1/*
2 * Copyright (c) 2020 - 2023 the ThorVG project. All rights reserved.
3
4 * Permission is hereby granted, free of charge, to any person obtaining a copy
5 * of this software and associated documentation files (the "Software"), to deal
6 * in the Software without restriction, including without limitation the rights
7 * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
8 * copies of the Software, and to permit persons to whom the Software is
9 * furnished to do so, subject to the following conditions:
10
11 * The above copyright notice and this permission notice shall be included in all
12 * copies or substantial portions of the Software.
13
14 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
15 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
16 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
17 * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
18 * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
19 * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
20 * SOFTWARE.
21 */
22
23#include "tvgMath.h"
24#include "tvgBezier.h"
25
26#define BEZIER_EPSILON 1e-4f
27
28/************************************************************************/
29/* Internal Class Implementation */
30/************************************************************************/
31
32static float _lineLength(const Point& pt1, const Point& pt2)
33{
34 /* approximate sqrt(x*x + y*y) using alpha max plus beta min algorithm.
35 With alpha = 1, beta = 3/8, giving results with the largest error less
36 than 7% compared to the exact value. */
37 Point diff = {pt2.x - pt1.x, pt2.y - pt1.y};
38 if (diff.x < 0) diff.x = -diff.x;
39 if (diff.y < 0) diff.y = -diff.y;
40 return (diff.x > diff.y) ? (diff.x + diff.y * 0.375f) : (diff.y + diff.x * 0.375f);
41}
42
43
44/************************************************************************/
45/* External Class Implementation */
46/************************************************************************/
47
48namespace tvg
49{
50
51void bezSplit(const Bezier&cur, Bezier& left, Bezier& right)
52{
53 auto c = (cur.ctrl1.x + cur.ctrl2.x) * 0.5f;
54 left.ctrl1.x = (cur.start.x + cur.ctrl1.x) * 0.5f;
55 right.ctrl2.x = (cur.ctrl2.x + cur.end.x) * 0.5f;
56 left.start.x = cur.start.x;
57 right.end.x = cur.end.x;
58 left.ctrl2.x = (left.ctrl1.x + c) * 0.5f;
59 right.ctrl1.x = (right.ctrl2.x + c) * 0.5f;
60 left.end.x = right.start.x = (left.ctrl2.x + right.ctrl1.x) * 0.5f;
61
62 c = (cur.ctrl1.y + cur.ctrl2.y) * 0.5f;
63 left.ctrl1.y = (cur.start.y + cur.ctrl1.y) * 0.5f;
64 right.ctrl2.y = (cur.ctrl2.y + cur.end.y) * 0.5f;
65 left.start.y = cur.start.y;
66 right.end.y = cur.end.y;
67 left.ctrl2.y = (left.ctrl1.y + c) * 0.5f;
68 right.ctrl1.y = (right.ctrl2.y + c) * 0.5f;
69 left.end.y = right.start.y = (left.ctrl2.y + right.ctrl1.y) * 0.5f;
70}
71
72
73float bezLength(const Bezier& cur)
74{
75 Bezier left, right;
76 auto len = _lineLength(cur.start, cur.ctrl1) + _lineLength(cur.ctrl1, cur.ctrl2) + _lineLength(cur.ctrl2, cur.end);
77 auto chord = _lineLength(cur.start, cur.end);
78
79 if (fabsf(len - chord) > BEZIER_EPSILON) {
80 bezSplit(cur, left, right);
81 return bezLength(left) + bezLength(right);
82 }
83 return len;
84}
85
86
87void bezSplitLeft(Bezier& cur, float at, Bezier& left)
88{
89 left.start = cur.start;
90
91 left.ctrl1.x = cur.start.x + at * (cur.ctrl1.x - cur.start.x);
92 left.ctrl1.y = cur.start.y + at * (cur.ctrl1.y - cur.start.y);
93
94 left.ctrl2.x = cur.ctrl1.x + at * (cur.ctrl2.x - cur.ctrl1.x); //temporary holding spot
95 left.ctrl2.y = cur.ctrl1.y + at * (cur.ctrl2.y - cur.ctrl1.y); //temporary holding spot
96
97 cur.ctrl2.x = cur.ctrl2.x + at * (cur.end.x - cur.ctrl2.x);
98 cur.ctrl2.y = cur.ctrl2.y + at * (cur.end.y - cur.ctrl2.y);
99
100 cur.ctrl1.x = left.ctrl2.x + at * (cur.ctrl2.x - left.ctrl2.x);
101 cur.ctrl1.y = left.ctrl2.y + at * (cur.ctrl2.y - left.ctrl2.y);
102
103 left.ctrl2.x = left.ctrl1.x + at * (left.ctrl2.x - left.ctrl1.x);
104 left.ctrl2.y = left.ctrl1.y + at * (left.ctrl2.y - left.ctrl1.y);
105
106 left.end.x = cur.start.x = left.ctrl2.x + at * (cur.ctrl1.x - left.ctrl2.x);
107 left.end.y = cur.start.y = left.ctrl2.y + at * (cur.ctrl1.y - left.ctrl2.y);
108}
109
110
111float bezAt(const Bezier& bz, float at, float length)
112{
113 auto biggest = 1.0f;
114 auto smallest = 0.0f;
115 auto t = 0.5f;
116
117 //just in case to prevent an infinite loop
118 if (at <= 0) return 0.0f;
119 if (at >= length) return length;
120
121 while (true) {
122 auto right = bz;
123 Bezier left;
124 bezSplitLeft(right, t, left);
125 length = bezLength(left);
126 if (fabsf(length - at) < BEZIER_EPSILON || fabsf(smallest - biggest) < BEZIER_EPSILON) {
127 break;
128 }
129 if (length < at) {
130 smallest = t;
131 t = (t + biggest) * 0.5f;
132 } else {
133 biggest = t;
134 t = (smallest + t) * 0.5f;
135 }
136 }
137 return t;
138}
139
140
141void bezSplitAt(const Bezier& cur, float at, Bezier& left, Bezier& right)
142{
143 right = cur;
144 auto t = bezAt(right, at, bezLength(right));
145 bezSplitLeft(right, t, left);
146}
147
148
149Point bezPointAt(const Bezier& bz, float t)
150{
151 Point cur;
152 auto it = 1.0f - t;
153
154 auto ax = bz.start.x * it + bz.ctrl1.x * t;
155 auto bx = bz.ctrl1.x * it + bz.ctrl2.x * t;
156 auto cx = bz.ctrl2.x * it + bz.end.x * t;
157 ax = ax * it + bx * t;
158 bx = bx * it + cx * t;
159 cur.x = ax * it + bx * t;
160
161 float ay = bz.start.y * it + bz.ctrl1.y * t;
162 float by = bz.ctrl1.y * it + bz.ctrl2.y * t;
163 float cy = bz.ctrl2.y * it + bz.end.y * t;
164 ay = ay * it + by * t;
165 by = by * it + cy * t;
166 cur.y = ay * it + by * t;
167
168 return cur;
169}
170
171
172float bezAngleAt(const Bezier& bz, float t)
173{
174 if (t < 0 || t > 1) return 0;
175
176 //derivate
177 // p'(t) = 3 * (-(1-2t+t^2) * p0 + (1 - 4 * t + 3 * t^2) * p1 + (2 * t - 3 *
178 // t^2) * p2 + t^2 * p3)
179 float mt = 1.0f - t;
180 float d = t * t;
181 float a = -mt * mt;
182 float b = 1 - 4 * t + 3 * d;
183 float c = 2 * t - 3 * d;
184
185 Point pt ={a * bz.start.x + b * bz.ctrl1.x + c * bz.ctrl2.x + d * bz.end.x, a * bz.start.y + b * bz.ctrl1.y + c * bz.ctrl2.y + d * bz.end.y};
186 pt.x *= 3;
187 pt.y *= 3;
188
189 return atan2(pt.x, pt.y) * 180.0f / 3.141592f;
190}
191
192
193}
194