class Shape:
def __init__(self):
self.transform = Identity()
self.material = Material()
self.parent = None
def set_material(self, material: Material):
self.material = material
def set_transform(self, t: Matrix):
self.transform *= t
def __eq__(self, other):
return (self.__class__ == other.__class__
and self.material == other.material
and self.parent == other.parent
and self.transform == other.transform)
def intersect(self, ray: Ray):
local_ray = ray.transform(self.transform.inverse())
return self.local_intersect(local_ray)
def normal_at(self, world_point: Point):
local_point = self.world_to_object(world_point)
local_normal = self.local_normal_at(local_point)
return self.normal_to_world(local_normal)
def world_to_object(self, point: Point):
if self.parent is not None:
point = self.parent.world_to_object(point)
return self.transform.inverse() * point
def normal_to_world(self, normal: Vector):
normalv = self.transform.inverse().transpose() * normal
normalv.w = 0
normalv = normalv.normalize()
if self.parent is not None:
normalv = self.parent.normal_to_world(normalv)
return normalv
def local_normal_at(self, local_point):
raise TypeError("Generic Shapes cannot be evaluated")
def local_intersect(self, ray):
raise TypeError("Generic Shapes cannot be evaluated")
def __str__(self):
return f"{self.__class__}: Transform:\n{self.transform}"
def test_default_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 == Identity()
def __init__(self, hsize: int, vsize: int, fov: float, transform: Matrix = None):
self.hsize = hsize
self.vsize = vsize
self.fov = fov
if transform is None:
self.transform = Identity()
else:
self.transform = transform
half_view = math.tan(self.fov / 2)
aspect = self.hsize / self.vsize
if aspect >= 1:
self.half_width = half_view
self.half_height = half_view / aspect
else:
self.half_width = half_view * aspect
self.half_height = half_view
self.pixel_size = (self.half_width * 2) / self.hsize
def test_camera_attributes():
hsize = 160
vsize = 120
fov = math.pi / 2
c = Camera(hsize, vsize, fov)
assert c.hsize == 160
assert c.vsize == 120
assert c.fov == math.pi / 2
assert c.transform == Identity()
class Camera:
def __init__(self, hsize: int, vsize: int, fov: float, transform: Matrix = None):
self.hsize = hsize
self.vsize = vsize
self.fov = fov
if transform is None:
self.transform = Identity()
else:
self.transform = transform
half_view = math.tan(self.fov / 2)
aspect = self.hsize / self.vsize
if aspect >= 1:
self.half_width = half_view
self.half_height = half_view / aspect
else:
self.half_width = half_view * aspect
self.half_height = half_view
self.pixel_size = (self.half_width * 2) / self.hsize
def ray_for_pixel(self, px, py):
x_offset = (px + 0.5) * self.pixel_size
y_offset = (py + 0.5) * self.pixel_size
world_x = self.half_width - x_offset
world_y = self.half_height - y_offset
pixel = self.transform.inverse() * Point(world_x, world_y, -1)
origin = self.transform.inverse() * Point(0, 0, 0)
direction = (pixel - origin).normalize()
return Ray(origin, direction)
def render(self, world: World):
image = Canvas(self.hsize, self.vsize)
for y in range(self.vsize):
print(y)
for x in range(self.hsize):
ray = self.ray_for_pixel(x, y)
color = world.color_at(ray)
image.write_pixel(x, y, color)
return image
class Pattern:
def __init__(self):
self.transform = Identity()
def set_pattern_transform(self, t: Matrix):
self.transform *= t
def pattern_at_shape(self, shape, world_point: Point):
object_point = shape.world_to_object(world_point)
pattern_point = self.transform.inverse() * object_point
return self.pattern_at(pattern_point)
def pattern_at(self, point):
raise TypeError("Generic Pattern Cannot be evaluated")
def __init__(self):
self.transform = Identity()
self.material = Material()
self.parent = None
def test_default_transform():
pattern = _TestPattern()
assert pattern.transform == Identity()
def __init__(self):
self.transform = Identity()
def test_group_creation():
g = Group()
assert g.transform == Identity()
assert len(g.objects) == 0
def test_default_transform():
s = _TestShape()
assert s.transform == Identity()
def test_identity_transpose():
m = Identity()
assert m == m.transpose()
def test_identity_mult():
m = Matrix([[0, 1, 2, 4], [1, 2, 4, 8], [2, 4, 8, 16], [4, 8, 16, 32]])
i = Identity()
assert m * i == m
def test_glassy_sphere():
s = GlassSphere()
assert s.transform == Identity()
assert s.material.transparency == 1.0
assert s.material.refractive_index == 1.5