1// Copyright 2014 The Chromium Authors. All rights reserved.
2// Use of this source code is governed by a BSD-style license that can be
3// found in the LICENSE file.
4
5#include "ui/gfx/geometry/cubic_bezier.h"
6
7#include "base/memory/scoped_ptr.h"
8#include "testing/gtest/include/gtest/gtest.h"
9
10namespace gfx {
11namespace {
12
13TEST(CubicBezierTest, Basic) {
14  CubicBezier function(0.25, 0.0, 0.75, 1.0);
15
16  double epsilon = 0.00015;
17
18  EXPECT_NEAR(function.Solve(0), 0, epsilon);
19  EXPECT_NEAR(function.Solve(0.05), 0.01136, epsilon);
20  EXPECT_NEAR(function.Solve(0.1), 0.03978, epsilon);
21  EXPECT_NEAR(function.Solve(0.15), 0.079780, epsilon);
22  EXPECT_NEAR(function.Solve(0.2), 0.12803, epsilon);
23  EXPECT_NEAR(function.Solve(0.25), 0.18235, epsilon);
24  EXPECT_NEAR(function.Solve(0.3), 0.24115, epsilon);
25  EXPECT_NEAR(function.Solve(0.35), 0.30323, epsilon);
26  EXPECT_NEAR(function.Solve(0.4), 0.36761, epsilon);
27  EXPECT_NEAR(function.Solve(0.45), 0.43345, epsilon);
28  EXPECT_NEAR(function.Solve(0.5), 0.5, epsilon);
29  EXPECT_NEAR(function.Solve(0.6), 0.63238, epsilon);
30  EXPECT_NEAR(function.Solve(0.65), 0.69676, epsilon);
31  EXPECT_NEAR(function.Solve(0.7), 0.75884, epsilon);
32  EXPECT_NEAR(function.Solve(0.75), 0.81764, epsilon);
33  EXPECT_NEAR(function.Solve(0.8), 0.87196, epsilon);
34  EXPECT_NEAR(function.Solve(0.85), 0.92021, epsilon);
35  EXPECT_NEAR(function.Solve(0.9), 0.96021, epsilon);
36  EXPECT_NEAR(function.Solve(0.95), 0.98863, epsilon);
37  EXPECT_NEAR(function.Solve(1), 1, epsilon);
38}
39
40// Tests that solving the bezier works with knots with y not in (0, 1).
41TEST(CubicBezierTest, UnclampedYValues) {
42  CubicBezier function(0.5, -1.0, 0.5, 2.0);
43
44  double epsilon = 0.00015;
45
46  EXPECT_NEAR(function.Solve(0.0), 0.0, epsilon);
47  EXPECT_NEAR(function.Solve(0.05), -0.08954, epsilon);
48  EXPECT_NEAR(function.Solve(0.1), -0.15613, epsilon);
49  EXPECT_NEAR(function.Solve(0.15), -0.19641, epsilon);
50  EXPECT_NEAR(function.Solve(0.2), -0.20651, epsilon);
51  EXPECT_NEAR(function.Solve(0.25), -0.18232, epsilon);
52  EXPECT_NEAR(function.Solve(0.3), -0.11992, epsilon);
53  EXPECT_NEAR(function.Solve(0.35), -0.01672, epsilon);
54  EXPECT_NEAR(function.Solve(0.4), 0.12660, epsilon);
55  EXPECT_NEAR(function.Solve(0.45), 0.30349, epsilon);
56  EXPECT_NEAR(function.Solve(0.5), 0.50000, epsilon);
57  EXPECT_NEAR(function.Solve(0.55), 0.69651, epsilon);
58  EXPECT_NEAR(function.Solve(0.6), 0.87340, epsilon);
59  EXPECT_NEAR(function.Solve(0.65), 1.01672, epsilon);
60  EXPECT_NEAR(function.Solve(0.7), 1.11992, epsilon);
61  EXPECT_NEAR(function.Solve(0.75), 1.18232, epsilon);
62  EXPECT_NEAR(function.Solve(0.8), 1.20651, epsilon);
63  EXPECT_NEAR(function.Solve(0.85), 1.19641, epsilon);
64  EXPECT_NEAR(function.Solve(0.9), 1.15613, epsilon);
65  EXPECT_NEAR(function.Solve(0.95), 1.08954, epsilon);
66  EXPECT_NEAR(function.Solve(1.0), 1.0, epsilon);
67}
68
69TEST(CubicBezierTest, Range) {
70  double epsilon = 0.00015;
71  double min, max;
72
73  // Derivative is a constant.
74  scoped_ptr<CubicBezier> function(
75      new CubicBezier(0.25, (1.0 / 3.0), 0.75, (2.0 / 3.0)));
76  function->Range(&min, &max);
77  EXPECT_EQ(0, min);
78  EXPECT_EQ(1, max);
79
80  // Derivative is linear.
81  function.reset(new CubicBezier(0.25, -0.5, 0.75, (-1.0 / 6.0)));
82  function->Range(&min, &max);
83  EXPECT_NEAR(min, -0.225, epsilon);
84  EXPECT_EQ(1, max);
85
86  // Derivative has no real roots.
87  function.reset(new CubicBezier(0.25, 0.25, 0.75, 0.5));
88  function->Range(&min, &max);
89  EXPECT_EQ(0, min);
90  EXPECT_EQ(1, max);
91
92  // Derivative has exactly one real root.
93  function.reset(new CubicBezier(0.0, 1.0, 1.0, 0.0));
94  function->Range(&min, &max);
95  EXPECT_EQ(0, min);
96  EXPECT_EQ(1, max);
97
98  // Derivative has one root < 0 and one root > 1.
99  function.reset(new CubicBezier(0.25, 0.1, 0.75, 0.9));
100  function->Range(&min, &max);
101  EXPECT_EQ(0, min);
102  EXPECT_EQ(1, max);
103
104  // Derivative has two roots in [0,1].
105  function.reset(new CubicBezier(0.25, 2.5, 0.75, 0.5));
106  function->Range(&min, &max);
107  EXPECT_EQ(0, min);
108  EXPECT_NEAR(max, 1.28818, epsilon);
109  function.reset(new CubicBezier(0.25, 0.5, 0.75, -1.5));
110  function->Range(&min, &max);
111  EXPECT_NEAR(min, -0.28818, epsilon);
112  EXPECT_EQ(1, max);
113
114  // Derivative has one root < 0 and one root in [0,1].
115  function.reset(new CubicBezier(0.25, 0.1, 0.75, 1.5));
116  function->Range(&min, &max);
117  EXPECT_EQ(0, min);
118  EXPECT_NEAR(max, 1.10755, epsilon);
119
120  // Derivative has one root in [0,1] and one root > 1.
121  function.reset(new CubicBezier(0.25, -0.5, 0.75, 0.9));
122  function->Range(&min, &max);
123  EXPECT_NEAR(min, -0.10755, epsilon);
124  EXPECT_EQ(1, max);
125
126  // Derivative has two roots < 0.
127  function.reset(new CubicBezier(0.25, 0.3, 0.75, 0.633));
128  function->Range(&min, &max);
129  EXPECT_EQ(0, min);
130  EXPECT_EQ(1, max);
131
132  // Derivative has two roots > 1.
133  function.reset(new CubicBezier(0.25, 0.367, 0.75, 0.7));
134  function->Range(&min, &max);
135  EXPECT_EQ(0.f, min);
136  EXPECT_EQ(1.f, max);
137}
138
139TEST(CubicBezierTest, Slope) {
140  CubicBezier function(0.25, 0.0, 0.75, 1.0);
141
142  double epsilon = 0.00015;
143
144  EXPECT_NEAR(function.Slope(0), 0, epsilon);
145  EXPECT_NEAR(function.Slope(0.05), 0.42170, epsilon);
146  EXPECT_NEAR(function.Slope(0.1), 0.69778, epsilon);
147  EXPECT_NEAR(function.Slope(0.15), 0.89121, epsilon);
148  EXPECT_NEAR(function.Slope(0.2), 1.03184, epsilon);
149  EXPECT_NEAR(function.Slope(0.25), 1.13576, epsilon);
150  EXPECT_NEAR(function.Slope(0.3), 1.21239, epsilon);
151  EXPECT_NEAR(function.Slope(0.35), 1.26751, epsilon);
152  EXPECT_NEAR(function.Slope(0.4), 1.30474, epsilon);
153  EXPECT_NEAR(function.Slope(0.45), 1.32628, epsilon);
154  EXPECT_NEAR(function.Slope(0.5), 1.33333, epsilon);
155  EXPECT_NEAR(function.Slope(0.55), 1.32628, epsilon);
156  EXPECT_NEAR(function.Slope(0.6), 1.30474, epsilon);
157  EXPECT_NEAR(function.Slope(0.65), 1.26751, epsilon);
158  EXPECT_NEAR(function.Slope(0.7), 1.21239, epsilon);
159  EXPECT_NEAR(function.Slope(0.75), 1.13576, epsilon);
160  EXPECT_NEAR(function.Slope(0.8), 1.03184, epsilon);
161  EXPECT_NEAR(function.Slope(0.85), 0.89121, epsilon);
162  EXPECT_NEAR(function.Slope(0.9), 0.69778, epsilon);
163  EXPECT_NEAR(function.Slope(0.95), 0.42170, epsilon);
164  EXPECT_NEAR(function.Slope(1), 0, epsilon);
165}
166
167}  // namespace
168}  // namespace gfx
169