def test_computing_a_point_from_a_distance():
# Given
r = Ray(Point(2, 3, 4), Vector(1, 0, 0))
# Then
assert r.position(0) == Point(2, 3, 4)
assert r.position(1) == Point(3, 3, 4)
assert r.position(-1) == Point(1, 3, 4)
assert r.position(2.5) == Point(4.5, 3, 4)
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_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_the_color_when_a_ray_misses__only_negative_intersection_t():
w = World()
w.light = PointLight(Point(-10, 10, -10), Color(1, 1, 1))
w.objects = [Plane()]
r = Ray(Point(0, 10, 0), Vector(0, 1, 1).normalize())
c = w.color_at(r)
assert c == Color(0, 0, 0)
def reflected_color(self, comps, remaining=4):
if comps.object.material.reflective == 0 or remaining <= 0:
return Color(0, 0, 0)
reflect_ray = Ray(comps.over_point, comps.reflectv)
color = self.color_at(reflect_ray, remaining - 1)
return color * comps.object.material.reflective
def test_intersect_with_a_coplanar_ray():
# Given
p = Plane()
r = Ray(Point(0, 0, 0), Vector(0, 0, 1))
# When
xs = p.local_intersect(r)
# Then
assert len(xs) == 0
def test_intersect_with_a_ray_parallel_to_the_plane():
# Given
p = Plane()
r = Ray(Point(0, 10, 0), Vector(0, 0, 1))
# When
xs = p.local_intersect(r)
# Then
assert len(xs) == 0
def test_the_color_when_a_ray_misses():
# Given
w = default_world()
r = Ray(Point(0, 0, -5), Vector(0, 1, 0))
# When
c = w.color_at(r)
# Then
assert c == Color(0, 0, 0)
def test_a_ray_misses_s_sphere():
# Given
r = Ray(Point(0, 2, -5), Vector(0, 0, 1))
s = Sphere()
# When
xs = s.intersect(r)
# Then
assert len(xs) == 0
def test_the_color_when_a_ray_hits():
# Given
w = default_world()
r = Ray(Point(0, 0, -5), Vector(0, 0, 1))
# When
c = w.color_at(r)
# Then
assert c == Color(0.38066, 0.47583, 0.2855)
def test_intersectinga_ray_with_an_empty_group():
# Given
g = Group()
r = Ray(Point(0, 0, 0), Vector(0, 0, 1))
# When
xs = g.local_intersect(r)
# Then
assert len(xs) == 0
def precomputing_the_reflection_vector():
# Given
shape = Plane()
r = Ray(Point(0, 1, -1), Vector(0, -sqrt(2) / 2, sqrt(2) / 2))
i = Intersection(sqrt(2), shape)
# When
comps = i.prepare_computations(r)
# Then
assert comps.reflectv == Vector(0, sqrt(2) / 2, sqrt(2) / 2)
def test_the_hit__when_an_intersection_occurs_on_the_outside():
# Given
r = Ray(Point(0, 0, -5), Vector(0, 0, 1))
shape = Sphere()
i = Intersection(4, shape)
# When
comps = i.prepare_computations(r)
# Then
assert comps.inside is False
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_creating_and_querying_a_ray():
# Given
origin = Point(1, 2, 3)
direction = Vector(4, 5, 6)
# When
r = Ray(origin, direction)
# Then
assert r.origin == origin
assert r.direction == direction
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_a_ray_intersects_a_sphere_at_two_points():
# Given
r = Ray(Point(0, 0, -5), Vector(0, 0, 1))
s = Sphere()
# When
xs = s.intersect(r)
# Then
assert len(xs) == 2
assert xs[0].t == 4.0
assert xs[1].t == 6.0
def test_intersect_sets_the_object_on_the_intersection():
# Given
r = Ray(Point(0, 0, -5), Vector(0, 0, 1))
s = Sphere()
# When
xs = s.intersect(r)
# Then
assert len(xs) == 2
assert xs[0].object == s
assert xs[1].object == s
def test_a_sphere_is_behind_a_ray():
# Given
r = Ray(Point(0, 0, 5), Vector(0, 0, 1))
s = Sphere()
# When
xs = s.intersect(r)
# Then
assert len(xs) == 2
assert xs[0].t == -6.0
assert xs[1].t == -4.0
def test_a_ray_originates_inside_a_sphere():
# Given
r = Ray(Point(0, 0, 0), Vector(0, 0, 1))
s = Sphere()
# When
xs = s.intersect(r)
# Then
assert len(xs) == 2
assert xs[0].t == -1.0
assert xs[1].t == 1.0
def test_a_ray_intersects_a_sphere_at_a_tangent():
# Then
r = Ray(Point(0, 1, -5), Vector(0, 0, 1))
s = Sphere()
# When
xs = s.intersect(r)
# Then
assert len(xs) == 2
assert xs[0].t == 5.0
assert xs[1].t == 5.0
def test_intersecting_a_cone_with_a_ray_parallel_to_one_of_its_halves():
# Given
shape = Cone()
direction = Vector(0, 1, 1).normalize()
r = Ray(Point(0, 0, -1), direction)
# When
xs = shape.local_intersect(r)
# Then
assert len(xs) == 1
assert equal(xs[0].t, 0.35355)
def test_a_ray_intersecting_a_plane_from_below():
# Given
p = Plane()
r = Ray(Point(0, -1, 0), Vector(0, 1, 0))
# When
xs = p.local_intersect(r)
# Then
assert len(xs) == 1
assert xs[0].t == 1
assert xs[0].object == p
def test_the_schlick_approximation_with_a_perpendicular_viewing_angle():
# Given
shape = glass_sphere()
r = Ray(Point(0, 0, 0), Vector(0, 1, 0))
xs = Intersections(Intersection(-1, shape), Intersection(1, shape))
# When
comps = xs[1].prepare_computations(r, xs)
reflectance = comps.schlick()
# Then
assert equal(reflectance, 0.04)
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_the_schlick_approximation_with_small_angle_and_n2_greater_than_n1():
# Given
shape = glass_sphere()
r = Ray(Point(0, 0.99, -2), Vector(0, 0, 1))
xs = Intersections(Intersection(1.8589, shape))
# When
comps = xs[0].prepare_computations(r, xs)
reflectance = comps.schlick()
# Then
assert equal(reflectance, 0.48873)
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_shading_an_intersection():
# Given
w = default_world()
r = Ray(Point(0, 0, -5), Vector(0, 0, 1))
shape = w.objects[0]
i = Intersection(4, shape)
# When
comps = i.prepare_computations(r)
c = w.shade_hit(comps)
# Then
assert c == Color(0.38066, 0.47583, 0.2855)
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_schlick_approximation_under_total_internal_reflection():
# Given
shape = glass_sphere()
r = Ray(Point(0, 0, sqrt(2) / 2), Vector(0, 1, 0))
xs = Intersections(Intersection(-sqrt(2) / 2, shape),
Intersection(sqrt(2) / 2, shape))
# When
comps = xs[1].prepare_computations(r, xs)
reflectance = comps.schlick()
# Then
assert reflectance == 1.0