1/*
2 * Copyright (C) 2008 Apple Inc. All Rights Reserved.
3 *
4 * Redistribution and use in source and binary forms, with or without
5 * modification, are permitted provided that the following conditions
6 * are met:
7 * 1. Redistributions of source code must retain the above copyright
8 * notice, this list of conditions and the following disclaimer.
9 * 2. Redistributions in binary form must reproduce the above copyright
10 * notice, this list of conditions and the following disclaimer in the
11 * documentation and/or other materials provided with the distribution.
12 *
13 * THIS SOFTWARE IS PROVIDED BY APPLE INC. ``AS IS'' AND ANY
14 * EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
15 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
16 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL APPLE INC. OR
17 * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
18 * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
19 * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
20 * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
21 * OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
22 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
23 * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
24 */
25
26#ifndef UnitBezier_h
27#define UnitBezier_h
28
29#include <math.h>
30
31namespace WebCore {
32
33 struct UnitBezier {
34 UnitBezier(double p1x, double p1y, double p2x, double p2y)
35 {
36 // Calculate the polynomial coefficients, implicit first and last control points are (0,0) and (1,1).
37 cx = 3.0 * p1x;
38 bx = 3.0 * (p2x - p1x) - cx;
39 ax = 1.0 - cx -bx;
40
41 cy = 3.0 * p1y;
42 by = 3.0 * (p2y - p1y) - cy;
43 ay = 1.0 - cy - by;
44 }
45
46 double sampleCurveX(double t)
47 {
48 // `ax t^3 + bx t^2 + cx t' expanded using Horner's rule.
49 return ((ax * t + bx) * t + cx) * t;
50 }
51
52 double sampleCurveY(double t)
53 {
54 return ((ay * t + by) * t + cy) * t;
55 }
56
57 double sampleCurveDerivativeX(double t)
58 {
59 return (3.0 * ax * t + 2.0 * bx) * t + cx;
60 }
61
62 // Given an x value, find a parametric value it came from.
63 double solveCurveX(double x, double epsilon)
64 {
65 double t0;
66 double t1;
67 double t2;
68 double x2;
69 double d2;
70 int i;
71
72 // First try a few iterations of Newton's method -- normally very fast.
73 for (t2 = x, i = 0; i < 8; i++) {
74 x2 = sampleCurveX(t2) - x;
75 if (fabs (x2) < epsilon)
76 return t2;
77 d2 = sampleCurveDerivativeX(t2);
78 if (fabs(d2) < 1e-6)
79 break;
80 t2 = t2 - x2 / d2;
81 }
82
83 // Fall back to the bisection method for reliability.
84 t0 = 0.0;
85 t1 = 1.0;
86 t2 = x;
87
88 if (t2 < t0)
89 return t0;
90 if (t2 > t1)
91 return t1;
92
93 while (t0 < t1) {
94 x2 = sampleCurveX(t2);
95 if (fabs(x2 - x) < epsilon)
96 return t2;
97 if (x > x2)
98 t0 = t2;
99 else
100 t1 = t2;
101 t2 = (t1 - t0) * .5 + t0;
102 }
103
104 // Failure.
105 return t2;
106 }
107
108 double solve(double x, double epsilon)
109 {
110 return sampleCurveY(solveCurveX(x, epsilon));
111 }
112
113 private:
114 double ax;
115 double bx;
116 double cx;
117
118 double ay;
119 double by;
120 double cy;
121 };
122}
123#endif
124