def test_assigning_a_transformation():
# Given
s = MockShape()
# When
s.transform = translation(2, 3, 4)
# Then
assert s.transform == translation(2, 3, 4)
def test_assigning_a_transformation():
# Given
pattern = MockPattern()
# When
pattern.transform = translation(1, 2, 3)
# Then
assert pattern.transform == translation(1, 2, 3)
def test_finding_n1_and_n2_at_various_intersections():
# Given
A = glass_sphere()
A.transform = scaling(2, 2, 2)
A.material.refractive_index = 1.5
B = glass_sphere()
B.transform = translation(0, 0, -0.25)
B.material.refractive_index = 2.0
C = glass_sphere()
C.transform = translation(0, 0, 0.25)
C.material.refractive_index = 2.5
r = Ray(Point(0, 0, -4), Vector(0, 0, 1))
xs = Intersections(Intersection(2, A), Intersection(2.75, B),
Intersection(3.25, C), Intersection(4.75, B),
Intersection(5.25, C), Intersection(6, A))
EXAMPLES = [
{
'n1': 1.0,
'n2': 1.5
}, # index: 0
{
'n1': 1.5,
'n2': 2.0
}, # index: 1
{
'n1': 2.0,
'n2': 2.5
}, # index: 2
{
'n1': 2.5,
'n2': 2.5
}, # index: 3
{
'n1': 2.5,
'n2': 1.5
}, # index: 4
{
'n1': 1.5,
'n2': 1.0
}, # index: 5
]
for index in range(len(EXAMPLES)):
# When
comps = xs[index].prepare_computations(r, xs=xs)
# Then
assert comps.n1 == EXAMPLES[index]['n1']
assert comps.n2 == EXAMPLES[index]['n2']
def test_multiplying_by_the_inverse_of_a_translation_matrix():
# Given
transform = translation(5, -3, 2)
inv = transform.inverse()
p = Point(-3, 4, 5)
# Then
assert inv * p == Point(-8, 7, 3)
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_constructing_a_ray_when_the_camera_is_transformed():
# Given
c = Camera(201, 101, pi / 2)
# When
c.transform = rotation_y(pi / 4) * translation(0, -2, 5)
r = c.ray_for_pixel(100, 50)
# Then
assert r.origin == Point(0, 2, -5)
assert r.direction == Vector(sqrt(2) / 2, 0, -sqrt(2) / 2)
def test_the_view_transformation_moves_the_world():
# Given
f = Point(0, 0, 8)
to = Point(0, 0, 0)
up = Vector(0, 1, 0)
# When
t = view_transform(f, to, up)
# Then
assert t == translation(0, 0, -8)
def test_translating_a_ray():
# Given
r = Ray(Point(1, 2, 3), Vector(0, 1, 0))
m = translation(3, 4, 5)
# When
r2 = r.transform(m)
# Then
assert r2.origin == Point(4, 6, 8)
assert r2.direction == Vector(0, 1, 0)
def test__color_at__with_mutually_reflective_surfaces():
# Given
w = World()
w.light = PointLight(Point(0, 0, 0), Color(1, 1, 1))
lower = Plane()
lower.material.reflective = 1
lower.transform = translation(0, -1, 0)
w.objects.append(lower)
upper = Plane()
upper.material.reflective = 1
upper.transform = translation(0, 1, 0)
w.objects.append(upper)
r = Ray(Point(0, 0, 0), Vector(0, 1, 0))
# Then
try:
w.color_at(r)
except RecursionError:
pytest.fail("Unexpected RecursionError ...")
def test_intersecting_a_translated_sphere_with_a_ray():
# Given
r = Ray(Point(0, 0, -5), Vector(0, 0, 1))
s = Sphere()
# When
s.transform = translation(5, 0, 0)
xs = s.intersect(r)
# Then
assert len(xs) == 0
def test_chained_transformations_must_be_applied_in_reverse_order():
# Given
p = Point(1, 0, 1)
A = rotation_x(pi / 2)
B = scaling(5, 5, 5)
C = translation(10, 5, 7)
# When
T = C * B * A
# Then
assert T * p == Point(15, 0, 7)
def test_intersecting_a_translated_shape_with_a_ray():
# Given
r = Ray(Point(0, 0, -5), Vector(0, 0, 1))
s = MockShape()
# When
s.transform = translation(5, 0, 0)
_ = s.intersect(r)
# Then
assert s.saved_ray.origin == Point(-5, 0, -5)
assert s.saved_ray.direction == Vector(0, 0, 1)
def test_a_pattern_with_both_an_object_and_a_pattern_transformation():
# Given
shape = Sphere()
shape.transform = scaling(2, 2, 2)
pattern = MockPattern()
pattern.transform = translation(0.5, 1, 1.5)
# When
c = pattern.pattern_at_shape(shape, Point(2.5, 3, 3.5))
# Then
assert c == Color(0.75, 0.5, 0.25)
def test_intersecting_a_ray_with_a_nonempty_group():
# Given
g = Group()
s1 = Sphere()
s2 = Sphere()
s2.transform = translation(0, 0, -3)
s3 = Sphere()
s3.transform = translation(5, 0, 0)
g.add_child(s1)
g.add_child(s2)
g.add_child(s3)
# When
r = Ray(Point(0, 0, -5), Vector(0, 0, 1))
xs = g.local_intersect(r)
# Then
assert len(xs) == 4
assert xs[0].object == s2
assert xs[1].object == s2
assert xs[2].object == s1
assert xs[3].object == s1
def test_the_hit_should_offset_the_point():
# Given
r = Ray(Point(0, 0, -5), Vector(0, 0, 1))
shape = Sphere()
shape.transform = translation(0, 0, 1)
i = Intersection(5, shape)
# When
comps = i.prepare_computations(r)
# Then
assert comps.over_point.z < -EPSILON / 2
assert comps.point.z > comps.over_point.z
def test_the_under_point_is_offset_below_the_surface():
# Given
r = Ray(Point(0, 0, -5), Vector(0, 0, 1))
shape = glass_sphere()
shape.transform = translation(0, 0, 1)
i = Intersection(5, shape)
xs = Intersections(i)
# When
comps = i.prepare_computations(r, xs)
# Then
assert comps.under_point.z > EPSILON / 2
assert comps.point.z < comps.under_point.z
def test_intersecting_a_transformed_group():
# Given
g = Group()
g.transform = scaling(2, 2, 2)
s = Sphere()
s.transform = translation(5, 0, 0)
g.add_child(s)
# When
r = Ray(Point(10, 0, -10), Vector(0, 0, 1))
xs = g.intersect(r)
# Then
assert len(xs) == 2
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)
def test_converting_a_point_from_world_to_object_space():
# Given
g1 = Group()
g1.transform = rotation_y(pi / 2)
g2 = Group()
g2.transform = scaling(2, 2, 2)
g1.add_child(g2)
s = Sphere()
s.transform = translation(5, 0, 0)
g2.add_child(s)
# When
p = s.world_to_object(Point(-2, 0, -10))
# Then
assert p == Point(0, 0, -1)
def test__shade_hit__with_a_reflective_material():
# Given
w = default_world()
shape = Plane()
shape.material.reflective = 0.5
shape.transform = translation(0, -1, 0)
w.objects.append(shape)
r = Ray(Point(0, 0, -3), Vector(0, -sqrt(2) / 2, sqrt(2) / 2))
i = Intersection(sqrt(2), shape)
# When
comps = i.prepare_computations(r)
color = w.shade_hit(comps)
# Then
assert color == Color(0.87675, 0.92434, 0.82918)
def test__shade_hit__with_a_transparent_material():
# Given
w = default_world()
floor = Plane()
floor.transform = translation(0, -1, 0)
floor.material.transparency = 0.5
floor.material.refractive_index = 1.5
w.objects.append(floor)
ball = Sphere()
ball.material.color = Color(1, 0, 0)
ball.material.ambient = 0.5
ball.transform = translation(0, -3.5, -0.5)
w.objects.append(ball)
r = Ray(Point(0, 0, -3), Vector(0, -sqrt(2) / 2, sqrt(2) / 2))
xs = Intersections(Intersection(sqrt(2), floor))
# When
comps = xs[0].prepare_computations(r, xs)
color = w.shade_hit(comps, 5)
# Then
assert color == Color(0.93642, 0.68642, 0.68642)
def test_the_reflected_color_at_the_maximum_recursive_depth():
# Given
w = default_world()
shape = Plane()
shape.material.reflective = 0.5
shape.transform = translation(0, -1, 0)
w.objects.append(shape)
r = Ray(Point(0, 0, -3), Vector(0, -sqrt(2) / 2, sqrt(2) / 2))
i = Intersection(sqrt(2), shape)
# When
comps = i.prepare_computations(r)
color = w.reflected_color(comps, 0)
# Then
assert color == Color(0, 0, 0)
def test_converting_a_normal_from_object_to_world_space():
# 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_to_world(Vector(sqrt(3) / 3, sqrt(3) / 3, sqrt(3) / 3))
# Then
assert n == Vector(0.28571, 0.42857, -0.85714)
def test__shade_hit__is_given_an_intersection_in_shadow():
# Given
w = World()
w.light = PointLight(Point(0, 0, -10), Color(1, 1, 1))
s1 = Sphere()
w.objects.append(s1)
s2 = Sphere()
s2.transform = translation(0, 0, 10)
w.objects.append(s2)
r = Ray(Point(0, 0, 5), Vector(0, 0, 1))
i = Intersection(4, s2)
# When
comps = i.prepare_computations(r)
c = w.shade_hit(comps)
# Then
assert c == Color(0.1, 0.1, 0.1)
def test_individual_transformations_are_applied_in_sequence():
# Given
p = Point(1, 0, 1)
A = rotation_x(pi / 2)
B = scaling(5, 5, 5)
C = translation(10, 5, 7)
# apply rotation first
# When
p2 = A * p
# Then
assert p2 == Point(1, -1, 0)
# then apply scaling
# When
p3 = B * p2
# Then
assert p3 == Point(5, -5, 0)
# then apply translation
# When
p4 = C * p3
# Then
assert p4 == Point(15, 0, 7)
def test_translation_does_not_affect_vectors():
# Given
transform = translation(5, -3, 2)
v = Vector(-3, 4, 5)
# Then
assert transform * v == v
if __name__ == "__main__":
# pattern = StripePattern(Color(1, 0, 0), Color(1, 1, 1))
# pattern = CheckersPattern(Color(1, 0, 0), Color(1, 1, 1))
pattern = GradientPattern(Color(1, 0, 0), Color(1, 1, 1))
# pattern = RingPattern(Color(1, 0, 0), Color(1, 1, 1))
pattern.transform = scaling(0.2, 0.2, 0.2)
floor = Plane()
floor.material = Material()
floor.material.color = Color(1, 0.9, 0.9)
# floor.material.pattern = pattern
backdrop = Plane()
backdrop.transform = \
rotation_y(pi / 3) * translation(0, 0, 5) * rotation_x(pi / 2)
backdrop2 = Plane()
backdrop2.transform = \
rotation_y(-pi / 3) * translation(0, 0, 5) * rotation_x(pi / 2)
middle = Sphere()
# middle = glass_sphere()
middle.transform = translation(-0.5, 1, 0.5)
# middle.reflective = 1.0
middle.material = Material()
middle.material.color = Color(0.1, 1, 0.5)
# middle.material.pattern = pattern
middle.material.diffuse = 0.7
middle.material.specular = 0.3
# middle.material.reflective = 1.0
def test_multiplying_by_a_translation_matrix():
# Given
transform = translation(5, -3, 2)
p = Point(-3, 4, 5)
# Then
assert transform * p == Point(2, 1, 7)
