cubic_bezier_unittest.cc 13 KB

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  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. #include "ui/gfx/geometry/cubic_bezier.h"
  5. #include <cmath>
  6. #include <memory>
  7. #include "testing/gtest/include/gtest/gtest.h"
  8. namespace gfx {
  9. namespace {
  10. TEST(CubicBezierTest, Basic) {
  11. CubicBezier function(0.25, 0.0, 0.75, 1.0);
  12. double epsilon = 0.00015;
  13. EXPECT_NEAR(function.Solve(0), 0, epsilon);
  14. EXPECT_NEAR(function.Solve(0.05), 0.01136, epsilon);
  15. EXPECT_NEAR(function.Solve(0.1), 0.03978, epsilon);
  16. EXPECT_NEAR(function.Solve(0.15), 0.079780, epsilon);
  17. EXPECT_NEAR(function.Solve(0.2), 0.12803, epsilon);
  18. EXPECT_NEAR(function.Solve(0.25), 0.18235, epsilon);
  19. EXPECT_NEAR(function.Solve(0.3), 0.24115, epsilon);
  20. EXPECT_NEAR(function.Solve(0.35), 0.30323, epsilon);
  21. EXPECT_NEAR(function.Solve(0.4), 0.36761, epsilon);
  22. EXPECT_NEAR(function.Solve(0.45), 0.43345, epsilon);
  23. EXPECT_NEAR(function.Solve(0.5), 0.5, epsilon);
  24. EXPECT_NEAR(function.Solve(0.6), 0.63238, epsilon);
  25. EXPECT_NEAR(function.Solve(0.65), 0.69676, epsilon);
  26. EXPECT_NEAR(function.Solve(0.7), 0.75884, epsilon);
  27. EXPECT_NEAR(function.Solve(0.75), 0.81764, epsilon);
  28. EXPECT_NEAR(function.Solve(0.8), 0.87196, epsilon);
  29. EXPECT_NEAR(function.Solve(0.85), 0.92021, epsilon);
  30. EXPECT_NEAR(function.Solve(0.9), 0.96021, epsilon);
  31. EXPECT_NEAR(function.Solve(0.95), 0.98863, epsilon);
  32. EXPECT_NEAR(function.Solve(1), 1, epsilon);
  33. CubicBezier basic_use(0.5, 1.0, 0.5, 1.0);
  34. EXPECT_EQ(0.875, basic_use.Solve(0.5));
  35. CubicBezier overshoot(0.5, 2.0, 0.5, 2.0);
  36. EXPECT_EQ(1.625, overshoot.Solve(0.5));
  37. CubicBezier undershoot(0.5, -1.0, 0.5, -1.0);
  38. EXPECT_EQ(-0.625, undershoot.Solve(0.5));
  39. }
  40. // Tests that solving the bezier works with knots with y not in (0, 1).
  41. TEST(CubicBezierTest, UnclampedYValues) {
  42. CubicBezier function(0.5, -1.0, 0.5, 2.0);
  43. double epsilon = 0.00015;
  44. EXPECT_NEAR(function.Solve(0.0), 0.0, epsilon);
  45. EXPECT_NEAR(function.Solve(0.05), -0.08954, epsilon);
  46. EXPECT_NEAR(function.Solve(0.1), -0.15613, epsilon);
  47. EXPECT_NEAR(function.Solve(0.15), -0.19641, epsilon);
  48. EXPECT_NEAR(function.Solve(0.2), -0.20651, epsilon);
  49. EXPECT_NEAR(function.Solve(0.25), -0.18232, epsilon);
  50. EXPECT_NEAR(function.Solve(0.3), -0.11992, epsilon);
  51. EXPECT_NEAR(function.Solve(0.35), -0.01672, epsilon);
  52. EXPECT_NEAR(function.Solve(0.4), 0.12660, epsilon);
  53. EXPECT_NEAR(function.Solve(0.45), 0.30349, epsilon);
  54. EXPECT_NEAR(function.Solve(0.5), 0.50000, epsilon);
  55. EXPECT_NEAR(function.Solve(0.55), 0.69651, epsilon);
  56. EXPECT_NEAR(function.Solve(0.6), 0.87340, epsilon);
  57. EXPECT_NEAR(function.Solve(0.65), 1.01672, epsilon);
  58. EXPECT_NEAR(function.Solve(0.7), 1.11992, epsilon);
  59. EXPECT_NEAR(function.Solve(0.75), 1.18232, epsilon);
  60. EXPECT_NEAR(function.Solve(0.8), 1.20651, epsilon);
  61. EXPECT_NEAR(function.Solve(0.85), 1.19641, epsilon);
  62. EXPECT_NEAR(function.Solve(0.9), 1.15613, epsilon);
  63. EXPECT_NEAR(function.Solve(0.95), 1.08954, epsilon);
  64. EXPECT_NEAR(function.Solve(1.0), 1.0, epsilon);
  65. }
  66. static void TestBezierFiniteRange(CubicBezier& function) {
  67. for (double i = 0; i <= 1.01; i += 0.05) {
  68. EXPECT_TRUE(std::isfinite(function.Solve(i)));
  69. EXPECT_TRUE(std::isfinite(function.Slope(i)));
  70. EXPECT_TRUE(std::isfinite(function.GetX2()));
  71. EXPECT_TRUE(std::isfinite(function.GetY2()));
  72. EXPECT_TRUE(std::isfinite(function.SampleCurveX(i)));
  73. EXPECT_TRUE(std::isfinite(function.SampleCurveY(i)));
  74. EXPECT_TRUE(std::isfinite(function.SampleCurveDerivativeX(i)));
  75. EXPECT_TRUE(std::isfinite(function.SampleCurveDerivativeY(i)));
  76. }
  77. }
  78. // Tests that solving the bezier works with huge value infinity evaluation
  79. TEST(CubicBezierTest, ClampInfinityEvaluation) {
  80. auto test_cases = {
  81. CubicBezier(0.5, std::numeric_limits<double>::max(), 0.5,
  82. std::numeric_limits<double>::max()),
  83. CubicBezier(0.5, std::numeric_limits<double>::lowest(), 0.5,
  84. std::numeric_limits<double>::max()),
  85. CubicBezier(0.5, std::numeric_limits<double>::max(), 0.5,
  86. std::numeric_limits<double>::lowest()),
  87. CubicBezier(0.5, std::numeric_limits<double>::lowest(), 0.5,
  88. std::numeric_limits<double>::lowest()),
  89. CubicBezier(0, std::numeric_limits<double>::max(), 0,
  90. std::numeric_limits<double>::max()),
  91. CubicBezier(0, std::numeric_limits<double>::lowest(), 0,
  92. std::numeric_limits<double>::max()),
  93. CubicBezier(0, std::numeric_limits<double>::max(), 0,
  94. std::numeric_limits<double>::lowest()),
  95. CubicBezier(0, std::numeric_limits<double>::lowest(), 0,
  96. std::numeric_limits<double>::lowest()),
  97. CubicBezier(1, std::numeric_limits<double>::max(), 1,
  98. std::numeric_limits<double>::max()),
  99. CubicBezier(1, std::numeric_limits<double>::lowest(), 1,
  100. std::numeric_limits<double>::max()),
  101. CubicBezier(1, std::numeric_limits<double>::max(), 1,
  102. std::numeric_limits<double>::lowest()),
  103. CubicBezier(1, std::numeric_limits<double>::lowest(), 1,
  104. std::numeric_limits<double>::lowest()),
  105. CubicBezier(0, 0, 0, std::numeric_limits<double>::max()),
  106. CubicBezier(0, std::numeric_limits<double>::lowest(), 0, 0),
  107. CubicBezier(1, 0, 0, std::numeric_limits<double>::lowest()),
  108. CubicBezier(0, std::numeric_limits<double>::lowest(), 1, 1),
  109. };
  110. for (auto tc : test_cases) {
  111. TestBezierFiniteRange(tc);
  112. }
  113. }
  114. TEST(CubicBezierTest, Range) {
  115. double epsilon = 0.00015;
  116. // Derivative is a constant.
  117. std::unique_ptr<CubicBezier> function =
  118. std::make_unique<CubicBezier>(0.25, (1.0 / 3.0), 0.75, (2.0 / 3.0));
  119. EXPECT_EQ(0, function->range_min());
  120. EXPECT_EQ(1, function->range_max());
  121. // Derivative is linear.
  122. function = std::make_unique<CubicBezier>(0.25, -0.5, 0.75, (-1.0 / 6.0));
  123. EXPECT_NEAR(function->range_min(), -0.225, epsilon);
  124. EXPECT_EQ(1, function->range_max());
  125. // Derivative has no real roots.
  126. function = std::make_unique<CubicBezier>(0.25, 0.25, 0.75, 0.5);
  127. EXPECT_EQ(0, function->range_min());
  128. EXPECT_EQ(1, function->range_max());
  129. // Derivative has exactly one real root.
  130. function = std::make_unique<CubicBezier>(0.0, 1.0, 1.0, 0.0);
  131. EXPECT_EQ(0, function->range_min());
  132. EXPECT_EQ(1, function->range_max());
  133. // Derivative has one root < 0 and one root > 1.
  134. function = std::make_unique<CubicBezier>(0.25, 0.1, 0.75, 0.9);
  135. EXPECT_EQ(0, function->range_min());
  136. EXPECT_EQ(1, function->range_max());
  137. // Derivative has two roots in [0,1].
  138. function = std::make_unique<CubicBezier>(0.25, 2.5, 0.75, 0.5);
  139. EXPECT_EQ(0, function->range_min());
  140. EXPECT_NEAR(function->range_max(), 1.28818, epsilon);
  141. function = std::make_unique<CubicBezier>(0.25, 0.5, 0.75, -1.5);
  142. EXPECT_NEAR(function->range_min(), -0.28818, epsilon);
  143. EXPECT_EQ(1, function->range_max());
  144. // Derivative has one root < 0 and one root in [0,1].
  145. function = std::make_unique<CubicBezier>(0.25, 0.1, 0.75, 1.5);
  146. EXPECT_EQ(0, function->range_min());
  147. EXPECT_NEAR(function->range_max(), 1.10755, epsilon);
  148. // Derivative has one root in [0,1] and one root > 1.
  149. function = std::make_unique<CubicBezier>(0.25, -0.5, 0.75, 0.9);
  150. EXPECT_NEAR(function->range_min(), -0.10755, epsilon);
  151. EXPECT_EQ(1, function->range_max());
  152. // Derivative has two roots < 0.
  153. function = std::make_unique<CubicBezier>(0.25, 0.3, 0.75, 0.633);
  154. EXPECT_EQ(0, function->range_min());
  155. EXPECT_EQ(1, function->range_max());
  156. // Derivative has two roots > 1.
  157. function = std::make_unique<CubicBezier>(0.25, 0.367, 0.75, 0.7);
  158. EXPECT_EQ(0.f, function->range_min());
  159. EXPECT_EQ(1.f, function->range_max());
  160. }
  161. TEST(CubicBezierTest, Slope) {
  162. CubicBezier function(0.25, 0.0, 0.75, 1.0);
  163. double epsilon = 0.00015;
  164. EXPECT_NEAR(function.Slope(-0.1), 0, epsilon);
  165. EXPECT_NEAR(function.Slope(0), 0, epsilon);
  166. EXPECT_NEAR(function.Slope(0.05), 0.42170, epsilon);
  167. EXPECT_NEAR(function.Slope(0.1), 0.69778, epsilon);
  168. EXPECT_NEAR(function.Slope(0.15), 0.89121, epsilon);
  169. EXPECT_NEAR(function.Slope(0.2), 1.03184, epsilon);
  170. EXPECT_NEAR(function.Slope(0.25), 1.13576, epsilon);
  171. EXPECT_NEAR(function.Slope(0.3), 1.21239, epsilon);
  172. EXPECT_NEAR(function.Slope(0.35), 1.26751, epsilon);
  173. EXPECT_NEAR(function.Slope(0.4), 1.30474, epsilon);
  174. EXPECT_NEAR(function.Slope(0.45), 1.32628, epsilon);
  175. EXPECT_NEAR(function.Slope(0.5), 1.33333, epsilon);
  176. EXPECT_NEAR(function.Slope(0.55), 1.32628, epsilon);
  177. EXPECT_NEAR(function.Slope(0.6), 1.30474, epsilon);
  178. EXPECT_NEAR(function.Slope(0.65), 1.26751, epsilon);
  179. EXPECT_NEAR(function.Slope(0.7), 1.21239, epsilon);
  180. EXPECT_NEAR(function.Slope(0.75), 1.13576, epsilon);
  181. EXPECT_NEAR(function.Slope(0.8), 1.03184, epsilon);
  182. EXPECT_NEAR(function.Slope(0.85), 0.89121, epsilon);
  183. EXPECT_NEAR(function.Slope(0.9), 0.69778, epsilon);
  184. EXPECT_NEAR(function.Slope(0.95), 0.42170, epsilon);
  185. EXPECT_NEAR(function.Slope(1), 0, epsilon);
  186. EXPECT_NEAR(function.Slope(1.1), 0, epsilon);
  187. }
  188. TEST(CubicBezierTest, InputOutOfRange) {
  189. CubicBezier simple(0.5, 1.0, 0.5, 1.0);
  190. EXPECT_EQ(-2.0, simple.Solve(-1.0));
  191. EXPECT_EQ(1.0, simple.Solve(2.0));
  192. CubicBezier at_edge_of_range(0.5, 1.0, 0.5, 1.0);
  193. EXPECT_EQ(0.0, at_edge_of_range.Solve(0.0));
  194. EXPECT_EQ(1.0, at_edge_of_range.Solve(1.0));
  195. CubicBezier large_epsilon(0.5, 1.0, 0.5, 1.0);
  196. EXPECT_EQ(-2.0, large_epsilon.SolveWithEpsilon(-1.0, 1.0));
  197. EXPECT_EQ(1.0, large_epsilon.SolveWithEpsilon(2.0, 1.0));
  198. CubicBezier coincident_endpoints(0.0, 0.0, 1.0, 1.0);
  199. EXPECT_EQ(-1.0, coincident_endpoints.Solve(-1.0));
  200. EXPECT_EQ(2.0, coincident_endpoints.Solve(2.0));
  201. CubicBezier vertical_gradient(0.0, 1.0, 1.0, 0.0);
  202. EXPECT_EQ(0.0, vertical_gradient.Solve(-1.0));
  203. EXPECT_EQ(1.0, vertical_gradient.Solve(2.0));
  204. CubicBezier vertical_trailing_gradient(0.5, 0.0, 1.0, 0.5);
  205. EXPECT_EQ(0.0, vertical_trailing_gradient.Solve(-1.0));
  206. EXPECT_EQ(1.0, vertical_trailing_gradient.Solve(2.0));
  207. CubicBezier distinct_endpoints(0.1, 0.2, 0.8, 0.8);
  208. EXPECT_EQ(-2.0, distinct_endpoints.Solve(-1.0));
  209. EXPECT_EQ(2.0, distinct_endpoints.Solve(2.0));
  210. CubicBezier coincident_leading_endpoint(0.0, 0.0, 0.5, 1.0);
  211. EXPECT_EQ(-2.0, coincident_leading_endpoint.Solve(-1.0));
  212. EXPECT_EQ(1.0, coincident_leading_endpoint.Solve(2.0));
  213. CubicBezier coincident_trailing_endpoint(1.0, 0.5, 1.0, 1.0);
  214. EXPECT_EQ(-0.5, coincident_trailing_endpoint.Solve(-1.0));
  215. EXPECT_EQ(1.0, coincident_trailing_endpoint.Solve(2.0));
  216. // Two special cases with three coincident points. Both are equivalent to
  217. // linear.
  218. CubicBezier all_zeros(0.0, 0.0, 0.0, 0.0);
  219. EXPECT_EQ(-1.0, all_zeros.Solve(-1.0));
  220. EXPECT_EQ(2.0, all_zeros.Solve(2.0));
  221. CubicBezier all_ones(1.0, 1.0, 1.0, 1.0);
  222. EXPECT_EQ(-1.0, all_ones.Solve(-1.0));
  223. EXPECT_EQ(2.0, all_ones.Solve(2.0));
  224. }
  225. TEST(CubicBezierTest, GetPoints) {
  226. double epsilon = 0.00015;
  227. CubicBezier cubic1(0.1, 0.2, 0.8, 0.9);
  228. EXPECT_NEAR(0.1, cubic1.GetX1(), epsilon);
  229. EXPECT_NEAR(0.2, cubic1.GetY1(), epsilon);
  230. EXPECT_NEAR(0.8, cubic1.GetX2(), epsilon);
  231. EXPECT_NEAR(0.9, cubic1.GetY2(), epsilon);
  232. CubicBezier cubic_zero(0, 0, 0, 0);
  233. EXPECT_NEAR(0, cubic_zero.GetX1(), epsilon);
  234. EXPECT_NEAR(0, cubic_zero.GetY1(), epsilon);
  235. EXPECT_NEAR(0, cubic_zero.GetX2(), epsilon);
  236. EXPECT_NEAR(0, cubic_zero.GetY2(), epsilon);
  237. CubicBezier cubic_one(1, 1, 1, 1);
  238. EXPECT_NEAR(1, cubic_one.GetX1(), epsilon);
  239. EXPECT_NEAR(1, cubic_one.GetY1(), epsilon);
  240. EXPECT_NEAR(1, cubic_one.GetX2(), epsilon);
  241. EXPECT_NEAR(1, cubic_one.GetY2(), epsilon);
  242. CubicBezier cubic_oor(-0.5, -1.5, 1.5, -1.6);
  243. EXPECT_NEAR(-0.5, cubic_oor.GetX1(), epsilon);
  244. EXPECT_NEAR(-1.5, cubic_oor.GetY1(), epsilon);
  245. EXPECT_NEAR(1.5, cubic_oor.GetX2(), epsilon);
  246. EXPECT_NEAR(-1.6, cubic_oor.GetY2(), epsilon);
  247. }
  248. void validateSolver(const CubicBezier& cubic_bezier) {
  249. const double epsilon = 1e-7;
  250. const double precision = 1e-5;
  251. for (double t = 0; t <= 1; t += 0.05) {
  252. double x = cubic_bezier.SampleCurveX(t);
  253. double root = cubic_bezier.SolveCurveX(x, epsilon);
  254. EXPECT_NEAR(t, root, precision);
  255. }
  256. }
  257. TEST(CubicBezierTest, CommonEasingFunctions) {
  258. validateSolver(CubicBezier(0.25, 0.1, 0.25, 1)); // ease
  259. validateSolver(CubicBezier(0.42, 0, 1, 1)); // ease-in
  260. validateSolver(CubicBezier(0, 0, 0.58, 1)); // ease-out
  261. validateSolver(CubicBezier(0.42, 0, 0.58, 1)); // ease-in-out
  262. }
  263. TEST(CubicBezierTest, LinearEquivalentBeziers) {
  264. validateSolver(CubicBezier(0.0, 0.0, 0.0, 0.0));
  265. validateSolver(CubicBezier(1.0, 1.0, 1.0, 1.0));
  266. }
  267. TEST(CubicBezierTest, ControlPointsOutsideUnitSquare) {
  268. validateSolver(CubicBezier(0.3, 1.5, 0.8, 1.5));
  269. validateSolver(CubicBezier(0.4, -0.8, 0.7, 1.7));
  270. validateSolver(CubicBezier(0.7, -2.0, 1.0, -1.5));
  271. validateSolver(CubicBezier(0, 4, 1, -3));
  272. }
  273. } // namespace
  274. } // namespace gfx