def test_positive_z_orientation_matrix():
f = Point(0, 0, 0)
to = Point(0, 0, 1)
up = Vector(0, 1, 0)
t = ViewTransform(f, to, up)
print(t)
assert t == Scaling(-1, 1, -1)
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_scaled_shape_intersection():
r = Ray(Point(0, 0, -5), Vector(0, 0, 1))
s = _TestShape()
s.set_transform(Scaling(2, 2, 2))
_ = s.intersect(r)
assert s.saved_ray.origin == Point(0, 0, -2.5)
assert s.saved_ray.direction == Vector(0, 0, 0.5)
def test_trans_chaining():
p = Point(1, 0, 1)
a = RotationX(math.pi / 2)
b = Scaling(5, 5, 5)
c = Translation(10, 5, 7)
t = c * b * a
print(t * p)
assert t * p == Point(15, 0, 7)
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_trans_sequence():
p = Point(1, 0, 1)
a = RotationX(math.pi / 2)
b = Scaling(5, 5, 5)
c = Translation(10, 5, 7)
p2 = a * p
assert p2 == Point(1, -1, 0)
p3 = b * p2
assert p3 == Point(5, -5, 0)
p4 = c * p3
assert p4 == Point(15, 0, 7)
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(cls):
world = cls()
world.light = PointLight(Point(-10, 10, -10), Color(1, 1, 1))
m = Material()
m.color = Color(0.8, 1.0, 0.6)
m.diffuse = 0.7
m.specular = 0.2
s1 = Sphere()
s1.set_material(m)
s2 = Sphere()
s2.set_transform(Scaling(0.5, 0.5, 0.5))
world.objects.extend([s1, s2])
return world
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_default_world():
light = PointLight(Point(-10, 10, -10), Color(1, 1, 1))
s1 = Sphere()
m = Material()
m.color = Color(0.8, 1.0, 0.6)
m.diffuse = 0.7
m.specular = 0.2
s1.set_material(m)
s2 = Sphere()
t = Scaling(0.5, 0.5, 0.5)
s2.set_transform(t)
w = World.default()
assert w.light == light
assert s1 in w.objects
assert s2 in w.objects
def check_n1_n2(index):
a = GlassSphere()
a.set_transform(Scaling(2, 2, 2))
a.material.refractive_index = 1.5
b = GlassSphere()
b.set_transform(Translation(0, 0, -0.25))
b.material.refractive_index = 2.0
c = GlassSphere()
c.set_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),
)
comps = xs[index].prepare_computation(r, xs)
return (comps.n1, comps.n2)
def test_reflection():
t = Scaling(-1, 1, 1)
p = Point(2, 3, 4)
assert t * p == Point(-2, 3, 4)
def test_transformed_shape_normal():
s = _TestShape()
t = Scaling(1, 0.5, 1) * RotationZ(math.pi / 5)
s.set_transform(t)
n = s.normal_at(Point(0, math.sqrt(2) / 2, -math.sqrt(2) / 2))
assert n == Vector(0, 0.97014, -0.24254)
def test_point_scaling():
t = Scaling(2, 3, 4)
p = Point(-4, 6, 8)
assert t * p == Point(-8, 18, 32)
def test_pattern_transform():
s = Sphere()
p = _TestPattern()
p.set_pattern_transform(Scaling(2, 2, 2))
c = p.pattern_at_shape(s, Point(2, 3, 4))
assert c == Color(1, 1.5, 2)
def test_object_transform():
s = Sphere()
s.set_transform(Scaling(2, 2, 2))
pattern = _TestPattern()
c = pattern.pattern_at_shape(s, Point(2, 3, 4))
assert c == Color(1, 1.5, 2)
def test_vector_scaling():
t = Scaling(2, 3, 4)
v = Vector(-4, 6, 8)
assert t * v == Vector(-8, 18, 32)
def test_ray_scaling():
r = Ray(Point(1, 2, 3), Vector(0, 1, 0))
m = Scaling(2, 3, 4)
r2 = r.transform(m)
assert r2.origin == Point(2, 6, 12)
assert r2.direction == Vector(0, 3, 0)
# color: [ 0.941, 0.322, 0.388 ] red = copy.deepcopy(white) red.color = Color(0.941, 0.322, 0.388) # - define: purple-material # extend: white-material # value: # color: [ 0.373, 0.404, 0.550 ] purple = copy.deepcopy(white) purple.color = Color(0.373, 0.322, 0.388) # - define: standard-transform # value: # - [ translate, 1, -1, 1 ] # - [ scale, 0.5, 0.5, 0.5 ] standard = Scaling(0.5, 0.5, 0.5) * Translation(1, -1, 1) # - define: large-object # value: # - standard-transform # - [ scale, 3.5, 3.5, 3.5 ] large = Scaling(3.5, 3.5, 3.5) * standard # - define: medium-object # value: # - standard-transform # - [ scale, 3, 3, 3 ] medium = Scaling(3, 3, 3) * standard # - define: small-object # value:
floor.material.color = Color(1.0, 0.9, 0.9)
floor.material.pattern = CheckersPattern(Color(1, 1, 1), Color(0, 0, 0))
floor.material.reflective = 0.5
floor.material.specular = 0
middle = Sphere()
middle.set_transform(Translation(-0.5, 1, 0.5))
middle.material.transparency = 0.9
middle.material.diffuse = 0.1
middle.material.reflective = 0.9
middle.material.refractive_index = 1.5
middle.material.specular = 1
middle.material.shininess = 300
right = Sphere()
right.set_transform(Translation(1.5, 0.5, -0.5) * Scaling(0.5, 1, 0.5))
right.material.pattern = StripePattern(Color(1, 1, 1), Color(0, 1, 0))
right.material.pattern.set_pattern_transform(
Scaling(0.1, 0.1, 0.1) * RotationY(math.pi / 4))
right.material.color = Color(0.1, 1, 0.5)
right.material.diffuse = 0.7
right.material.specular = 0.3
left = Sphere()
left.transform = Translation(-1.5, 0.33, -0.75) * Scaling(0.33, 0.33, 0.33)
left.material.color = Color(1, 0.8, 0.1)
left.material.diffuse = 0.7
left.material.specular = 0.3
world = World()
world.objects.extend([floor, middle, right, left])
def test_inverse_scaling():
t = Scaling(2, 3, 4)
i = t.inverse()
v = Vector(-4, 6, 8)
assert i * v == Vector(-2, 2, 2)