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- /*
- * DoRayMe - a quick and dirty Raytracer
- * Matrix unit tests
- *
- * Created by Manoël Trapier
- * Copyright (c) 2020 986-Studio.
- *
- */
- #include <matrix.h>
- #include <tuple.h>
- #include <math.h>
- #include <gtest/gtest.h>
- 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);
- }
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