/* * DoRayMe - a quick and dirty Raytracer * Transformations unit tests * * Created by Manoƫl Trapier * Copyright (c) 2020 986-Studio. * */ #include #include #include #include TEST(TransformationTest, Multiplying_by_a_translation_matrix) { Matrix transform = translation(5, -3, 2); Point p = Point(-3, 4, 5); ASSERT_EQ(transform * p, Point(2, 1, 7)); } TEST(TransformationTest, Multiplying_by_the_inverse_of_a_translation_matrix) { Matrix transform = translation(5, -3, 2); Matrix inv = transform.inverse(); Point p = Point(-3, 4, 5); ASSERT_EQ(inv * p, Point(-8, 7, 3)); } TEST(TransformationTest, Translation_does_not_affect_vectors) { Matrix transform = translation(5, -3, 2); Vector v = Vector(-3, 4, 5); ASSERT_EQ(transform * v, Vector(-3, 4, 5)); } TEST(TransformationTest, A_scaling_matrix_applied_to_a_point) { Matrix transform = scaling(2, 3, 4); Point p = Point(-4, 6, 8); ASSERT_EQ(transform * p, Point(-8, 18, 32)); } TEST(TransformationTest, A_scaling_matrix_applied_to_a_vector) { Matrix transform = scaling(2, 3, 4); Vector v = Vector(-4, 6, 8); ASSERT_EQ(transform * v, Vector(-8, 18, 32)); } TEST(TransformationTest, Multiplaying_by_the_inverse_of_a_scaling_matrix) { Matrix transform = scaling(2, 3, 4); Matrix inv = transform.inverse(); Vector v = Vector(-4, 6, 8); ASSERT_EQ(inv * v, Vector(-2, 2, 2)); } TEST(TransformationTest, Reflexion_is_scaling_by_a_negative_value) { Matrix transform = scaling(-1, 1, 1); Point p = Point(2, 3, 4); ASSERT_EQ(transform * p, Point(-2, 3, 4)); } TEST(TransformationTest, Rotating_a_point_around_the_X_axis) { Point p = Point(0, 1, 0); Matrix half_quarter = rotationX(M_PI / 4.); Matrix full_quarter = rotationX(M_PI / 2.); ASSERT_EQ(half_quarter * p, Point(0, sqrt(2)/2, sqrt(2)/2)); ASSERT_EQ(full_quarter * p, Point(0, 0, 1)); } TEST(TransformationTest, The_inverse_of_an_x_rotation_rotates_in_the_opposite_direction) { Point p = Point(0, 1, 0); Matrix half_quarter = rotationX(M_PI / 4.); Matrix inv = half_quarter.inverse(); ASSERT_EQ(inv * p, Point(0, sqrt(2)/2, -sqrt(2)/2)); } TEST(TransformationTest, Rotating_a_point_around_the_Y_axis) { Point p = Point(0, 0, 1); Matrix half_quarter = rotationY(M_PI / 4.); Matrix full_quarter = rotationY(M_PI / 2.); ASSERT_EQ(half_quarter * p, Point(sqrt(2)/2, 0, sqrt(2)/2)); ASSERT_EQ(full_quarter * p, Point(1, 0, 0)); } TEST(TransformationTest, Rotating_a_point_around_the_Z_axis) { Point p = Point(0, 1, 0); Matrix half_quarter = rotationZ(M_PI / 4.); Matrix full_quarter = rotationZ(M_PI / 2.); ASSERT_EQ(half_quarter * p, Point(-sqrt(2)/2, sqrt(2)/2, 0)); ASSERT_EQ(full_quarter * p, Point(-1, 0, 0)); } TEST(TransformationTest, A_shearing_transformation_moves_x_in_proportion_to_y) { Matrix transform = shearing(1, 0, 0, 0, 0, 0); Point p = Point(2, 3, 4); ASSERT_EQ(transform * p, Point(5, 3, 4)); } TEST(TransformationTest, A_shearing_transformation_moves_x_in_proportion_to_z) { Matrix transform = shearing(0, 1, 0, 0, 0, 0); Point p = Point(2, 3, 4); ASSERT_EQ(transform * p, Point(6, 3, 4)); } TEST(TransformationTest, A_shearing_transformation_moves_y_in_proportion_to_x) { Matrix transform = shearing(0, 0, 1, 0, 0, 0); Point p = Point(2, 3, 4); ASSERT_EQ(transform * p, Point(2, 5, 4)); } TEST(TransformationTest, A_shearing_transformation_moves_y_in_proportion_to_z) { Matrix transform = shearing(0, 0, 0, 1, 0, 0); Point p = Point(2, 3, 4); ASSERT_EQ(transform * p, Point(2, 7, 4)); } TEST(TransformationTest, A_shearing_transformation_moves_z_in_proportion_to_x) { Matrix transform = shearing(0, 0, 0, 0, 1, 0); Point p = Point(2, 3, 4); ASSERT_EQ(transform * p, Point(2, 3, 6)); } TEST(TransformationTest, A_shearing_transformation_moves_z_in_proportion_to_y) { Matrix transform = shearing(0, 0, 0, 0, 0, 1); Point p = Point(2, 3, 4); ASSERT_EQ(transform * p, Point(2, 3, 7)); } TEST(TransformationTest, Individual_trnasformations_are_applied_in_sequence) { Point p = Point(1, 0, 1); Matrix A = rotationX(M_PI / 2.); Matrix B = scaling(5, 5, 5); Matrix C = translation(10, 5, 7); Tuple p2 = A * p; ASSERT_EQ(p2, Point(1, -1, 0)); Tuple p3 = B * p2; ASSERT_EQ(p3, Point(5, -5, 0)); Tuple p4 = C * p3; ASSERT_EQ(p4, Point(15, 0, 7)); } TEST(TransformationTest, Chained_transformation_must_be_applied_in_reverse_order) { Point p = Point(1, 0, 1); Matrix A = rotationX(M_PI / 2.); Matrix B = scaling(5, 5, 5); Matrix C = translation(10, 5, 7); Matrix T = C * B * A; ASSERT_EQ(T * p, Point(15, 0, 7)); } TEST(TransformationTest, The_transformation_matrix_for_the_default_orientation) { Tuple from = Point(0, 0, 0); Tuple to = Point(0, 0, -1); Tuple up = Vector(0, 1, 0); Matrix t = viewTransform(from, to, up); ASSERT_EQ(t, Matrix4().identity()); } TEST(TransformationTest, A_view_transformation_matrix_looking_in_positive_z_direction) { Tuple from = Point(0, 0, 0); Tuple to = Point(0, 0, 1); Tuple up = Vector(0, 1, 0); Matrix t = viewTransform(from, to, up); ASSERT_EQ(t, scaling(-1, 1, -1)); } TEST(TransformationTest, The_view_transformation_move_the_world) { Tuple from = Point(0, 0, 8); Tuple to = Point(0, 0, 0); Tuple up = Vector(0, 1, 0); Matrix t = viewTransform(from, to, up); ASSERT_EQ(t, translation(0, 0, -8)); } TEST(TransformationTest, An_arbitrary_view_transformation) { Tuple from = Point(1, 3, 2); Tuple to = Point(4, -2, 8); Tuple up = Vector(1, 1, 0); Matrix t = viewTransform(from, to, up); double values[] = {-0.50709, 0.50709, 0.67612, -2.36643, 0.76772, 0.60609, 0.12122, -2.82843, -0.35857, 0.59761, -0.71714, 0.00000, 0.00000, 0.00000, 0.00000, 1.00000}; /* Temporary lower the precision */ set_equal_precision(0.00001); ASSERT_EQ(t, Matrix4(values)); set_equal_precision(FLT_EPSILON); }