136 lines
3.6 KiB
C++
136 lines
3.6 KiB
C++
/*
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* Copyright (c) 2020 Samsung Electronics Co., Ltd. All rights reserved.
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* Permission is hereby granted, free of charge, to any person obtaining a copy
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* of this software and associated documentation files (the "Software"), to deal
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* in the Software without restriction, including without limitation the rights
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* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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* copies of the Software, and to permit persons to whom the Software is
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* furnished to do so, subject to the following conditions:
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* The above copyright notice and this permission notice shall be included in all
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* copies or substantial portions of the Software.
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* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
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* SOFTWARE.
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*/
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#include "vector_vbezier.h"
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#include <cmath>
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#include "vector_vline.h"
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V_BEGIN_NAMESPACE
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VBezier VBezier::fromPoints(const VPointF &p1, const VPointF &p2,
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const VPointF &p3, const VPointF &p4)
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{
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VBezier b;
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b.x1 = p1.x();
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b.y1 = p1.y();
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b.x2 = p2.x();
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b.y2 = p2.y();
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b.x3 = p3.x();
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b.y3 = p3.y();
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b.x4 = p4.x();
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b.y4 = p4.y();
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return b;
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}
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float VBezier::length() const
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{
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const auto len = VLine::length(x1, y1, x2, y2) +
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VLine::length(x2, y2, x3, y3) +
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VLine::length(x3, y3, x4, y4);
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const auto chord = VLine::length(x1, y1, x4, y4);
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if ((len - chord) > 0.01) {
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VBezier left, right;
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split(&left, &right);
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return left.length() + right.length();
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}
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return len;
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}
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VBezier VBezier::onInterval(float t0, float t1) const
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{
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if (t0 == 0 && t1 == 1) return *this;
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VBezier bezier = *this;
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VBezier result;
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bezier.parameterSplitLeft(t0, &result);
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float trueT = (t1 - t0) / (1 - t0);
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bezier.parameterSplitLeft(trueT, &result);
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return result;
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}
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float VBezier::tAtLength(float l, float totalLength) const
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{
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float t = 1.0;
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const float error = 0.01f;
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if (l > totalLength || vCompare(l, totalLength)) return t;
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t *= 0.5;
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float lastBigger = 1.0;
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for (int num = 0; num < 100500; num++) {
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VBezier right = *this;
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VBezier left;
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right.parameterSplitLeft(t, &left);
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float lLen = left.length();
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if (fabs(lLen - l) < error) return t;
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if (lLen < l) {
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t += (lastBigger - t) * 0.5f;
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} else {
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lastBigger = t;
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t -= t * 0.5f;
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}
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}
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vWarning << "no convergence";
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return t;
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}
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void VBezier::splitAtLength(float len, VBezier *left, VBezier *right)
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{
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float t;
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*right = *this;
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t = right->tAtLength(len);
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right->parameterSplitLeft(t, left);
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}
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VPointF VBezier::derivative(float t) const
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{
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// p'(t) = 3 * (-(1-2t+t^2) * p0 + (1 - 4 * t + 3 * t^2) * p1 + (2 * t - 3 *
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// t^2) * p2 + t^2 * p3)
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float m_t = 1.0f - t;
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float d = t * t;
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float a = -m_t * m_t;
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float b = 1 - 4 * t + 3 * d;
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float c = 2 * t - 3 * d;
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return 3 * VPointF(a * x1 + b * x2 + c * x3 + d * x4,
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a * y1 + b * y2 + c * y3 + d * y4);
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}
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float VBezier::angleAt(float t) const
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{
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if (t < 0 || t > 1) {
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return 0;
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}
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return VLine({}, derivative(t)).angle();
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}
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V_END_NAMESPACE
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