696 lines
19 KiB
Go
696 lines
19 KiB
Go
// 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:
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// p1,p3,p4 are collinear, p2 is significant
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//----------------------
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if d2*d2 <= 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[5]-c[3], c[4]-c[2]) - math.Atan2(c[3]-c[1], c[2]-c[0]))
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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[2], c[3])
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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:
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// Regular case
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//-----------------
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if (d2+d3)*(d2+d3) <= distanceToleranceSquare*(dx*dx+dy*dy) {
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// If the curvature doesn't exceed the distanceTolerance value
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// we tend to finish subdivisions.
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//----------------------
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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 & Cusp Condition
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//----------------------
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k := math.Atan2(c[5]-c[3], c[4]-c[2])
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da1 := math.Abs(k - math.Atan2(c[3]-c[1], c[2]-c[0]))
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da2 := math.Abs(math.Atan2(c[7]-c[5], c[6]-c[4]) - k)
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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 da2 >= math.Pi {
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da2 = 2*math.Pi - da2
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}
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if da1+da2 < angleTolerance {
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// Finally we can stop the recursion
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//----------------------
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t.LineTo(x23, y23)
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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[2], c[3])
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return
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}
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if da2 > 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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}
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// Continue subdivision
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//----------------------
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c1.adaptiveSegmentRec(t, level+1, distanceToleranceSquare, angleTolerance, cuspLimit)
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c2.adaptiveSegmentRec(t, level+1, distanceToleranceSquare, angleTolerance, cuspLimit)
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}
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func (curve *CubicCurveFloat64) AdaptiveSegment(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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var curves [CurveRecursionLimit]CubicCurveFloat64
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curves[0] = *curve
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i := 0
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// current curve
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var c *CubicCurveFloat64
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var c1, c2 CubicCurveFloat64
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var dx, dy, d2, d3, k, x23, y23 float64
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for i >= 0 {
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c = &curves[i]
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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 i == len(curves)-1:
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t.LineTo(c[6], c[7])
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i--
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continue
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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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i--
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continue
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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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i--
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continue
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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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i--
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continue
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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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i--
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continue
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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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i--
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continue
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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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i--
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continue
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}
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}
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}
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case d2 > CurveCollinearityEpsilon && d3 <= CurveCollinearityEpsilon:
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// p1,p3,p4 are collinear, p2 is significant
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//----------------------
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if d2*d2 <= distanceToleranceSquare*(dx*dx+dy*dy) {
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if angleTolerance < CurveAngleToleranceEpsilon {
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t.LineTo(x23, y23)
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i--
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continue
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}
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// Angle Condition
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//----------------------
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da1 := math.Abs(math.Atan2(c[5]-c[3], c[4]-c[2]) - math.Atan2(c[3]-c[1], c[2]-c[0]))
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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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i--
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continue
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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[2], c[3])
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i--
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continue
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}
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}
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}
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case d2 > CurveCollinearityEpsilon && d3 > CurveCollinearityEpsilon:
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// Regular case
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//-----------------
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if (d2+d3)*(d2+d3) <= distanceToleranceSquare*(dx*dx+dy*dy) {
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// If the curvature doesn't exceed the distanceTolerance value
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// we tend to finish subdivisions.
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//----------------------
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if angleTolerance < CurveAngleToleranceEpsilon {
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t.LineTo(x23, y23)
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i--
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continue
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}
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// Angle & Cusp Condition
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//----------------------
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k := math.Atan2(c[5]-c[3], c[4]-c[2])
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da1 := math.Abs(k - math.Atan2(c[3]-c[1], c[2]-c[0]))
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da2 := math.Abs(math.Atan2(c[7]-c[5], c[6]-c[4]) - k)
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if da1 >= math.Pi {
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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
|
|
}
|