def test_the_inverse_of_an_x_rotation_rotates_in_the_opposite_direction(): p = point(0, 1, 0) half_quarter = transformations.rotation_x(math.pi / 4) inverse = transformations.invert(half_quarter) assert (np.allclose(point(0, math.sqrt(2) / 2, -math.sqrt(2) / 2), inverse(p)))
def test_rotating_a_point_around_the_z_axis(): p = point(0, 1, 0) half_quarter = transformations.rotation_z(math.pi / 4) full_quarter = transformations.rotation_z(math.pi / 2) assert (np.allclose(point(-math.sqrt(2) / 2, math.sqrt(2) / 2, 0), half_quarter(p))) assert (np.allclose(point(-1, 0, 0), full_quarter(p)))
def test_chained_transofrmations_must_be_applied_in_reverse_order(): p = point(1, 0, 1) A = transformations.rotation_x(math.pi / 2) B = transformations.scaling(5, 5, 5) C = transformations.translation(10, 5, 7) CBA = transformations.concat(C, B, A) assert (np.allclose(point(15, 0, 7), CBA(p)))
def test_computing_a_point_from_a_distance(): origin = point(2, 3, 4) direction = vector(1, 0, 0) r = Ray(origin, direction) assert ((point(2, 3, 4) == r.position(0)).all()) assert ((point(3, 3, 4) == r.position(1)).all()) assert ((point(1, 3, 4) == r.position(-1)).all()) assert ((point(4.5, 3, 4) == r.position(2.5)).all())
def test_scaling_a_ray(): origin = point(1, 2, 3) direction = vector(0, 1, 0) r = Ray(origin, direction) m = transformations.scaling(2, 3, 4) scaled_ray = r.transform(m) assert (np.allclose(point(2, 6, 12), scaled_ray.origin)) assert (np.allclose(vector(0, 3, 0), scaled_ray.direction))
def test_translating_a_ray(): origin = point(1, 2, 3) direction = vector(0, 1, 0) r = Ray(origin, direction) m = transformations.translation(3, 4, 5) translated_ray = r.transform(m) assert (np.allclose(point(4, 6, 8), translated_ray.origin)) assert (np.allclose(vector(0, 1, 0), translated_ray.direction))
def test_the_hit_when_an_intersection_occurs_on_the_inside(): r = Ray(point(0, 0, 0), vector(0, 0, 1)) shape = Sphere() i = Intersection(1, shape) comps = i.prepare_computations(r) assert(np.allclose(point(0, 0, 1), comps.point)) assert(np.allclose(vector(0, 0, -1), comps.eyev)) assert(comps.inside == True) assert(np.allclose(vector(0, 0, -1), comps.normalv))
def test_shade_hit_is_given_an_intersection_in_shadow(): light = PointLight(point(0, 0, -10), color(1, 1, 1)) s1 = Sphere() s2 = Sphere(transformation=translation(0, 0, 10)) w = World(light, s1, s2) r = Ray(point(0, 0, 5), vector(0, 0, 1)) i = Intersection(4, s2) comps = i.prepare_computations(r) c = w.shade_hit(comps) assert(np.allclose(color(0.1, 0.1, 0.1), c))
def test_rendering_a_world_with_a_camera(): w = default_world() from_ = point(0, 0, -5) to = point(0, 0, 0) up = vector(0, 1, 0) c = Camera(11, 11, math.pi/2, transform=view_transformation(from_, to, up)) image = c.render(w) assert(np.allclose(image.pixel_at(5, 5), color( 0.38066, 0.47583, 0.2855), atol=0.00001))
def test_the_view_transformation_moves_the_world(): from_ = point(0, 0, 8) to = point(0, 0, 0) up = vector(0, 1, 0) t = view_transformation(from_, to, up) actual_transform_matrix = t(identity_matrix()) expected_transform_matrix = translation(0, 0, -8)(identity_matrix()) assert (np.allclose(actual_transform_matrix, expected_transform_matrix))
def test_a_transformation_matrix_looking_in_positive_z_direction(): from_ = point(0, 0, 0) to = point(0, 0, 1) up = vector(0, 1, 0) t = view_transformation(from_, to, up) actual_transform_matrix = t(identity_matrix()) expected_transform_matrix = scaling(-1, 1, -1)(identity_matrix()) assert (np.allclose(actual_transform_matrix, expected_transform_matrix))
def test_the_view_transformation_matrix_for_the_default_orientation(): from_ = point(0, 0, 0) to = point(0, 0, -1) up = vector(0, 1, 0) t = view_transformation(from_, to, up) actual_transform_matrix = t(identity_matrix()) expected_transform_matrix = identity_matrix() assert (np.allclose(actual_transform_matrix, expected_transform_matrix))
def test_shading_an_intersection_from_the_inside(): w = default_world() w._light = PointLight(point(0, 0.25, 0), color(1, 1, 1)) r = Ray(point(0, 0, 0), vector(0, 0, 1)) shape = w[1] i = Intersection(0.5, shape) comps = i.prepare_computations(r) c = w.shade_hit(comps) assert(np.allclose(color(0.90498, 0.90498, 0.90498), c))
def test_precompute_the_state_of_an_intersection(): r = Ray(point(0, 0, -5), vector(0, 0, 1)) shape = Sphere() i = Intersection(4, shape) comps = i.prepare_computations(r) assert(comps.t == i.t) assert(comps.object is i.object) assert(np.allclose(point(0, 0, -1), comps.point)) assert(np.allclose(vector(0, 0, -1), comps.eyev)) assert(np.allclose(vector(0, 0, -1), comps.normalv))
def ray_for_pixel(self, px, py): xoffset = (px + 0.5) * self.pixel_size yoffset = (py + 0.5) * self.pixel_size world_x = self._half_width - xoffset world_y = self._half_height - yoffset inverse_camera_transform = invert(self._transform) pixel = inverse_camera_transform(point(world_x, world_y, -1)) origin = inverse_camera_transform(point(0, 0, 0)) direction = normalize(pixel - origin) return Ray(origin, direction)
def test_individual_transformations_are_applied_in_sequence(): p = point(1, 0, 1) A = transformations.rotation_x(math.pi / 2) B = transformations.scaling(5, 5, 5) C = transformations.translation(10, 5, 7) p2 = A(p) assert (np.allclose(point(1, -1, 0), p2)) p3 = B(p2) assert (np.allclose(point(5, -5, 0), p3)) p4 = C(p3) assert (np.allclose(point(15, 0, 7), p4))
def test_constructing_a_ray_when_the_camera_is_transformed(): c = Camera(201, 101, math.pi/2, transform=concat(rotation_y(math.pi/4), translation(0, -2, 5))) r = c.ray_for_pixel(100, 50) assert(np.allclose(point(0, 2, -5), r.origin)) assert(np.allclose(vector(math.sqrt(2)/2, 0, -math.sqrt(2)/2), r.direction))
def default_world(): light = PointLight(point(-10, 10, -10), white) m = Material(color=color(0.8, 1.0, 0.6), diffuse=0.7, specular=0.2) s1 = Sphere(material=m) s2 = Sphere(transformation=scaling(0.5, 0.5, 0.5)) return World(light, s1, s2)
def normal_at(self, p): transformation = invert(self.transformation) object_point = transformation(p) object_normal = object_point - point(0, 0, 0) world_normal = transpose(transformation)(object_normal) world_normal[3] = 0 return normalize(world_normal)
def test_intersecting_a_translated_sphere_with_a_ray(): sphere = Sphere(transformation=transformations.translation(5, 0, 0)) ray = Ray(point(0, 0, -5), vector(0, 0, 1)) xs = sphere.intersect(ray) assert(len(xs) == 0)
def test_hit_should_offset_the_point(): r = Ray(point(0, 0, -5), vector(0, 0, 1)) shape = Sphere(transformation=translation(0, 0, 1)) i = Intersection(5, shape) comps = i.prepare_computations(r) assert(comps.point[2] < -EPSILON/2)
def test_lighting_with_the_light_behind_the_surface(material, position): eyev = vector(0, 0, -1) normalv = vector(0, 0, -1) light = PointLight(point(0, 0, 10), color(1, 1, 1)) result = material.lighting(light, position, eyev, normalv, False) assert (np.array_equal(color(0.1, 0.1, 0.1), result))
def test_the_hit_when_an_intersection_occurs_on_the_outside(): r = Ray(point(0, 0, -5), vector(0, 0, 1)) shape = Sphere() i = Intersection(4, shape) comps = i.prepare_computations(r) assert(comps.inside == False)
def test_intersecting_a_scaled_sphere_with_a_ray(): sphere = Sphere(transformation=transformations.scaling(2, 2, 2)) ray = Ray(point(0, 0, -5), vector(0, 0, 1)) xs = sphere.intersect(ray) assert(xs[0].t == 3) assert(xs[1].t == 7)
def test_lighting_with_the_surface_in_shadow(material, position): eyev = vector(0, 0, -1) normalv = vector(0, 0, -1) light = PointLight(point(0, 0, -10), color(1, 1, 1)) in_shadow = True result = material.lighting(light, position, eyev, normalv, in_shadow) assert (np.allclose(color(0.1, 0.1, 0.1), result))
def test_intersect_sets_the_object_on_the_intersection(): r = Ray(point(0, 0, -5), vector(0, 0, 1)) s = Sphere() xs = s.intersect(r) assert(len(xs) == 2) assert(xs[0].object is s) assert(xs[1].object is s)
def test_lighting_with_the_eye_between_the_light_and_the_surface_and_wyw_offset_45_degrees( material, position): eyev = vector(0, math.sqrt(2) / 2, -math.sqrt(2) / 2) normalv = vector(0, 0, -1) light = PointLight(point(0, 0, -10), color(1, 1, 1)) result = material.lighting(light, position, eyev, normalv, False) assert (np.array_equal(color(1.0, 1.0, 1.0), result))
def test_computing_the_normal_on_a_transformed_sphere(): s = transformations.scaling(1, 0.5, 1) r = transformations.rotation_z(math.pi/5) transform = transformations.concat(s, r) sphere = Sphere(transform) n = sphere.normal_at(point(0, math.sqrt(2)/2, -math.sqrt(2)/2)) assert(np.allclose(vector(0, 0.97014, -0.242535), n))
def test_lighting_with_the_eye_opposite_surface_light_offest_45_degrees( material, position): eyev = vector(0, 0, -1) normalv = vector(0, 0, -1) light = PointLight(point(0, 10, -10), color(1, 1, 1)) result = material.lighting(light, position, eyev, normalv, False) assert (np.allclose(color(0.7364, 0.7364, 0.7364), result))
def test_lighting_with_the_eye_in_the_path_of_the_reflection_vector( material, position): eyev = vector(0, -math.sqrt(2) / 2, -math.sqrt(2) / 2) normalv = vector(0, 0, -1) light = PointLight(point(0, 10, -10), color(1, 1, 1)) result = material.lighting(light, position, eyev, normalv, False) assert (np.allclose(color(1.6364, 1.6364, 1.6364), result))