGBA{0xff, 0, 0, 0xff}, curve[:]...)
|
|
||||||
raster.PolylineBresenham(img, image.Black, p.points...)
|
|
||||||
//drawPoints(img, image.NRGBAColor{0, 0, 0, 0xff}, curve[:]...)
|
|
||||||
drawPoints(img, color.NRGBA{0, 0, 0, 0xff}, p.points...)
|
|
||||||
savepng(fmt.Sprintf("_testRec%d.png", i), img)
|
|
||||||
log.Printf("Num of points: %d\n", len(p.points))
|
|
||||||
}
|
|
||||||
fmt.Println()
|
|
||||||
}
|
|
||||||
|
|
||||||
func TestCubicCurve(t *testing.T) {
|
func TestCubicCurve(t *testing.T) {
|
||||||
for i, curve := range testsCubicFloat64 {
|
for i, curve := range testsCubicFloat64 {
|
||||||
var p Path
|
var p Path
|
||||||
p.LineTo(curve[0], curve[1])
|
p.LineTo(curve[0], curve[1])
|
||||||
curve.Segment(&p, flattening_threshold)
|
curve.Trace(&p, flattening_threshold)
|
||||||
img := image.NewNRGBA(image.Rect(0, 0, 300, 300))
|
img := image.NewNRGBA(image.Rect(0, 0, 300, 300))
|
||||||
raster.PolylineBresenham(img, color.NRGBA{0xff, 0, 0, 0xff}, curve[:]...)
|
raster.PolylineBresenham(img, color.NRGBA{0xff, 0, 0, 0xff}, curve[:]...)
|
||||||
raster.PolylineBresenham(img, image.Black, p.points...)
|
raster.PolylineBresenham(img, image.Black, p.points...)
|
||||||
//drawPoints(img, image.NRGBAColor{0, 0, 0, 0xff}, curve[:]...)
|
//drawPoints(img, image.NRGBAColor{0, 0, 0, 0xff}, curve[:]...)
|
||||||
drawPoints(img, color.NRGBA{0, 0, 0, 0xff}, p.points...)
|
drawPoints(img, color.NRGBA{0, 0, 0, 0xff}, p.points...)
|
||||||
savepng(fmt.Sprintf("_test%d.png", i), img)
|
draw2d.SaveToPngFile(fmt.Sprintf("test_results/_test%d.png", i), img)
|
||||||
log.Printf("Num of points: %d\n", len(p.points))
|
|
||||||
}
|
|
||||||
fmt.Println()
|
|
||||||
}
|
|
||||||
|
|
||||||
func TestCubicCurveAdaptiveRec(t *testing.T) {
|
|
||||||
for i, curve := range testsCubicFloat64 {
|
|
||||||
var p Path
|
|
||||||
p.LineTo(curve[0], curve[1])
|
|
||||||
curve.AdaptiveSegmentRec(&p, 1, 0, 0)
|
|
||||||
img := image.NewNRGBA(image.Rect(0, 0, 300, 300))
|
|
||||||
raster.PolylineBresenham(img, color.NRGBA{0xff, 0, 0, 0xff}, curve[:]...)
|
|
||||||
raster.PolylineBresenham(img, image.Black, p.points...)
|
|
||||||
//drawPoints(img, image.NRGBAColor{0, 0, 0, 0xff}, curve[:]...)
|
|
||||||
drawPoints(img, color.NRGBA{0, 0, 0, 0xff}, p.points...)
|
|
||||||
savepng(fmt.Sprintf("_testAdaptiveRec%d.png", i), img)
|
|
||||||
log.Printf("Num of points: %d\n", len(p.points))
|
|
||||||
}
|
|
||||||
fmt.Println()
|
|
||||||
}
|
|
||||||
|
|
||||||
func TestCubicCurveAdaptive(t *testing.T) {
|
|
||||||
for i, curve := range testsCubicFloat64 {
|
|
||||||
var p Path
|
|
||||||
p.LineTo(curve[0], curve[1])
|
|
||||||
curve.AdaptiveSegment(&p, 1, 0, 0)
|
|
||||||
img := image.NewNRGBA(image.Rect(0, 0, 300, 300))
|
|
||||||
raster.PolylineBresenham(img, color.NRGBA{0xff, 0, 0, 0xff}, curve[:]...)
|
|
||||||
raster.PolylineBresenham(img, image.Black, p.points...)
|
|
||||||
//drawPoints(img, image.NRGBAColor{0, 0, 0, 0xff}, curve[:]...)
|
|
||||||
drawPoints(img, color.NRGBA{0, 0, 0, 0xff}, p.points...)
|
|
||||||
savepng(fmt.Sprintf("_testAdaptive%d.png", i), img)
|
|
||||||
log.Printf("Num of points: %d\n", len(p.points))
|
|
||||||
}
|
|
||||||
fmt.Println()
|
|
||||||
}
|
|
||||||
|
|
||||||
func TestCubicCurveParabolic(t *testing.T) {
|
|
||||||
for i, curve := range testsCubicFloat64 {
|
|
||||||
var p Path
|
|
||||||
p.LineTo(curve[0], curve[1])
|
|
||||||
curve.ParabolicSegment(&p, flattening_threshold)
|
|
||||||
img := image.NewNRGBA(image.Rect(0, 0, 300, 300))
|
|
||||||
raster.PolylineBresenham(img, color.NRGBA{0xff, 0, 0, 0xff}, curve[:]...)
|
|
||||||
raster.PolylineBresenham(img, image.Black, p.points...)
|
|
||||||
//drawPoints(img, image.NRGBAColor{0, 0, 0, 0xff}, curve[:]...)
|
|
||||||
drawPoints(img, color.NRGBA{0, 0, 0, 0xff}, p.points...)
|
|
||||||
savepng(fmt.Sprintf("_testParabolic%d.png", i), img)
|
|
||||||
log.Printf("Num of points: %d\n", len(p.points))
|
log.Printf("Num of points: %d\n", len(p.points))
|
||||||
}
|
}
|
||||||
fmt.Println()
|
fmt.Println()
|
||||||
|
|
@ -190,74 +106,24 @@ func TestQuadCurve(t *testing.T) {
|
||||||
for i, curve := range testsQuadFloat64 {
|
for i, curve := range testsQuadFloat64 {
|
||||||
var p Path
|
var p Path
|
||||||
p.LineTo(curve[0], curve[1])
|
p.LineTo(curve[0], curve[1])
|
||||||
curve.Segment(&p, flattening_threshold)
|
curve.Trace(&p, flattening_threshold)
|
||||||
img := image.NewNRGBA(image.Rect(0, 0, 300, 300))
|
img := image.NewNRGBA(image.Rect(0, 0, 300, 300))
|
||||||
raster.PolylineBresenham(img, color.NRGBA{0xff, 0, 0, 0xff}, curve[:]...)
|
raster.PolylineBresenham(img, color.NRGBA{0xff, 0, 0, 0xff}, curve[:]...)
|
||||||
raster.PolylineBresenham(img, image.Black, p.points...)
|
raster.PolylineBresenham(img, image.Black, p.points...)
|
||||||
//drawPoints(img, image.NRGBAColor{0, 0, 0, 0xff}, curve[:]...)
|
//drawPoints(img, image.NRGBAColor{0, 0, 0, 0xff}, curve[:]...)
|
||||||
drawPoints(img, color.NRGBA{0, 0, 0, 0xff}, p.points...)
|
drawPoints(img, color.NRGBA{0, 0, 0, 0xff}, p.points...)
|
||||||
savepng(fmt.Sprintf("_testQuad%d.png", i), img)
|
draw2d.SaveToPngFile(fmt.Sprintf("test_results/_testQuad%d.png", i), img)
|
||||||
log.Printf("Num of points: %d\n", len(p.points))
|
log.Printf("Num of points: %d\n", len(p.points))
|
||||||
}
|
}
|
||||||
fmt.Println()
|
fmt.Println()
|
||||||
}
|
}
|
||||||
|
|
||||||
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[0], curve[1])
|
|
||||||
curve.SegmentRec(&p, flattening_threshold)
|
|
||||||
}
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
func BenchmarkCubicCurve(b *testing.B) {
|
func BenchmarkCubicCurve(b *testing.B) {
|
||||||
for i := 0; i < b.N; i++ {
|
for i := 0; i < b.N; i++ {
|
||||||
for _, curve := range testsCubicFloat64 {
|
for _, curve := range testsCubicFloat64 {
|
||||||
p := Path{make([]float64, 0, 32)}
|
p := Path{make([]float64, 0, 32)}
|
||||||
p.LineTo(curve[0], curve[1])
|
p.LineTo(curve[0], curve[1])
|
||||||
curve.Segment(&p, flattening_threshold)
|
curve.Trace(&p, flattening_threshold)
|
||||||
}
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
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[0], curve[1])
|
|
||||||
curve.AdaptiveSegmentRec(&p, 1, 0, 0)
|
|
||||||
}
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
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[0], curve[1])
|
|
||||||
curve.AdaptiveSegment(&p, 1, 0, 0)
|
|
||||||
}
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
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[0], curve[1])
|
|
||||||
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)}
|
|
||||||
p.LineTo(curve[0], curve[1])
|
|
||||||
curve.Segment(&p, flattening_threshold)
|
|
||||||
}
|
}
|
||||||
}
|
}
|
||||||
}
|
}
|
||||||
|
|
|
||||||
|
|
@ -1,19 +1,25 @@
|
||||||
// Copyright 2010 The draw2d Authors. All rights reserved.
|
// Copyright 2010 The draw2d Authors. All rights reserved.
|
||||||
// created: 17/05/2011 by Laurent Le Goff
|
// created: 17/05/2011 by Laurent Le Goff
|
||||||
|
|
||||||
package curve
|
package curve
|
||||||
|
|
||||||
import (
|
import (
|
||||||
"math"
|
"math"
|
||||||
)
|
)
|
||||||
|
|
||||||
//X1, Y1, X2, Y2, X3, Y3 float64
|
//x1, y1, cpx1, cpy2, x2, y2 float64
|
||||||
type QuadCurveFloat64 [6]float64
|
type QuadCurveFloat64 [6]float64
|
||||||
|
|
||||||
|
// Subdivide a Bezier quad curve in 2 equivalents Bezier quad curves.
|
||||||
|
// c1 and c2 parameters are the resulting curves
|
||||||
func (c *QuadCurveFloat64) Subdivide(c1, c2 *QuadCurveFloat64) {
|
func (c *QuadCurveFloat64) Subdivide(c1, c2 *QuadCurveFloat64) {
|
||||||
// Calculate all the mid-points of the line segments
|
|
||||||
//----------------------
|
// First point of c is the first point of c1
|
||||||
c1[0], c1[1] = c[0], c[1]
|
c1[0], c1[1] = c[0], c[1]
|
||||||
|
// Last point of c is the last point of c2
|
||||||
c2[4], c2[5] = c[4], c[5]
|
c2[4], c2[5] = c[4], c[5]
|
||||||
|
|
||||||
|
// Subdivide segment using midpoints
|
||||||
c1[2] = (c[0] + c[2]) / 2
|
c1[2] = (c[0] + c[2]) / 2
|
||||||
c1[3] = (c[1] + c[3]) / 2
|
c1[3] = (c[1] + c[3]) / 2
|
||||||
c2[2] = (c[2] + c[4]) / 2
|
c2[2] = (c[2] + c[4]) / 2
|
||||||
|
|
@ -24,7 +30,10 @@ func (c *QuadCurveFloat64) Subdivide(c1, c2 *QuadCurveFloat64) {
|
||||||
return
|
return
|
||||||
}
|
}
|
||||||
|
|
||||||
func (curve *QuadCurveFloat64) Segment(t LineTracer, flattening_threshold float64) {
|
// Trace generate lines subdividing the curve using a LineTracer
|
||||||
|
// flattening_threshold helps determines the flattening expectation of the curve
|
||||||
|
func (curve *QuadCurveFloat64) Trace(t LineTracer, flattening_threshold float64) {
|
||||||
|
// Allocates curves stack
|
||||||
var curves [CurveRecursionLimit]QuadCurveFloat64
|
var curves [CurveRecursionLimit]QuadCurveFloat64
|
||||||
curves[0] = *curve
|
curves[0] = *curve
|
||||||
i := 0
|
i := 0
|
||||||
|
|
@ -39,6 +48,7 @@ func (curve *QuadCurveFloat64) Segment(t LineTracer, flattening_threshold float6
|
||||||
|
|
||||||
d = math.Abs(((c[2]-c[4])*dy - (c[3]-c[5])*dx))
|
d = math.Abs(((c[2]-c[4])*dy - (c[3]-c[5])*dx))
|
||||||
|
|
||||||
|
// if it's flat then trace a line
|
||||||
if (d*d) < flattening_threshold*(dx*dx+dy*dy) || i == len(curves)-1 {
|
if (d*d) < flattening_threshold*(dx*dx+dy*dy) || i == len(curves)-1 {
|
||||||
t.LineTo(c[4], c[5])
|
t.LineTo(c[4], c[5])
|
||||||
i--
|
i--
|
||||||
|
|
|
||||||
6
curve/tracer.go
Normal file
6
curve/tracer.go
Normal file
|
|
@ -0,0 +1,6 @@
|
||||||
|
package curve
|
||||||
|
|
||||||
|
// LineTracer is an interface that help segmenting curve into small lines
|
||||||
|
type LineTracer interface {
|
||||||
|
LineTo(x, y float64)
|
||||||
|
}
|
||||||
Loading…
Reference in a new issue