81 lines
1.9 KiB
Go
81 lines
1.9 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 implements Bezier Curve Subdivision using De Casteljau's algorithm
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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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CurveRecursionLimit = 32
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)
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// x1, y1, cpx1, cpy1, cpx2, cpy2, x2, y2 float64
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// type Cubic []float64
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// Subdivide a Bezier cubic curve in 2 equivalents Bezier cubic curves.
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// c1 and c2 parameters are the resulting curves
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func SubdivideCubic(c, c1, c2 []float64) {
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// First point of c is the first point of c1
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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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// Subdivide segment using midpoints
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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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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[5] = (c[5] + c[7]) / 2
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c1[4] = (c1[2] + midX) / 2
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c1[5] = (c1[3] + midY) / 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[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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}
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// TraceCubic generate lines subdividing the cubic curve using a LineBuilder
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// flattening_threshold helps determines the flattening expectation of the curve
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func TraceCubic(t LineBuilder, cubic []float64, flattening_threshold float64) {
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// Allocation curves
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var curves [CurveRecursionLimit * 8]float64
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copy(curves[0:8], cubic[0:8])
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i := 0
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// current curve
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var c []float64
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var dx, dy, d2, d3 float64
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for i >= 0 {
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c = curves[i*8:]
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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 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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t.LineTo(c[6], c[7])
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i--
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} else {
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// second half of bezier go lower onto the stack
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SubdivideCubic(c, curves[(i+1)*8:], curves[i*8:])
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i++
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}
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}
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}
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