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_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_multiplying_the_inverse_of_a_scaling_matrix():
transform = transformations.scaling(2, 3, 4)
inverse = transformations.invert(transform)
v = vector(-4, 6, 8)
expected = vector(-2, 2, 2)
actual = inverse(v)
assert ((expected == actual).all())
def intersect(self, ray):
transformation = invert(self.transformation)
transformed_ray = ray.transform(transformation)
ts = intersect_fast(transformed_ray.origin, transformed_ray.direction)
if len(ts) == 2:
i1 = Intersection(ts[0], self)
i2 = Intersection(ts[1], self)
return Intersections(i1, i2)
return []
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_multiplying_by_the_inverse_of_a_translation_matrix():
transform = transformations.translation(5, -3, 2)
transform = transformations.invert(transform)
p = point(-3, 4, 5)
assert ((point(-8, 7, 3) == transform(p)).all())