def test_finding_normal_on_child_object(self):
g1 = Group()
g1.transform = Transformations.rotation_y(math.pi / 2)
g2 = Group()
g2.transform = Transformations.scaling(1, 2, 3)
g1.add_child(g2)
s = Sphere()
s.transform = Transformations.translation(5, 0, 0)
g2.add_child(s)
n = s.normal_at(Point(1.7321, 1.1547, -5.5774))
self.assertEqual(n, Vector(0.2857, 0.4286, -0.8571))
def test_normal_sphere_z(self):
s = Sphere()
n = s.normal_at(Point(0, 0, 1))
self.assertEqual(n, Vector(0, 0, 1))
def test_normal_transformed_sphere(self):
s = Sphere()
m = Transformations.scaling(1, 0.5, 1).dot(Transformations.rotation_z(math.pi / 5))
s.transform = m
n = s.normal_at(Point(0, math.sqrt(2) / 2, -(math.sqrt(2) / 2)))
self.assertEqual(n, Vector(0, 0.97014, -0.24254))
def test_normal_translated_sphere(self):
s = Sphere()
s.transform = Transformations.translation(0, 1, 0)
n = s.normal_at(Point(0, 1.70711, -0.70711))
self.assertEqual(n, Vector(0, 0.70711, -0.70711))
def test_normalized_vector(self):
s = Sphere()
n = s.normal_at(Point(math.sqrt(3) / 3, math.sqrt(3) / 3, math.sqrt(3) / 3))
self.assertEqual(n, Tuple.normalize(n))
def test_normal_sphere_nonaxial(self):
s = Sphere()
n = s.normal_at(Point(math.sqrt(3) / 3, math.sqrt(3) / 3, math.sqrt(3) / 3))
self.assertEqual(n, Vector(math.sqrt(3) / 3, math.sqrt(3) / 3, math.sqrt(3) / 3))
for x in range(canvas_pixels):
world_x = -half + pixel_size * x
position = Point(world_x, world_y, wall_z)
r = Ray(ray_origin, Vector.normalize(position - ray_origin))
# shrink along y-axis
# r = r.transform(Transformations.scaling(1, 0.5, 1))
# shrink along x-axis
# r = r.transform(Transformations.scaling(0.5, 1, 1))
# shrink and rotate
# r = r.transform(Transformations.rotation_z(math.pi / 4)).transform(Transformations.scaling(0.5, 1, 1))
# shrink and skew
# r = r.transform(Transformations.shearing(1, 0, 0, 0, 0, 0)).transform(Transformations.scaling(0.5, 1, 1))
xs = shape.intersect(r)
hit = Intersection.hit(xs)
if hit is not None:
point = Ray.position(r, hit.t)
normal = shape.normal_at(point)
eye = -r.direction
color = PointLight.lighting(hit.object.material, hit.object,
light, point, eye, normal, False)
canvas.write_pixel(x, y, color)
canvas.canvas_to_ppm()
def test_normal6(self):
s = Sphere()
s.set_transform(scale(1, 0.5, 1) * rotate_z(pi / 5))
n = s.normal_at(Point(0, sqrt(2) / 2, -sqrt(2) / 2))
self.assertTrue(n.equals(Vector(0, 0.97014, -0.24254)))
def test_normal5(self):
s = Sphere()
s.set_transform(translate(0, 1, 0))
n = s.normal_at(Point(0, 1.70711, -0.70711))
self.assertTrue(n.equals(Vector(0, 0.70711, -0.70711)))
def test_normal4(self):
s = Sphere()
n = s.normal_at(Point(sqrt(3) / 3, sqrt(3) / 3, sqrt(3) / 3))
self.assertTrue(n.equals(Vector(sqrt(3) / 3,
sqrt(3) / 3,
sqrt(3) / 3)))
def test_normal3(self):
s = Sphere()
n = s.normal_at(Point(0, 0, 1))
self.assertTrue(n.equals(Vector(0, 0, 1)))
