2  * Copyright (c) 2021 - 2024 the ThorVG project. All rights reserved.
28 #define BEZIER_EPSILON 1e-2f
40     Point diff = {pt2.x - pt1.x, pt2.y - pt1.y};  in _lineLengthApprox()
41     if (diff.x < 0) diff.x = -diff.x;  in _lineLengthApprox()
42     if (diff.y < 0) diff.y = -diff.y;  in _lineLengthApprox()
49     Point diff = {pt2.x - pt1.x, pt2.y - pt1.y};  in _lineLength()
61     if (fabsf(len - chord) > BEZIER_EPSILON) {  in _bezLength()
85         if (fabsf(length - at) < BEZIER_EPSILON || fabsf(smallest - biggest) < 1e-3f) {  in _bezAt()
112     auto r = ((-0.0464964749f * s + 0.15931422f) * s - 0.327622764f) * s * a + a;  in atan2()
113     if (fabsf(y) > fabsf(x)) r = 1.57079637f - r;  in atan2()
114     if (x < 0) r = 3.14159274f - r;  in atan2()
115     if (y < 0) return -r;  in atan2()
120 bool inverse(const Matrix* m, Matrix* out)  in inverse()  argument
122     auto det = m->e11 * (m->e22 * m->e33 - m->e32 * m->e23) -  in inverse()
123                m->e12 * (m->e21 * m->e33 - m->e23 * m->e31) +  in inverse()
124                m->e13 * (m->e21 * m->e32 - m->e22 * m->e31);  in inverse()
129     out->e11 = (m->e22 * m->e33 - m->e32 * m->e23) * invDet;  in inverse()
130     out->e12 = (m->e13 * m->e32 - m->e12 * m->e33) * invDet;  in inverse()
131     out->e13 = (m->e12 * m->e23 - m->e13 * m->e22) * invDet;  in inverse()
132     out->e21 = (m->e23 * m->e31 - m->e21 * m->e33) * invDet;  in inverse()
133     out->e22 = (m->e11 * m->e33 - m->e13 * m->e31) * invDet;  in inverse()
134     out->e23 = (m->e21 * m->e13 - m->e11 * m->e23) * invDet;  in inverse()
135     out->e31 = (m->e21 * m->e32 - m->e31 * m->e22) * invDet;  in inverse()
136     out->e32 = (m->e31 * m->e12 - m->e11 * m->e32) * invDet;  in inverse()
137     out->e33 = (m->e11 * m->e22 - m->e21 * m->e12) * invDet;  in inverse()
143 bool identity(const Matrix* m)  in identity()  argument
145     if (m->e11 != 1.0f || m->e12 != 0.0f || m->e13 != 0.0f ||  in identity()
146         m->e21 != 0.0f || m->e22 != 1.0f || m->e23 != 0.0f ||  in identity()
147         m->e31 != 0.0f || m->e32 != 0.0f || m->e33 != 1.0f) {  in identity()
154 void rotate(Matrix* m, float degree)  in rotate()  argument
162     m->e12 = m->e11 * -sinVal;  in rotate()
163     m->e11 *= cosVal;  in rotate()
164     m->e21 = m->e22 * sinVal;  in rotate()
165     m->e22 *= cosVal;  in rotate()
171     Matrix m;  in operator *()  local
173     m.e11 = lhs.e11 * rhs.e11 + lhs.e12 * rhs.e21 + lhs.e13 * rhs.e31;  in operator *()
174     m.e12 = lhs.e11 * rhs.e12 + lhs.e12 * rhs.e22 + lhs.e13 * rhs.e32;  in operator *()
175     m.e13 = lhs.e11 * rhs.e13 + lhs.e12 * rhs.e23 + lhs.e13 * rhs.e33;  in operator *()
177     m.e21 = lhs.e21 * rhs.e11 + lhs.e22 * rhs.e21 + lhs.e23 * rhs.e31;  in operator *()
178     m.e22 = lhs.e21 * rhs.e12 + lhs.e22 * rhs.e22 + lhs.e23 * rhs.e32;  in operator *()
179     m.e23 = lhs.e21 * rhs.e13 + lhs.e22 * rhs.e23 + lhs.e23 * rhs.e33;  in operator *()
181     m.e31 = lhs.e31 * rhs.e11 + lhs.e32 * rhs.e21 + lhs.e33 * rhs.e31;  in operator *()
182     m.e32 = lhs.e31 * rhs.e12 + lhs.e32 * rhs.e22 + lhs.e33 * rhs.e32;  in operator *()
183     m.e33 = lhs.e31 * rhs.e13 + lhs.e32 * rhs.e23 + lhs.e33 * rhs.e33;  in operator *()
185     return m;  in operator *()
200 void operator*=(Point& pt, const Matrix& m)  in operator *=()  argument
202     auto tx = pt.x * m.e11 + pt.y * m.e12 + m.e13;  in operator *=()
203     auto ty = pt.x * m.e21 + pt.y * m.e22 + m.e23;  in operator *=()
209 Point operator*(const Point& pt, const Matrix& m)  in operator *()  argument
211     auto tx = pt.x * m.e11 + pt.y * m.e12 + m.e13;  in operator *()
212     auto ty = pt.x * m.e21 + pt.y * m.e22 + m.e23;  in operator *()
219     auto dir = p2 - p1;  in normal()
224     return {-unitDir.y, unitDir.x};  in normal()
237     auto dx = ((pt2.x - pt1.x) / len) * at;  in split()
238     auto dy = ((pt2.y - pt1.y) / len) * at;  in split()
293     left.ctrl1.x = start.x + t * (ctrl1.x - start.x);  in split()
294     left.ctrl1.y = start.y + t * (ctrl1.y - start.y);  in split()
296     left.ctrl2.x = ctrl1.x + t * (ctrl2.x - ctrl1.x); //temporary holding spot  in split()
297     left.ctrl2.y = ctrl1.y + t * (ctrl2.y - ctrl1.y); //temporary holding spot  in split()
299     ctrl2.x = ctrl2.x + t * (end.x - ctrl2.x);  in split()
300     ctrl2.y = ctrl2.y + t * (end.y - ctrl2.y);  in split()
302     ctrl1.x = left.ctrl2.x + t * (ctrl2.x - left.ctrl2.x);  in split()
303     ctrl1.y = left.ctrl2.y + t * (ctrl2.y - left.ctrl2.y);  in split()
305     left.ctrl2.x = left.ctrl1.x + t * (left.ctrl2.x - left.ctrl1.x);  in split()
306     left.ctrl2.y = left.ctrl1.y + t * (left.ctrl2.y - left.ctrl1.y);  in split()
308     left.end.x = start.x = left.ctrl2.x + t * (ctrl1.x - left.ctrl2.x);  in split()
309     left.end.y = start.y = left.ctrl2.y + t * (ctrl1.y - left.ctrl2.y);  in split()
328     auto it = 1.0f - t;  in at()
353     // p'(t) = 3 * (-(1-2t+t^2) * p0 + (1 - 4 * t + 3 * t^2) * p1 + (2 * t - 3 *  in angle()
355     float mt = 1.0f - t;  in angle()
357     float a = -mt * mt;  in angle()
358     float b = 1 - 4 * t + 3 * d;  in angle()
359     float c = 2 * t - 3 * d;  in angle()
371     auto result = static_cast<int>(start + (end - start) * t);  in lerp()