xref: /aosp_15_r20/external/libchrome/ui/gfx/geometry/cubic_bezier_unittest.cc (revision 635a864187cb8b6c713ff48b7e790a6b21769273) 
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 <memory>
8 
9 #include "testing/gtest/include/gtest/gtest.h"
10 
11 namespace gfx {
12 namespace {
13 
TEST(CubicBezierTest,Basic)14 TEST(CubicBezierTest, Basic) {
15   CubicBezier function(0.25, 0.0, 0.75, 1.0);
16 
17   double epsilon = 0.00015;
18 
19   EXPECT_NEAR(function.Solve(0), 0, epsilon);
20   EXPECT_NEAR(function.Solve(0.05), 0.01136, epsilon);
21   EXPECT_NEAR(function.Solve(0.1), 0.03978, epsilon);
22   EXPECT_NEAR(function.Solve(0.15), 0.079780, epsilon);
23   EXPECT_NEAR(function.Solve(0.2), 0.12803, epsilon);
24   EXPECT_NEAR(function.Solve(0.25), 0.18235, epsilon);
25   EXPECT_NEAR(function.Solve(0.3), 0.24115, epsilon);
26   EXPECT_NEAR(function.Solve(0.35), 0.30323, epsilon);
27   EXPECT_NEAR(function.Solve(0.4), 0.36761, epsilon);
28   EXPECT_NEAR(function.Solve(0.45), 0.43345, epsilon);
29   EXPECT_NEAR(function.Solve(0.5), 0.5, epsilon);
30   EXPECT_NEAR(function.Solve(0.6), 0.63238, epsilon);
31   EXPECT_NEAR(function.Solve(0.65), 0.69676, epsilon);
32   EXPECT_NEAR(function.Solve(0.7), 0.75884, epsilon);
33   EXPECT_NEAR(function.Solve(0.75), 0.81764, epsilon);
34   EXPECT_NEAR(function.Solve(0.8), 0.87196, epsilon);
35   EXPECT_NEAR(function.Solve(0.85), 0.92021, epsilon);
36   EXPECT_NEAR(function.Solve(0.9), 0.96021, epsilon);
37   EXPECT_NEAR(function.Solve(0.95), 0.98863, epsilon);
38   EXPECT_NEAR(function.Solve(1), 1, epsilon);
39 
40   CubicBezier basic_use(0.5, 1.0, 0.5, 1.0);
41   EXPECT_EQ(0.875, basic_use.Solve(0.5));
42 
43   CubicBezier overshoot(0.5, 2.0, 0.5, 2.0);
44   EXPECT_EQ(1.625, overshoot.Solve(0.5));
45 
46   CubicBezier undershoot(0.5, -1.0, 0.5, -1.0);
47   EXPECT_EQ(-0.625, undershoot.Solve(0.5));
48 }
49 
50 // Tests that solving the bezier works with knots with y not in (0, 1).
TEST(CubicBezierTest,UnclampedYValues)51 TEST(CubicBezierTest, UnclampedYValues) {
52   CubicBezier function(0.5, -1.0, 0.5, 2.0);
53 
54   double epsilon = 0.00015;
55 
56   EXPECT_NEAR(function.Solve(0.0), 0.0, epsilon);
57   EXPECT_NEAR(function.Solve(0.05), -0.08954, epsilon);
58   EXPECT_NEAR(function.Solve(0.1), -0.15613, epsilon);
59   EXPECT_NEAR(function.Solve(0.15), -0.19641, epsilon);
60   EXPECT_NEAR(function.Solve(0.2), -0.20651, epsilon);
61   EXPECT_NEAR(function.Solve(0.25), -0.18232, epsilon);
62   EXPECT_NEAR(function.Solve(0.3), -0.11992, epsilon);
63   EXPECT_NEAR(function.Solve(0.35), -0.01672, epsilon);
64   EXPECT_NEAR(function.Solve(0.4), 0.12660, epsilon);
65   EXPECT_NEAR(function.Solve(0.45), 0.30349, epsilon);
66   EXPECT_NEAR(function.Solve(0.5), 0.50000, epsilon);
67   EXPECT_NEAR(function.Solve(0.55), 0.69651, epsilon);
68   EXPECT_NEAR(function.Solve(0.6), 0.87340, epsilon);
69   EXPECT_NEAR(function.Solve(0.65), 1.01672, epsilon);
70   EXPECT_NEAR(function.Solve(0.7), 1.11992, epsilon);
71   EXPECT_NEAR(function.Solve(0.75), 1.18232, epsilon);
72   EXPECT_NEAR(function.Solve(0.8), 1.20651, epsilon);
73   EXPECT_NEAR(function.Solve(0.85), 1.19641, epsilon);
74   EXPECT_NEAR(function.Solve(0.9), 1.15613, epsilon);
75   EXPECT_NEAR(function.Solve(0.95), 1.08954, epsilon);
76   EXPECT_NEAR(function.Solve(1.0), 1.0, epsilon);
77 }
78 
TEST(CubicBezierTest,Range)79 TEST(CubicBezierTest, Range) {
80   double epsilon = 0.00015;
81 
82   // Derivative is a constant.
83   std::unique_ptr<CubicBezier> function(
84       new CubicBezier(0.25, (1.0 / 3.0), 0.75, (2.0 / 3.0)));
85   EXPECT_EQ(0, function->range_min());
86   EXPECT_EQ(1, function->range_max());
87 
88   // Derivative is linear.
89   function.reset(new CubicBezier(0.25, -0.5, 0.75, (-1.0 / 6.0)));
90   EXPECT_NEAR(function->range_min(), -0.225, epsilon);
91   EXPECT_EQ(1, function->range_max());
92 
93   // Derivative has no real roots.
94   function.reset(new CubicBezier(0.25, 0.25, 0.75, 0.5));
95   EXPECT_EQ(0, function->range_min());
96   EXPECT_EQ(1, function->range_max());
97 
98   // Derivative has exactly one real root.
99   function.reset(new CubicBezier(0.0, 1.0, 1.0, 0.0));
100   EXPECT_EQ(0, function->range_min());
101   EXPECT_EQ(1, function->range_max());
102 
103   // Derivative has one root < 0 and one root > 1.
104   function.reset(new CubicBezier(0.25, 0.1, 0.75, 0.9));
105   EXPECT_EQ(0, function->range_min());
106   EXPECT_EQ(1, function->range_max());
107 
108   // Derivative has two roots in [0,1].
109   function.reset(new CubicBezier(0.25, 2.5, 0.75, 0.5));
110   EXPECT_EQ(0, function->range_min());
111   EXPECT_NEAR(function->range_max(), 1.28818, epsilon);
112   function.reset(new CubicBezier(0.25, 0.5, 0.75, -1.5));
113   EXPECT_NEAR(function->range_min(), -0.28818, epsilon);
114   EXPECT_EQ(1, function->range_max());
115 
116   // Derivative has one root < 0 and one root in [0,1].
117   function.reset(new CubicBezier(0.25, 0.1, 0.75, 1.5));
118   EXPECT_EQ(0, function->range_min());
119   EXPECT_NEAR(function->range_max(), 1.10755, epsilon);
120 
121   // Derivative has one root in [0,1] and one root > 1.
122   function.reset(new CubicBezier(0.25, -0.5, 0.75, 0.9));
123   EXPECT_NEAR(function->range_min(), -0.10755, epsilon);
124   EXPECT_EQ(1, function->range_max());
125 
126   // Derivative has two roots < 0.
127   function.reset(new CubicBezier(0.25, 0.3, 0.75, 0.633));
128   EXPECT_EQ(0, function->range_min());
129   EXPECT_EQ(1, function->range_max());
130 
131   // Derivative has two roots > 1.
132   function.reset(new CubicBezier(0.25, 0.367, 0.75, 0.7));
133   EXPECT_EQ(0.f, function->range_min());
134   EXPECT_EQ(1.f, function->range_max());
135 }
136 
TEST(CubicBezierTest,Slope)137 TEST(CubicBezierTest, Slope) {
138   CubicBezier function(0.25, 0.0, 0.75, 1.0);
139 
140   double epsilon = 0.00015;
141 
142   EXPECT_NEAR(function.Slope(-0.1), 0, epsilon);
143   EXPECT_NEAR(function.Slope(0), 0, epsilon);
144   EXPECT_NEAR(function.Slope(0.05), 0.42170, epsilon);
145   EXPECT_NEAR(function.Slope(0.1), 0.69778, epsilon);
146   EXPECT_NEAR(function.Slope(0.15), 0.89121, epsilon);
147   EXPECT_NEAR(function.Slope(0.2), 1.03184, epsilon);
148   EXPECT_NEAR(function.Slope(0.25), 1.13576, epsilon);
149   EXPECT_NEAR(function.Slope(0.3), 1.21239, epsilon);
150   EXPECT_NEAR(function.Slope(0.35), 1.26751, epsilon);
151   EXPECT_NEAR(function.Slope(0.4), 1.30474, epsilon);
152   EXPECT_NEAR(function.Slope(0.45), 1.32628, epsilon);
153   EXPECT_NEAR(function.Slope(0.5), 1.33333, epsilon);
154   EXPECT_NEAR(function.Slope(0.55), 1.32628, epsilon);
155   EXPECT_NEAR(function.Slope(0.6), 1.30474, epsilon);
156   EXPECT_NEAR(function.Slope(0.65), 1.26751, epsilon);
157   EXPECT_NEAR(function.Slope(0.7), 1.21239, epsilon);
158   EXPECT_NEAR(function.Slope(0.75), 1.13576, epsilon);
159   EXPECT_NEAR(function.Slope(0.8), 1.03184, epsilon);
160   EXPECT_NEAR(function.Slope(0.85), 0.89121, epsilon);
161   EXPECT_NEAR(function.Slope(0.9), 0.69778, epsilon);
162   EXPECT_NEAR(function.Slope(0.95), 0.42170, epsilon);
163   EXPECT_NEAR(function.Slope(1), 0, epsilon);
164   EXPECT_NEAR(function.Slope(1.1), 0, epsilon);
165 }
166 
TEST(CubicBezierTest,InputOutOfRange)167 TEST(CubicBezierTest, InputOutOfRange) {
168   CubicBezier simple(0.5, 1.0, 0.5, 1.0);
169   EXPECT_EQ(-2.0, simple.Solve(-1.0));
170   EXPECT_EQ(1.0, simple.Solve(2.0));
171 
172   CubicBezier at_edge_of_range(0.5, 1.0, 0.5, 1.0);
173   EXPECT_EQ(0.0, at_edge_of_range.Solve(0.0));
174   EXPECT_EQ(1.0, at_edge_of_range.Solve(1.0));
175 
176   CubicBezier large_epsilon(0.5, 1.0, 0.5, 1.0);
177   EXPECT_EQ(-2.0, large_epsilon.SolveWithEpsilon(-1.0, 1.0));
178   EXPECT_EQ(1.0, large_epsilon.SolveWithEpsilon(2.0, 1.0));
179 
180   CubicBezier coincident_endpoints(0.0, 0.0, 1.0, 1.0);
181   EXPECT_EQ(-1.0, coincident_endpoints.Solve(-1.0));
182   EXPECT_EQ(2.0, coincident_endpoints.Solve(2.0));
183 
184   CubicBezier vertical_gradient(0.0, 1.0, 1.0, 0.0);
185   EXPECT_EQ(0.0, vertical_gradient.Solve(-1.0));
186   EXPECT_EQ(1.0, vertical_gradient.Solve(2.0));
187 
188   CubicBezier distinct_endpoints(0.1, 0.2, 0.8, 0.8);
189   EXPECT_EQ(-2.0, distinct_endpoints.Solve(-1.0));
190   EXPECT_EQ(2.0, distinct_endpoints.Solve(2.0));
191 
192   CubicBezier coincident_endpoint(0.0, 0.0, 0.8, 0.8);
193   EXPECT_EQ(-1.0, coincident_endpoint.Solve(-1.0));
194   EXPECT_EQ(2.0, coincident_endpoint.Solve(2.0));
195 
196   CubicBezier three_coincident_points(0.0, 0.0, 0.0, 0.0);
197   EXPECT_EQ(0, three_coincident_points.Solve(-1.0));
198   EXPECT_EQ(2.0, three_coincident_points.Solve(2.0));
199 }
200 
TEST(CubicBezierTest,GetPoints)201 TEST(CubicBezierTest, GetPoints) {
202   double epsilon = 0.00015;
203 
204   CubicBezier cubic1(0.1, 0.2, 0.8, 0.9);
205   EXPECT_NEAR(0.1, cubic1.GetX1(), epsilon);
206   EXPECT_NEAR(0.2, cubic1.GetY1(), epsilon);
207   EXPECT_NEAR(0.8, cubic1.GetX2(), epsilon);
208   EXPECT_NEAR(0.9, cubic1.GetY2(), epsilon);
209 
210   CubicBezier cubic_zero(0, 0, 0, 0);
211   EXPECT_NEAR(0, cubic_zero.GetX1(), epsilon);
212   EXPECT_NEAR(0, cubic_zero.GetY1(), epsilon);
213   EXPECT_NEAR(0, cubic_zero.GetX2(), epsilon);
214   EXPECT_NEAR(0, cubic_zero.GetY2(), epsilon);
215 
216   CubicBezier cubic_one(1, 1, 1, 1);
217   EXPECT_NEAR(1, cubic_one.GetX1(), epsilon);
218   EXPECT_NEAR(1, cubic_one.GetY1(), epsilon);
219   EXPECT_NEAR(1, cubic_one.GetX2(), epsilon);
220   EXPECT_NEAR(1, cubic_one.GetY2(), epsilon);
221 
222   CubicBezier cubic_oor(-0.5, -1.5, 1.5, -1.6);
223   EXPECT_NEAR(-0.5, cubic_oor.GetX1(), epsilon);
224   EXPECT_NEAR(-1.5, cubic_oor.GetY1(), epsilon);
225   EXPECT_NEAR(1.5, cubic_oor.GetX2(), epsilon);
226   EXPECT_NEAR(-1.6, cubic_oor.GetY2(), epsilon);
227 }
228 
229 }  // namespace
230 }  // namespace gfx
231