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