def test_pattern_with_both_object_and_pattern_transformation(self):
obj = Sphere()
obj.transformation = scaling(2, 2, 2)
pattern = test_pattern()
pattern.transformation = translation(0.5, 1, 1.5)
c = pattern.pattern_at_shape(obj, Point(2.5, 3, 3.5))
assert c == Color(0.75, 0.5, 0.25)
def test_both_transform():
s = Sphere()
s.set_transform(Scaling(2, 2, 2))
pattern = _TestPattern()
pattern.set_pattern_transform(Translation(0.5, 1, 1.5))
c = pattern.pattern_at_shape(s, Point(2.5, 3, 3.5))
assert c == Color(0.75, 0.5, 0.25)
def test_ray_sphere_intersect():
r = Ray(Point(0, 0, -5), Vector(0, 0, 1))
s = Sphere()
i = s.intersect(r)
assert len(i) == 2
assert i[0].t == 4.0
assert i[1].t == 6.0
def test_sphere_behind_ray():
r = Ray(Point(0, 0, 5), Vector(0, 0, 1))
s = Sphere()
i = s.intersect(r)
assert len(i) == 2
assert i[0].t == -6.0
assert i[1].t == -4.0
def test_object_intersect():
r = Ray(Point(0, 0, -5), Vector(0, 0, 1))
s = Sphere()
xs = s.intersect(r)
assert len(xs) == 2
assert xs[0].object == s
assert xs[1].object == s
def test_ray_in_sphere():
r = Ray(Point(0, 0, 0), Vector(0, 0, 1))
s = Sphere()
i = s.intersect(r)
assert len(i) == 2
assert i[0].t == -1
assert i[1].t == 1
def test_ray_tangent_intersect():
r = Ray(Point(0, 1, -5), Vector(0, 0, 1))
s = Sphere()
i = s.intersect(r)
assert len(i) == 2
assert i[0].t == 5.0
assert i[1].t == 5.0
def test_hit_offset():
r = Ray(Point(0, 0, -5), Vector(0, 0, 1))
shape = Sphere()
shape.set_transform(Translation(0, 0, 1))
i = Intersection(5, shape)
comps = i.prepare_computation(r)
assert comps.over_point.z < -EPSILON / 2
assert comps.point.z > comps.over_point.z
def test_hit_should_offset_the_point(self):
r = Ray(Point(0, 0, -5), Vector(0, 0, 1))
shape = Sphere()
shape.transformation = translation(0, 0, 1)
i = Intersection(5, shape)
comps = i.prepare_computations(r)
assert comps.over_point.z < -EPSILON / 2
assert comps.point.z > comps.over_point.z
def test_transformed_group():
g = Group()
g.set_transform(Scaling(2, 2, 2))
s = Sphere()
s.set_transform(Translation(5, 0, 0))
g.add_child(s)
r = Ray(Point(10, 0, -10), Vector(0, 0, 1))
xs = g.intersect(r)
assert len(xs) == 2
def test_world_to_object():
g1 = Group()
g1.set_transform(RotationY(math.pi / 2))
g2 = Group()
g2.set_transform(Scaling(2, 2, 2))
g1.add_child(g2)
s = Sphere()
s.set_transform(Translation(5, 0, 0))
g2.add_child(s)
p = s.world_to_object(Point(-2, 0, -10))
assert p == Point(0, 0, -1)
def test_child_normal():
g1 = Group()
g1.set_transform(RotationY(math.pi / 2))
g2 = Group()
g2.set_transform(Scaling(1, 2, 3))
g1.add_child(g2)
s = Sphere()
s.set_transform(Translation(5, 0, 0))
g2.add_child(s)
n = s.normal_at(Point(1.7321, 1.1547, -5.5774))
assert n == Vector(0.2857, 0.4286, -0.8571)
def default_world():
w = World()
w.light_source = PointLight(Point(-10, 10, -10), Color.white())
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.transformation = scaling(0.5, 0.5, 0.5)
w.add(s1, s2)
return w
def test_shade_hit_is_given_an_intersection_in_shadow(self):
w = World()
w.light_source = PointLight(Point(0, 0, -10), Color.white())
s1 = Sphere()
s2 = Sphere()
s2.transformation = translation(0, 0, 10)
w.add(s1, s2)
r = Ray(Point(0, 0, 5), Vector(0, 0, 1))
i = Intersection(4, s2)
comps = i.prepare_computations(r)
c = w.shade_hit(comps)
assert c == Color(0.1, 0.1, 0.1)
def test_lighting_with_pattern_applied(self):
m = Material()
m.pattern = StripePattern(Color.white(), Color.black())
m.ambient = 1
m.diffuse = 0
m.specular = 0
eyev = Vector(0, 0, -1)
normalv = Vector(0, 0, -1)
light = PointLight(Point(0, 0, -10), Color.white())
c1 = m.lighting(Sphere(), light, Point(0.9, 0, 0), eyev, normalv, False)
c2 = m.lighting(Sphere(), light, Point(1.1, 0, 0), eyev, normalv, False)
assert c1 == Color.white()
assert c2 == Color.black()
def test_shadow_shade_hit():
w = World()
w.light = PointLight(Point(0, 0, -10), Color(1, 1, 1))
s1 = Sphere()
s2 = Sphere()
s2.set_transform(Translation(0, 0, 10))
w.objects.extend([s1, s2])
r = Ray(Point(0, 0, 5), Vector(0, 0, 1))
i = Intersection(4, s2)
comps = i.prepare_computation(r)
c = w.shade_hit(comps)
print(c)
assert c == Color(0.1, 0.1, 0.1)
def test_normal_object_to_world():
g1 = Group()
g1.set_transform(RotationY(math.pi / 2))
g2 = Group()
g2.set_transform(Scaling(1, 2, 3))
g1.add_child(g2)
s = Sphere()
s.set_transform(Translation(5, 0, 0))
g2.add_child(s)
n = s.normal_to_world(
Vector(math.sqrt(3) / 3,
math.sqrt(3) / 3,
math.sqrt(3) / 3))
assert n == Vector(0.2857, 0.4286, -0.8571)
def test_positive_hit():
s = Sphere()
i1 = Intersection(1, s)
i2 = Intersection(2, s)
xs = Intersections(i1, i2)
i = xs.hit()
assert i == i1
def test_lighting_with_surface_in_shadow(self, background):
eyev = Vector(0, 0, -1)
normalv = Vector(0, 0, -1)
light = PointLight(Point(0, 0, -10), Color(1, 1, 1))
in_shadow = True
result = background['m'].lighting(Sphere(), light, background['position'], eyev, normalv, in_shadow)
assert result == Color(0.1, 0.1, 0.1)
def test_mixed_hit():
s = Sphere()
i1 = Intersection(-1, s)
i2 = Intersection(1, s)
xs = Intersections(i1, i2)
i = xs.hit()
assert i == i2
def test_shade_hit_with_transparent_material(self, default_world):
w = default_world
floor = Plane()
floor.transformation = translation(0, -1, 0)
floor.material.transparency = 0.5
floor.material.refractive_index = 1.5
ball = Sphere()
ball.material.color = Color(1, 0, 0)
ball.material.ambient = 0.5
ball.transformation = translation(0, -3.5, -0.5)
w.add(floor, ball)
r = Ray(Point(0, 0, -3), Vector(0, -sqrt(2) / 2, sqrt(2) / 2))
xs = Intersections(Intersection(sqrt(2), floor))
comps = xs[0].prepare_computations(r, xs)
color = w.shade_hit(comps, 5)
assert color == Color(0.93642, 0.68642, 0.68642)
def test_negative_hit():
s = Sphere()
i1 = Intersection(-2, s)
i2 = Intersection(-1, s)
xs = Intersections(i1, i2)
i = xs.hit()
assert i is None
def test_aggregate_intersections():
s = Sphere()
i1 = Intersection(1, s)
i2 = Intersection(2, s)
xs = Intersections(i1, i2)
assert len(xs) == 2
assert xs[0].t == 1
assert xs[1].t == 2
def test_hit_is_always_lowest_nonnegative_intersection(self):
s = Sphere()
i1 = Intersection(5, s)
i2 = Intersection(7, s)
i3 = Intersection(-3, s)
i4 = Intersection(2, s)
xs = Intersections(i1, i2, i3, i4)
assert xs.hit() == i4
def shade_hit_transparent():
w = World().default()
floor = Plane()
floor.set_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.set_transform(Translation(0, -3.5, -0.5))
w.objects.append(ball)
r = Ray(Point(0, 0, -3), Vector(0, -math.sqrt(2) / 2, math.sqrt(2) / 2))
xs = Intersections(Intersection(math.sqrt(2), floor))
comps = xs[0].prepare_computations(r, xs)
color = w.shade_hit(comps, 5)
assert color == Color(0.93642, 0.68642, 0.68642)
def test_aggregate_intersections(self):
s = Sphere()
i1 = Intersection(1, s)
i2 = Intersection(2, s)
xs = Intersections(i1, i2)
assert xs.count == 2
assert xs[0].t == 1
assert xs[1].t == 2
def test_lighting_eye_offset(): # eye between light and surface, 45 offset
s = Sphere()
m = Material()
p = Point(0, 0, 0)
eyev = Vector(0, math.sqrt(2) / 2, -math.sqrt(2) / 2)
normalv = Vector(0, 0, -1)
light = PointLight(Point(0, 0, -10), Color(1, 1, 1))
res = m.lighting(s, light, p, eyev, normalv)
assert res == Color(1.0, 1.0, 1.0)
def test_lighting_eye_in_path(): # eye in reflection path
s = Sphere()
m = Material()
p = Point(0, 0, 0)
eyev = Vector(0, -math.sqrt(2) / 2, -math.sqrt(2) / 2)
normalv = Vector(0, 0, -1)
light = PointLight(Point(0, 10, -10), Color(1, 1, 1))
res = m.lighting(s, light, p, eyev, normalv)
assert res == Color(1.6364, 1.6364, 1.6364)
def test_lighting_eye_opposite(): # eye opposite surface, 45 offset
s = Sphere()
m = Material()
p = Point(0, 0, 0)
eyev = Vector(0, 0, -1)
normalv = Vector(0, 0, -1)
light = PointLight(Point(0, 10, -10), Color(1, 1, 1))
res = m.lighting(s, light, p, eyev, normalv)
assert res == Color(0.7364, 0.7364, 0.7364)
def test_lighting_behind_surface(): # eye behind surface
s = Sphere()
m = Material()
p = Point(0, 0, 0)
eyev = Vector(0, 0, -1)
normalv = Vector(0, 0, -1)
light = PointLight(Point(0, 0, 10), Color(1, 1, 1))
res = m.lighting(s, light, p, eyev, normalv)
assert res == Color(0.1, 0.1, 0.1)