def test_the_normal_is_a_normalized_vector():
# Given
s = Sphere()
# When
n = s.normal_at(Point(sqrt(3) / 3, sqrt(3) / 3, sqrt(3) / 3))
# Then
assert n == n.normalize()
def test_the_normal_on_a_sphere_at_a_point_at_a_nonaxial_axis():
# Given
s = Sphere()
# When
n = s.normal_at(Point(sqrt(3) / 3, sqrt(3) / 3, sqrt(3) / 3))
# Then
assert n == Vector(sqrt(3) / 3, sqrt(3) / 3, sqrt(3) / 3)
def test_the_normal_on_a_sphere_at_a_point_on_the_z_axis():
# Given
s = Sphere()
# When
n = s.normal_at(Point(0, 0, 1))
# Then
assert n == Vector(0, 0, 1)
def test_computing_the_normal_on_a_translated_sphere():
# Given
s = Sphere()
s.transform = translation(0, 1, 0)
# When
n = s.normal_at(Point(0, 1.70711, -0.70711))
# Then
assert n == Vector(0, 0.70711, -0.70711)
def test_commputing_the_normal_on_a_transformed_sphere():
# Given
s = Sphere()
m = scaling(1, 0.5, 1) * rotation_z(pi / 5)
s.transform = m
# When
n = s.normal_at(Point(0, sqrt(2) / 2, -sqrt(2) / 2))
# Then
assert n == Vector(0, 0.97014, -0.24254)
def test_finding_the_normal_on_a_child_object():
# Given
g1 = Group()
g1.transform = rotation_y(pi / 2)
g2 = Group()
g2.transform = scaling(1, 2, 3)
g1.add_child(g2)
s = Sphere()
s.transform = translation(5, 0, 0)
g2.add_child(s)
# When
n = s.normal_at(Point(1.7321, 1.1547, -5.5774))
# Then
assert n == Vector(0.2857, 0.42854, -0.85716)
