40 lines
1.3 KiB
C++
40 lines
1.3 KiB
C++
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/*
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* Copyright 2012 Google Inc.
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*
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* Use of this source code is governed by a BSD-style license that can be
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* found in the LICENSE file.
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*/
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#include "CubicLineSegments.h"
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#include "QuadraticLineSegments.h"
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#include <algorithm> // used for std::max
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// http://cagd.cs.byu.edu/~557/text/cagd.pdf 2.7
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// A hodograph is the first derivative curve
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void hodograph(const Cubic& cubic, Quadratic& hodo) {
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hodo[0].x = 3 * (cubic[1].x - cubic[0].x);
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hodo[0].y = 3 * (cubic[1].y - cubic[0].y);
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hodo[1].x = 3 * (cubic[2].x - cubic[1].x);
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hodo[1].y = 3 * (cubic[2].y - cubic[1].y);
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hodo[2].x = 3 * (cubic[3].x - cubic[2].x);
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hodo[2].y = 3 * (cubic[3].y - cubic[2].y);
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}
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// A 2nd hodograph is the second derivative curve
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void secondHodograph(const Cubic& cubic, _Line& hodo2) {
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Quadratic hodo;
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hodograph(cubic, hodo);
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hodograph(hodo, hodo2);
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}
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// The number of line segments required to approximate the cubic
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// see http://cagd.cs.byu.edu/~557/text/cagd.pdf 10.6
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double subDivisions(const Cubic& cubic) {
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_Line hodo2;
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secondHodograph(cubic, hodo2);
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double maxX = std::max(hodo2[1].x, hodo2[1].x);
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double maxY = std::max(hodo2[1].y, hodo2[1].y);
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double dist = sqrt(maxX * maxX + maxY * maxY);
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double segments = sqrt(dist / (8 * FLT_EPSILON));
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return segments;
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}
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