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1 /* | |
2 * Copyright 2012 Google Inc. | |
3 * | |
4 * Use of this source code is governed by a BSD-style license that can be | |
5 * found in the LICENSE file. | |
6 */ | |
7 #include "CubicLineSegments.h" | |
8 #include "QuadraticLineSegments.h" | |
9 | |
10 // http://cagd.cs.byu.edu/~557/text/cagd.pdf 2.7 | |
11 // A hodograph is the first derivative curve | |
12 void hodograph(const Cubic& cubic, Quadratic& hodo) { | |
13 hodo[0].x = 3 * (cubic[1].x - cubic[0].x); | |
14 hodo[0].y = 3 * (cubic[1].y - cubic[0].y); | |
15 hodo[1].x = 3 * (cubic[2].x - cubic[1].x); | |
16 hodo[1].y = 3 * (cubic[2].y - cubic[1].y); | |
17 hodo[2].x = 3 * (cubic[3].x - cubic[2].x); | |
18 hodo[2].y = 3 * (cubic[3].y - cubic[2].y); | |
19 } | |
20 | |
21 // A 2nd hodograph is the second derivative curve | |
22 void secondHodograph(const Cubic& cubic, _Line& hodo2) { | |
23 Quadratic hodo; | |
24 hodograph(cubic, hodo); | |
25 hodograph(hodo, hodo2); | |
26 } | |
27 | |
28 // The number of line segments required to approximate the cubic | |
29 // see http://cagd.cs.byu.edu/~557/text/cagd.pdf 10.6 | |
30 double subDivisions(const Cubic& cubic) { | |
31 _Line hodo2; | |
32 secondHodograph(cubic, hodo2); | |
33 double maxX = SkTMax(hodo2[1].x, hodo2[1].x); | |
34 double maxY = SkTMax(hodo2[1].y, hodo2[1].y); | |
35 double dist = sqrt(maxX * maxX + maxY * maxY); | |
36 double segments = sqrt(dist / (8 * FLT_EPSILON)); | |
37 return segments; | |
38 } | |
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