| // Copyright 2014 The Chromium Authors. All rights reserved. |
| // Use of this source code is governed by a BSD-style license that can be |
| // found in the LICENSE file. |
| |
| #include <memory> |
| |
| #include "cobalt/math/cubic_bezier.h" |
| |
| #include "testing/gtest/include/gtest/gtest.h" |
| |
| namespace cobalt { |
| namespace math { |
| namespace { |
| |
| TEST(CubicBezierTest, Basic) { |
| CubicBezier function(0.25, 0.0, 0.75, 1.0); |
| |
| double epsilon = 0.00015; |
| |
| EXPECT_NEAR(function.Solve(0), 0, epsilon); |
| EXPECT_NEAR(function.Solve(0.05), 0.01136, epsilon); |
| EXPECT_NEAR(function.Solve(0.1), 0.03978, epsilon); |
| EXPECT_NEAR(function.Solve(0.15), 0.079780, epsilon); |
| EXPECT_NEAR(function.Solve(0.2), 0.12803, epsilon); |
| EXPECT_NEAR(function.Solve(0.25), 0.18235, epsilon); |
| EXPECT_NEAR(function.Solve(0.3), 0.24115, epsilon); |
| EXPECT_NEAR(function.Solve(0.35), 0.30323, epsilon); |
| EXPECT_NEAR(function.Solve(0.4), 0.36761, epsilon); |
| EXPECT_NEAR(function.Solve(0.45), 0.43345, epsilon); |
| EXPECT_NEAR(function.Solve(0.5), 0.5, epsilon); |
| EXPECT_NEAR(function.Solve(0.6), 0.63238, epsilon); |
| EXPECT_NEAR(function.Solve(0.65), 0.69676, epsilon); |
| EXPECT_NEAR(function.Solve(0.7), 0.75884, epsilon); |
| EXPECT_NEAR(function.Solve(0.75), 0.81764, epsilon); |
| EXPECT_NEAR(function.Solve(0.8), 0.87196, epsilon); |
| EXPECT_NEAR(function.Solve(0.85), 0.92021, epsilon); |
| EXPECT_NEAR(function.Solve(0.9), 0.96021, epsilon); |
| EXPECT_NEAR(function.Solve(0.95), 0.98863, epsilon); |
| EXPECT_NEAR(function.Solve(1), 1, epsilon); |
| } |
| |
| // Tests that solving the bezier works with knots with y not in (0, 1). |
| TEST(CubicBezierTest, UnclampedYValues) { |
| CubicBezier function(0.5, -1.0, 0.5, 2.0); |
| |
| double epsilon = 0.00015; |
| |
| EXPECT_NEAR(function.Solve(0.0), 0.0, epsilon); |
| EXPECT_NEAR(function.Solve(0.05), -0.08954, epsilon); |
| EXPECT_NEAR(function.Solve(0.1), -0.15613, epsilon); |
| EXPECT_NEAR(function.Solve(0.15), -0.19641, epsilon); |
| EXPECT_NEAR(function.Solve(0.2), -0.20651, epsilon); |
| EXPECT_NEAR(function.Solve(0.25), -0.18232, epsilon); |
| EXPECT_NEAR(function.Solve(0.3), -0.11992, epsilon); |
| EXPECT_NEAR(function.Solve(0.35), -0.01672, epsilon); |
| EXPECT_NEAR(function.Solve(0.4), 0.12660, epsilon); |
| EXPECT_NEAR(function.Solve(0.45), 0.30349, epsilon); |
| EXPECT_NEAR(function.Solve(0.5), 0.50000, epsilon); |
| EXPECT_NEAR(function.Solve(0.55), 0.69651, epsilon); |
| EXPECT_NEAR(function.Solve(0.6), 0.87340, epsilon); |
| EXPECT_NEAR(function.Solve(0.65), 1.01672, epsilon); |
| EXPECT_NEAR(function.Solve(0.7), 1.11992, epsilon); |
| EXPECT_NEAR(function.Solve(0.75), 1.18232, epsilon); |
| EXPECT_NEAR(function.Solve(0.8), 1.20651, epsilon); |
| EXPECT_NEAR(function.Solve(0.85), 1.19641, epsilon); |
| EXPECT_NEAR(function.Solve(0.9), 1.15613, epsilon); |
| EXPECT_NEAR(function.Solve(0.95), 1.08954, epsilon); |
| EXPECT_NEAR(function.Solve(1.0), 1.0, epsilon); |
| } |
| |
| TEST(CubicBezierTest, Range) { |
| double epsilon = 0.00015; |
| double min, max; |
| |
| // Derivative is a constant. |
| std::unique_ptr<CubicBezier> function( |
| new CubicBezier(0.25, (1.0 / 3.0), 0.75, (2.0 / 3.0))); |
| function->Range(&min, &max); |
| EXPECT_EQ(0, min); |
| EXPECT_EQ(1, max); |
| |
| // Derivative is linear. |
| function.reset(new CubicBezier(0.25, -0.5, 0.75, (-1.0 / 6.0))); |
| function->Range(&min, &max); |
| EXPECT_NEAR(min, -0.225, epsilon); |
| EXPECT_EQ(1, max); |
| |
| // Derivative has no real roots. |
| function.reset(new CubicBezier(0.25, 0.25, 0.75, 0.5)); |
| function->Range(&min, &max); |
| EXPECT_EQ(0, min); |
| EXPECT_EQ(1, max); |
| |
| // Derivative has exactly one real root. |
| function.reset(new CubicBezier(0.0, 1.0, 1.0, 0.0)); |
| function->Range(&min, &max); |
| EXPECT_EQ(0, min); |
| EXPECT_EQ(1, max); |
| |
| // Derivative has one root < 0 and one root > 1. |
| function.reset(new CubicBezier(0.25, 0.1, 0.75, 0.9)); |
| function->Range(&min, &max); |
| EXPECT_EQ(0, min); |
| EXPECT_EQ(1, max); |
| |
| // Derivative has two roots in [0,1]. |
| function.reset(new CubicBezier(0.25, 2.5, 0.75, 0.5)); |
| function->Range(&min, &max); |
| EXPECT_EQ(0, min); |
| EXPECT_NEAR(max, 1.28818, epsilon); |
| function.reset(new CubicBezier(0.25, 0.5, 0.75, -1.5)); |
| function->Range(&min, &max); |
| EXPECT_NEAR(min, -0.28818, epsilon); |
| EXPECT_EQ(1, max); |
| |
| // Derivative has one root < 0 and one root in [0,1]. |
| function.reset(new CubicBezier(0.25, 0.1, 0.75, 1.5)); |
| function->Range(&min, &max); |
| EXPECT_EQ(0, min); |
| EXPECT_NEAR(max, 1.10755, epsilon); |
| |
| // Derivative has one root in [0,1] and one root > 1. |
| function.reset(new CubicBezier(0.25, -0.5, 0.75, 0.9)); |
| function->Range(&min, &max); |
| EXPECT_NEAR(min, -0.10755, epsilon); |
| EXPECT_EQ(1, max); |
| |
| // Derivative has two roots < 0. |
| function.reset(new CubicBezier(0.25, 0.3, 0.75, 0.633)); |
| function->Range(&min, &max); |
| EXPECT_EQ(0, min); |
| EXPECT_EQ(1, max); |
| |
| // Derivative has two roots > 1. |
| function.reset(new CubicBezier(0.25, 0.367, 0.75, 0.7)); |
| function->Range(&min, &max); |
| EXPECT_EQ(0.f, min); |
| EXPECT_EQ(1.f, max); |
| } |
| |
| TEST(CubicBezierTest, Slope) { |
| CubicBezier function(0.25, 0.0, 0.75, 1.0); |
| |
| double epsilon = 0.00015; |
| |
| EXPECT_NEAR(function.Slope(0), 0, epsilon); |
| EXPECT_NEAR(function.Slope(0.05), 0.42170, epsilon); |
| EXPECT_NEAR(function.Slope(0.1), 0.69778, epsilon); |
| EXPECT_NEAR(function.Slope(0.15), 0.89121, epsilon); |
| EXPECT_NEAR(function.Slope(0.2), 1.03184, epsilon); |
| EXPECT_NEAR(function.Slope(0.25), 1.13576, epsilon); |
| EXPECT_NEAR(function.Slope(0.3), 1.21239, epsilon); |
| EXPECT_NEAR(function.Slope(0.35), 1.26751, epsilon); |
| EXPECT_NEAR(function.Slope(0.4), 1.30474, epsilon); |
| EXPECT_NEAR(function.Slope(0.45), 1.32628, epsilon); |
| EXPECT_NEAR(function.Slope(0.5), 1.33333, epsilon); |
| EXPECT_NEAR(function.Slope(0.55), 1.32628, epsilon); |
| EXPECT_NEAR(function.Slope(0.6), 1.30474, epsilon); |
| EXPECT_NEAR(function.Slope(0.65), 1.26751, epsilon); |
| EXPECT_NEAR(function.Slope(0.7), 1.21239, epsilon); |
| EXPECT_NEAR(function.Slope(0.75), 1.13576, epsilon); |
| EXPECT_NEAR(function.Slope(0.8), 1.03184, epsilon); |
| EXPECT_NEAR(function.Slope(0.85), 0.89121, epsilon); |
| EXPECT_NEAR(function.Slope(0.9), 0.69778, epsilon); |
| EXPECT_NEAR(function.Slope(0.95), 0.42170, epsilon); |
| EXPECT_NEAR(function.Slope(1), 0, epsilon); |
| } |
| |
| } // namespace |
| } // namespace math |
| } // namespace cobalt |