matrix_test.cpp 9.9 KB

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  1. /*
  2. * DoRayMe - a quick and dirty Raytracer
  3. * Matric unit tests
  4. *
  5. * Created by Manoël Trapier
  6. * Copyright (c) 2020 986-Studio.
  7. *
  8. */
  9. #include <matrix.h>
  10. #include <tuple.h>
  11. #include <math.h>
  12. #include <gtest/gtest.h>
  13. TEST(MatrixTest, Constructing_and_inspecting_a_4x4_Matrix)
  14. {
  15. double values[] = {1, 2, 3, 4,
  16. 5.5, 6.5, 7.5, 8.5,
  17. 9, 10, 11, 12,
  18. 13.5, 14.5, 15.5, 16.5};
  19. Matrix4 m = Matrix4(values);
  20. ASSERT_EQ(m.get(0, 0), 1);
  21. ASSERT_EQ(m.get(0, 3), 4);
  22. ASSERT_EQ(m.get(1, 0), 5.5);
  23. ASSERT_EQ(m.get(1, 2), 7.5);
  24. ASSERT_EQ(m.get(2, 2), 11);
  25. ASSERT_EQ(m.get(3, 0), 13.5);
  26. ASSERT_EQ(m.get(3, 2), 15.5);
  27. }
  28. TEST(MatrixTest, A_2x2_matric_ought_to_be_representable)
  29. {
  30. double values[] = {-3, 5,
  31. 1, -2};
  32. Matrix2 m = Matrix2(values);
  33. ASSERT_EQ(m.get(0, 0), -3);
  34. ASSERT_EQ(m.get(0, 1), 5);
  35. ASSERT_EQ(m.get(1, 0), 1);
  36. ASSERT_EQ(m.get(1, 1), -2);
  37. }
  38. TEST(MatrixTest, A_3x3_matric_ought_to_be_representable)
  39. {
  40. double values[] = {-3, 5, 0,
  41. 1, -2, -7,
  42. 0, 1, 1};
  43. Matrix3 m = Matrix3(values);
  44. ASSERT_EQ(m.get(0, 0), -3);
  45. ASSERT_EQ(m.get(1, 1), -2);
  46. ASSERT_EQ(m.get(2, 2), 1);
  47. }
  48. TEST(MatrixTest, Matrix_equality_with_identical_matrix)
  49. {
  50. double values1[] = {1, 2, 3, 4,
  51. 5, 6, 7, 8,
  52. 9, 8, 7, 6,
  53. 5, 4, 3, 2};
  54. double values2[] = {1, 2, 3, 4,
  55. 5, 6, 7, 8,
  56. 9, 8, 7, 6,
  57. 5, 4, 3, 2};
  58. Matrix4 A = Matrix4(values1);
  59. Matrix4 B = Matrix4(values2);
  60. ASSERT_EQ(A, B);
  61. }
  62. TEST(MatrixTest, Matrix_equality_with_different_matrix)
  63. {
  64. double values1[] = {1, 2, 3, 4,
  65. 5, 6, 7, 8,
  66. 9, 8, 7, 6,
  67. 5, 4, 3, 2};
  68. double values2[] = {2, 3, 4, 5,
  69. 6, 7, 8, 9,
  70. 8, 7, 6, 5,
  71. 4, 3, 2, 1};
  72. Matrix4 A = Matrix4(values1);
  73. Matrix4 B = Matrix4(values2);
  74. ASSERT_NE(A, B);
  75. }
  76. TEST(MatrixTest, Multiplying_two_matrices)
  77. {
  78. double values1[] = {1, 2, 3, 4,
  79. 5, 6, 7, 8,
  80. 9, 8, 7, 6,
  81. 5, 4, 3, 2};
  82. double values2[] = {-2, 1, 2, 3,
  83. 3, 2, 1, -1,
  84. 4, 3, 6, 5,
  85. 1, 2, 7, 8};
  86. double results[] = {20, 22, 50, 48,
  87. 44, 54, 114, 108,
  88. 40, 58, 110, 102,
  89. 16, 26, 46, 42};
  90. Matrix4 A = Matrix4(values1);
  91. Matrix4 B = Matrix4(values2);
  92. ASSERT_EQ(A * B, Matrix4(results));
  93. }
  94. TEST(MatrixTest, A_matrix_multiplyed_by_a_tuple)
  95. {
  96. double valuesA[] = {1, 2, 3, 4,
  97. 2, 4, 4, 2,
  98. 8, 6, 4, 1,
  99. 0, 0, 0, 1};
  100. Matrix4 A = Matrix4(valuesA);
  101. Tuple b = Tuple(1, 2, 3, 1);
  102. ASSERT_EQ(A * b, Tuple(18, 24, 33, 1));
  103. }
  104. TEST(MatrixTest, Multiplying_a_matrix_by_the_identity_matrix)
  105. {
  106. double valuesA[] = {0, 1, 2, 4,
  107. 1, 2, 4, 8,
  108. 2, 4, 8, 16,
  109. 4, 8, 16, 32};
  110. Matrix4 A = Matrix4(valuesA);
  111. Matrix ident = Matrix4().identity();
  112. ASSERT_EQ(A * ident, A);
  113. }
  114. TEST(MatrixTest, Multiplying_the_identity_matrix_by_a_tuple)
  115. {
  116. Tuple a = Tuple(1, 2, 3, 4);
  117. Matrix ident = Matrix4().identity();
  118. ASSERT_EQ(ident * a, a);
  119. }
  120. TEST(MatrixTest, Transposing_a_matrix)
  121. {
  122. double valuesA[] = {0, 9, 3, 0,
  123. 9, 8, 0, 8,
  124. 1, 8, 5, 3,
  125. 0, 0, 5, 8};
  126. double results[] = {0, 9, 1, 0,
  127. 9, 8, 8, 0,
  128. 3, 0, 5, 5,
  129. 0, 8, 3, 8};
  130. Matrix A = Matrix4(valuesA);
  131. ASSERT_EQ(A.transpose(), Matrix4(results));
  132. }
  133. TEST(MatrixTest, Transposing_this_identity_matrix)
  134. {
  135. Matrix ident = Matrix4().identity();
  136. ASSERT_EQ(ident.transpose(), ident);
  137. }
  138. TEST(MatrixTest, Calculating_the_determinant_of_a_2x2_matrix)
  139. {
  140. double valuesA[] = { 1, 5,
  141. -3, 2 };
  142. Matrix2 A = Matrix2(valuesA);
  143. ASSERT_EQ(A.determinant(), 17);
  144. }
  145. TEST(MatrixTest, A_submatrix_of_a_3x3_matrix_is_a_2x2_matrix)
  146. {
  147. double valuesA[] = { 1, 5, 0,
  148. -3, 2, 7,
  149. 0, 6, -3 };
  150. double results[] = { -3, 2,
  151. 0, 6 };
  152. Matrix3 A = Matrix3(valuesA);
  153. ASSERT_EQ(A.submatrix(0, 2), Matrix2(results));
  154. }
  155. TEST(MatrixTest, A_submatrix_of_a_4x4_matrix_is_a_3x3_matrix)
  156. {
  157. double valuesA[] = { -6, 1, 1, 6,
  158. -8, 5, 8, 6,
  159. -1, 0, 8, 2,
  160. -7, 1, -1, 1 };
  161. double results[] = { -6, 1, 6,
  162. -8, 8, 6,
  163. -7,-1, 1 };
  164. Matrix4 A = Matrix4(valuesA);
  165. ASSERT_EQ(A.submatrix(2, 1), Matrix3(results));
  166. }
  167. TEST(MatrixTest, Calculate_a_minor_of_a_3x3_matrix)
  168. {
  169. double valuesA[] = { 3, 5, 0,
  170. 2, -1, -7,
  171. 6, -1, 5 };
  172. Matrix3 A = Matrix3(valuesA);
  173. Matrix B = A.submatrix(1, 0);
  174. ASSERT_EQ(B.determinant(), 25);
  175. ASSERT_EQ(A.minor(1, 0), 25);
  176. }
  177. TEST(MatrixTest, Calculating_a_cofactor_of_a_3x3_matrix)
  178. {
  179. double valuesA[] = { 3, 5, 0,
  180. 2, -1, -7,
  181. 6, -1, 5 };
  182. Matrix3 A = Matrix3(valuesA);
  183. ASSERT_EQ(A.minor(0, 0), -12);
  184. ASSERT_EQ(A.cofactor(0, 0), -12);
  185. ASSERT_EQ(A.minor(1, 0), 25);
  186. ASSERT_EQ(A.cofactor(1, 0), -25);
  187. }
  188. TEST(MatrixTest, Calculating_the_determinant_of_a_3x3_matrix)
  189. {
  190. double valuesA[] = { 1, 2, 6,
  191. -5, 8, -4,
  192. 2, 6, 4 };
  193. Matrix A = Matrix3(valuesA);
  194. ASSERT_EQ(A.cofactor(0, 0), 56);
  195. ASSERT_EQ(A.cofactor(0, 1), 12);
  196. ASSERT_EQ(A.minor(0, 2), -46);
  197. ASSERT_EQ(A.determinant(), -196);
  198. }
  199. TEST(MatrixTest, Calculating_the_determinant_of_a_4x4_matrix)
  200. {
  201. double valuesA[] = { -2, -8, 3, 5,
  202. -3, 1, 7, 3,
  203. 1, 2, -9, 6,
  204. -6, 7, 7, -9 };
  205. Matrix A = Matrix4(valuesA);
  206. ASSERT_EQ(A.cofactor(0, 0), 690);
  207. ASSERT_EQ(A.cofactor(0, 1), 447);
  208. ASSERT_EQ(A.cofactor(0, 2), 210);
  209. ASSERT_EQ(A.minor(0, 3), -51);
  210. ASSERT_EQ(A.determinant(), -4071);
  211. }
  212. TEST(MatrixTest, Testing_an_invertible_matrix_for_invertibility)
  213. {
  214. double valuesA[] = { 6, 4, 4, 4,
  215. 5, 5, 7, 6,
  216. 4, -9, 3, -7,
  217. 9, 1, 7, -6 };
  218. Matrix A = Matrix4(valuesA);
  219. ASSERT_EQ(A.determinant(), -2120);
  220. ASSERT_TRUE(A.isInvertible());
  221. }
  222. TEST(MatrixTest, Testing_an_noninvertible_matrix_for_invertibility)
  223. {
  224. double valuesA[] = { -4, 2, -2, -3,
  225. 9, 6, 2, 6,
  226. 0, -5, 1, -5,
  227. 0, 0, 0, 0 };
  228. Matrix A = Matrix4(valuesA);
  229. ASSERT_EQ(A.determinant(), 0);
  230. ASSERT_FALSE(A.isInvertible());
  231. }
  232. TEST(MatrixTest, Calculating_the_inverse_of_a_matrix)
  233. {
  234. double valuesA[] = { -5, 2, 6, -8,
  235. 1, -5, 1, 8,
  236. 7, 7, -6, -7,
  237. 1, -3, 7, 4 };
  238. double results[] = { 0.21805, 0.45113, 0.24060, -0.04511,
  239. -0.80827, -1.45677, -0.44361, 0.52068,
  240. -0.07895, -0.22368, -0.05263, 0.19737,
  241. -0.52256, -0.81391, -0.30075, 0.30639 };
  242. Matrix A = Matrix4(valuesA);
  243. Matrix B = A.inverse();
  244. ASSERT_EQ(A.determinant(), 532);
  245. ASSERT_EQ(A.cofactor(2, 3), -160);
  246. ASSERT_NEAR(B.get(3, 2), -160./532., DBL_EPSILON);
  247. ASSERT_EQ(A.cofactor(3, 2), 105);
  248. ASSERT_NEAR(B.get(2, 3), 105./532., DBL_EPSILON);
  249. /* Temporary lower the precision */
  250. set_equal_precision(0.00001);
  251. ASSERT_EQ(B, Matrix4(results));
  252. /* Revert to default */
  253. set_equal_precision(FLT_EPSILON);
  254. }
  255. TEST(MatrixTest, Calculating_the_inverse_of_another_matrix)
  256. {
  257. double valuesA[] = { 8, -5, 9, 2,
  258. 7, 5, 6, 1,
  259. -6, 0, 9, 6,
  260. -3, 0, -9, -4 };
  261. double results[] = { -0.15385, -0.15385, -0.28205, -0.53846,
  262. -0.07692, 0.12308, 0.02564, 0.03077,
  263. 0.35897, 0.35897, 0.43590, 0.92308,
  264. -0.69231, -0.69231, -0.76923, -1.92308 };
  265. Matrix A = Matrix4(valuesA);
  266. Matrix B = A.inverse();
  267. /* Temporary lower the precision */
  268. set_equal_precision(0.00001);
  269. ASSERT_EQ(B, Matrix4(results));
  270. /* Revert to default */
  271. set_equal_precision(FLT_EPSILON);
  272. }
  273. TEST(MatrixTest, Calculating_the_inverse_of_third_matrix)
  274. {
  275. double valuesA[] = { 9, 3, 0, 9,
  276. -5, -2, -6, -3,
  277. -4, 9, 6, 4,
  278. -7, 6, 6, 2 };
  279. double results[] = { -0.04074, -0.07778, 0.14444, -0.22222,
  280. -0.07778, 0.03333, 0.36667, -0.33333,
  281. -0.02901, -0.14630, -0.10926, 0.12963,
  282. 0.17778, 0.06667, -0.26667, 0.33333 };
  283. Matrix A = Matrix4(valuesA);
  284. Matrix B = A.inverse();
  285. /* Temporary lower the precision */
  286. set_equal_precision(0.00001);
  287. ASSERT_EQ(B, Matrix4(results));
  288. /* Revert to default */
  289. set_equal_precision(FLT_EPSILON);
  290. }
  291. TEST(MatrixTest, Multiplying_a_product_by_its_inverse)
  292. {
  293. double valuesA[] = { 3, -9, 7, 3,
  294. 3, -8, 2, -9,
  295. -4, 4, 4, 1,
  296. -6, 5, -1, 1 };
  297. double valuesB[] = { 8, 2, 2, 2,
  298. 3, -1, 7, 0,
  299. 7, 0, 5, 4,
  300. 6, -2, 0, 5 };
  301. Matrix A = Matrix4(valuesA);
  302. Matrix B = Matrix4(valuesB);
  303. Matrix C = A * B;
  304. ASSERT_EQ(C * B.inverse(), A);
  305. }