mirror of
https://github.com/thorvg/thorvg.git
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ecabdc5ebc
Replaced the transformation with a strong associated data field. This helps to reduce the binary size (-1k).
355 lines
No EOL
10 KiB
C++
355 lines
No EOL
10 KiB
C++
/*
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* Copyright (c) 2021 - 2024 the ThorVG project. 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 "tvgMath.h"
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#define BEZIER_EPSILON 1e-2f
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/************************************************************************/
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/* Internal Class Implementation */
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/************************************************************************/
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static float _lineLengthApprox(const Point& pt1, const Point& pt2)
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{
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/* approximate sqrt(x*x + y*y) using alpha max plus beta min algorithm.
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With alpha = 1, beta = 3/8, giving results with the largest error less
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than 7% compared to the exact value. */
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Point diff = {pt2.x - pt1.x, pt2.y - pt1.y};
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if (diff.x < 0) diff.x = -diff.x;
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if (diff.y < 0) diff.y = -diff.y;
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return (diff.x > diff.y) ? (diff.x + diff.y * 0.375f) : (diff.y + diff.x * 0.375f);
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}
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static float _lineLength(const Point& pt1, const Point& pt2)
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{
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Point diff = {pt2.x - pt1.x, pt2.y - pt1.y};
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return sqrtf(diff.x * diff.x + diff.y * diff.y);
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}
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template<typename LengthFunc>
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float _bezLength(const Bezier& cur, LengthFunc lineLengthFunc)
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{
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Bezier left, right;
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auto len = lineLengthFunc(cur.start, cur.ctrl1) + lineLengthFunc(cur.ctrl1, cur.ctrl2) + lineLengthFunc(cur.ctrl2, cur.end);
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auto chord = lineLengthFunc(cur.start, cur.end);
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if (fabsf(len - chord) > BEZIER_EPSILON) {
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cur.split(left, right);
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return _bezLength(left, lineLengthFunc) + _bezLength(right, lineLengthFunc);
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}
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return len;
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}
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template<typename LengthFunc>
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float _bezAt(const Bezier& bz, float at, float length, LengthFunc lineLengthFunc)
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{
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auto biggest = 1.0f;
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auto smallest = 0.0f;
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auto t = 0.5f;
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//just in case to prevent an infinite loop
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if (at <= 0) return 0.0f;
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if (at >= length) return 1.0f;
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while (true) {
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auto right = bz;
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Bezier left;
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right.split(t, left);
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length = _bezLength(left, lineLengthFunc);
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if (fabsf(length - at) < BEZIER_EPSILON || fabsf(smallest - biggest) < BEZIER_EPSILON) {
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break;
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}
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if (length < at) {
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smallest = t;
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t = (t + biggest) * 0.5f;
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} else {
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biggest = t;
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t = (smallest + t) * 0.5f;
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}
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}
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return t;
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}
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/************************************************************************/
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/* External Class Implementation */
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/************************************************************************/
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namespace tvg {
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//https://en.wikipedia.org/wiki/Remez_algorithm
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float atan2(float y, float x)
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{
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if (y == 0.0f && x == 0.0f) return 0.0f;
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auto a = std::min(fabsf(x), fabsf(y)) / std::max(fabsf(x), fabsf(y));
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auto s = a * a;
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auto r = ((-0.0464964749f * s + 0.15931422f) * s - 0.327622764f) * s * a + a;
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if (fabsf(y) > fabsf(x)) r = 1.57079637f - r;
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if (x < 0) r = 3.14159274f - r;
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if (y < 0) return -r;
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return r;
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}
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bool inverse(const Matrix* m, Matrix* out)
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{
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auto det = m->e11 * (m->e22 * m->e33 - m->e32 * m->e23) -
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m->e12 * (m->e21 * m->e33 - m->e23 * m->e31) +
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m->e13 * (m->e21 * m->e32 - m->e22 * m->e31);
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if (tvg::zero(det)) return false;
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auto invDet = 1 / det;
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out->e11 = (m->e22 * m->e33 - m->e32 * m->e23) * invDet;
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out->e12 = (m->e13 * m->e32 - m->e12 * m->e33) * invDet;
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out->e13 = (m->e12 * m->e23 - m->e13 * m->e22) * invDet;
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out->e21 = (m->e23 * m->e31 - m->e21 * m->e33) * invDet;
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out->e22 = (m->e11 * m->e33 - m->e13 * m->e31) * invDet;
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out->e23 = (m->e21 * m->e13 - m->e11 * m->e23) * invDet;
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out->e31 = (m->e21 * m->e32 - m->e31 * m->e22) * invDet;
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out->e32 = (m->e31 * m->e12 - m->e11 * m->e32) * invDet;
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out->e33 = (m->e11 * m->e22 - m->e21 * m->e12) * invDet;
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return true;
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}
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bool identity(const Matrix* m)
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{
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if (m->e11 != 1.0f || m->e12 != 0.0f || m->e13 != 0.0f ||
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m->e21 != 0.0f || m->e22 != 1.0f || m->e23 != 0.0f ||
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m->e31 != 0.0f || m->e32 != 0.0f || m->e33 != 1.0f) {
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return false;
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}
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return true;
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}
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void rotate(Matrix* m, float degree)
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{
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if (degree == 0.0f) return;
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auto radian = degree / 180.0f * MATH_PI;
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auto cosVal = cosf(radian);
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auto sinVal = sinf(radian);
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m->e12 = m->e11 * -sinVal;
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m->e11 *= cosVal;
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m->e21 = m->e22 * sinVal;
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m->e22 *= cosVal;
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}
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Matrix operator*(const Matrix& lhs, const Matrix& rhs)
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{
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Matrix m;
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m.e11 = lhs.e11 * rhs.e11 + lhs.e12 * rhs.e21 + lhs.e13 * rhs.e31;
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m.e12 = lhs.e11 * rhs.e12 + lhs.e12 * rhs.e22 + lhs.e13 * rhs.e32;
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m.e13 = lhs.e11 * rhs.e13 + lhs.e12 * rhs.e23 + lhs.e13 * rhs.e33;
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m.e21 = lhs.e21 * rhs.e11 + lhs.e22 * rhs.e21 + lhs.e23 * rhs.e31;
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m.e22 = lhs.e21 * rhs.e12 + lhs.e22 * rhs.e22 + lhs.e23 * rhs.e32;
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m.e23 = lhs.e21 * rhs.e13 + lhs.e22 * rhs.e23 + lhs.e23 * rhs.e33;
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m.e31 = lhs.e31 * rhs.e11 + lhs.e32 * rhs.e21 + lhs.e33 * rhs.e31;
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m.e32 = lhs.e31 * rhs.e12 + lhs.e32 * rhs.e22 + lhs.e33 * rhs.e32;
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m.e33 = lhs.e31 * rhs.e13 + lhs.e32 * rhs.e23 + lhs.e33 * rhs.e33;
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return m;
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}
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bool operator==(const Matrix& lhs, const Matrix& rhs)
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{
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if (!tvg::equal(lhs.e11, rhs.e11) || !tvg::equal(lhs.e12, rhs.e12) || !tvg::equal(lhs.e13, rhs.e13) ||
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!tvg::equal(lhs.e21, rhs.e21) || !tvg::equal(lhs.e22, rhs.e22) || !tvg::equal(lhs.e23, rhs.e23) ||
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!tvg::equal(lhs.e31, rhs.e31) || !tvg::equal(lhs.e32, rhs.e32) || !tvg::equal(lhs.e33, rhs.e33)) {
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return false;
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}
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return true;
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}
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void operator*=(Point& pt, const Matrix& m)
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{
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auto tx = pt.x * m.e11 + pt.y * m.e12 + m.e13;
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auto ty = pt.x * m.e21 + pt.y * m.e22 + m.e23;
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pt.x = tx;
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pt.y = ty;
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}
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Point operator*(const Point& pt, const Matrix& m)
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{
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auto tx = pt.x * m.e11 + pt.y * m.e12 + m.e13;
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auto ty = pt.x * m.e21 + pt.y * m.e22 + m.e23;
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return {tx, ty};
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}
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float Line::length() const
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{
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return _lineLength(pt1, pt2);
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}
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void Line::split(float at, Line& left, Line& right) const
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{
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auto len = length();
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auto dx = ((pt2.x - pt1.x) / len) * at;
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auto dy = ((pt2.y - pt1.y) / len) * at;
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left.pt1 = pt1;
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left.pt2.x = left.pt1.x + dx;
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left.pt2.y = left.pt1.y + dy;
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right.pt1 = left.pt2;
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right.pt2 = pt2;
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}
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void Bezier::split(Bezier& left, Bezier& right) const
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{
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auto c = (ctrl1.x + ctrl2.x) * 0.5f;
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left.ctrl1.x = (start.x + ctrl1.x) * 0.5f;
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right.ctrl2.x = (ctrl2.x + end.x) * 0.5f;
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left.start.x = start.x;
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right.end.x = end.x;
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left.ctrl2.x = (left.ctrl1.x + c) * 0.5f;
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right.ctrl1.x = (right.ctrl2.x + c) * 0.5f;
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left.end.x = right.start.x = (left.ctrl2.x + right.ctrl1.x) * 0.5f;
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c = (ctrl1.y + ctrl2.y) * 0.5f;
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left.ctrl1.y = (start.y + ctrl1.y) * 0.5f;
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right.ctrl2.y = (ctrl2.y + end.y) * 0.5f;
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left.start.y = start.y;
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right.end.y = end.y;
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left.ctrl2.y = (left.ctrl1.y + c) * 0.5f;
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right.ctrl1.y = (right.ctrl2.y + c) * 0.5f;
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left.end.y = right.start.y = (left.ctrl2.y + right.ctrl1.y) * 0.5f;
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}
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void Bezier::split(float at, Bezier& left, Bezier& right) const
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{
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right = *this;
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auto t = right.at(at, right.length());
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right.split(t, left);
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}
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float Bezier::length() const
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{
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return _bezLength(*this, _lineLength);
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}
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float Bezier::lengthApprox() const
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{
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return _bezLength(*this, _lineLengthApprox);
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}
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void Bezier::split(float at, Bezier& left)
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{
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left.start = start;
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left.ctrl1.x = start.x + at * (ctrl1.x - start.x);
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left.ctrl1.y = start.y + at * (ctrl1.y - start.y);
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left.ctrl2.x = ctrl1.x + at * (ctrl2.x - ctrl1.x); //temporary holding spot
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left.ctrl2.y = ctrl1.y + at * (ctrl2.y - ctrl1.y); //temporary holding spot
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ctrl2.x = ctrl2.x + at * (end.x - ctrl2.x);
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ctrl2.y = ctrl2.y + at * (end.y - ctrl2.y);
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ctrl1.x = left.ctrl2.x + at * (ctrl2.x - left.ctrl2.x);
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ctrl1.y = left.ctrl2.y + at * (ctrl2.y - left.ctrl2.y);
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left.ctrl2.x = left.ctrl1.x + at * (left.ctrl2.x - left.ctrl1.x);
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left.ctrl2.y = left.ctrl1.y + at * (left.ctrl2.y - left.ctrl1.y);
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left.end.x = start.x = left.ctrl2.x + at * (ctrl1.x - left.ctrl2.x);
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left.end.y = start.y = left.ctrl2.y + at * (ctrl1.y - left.ctrl2.y);
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}
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float Bezier::at(float at, float length) const
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{
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return _bezAt(*this, at, length, _lineLength);
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}
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float Bezier::atApprox(float at, float length) const
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{
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return _bezAt(*this, at, length, _lineLengthApprox);
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}
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Point Bezier::at(float t) const
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{
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Point cur;
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auto it = 1.0f - t;
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auto ax = start.x * it + ctrl1.x * t;
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auto bx = ctrl1.x * it + ctrl2.x * t;
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auto cx = ctrl2.x * it + end.x * t;
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ax = ax * it + bx * t;
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bx = bx * it + cx * t;
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cur.x = ax * it + bx * t;
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float ay = start.y * it + ctrl1.y * t;
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float by = ctrl1.y * it + ctrl2.y * t;
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float cy = ctrl2.y * it + end.y * t;
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ay = ay * it + by * t;
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by = by * it + cy * t;
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cur.y = ay * it + by * t;
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return cur;
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}
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float Bezier::angle(float t) const
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{
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if (t < 0 || t > 1) return 0;
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//derivate
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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 mt = 1.0f - t;
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float d = t * t;
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float a = -mt * mt;
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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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Point pt ={a * start.x + b * ctrl1.x + c * ctrl2.x + d * end.x, a * start.y + b * ctrl1.y + c * ctrl2.y + d * end.y};
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pt.x *= 3;
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pt.y *= 3;
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return rad2deg(tvg::atan2(pt.y, pt.x));
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}
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} |