def test_multiplying_by_the_inverse_of_a_scaling_matrix():
# Given
transform = scaling(2, 3, 4)
inv = transform.inverse()
v = Vector(-4, 6, 8)
# Then
assert inv * v == Vector(-2, 2, 2)
def test_scaling_a_ray():
# Given
r = Ray(Point(1, 2, 3), Vector(0, 1, 0))
m = scaling(2, 3, 4)
# When
r2 = r.transform(m)
# Then
assert r2.origin == Point(2, 6, 12)
assert r2.direction == Vector(0, 3, 0)
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_a_pattern_with_a_pattern_transformation():
# Given
shape = Sphere()
pattern = MockPattern()
pattern.transform = scaling(2, 2, 2)
# When
c = pattern.pattern_at_shape(shape, Point(2, 3, 4))
# Then
assert c == Color(1, 1.5, 2)
def test_a_view_transformation_matrix_looking_in_positive_z_direction():
# Given
f = Point(0, 0, 0)
to = Point(0, 0, 1)
up = Vector(0, 1, 0)
# When
t = view_transform(f, to, up)
# Then
assert t == scaling(-1, 1, -1)
def test_intersecting_a_scaled_shape_with_a_ray():
# Given
r = Ray(Point(0, 0, -5), Vector(0, 0, 1))
s = MockShape()
# When
s.transform = scaling(2, 2, 2)
_ = s.intersect(r)
# Then
assert s.saved_ray.origin == Point(0, 0, -2.5)
assert s.saved_ray.direction == Vector(0, 0, 0.5)
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_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_scaled_sphere_with_a_ray():
# Given
r = Ray(Point(0, 0, -5), Vector(0, 0, 1))
s = Sphere()
# When
s.transform = scaling(2, 2, 2)
xs = s.intersect(r)
# Then
assert len(xs) == 2
assert xs[0].t == 3
assert xs[1].t == 7
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 default_world():
light = PointLight(Point(-10, 10, -10), Color(1, 1, 1))
s1 = Sphere()
s1.material.color = Color(0.8, 1.0, 0.6)
s1.material.diffuse = 0.7
s1.material.specular = 0.2
s2 = Sphere()
s2.transform = scaling(0.5, 0.5, 0.5)
w = World()
w.light = light
w.objects = [s1, s2]
return w
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_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_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_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_default_world():
# Given
light = PointLight(Point(-10, 10, -10), Color(1, 1, 1))
s1 = Sphere()
s1.material.color = Color(0.8, 1.0, 0.6)
s1.material.diffuse = 0.7
s1.material.specular = 0.2
s2 = Sphere()
s2.transform = scaling(0.5, 0.5, 0.5)
# When
w = default_world()
# Then
assert w.light == light
assert s1 in w.objects
assert s2 in w.objects
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_reflection_is_scaling_by_a_negative_value():
# Given
transform = scaling(-1, 1, 1)
p = Point(2, 3, 4)
# Then
assert transform * p == Point(-2, 3, 4)
def test_a_scaling_matrix_applied_to_a_vector():
# Given
tranform = scaling(2, 3, 4)
v = Vector(-4, 6, 8)
# Then
assert tranform * v == Vector(-8, 18, 32)
def test_scaling_matrix_applied_to_a_point():
# Given
trasform = scaling(2, 3, 4)
p = Point(-4, 6, 8)
# Then
assert trasform * p == Point(-8, 18, 32)
from raytracerchallenge_python.tuple import Color, Point, Vector
from raytracerchallenge_python.material import Material
from raytracerchallenge_python.sphere import Sphere, glass_sphere
from raytracerchallenge_python.plane import Plane
from raytracerchallenge_python.cube import Cube
# from raytracerchallenge_python.stripe_pattern import StripePattern
# from raytracerchallenge_python.checkers_pattern import CheckersPattern
# from raytracerchallenge_python.ring_pattern import RingPattern
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()
