1/*
2 * Copyright (C) 2014 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. AND ITS CONTRIBUTORS ``AS IS''
14 * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO,
15 * THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
16 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL APPLE INC. OR ITS CONTRIBUTORS
17 * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
18 * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
19 * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
20 * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
21 * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
22 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF
23 * THE POSSIBILITY OF SUCH DAMAGE.
24 */
25
26WebInspector.UnitBezier = function(x1, y1, x2, y2)
27{
28    WebInspector.Object.call(this);
29
30    // Calculate the polynomial coefficients, implicit first and last control points are (0,0) and (1,1).
31    this._cx = 3.0 * x1;
32    this._bx = 3.0 * (x2 - x1) - this._cx;
33    this._ax = 1.0 - this._cx - this._bx;
34
35    this._cy = 3.0 * y1;
36    this._by = 3.0 * (y2 - y1) - this._cy;
37    this._ay = 1.0 - this._cy - this._by;
38};
39
40WebInspector.UnitBezier.prototype = {
41    constructor: WebInspector.UnitBezier,
42
43    // Public
44
45    solve: function(x, epsilon)
46    {
47        return this._sampleCurveY(this._solveCurveX(x, epsilon));
48    },
49
50    // Private
51
52    _sampleCurveX: function(t)
53    {
54        // `ax t^3 + bx t^2 + cx t' expanded using Horner's rule.
55        return ((this._ax * t + this._bx) * t + this._cx) * t;
56    },
57
58    _sampleCurveY: function(t)
59    {
60        return ((this._ay * t + this._by) * t + this._cy) * t;
61    },
62
63    _sampleCurveDerivativeX: function(t)
64    {
65        return (3.0 * this._ax * t + 2.0 * this._bx) * t + this._cx;
66    },
67
68    // Given an x value, find a parametric value it came from.
69    _solveCurveX: function(x, epsilon)
70    {
71        var t0, t1, t2, x2, d2, i;
72
73        // First try a few iterations of Newton's method -- normally very fast.
74        for (t2 = x, i = 0; i < 8; i++) {
75            x2 = this._sampleCurveX(t2) - x;
76            if (Math.abs(x2) < epsilon)
77                return t2;
78            d2 = this._sampleCurveDerivativeX(t2);
79            if (Math.abs(d2) < 1e-6)
80                break;
81            t2 = t2 - x2 / d2;
82        }
83
84        // Fall back to the bisection method for reliability.
85        t0 = 0.0;
86        t1 = 1.0;
87        t2 = x;
88
89        if (t2 < t0)
90            return t0;
91        if (t2 > t1)
92            return t1;
93
94        while (t0 < t1) {
95            x2 = this._sampleCurveX(t2);
96            if (Math.abs(x2 - x) < epsilon)
97                return t2;
98            if (x > x2)
99                t0 = t2;
100            else
101                t1 = t2;
102            t2 = (t1 - t0) * 0.5 + t0;
103        }
104
105        // Failure.
106        return t2;
107    }
108};
109