/* * DoRayMe - a quick and dirty Raytracer * Matrix unit tests * * Created by Manoƫl Trapier * Copyright (c) 2020 986-Studio. * */ #include #include #include #include TEST(MatrixTest, Constructing_and_inspecting_a_4x4_Matrix) { double values[] = {1, 2, 3, 4, 5.5, 6.5, 7.5, 8.5, 9, 10, 11, 12, 13.5, 14.5, 15.5, 16.5}; Matrix4 m = Matrix4(values); ASSERT_EQ(m.get(0, 0), 1); ASSERT_EQ(m.get(0, 3), 4); ASSERT_EQ(m.get(1, 0), 5.5); ASSERT_EQ(m.get(1, 2), 7.5); ASSERT_EQ(m.get(2, 2), 11); ASSERT_EQ(m.get(3, 0), 13.5); ASSERT_EQ(m.get(3, 2), 15.5); } TEST(MatrixTest, Change_a_single_value_and_check_it) { double values[] = {-3, 5, 1, -2}; Matrix2 m = Matrix2(values); ASSERT_EQ(m.get(0, 0), -3); ASSERT_EQ(m.get(0, 1), 5); ASSERT_EQ(m.get(1, 0), 1); ASSERT_EQ(m.get(1, 1), -2); m.set(0, 0, 12); ASSERT_EQ(m.get(0, 0), 12); } TEST(MatrixTest, A_3x3_matrix_ought_to_be_representable) { double values[] = {-3, 5, 0, 1, -2, -7, 0, 1, 1}; Matrix3 m = Matrix3(values); ASSERT_EQ(m.get(0, 0), -3); ASSERT_EQ(m.get(1, 1), -2); ASSERT_EQ(m.get(2, 2), 1); } TEST(MatrixTest, A_2x2_matrix_ought_to_be_representable) { double values[] = {-3, 5, 1, -2}; Matrix2 m = Matrix2(values); ASSERT_EQ(m.get(0, 0), -3); ASSERT_EQ(m.get(0, 1), 5); ASSERT_EQ(m.get(1, 0), 1); ASSERT_EQ(m.get(1, 1), -2); } TEST(MatrixTest, Matrix_equality_with_identical_matrix) { double values1[] = {1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2}; double values2[] = {1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2}; Matrix4 A = Matrix4(values1); Matrix4 B = Matrix4(values2); ASSERT_EQ(A, B); } TEST(MatrixTest, Matrix_equality_with_different_matrix) { double values1[] = {1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2}; double values2[] = {2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1}; Matrix4 A = Matrix4(values1); Matrix4 B = Matrix4(values2); ASSERT_NE(A, B); } TEST(MatrixTest, Multiplying_two_matrices) { double values1[] = {1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2}; double values2[] = {-2, 1, 2, 3, 3, 2, 1, -1, 4, 3, 6, 5, 1, 2, 7, 8}; double results[] = {20, 22, 50, 48, 44, 54, 114, 108, 40, 58, 110, 102, 16, 26, 46, 42}; Matrix4 A = Matrix4(values1); Matrix4 B = Matrix4(values2); ASSERT_EQ(A * B, Matrix4(results)); } TEST(MatrixTest, A_matrix_multiplyed_by_a_tuple) { double valuesA[] = {1, 2, 3, 4, 2, 4, 4, 2, 8, 6, 4, 1, 0, 0, 0, 1}; Matrix4 A = Matrix4(valuesA); Tuple b = Tuple(1, 2, 3, 1); ASSERT_EQ(A * b, Tuple(18, 24, 33, 1)); } TEST(MatrixTest, Multiplying_a_matrix_by_the_identity_matrix) { double valuesA[] = {0, 1, 2, 4, 1, 2, 4, 8, 2, 4, 8, 16, 4, 8, 16, 32}; Matrix4 A = Matrix4(valuesA); Matrix ident = Matrix4().identity(); ASSERT_EQ(A * ident, A); } TEST(MatrixTest, Multiplying_the_identity_matrix_by_a_tuple) { Tuple a = Tuple(1, 2, 3, 4); Matrix ident = Matrix4().identity(); ASSERT_EQ(ident * a, a); } TEST(MatrixTest, Transposing_a_matrix) { double valuesA[] = {0, 9, 3, 0, 9, 8, 0, 8, 1, 8, 5, 3, 0, 0, 5, 8}; double results[] = {0, 9, 1, 0, 9, 8, 8, 0, 3, 0, 5, 5, 0, 8, 3, 8}; Matrix A = Matrix4(valuesA); ASSERT_EQ(A.transpose(), Matrix4(results)); } TEST(MatrixTest, Transposing_this_identity_matrix) { Matrix ident = Matrix4().identity(); ASSERT_EQ(ident.transpose(), ident); } TEST(MatrixTest, Calculating_the_determinant_of_a_2x2_matrix) { double valuesA[] = { 1, 5, -3, 2 }; Matrix2 A = Matrix2(valuesA); ASSERT_EQ(A.determinant(), 17); } TEST(MatrixTest, A_submatrix_of_a_3x3_matrix_is_a_2x2_matrix) { double valuesA[] = { 1, 5, 0, -3, 2, 7, 0, 6, -3 }; double results[] = { -3, 2, 0, 6 }; Matrix3 A = Matrix3(valuesA); ASSERT_EQ(A.submatrix(0, 2), Matrix2(results)); } TEST(MatrixTest, A_submatrix_of_a_4x4_matrix_is_a_3x3_matrix) { double valuesA[] = { -6, 1, 1, 6, -8, 5, 8, 6, -1, 0, 8, 2, -7, 1, -1, 1 }; double results[] = { -6, 1, 6, -8, 8, 6, -7,-1, 1 }; Matrix4 A = Matrix4(valuesA); ASSERT_EQ(A.submatrix(2, 1), Matrix3(results)); } TEST(MatrixTest, Calculate_a_minor_of_a_3x3_matrix) { double valuesA[] = { 3, 5, 0, 2, -1, -7, 6, -1, 5 }; Matrix3 A = Matrix3(valuesA); Matrix B = A.submatrix(1, 0); ASSERT_EQ(B.determinant(), 25); ASSERT_EQ(A.minor(1, 0), 25); } TEST(MatrixTest, Calculating_a_cofactor_of_a_3x3_matrix) { double valuesA[] = { 3, 5, 0, 2, -1, -7, 6, -1, 5 }; Matrix3 A = Matrix3(valuesA); ASSERT_EQ(A.minor(0, 0), -12); ASSERT_EQ(A.cofactor(0, 0), -12); ASSERT_EQ(A.minor(1, 0), 25); ASSERT_EQ(A.cofactor(1, 0), -25); } TEST(MatrixTest, Calculating_the_determinant_of_a_3x3_matrix) { double valuesA[] = { 1, 2, 6, -5, 8, -4, 2, 6, 4 }; Matrix A = Matrix3(valuesA); ASSERT_EQ(A.cofactor(0, 0), 56); ASSERT_EQ(A.cofactor(0, 1), 12); ASSERT_EQ(A.minor(0, 2), -46); ASSERT_EQ(A.determinant(), -196); } TEST(MatrixTest, Calculating_the_determinant_of_a_4x4_matrix) { double valuesA[] = { -2, -8, 3, 5, -3, 1, 7, 3, 1, 2, -9, 6, -6, 7, 7, -9 }; Matrix A = Matrix4(valuesA); ASSERT_EQ(A.cofactor(0, 0), 690); ASSERT_EQ(A.cofactor(0, 1), 447); ASSERT_EQ(A.cofactor(0, 2), 210); ASSERT_EQ(A.minor(0, 3), -51); ASSERT_EQ(A.determinant(), -4071); } TEST(MatrixTest, Testing_an_invertible_matrix_for_invertibility) { double valuesA[] = { 6, 4, 4, 4, 5, 5, 7, 6, 4, -9, 3, -7, 9, 1, 7, -6 }; Matrix A = Matrix4(valuesA); ASSERT_EQ(A.determinant(), -2120); ASSERT_TRUE(A.isInvertible()); } TEST(MatrixTest, Testing_an_noninvertible_matrix_for_invertibility) { double valuesA[] = { -4, 2, -2, -3, 9, 6, 2, 6, 0, -5, 1, -5, 0, 0, 0, 0 }; Matrix A = Matrix4(valuesA); ASSERT_EQ(A.determinant(), 0); ASSERT_FALSE(A.isInvertible()); } TEST(MatrixTest, Calculating_the_inverse_of_a_matrix) { double valuesA[] = { -5, 2, 6, -8, 1, -5, 1, 8, 7, 7, -6, -7, 1, -3, 7, 4 }; double results[] = { 0.21805, 0.45113, 0.24060, -0.04511, -0.80827, -1.45677, -0.44361, 0.52068, -0.07895, -0.22368, -0.05263, 0.19737, -0.52256, -0.81391, -0.30075, 0.30639 }; Matrix A = Matrix4(valuesA); Matrix B = A.inverse(); ASSERT_EQ(A.determinant(), 532); ASSERT_EQ(A.cofactor(2, 3), -160); ASSERT_NEAR(B.get(3, 2), -160./532., DBL_EPSILON); ASSERT_EQ(A.cofactor(3, 2), 105); ASSERT_NEAR(B.get(2, 3), 105./532., DBL_EPSILON); /* Temporary lower the precision */ set_equal_precision(0.00001); ASSERT_EQ(B, Matrix4(results)); /* Revert to default */ set_equal_precision(FLT_EPSILON); } TEST(MatrixTest, Calculating_the_inverse_of_another_matrix) { double valuesA[] = { 8, -5, 9, 2, 7, 5, 6, 1, -6, 0, 9, 6, -3, 0, -9, -4 }; double results[] = { -0.15385, -0.15385, -0.28205, -0.53846, -0.07692, 0.12308, 0.02564, 0.03077, 0.35897, 0.35897, 0.43590, 0.92308, -0.69231, -0.69231, -0.76923, -1.92308 }; Matrix A = Matrix4(valuesA); Matrix B = A.inverse(); /* Temporary lower the precision */ set_equal_precision(0.00001); ASSERT_EQ(B, Matrix4(results)); /* Revert to default */ set_equal_precision(FLT_EPSILON); } TEST(MatrixTest, Calculating_the_inverse_of_third_matrix) { double valuesA[] = { 9, 3, 0, 9, -5, -2, -6, -3, -4, 9, 6, 4, -7, 6, 6, 2 }; double results[] = { -0.04074, -0.07778, 0.14444, -0.22222, -0.07778, 0.03333, 0.36667, -0.33333, -0.02901, -0.14630, -0.10926, 0.12963, 0.17778, 0.06667, -0.26667, 0.33333 }; Matrix A = Matrix4(valuesA); Matrix B = A.inverse(); /* Temporary lower the precision */ set_equal_precision(0.00001); ASSERT_EQ(B, Matrix4(results)); /* Revert to default */ set_equal_precision(FLT_EPSILON); } TEST(MatrixTest, Multiplying_a_product_by_its_inverse) { double valuesA[] = { 3, -9, 7, 3, 3, -8, 2, -9, -4, 4, 4, 1, -6, 5, -1, 1 }; double valuesB[] = { 8, 2, 2, 2, 3, -1, 7, 0, 7, 0, 5, 4, 6, -2, 0, 5 }; Matrix A = Matrix4(valuesA); Matrix B = Matrix4(valuesB); Matrix C = A * B; ASSERT_EQ(C * B.inverse(), A); }