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#pragma once
27
28#include <cmath>
29#include <tuple>
30
31namespace mbgl {
32namespace util {
33
34struct UnitBezier {
35 // Calculate the polynomial coefficients, implicit first and last control points are (0,0) and (1,1).
36 constexpr UnitBezier(double p1x, double p1y, double p2x, double p2y)
37 : cx(3.0 * p1x)
38 , bx(3.0 * (p2x - p1x) - (3.0 * p1x))
39 , ax(1.0 - (3.0 * p1x) - (3.0 * (p2x - p1x) - (3.0 * p1x)))
40 , cy(3.0 * p1y)
41 , by(3.0 * (p2y - p1y) - (3.0 * p1y))
42 , ay(1.0 - (3.0 * p1y) - (3.0 * (p2y - p1y) - (3.0 * p1y))) {
43 }
44
45 std::pair<double, double> getP1() const {
46 return { cx / 3.0, cy / 3.0 };
47 }
48
49 std::pair<double, double> getP2() const {
50 return {
51 (bx + (3.0 * cx / 3.0) + cx) / 3.0,
52 (by + (3.0 * cy / 3.0) + cy) / 3.0,
53 };
54 }
55
56 double sampleCurveX(double t) const {
57 // `ax t^3 + bx t^2 + cx t' expanded using Horner's rule.
58 return ((ax * t + bx) * t + cx) * t;
59 }
60
61 double sampleCurveY(double t) const {
62 return ((ay * t + by) * t + cy) * t;
63 }
64
65 double sampleCurveDerivativeX(double t) const {
66 return (3.0 * ax * t + 2.0 * bx) * t + cx;
67 }
68
69 // Given an x value, find a parametric value it came from.
70 double solveCurveX(double x, double epsilon) const {
71 double t0;
72 double t1;
73 double t2;
74 double x2;
75 double d2;
76 int i;
77
78 // First try a few iterations of Newton's method -- normally very fast.
79 for (t2 = x, i = 0; i < 8; ++i) {
80 x2 = sampleCurveX(t: t2) - x;
81 if (fabs (x: x2) < epsilon)
82 return t2;
83 d2 = sampleCurveDerivativeX(t: t2);
84 if (fabs(x: d2) < 1e-6)
85 break;
86 t2 = t2 - x2 / d2;
87 }
88
89 // Fall back to the bisection method for reliability.
90 t0 = 0.0;
91 t1 = 1.0;
92 t2 = x;
93
94 if (t2 < t0)
95 return t0;
96 if (t2 > t1)
97 return t1;
98
99 while (t0 < t1) {
100 x2 = sampleCurveX(t: t2);
101 if (fabs(x: x2 - x) < epsilon)
102 return t2;
103 if (x > x2)
104 t0 = t2;
105 else
106 t1 = t2;
107 t2 = (t1 - t0) * .5 + t0;
108 }
109
110 // Failure.
111 return t2;
112 }
113
114 double solve(double x, double epsilon) const {
115 return sampleCurveY(t: solveCurveX(x, epsilon));
116 }
117
118 bool operator==(const UnitBezier& rhs) const {
119 return std::tie(args: cx, args: bx, args: ax, args: cy, args: by, args: ay) ==
120 std::tie(args: rhs.cx, args: rhs.bx, args: rhs.ax, args: rhs.cy, args: rhs.by, args: rhs.ay);
121 }
122
123private:
124 const double cx;
125 const double bx;
126 const double ax;
127
128 const double cy;
129 const double by;
130 const double ay;
131};
132
133} // namespace util
134} // namespace mbgl
135

source code of qtlocation/src/3rdparty/mapbox-gl-native/include/mbgl/util/unitbezier.hpp