def ray_for_pixel(self, pixel_x, pixel_y):
xoffset = (pixel_x + 0.5) * self.pixel_size
yoffset = (pixel_y + 0.5) * self.pixel_size
world_x = self.half_width - xoffset
world_y = self.half_height - yoffset
pixel = multiply_tuple(self.__inverse_transform,
point(world_x, world_y, -1))
origin = multiply_tuple(self.__inverse_transform, point(0, 0, 0))
direction = normalize(subtract(pixel, origin))
return Ray(origin, direction)
def normal_to_world(self, normal):
normal = multiply_tuple(transpose(self.__inverse_transform), normal)
normal[3] = 0
normal = normalize(normal)
if self.parent:
normal = self.parent.normal_to_world(normal)
return normal
def main():
print("What happens when you invert the identity matrix?")
a = identity_matrix()
print(inverse(a))
print()
print("What do you get when you multiply a matrix by its inverse?")
a = identity_matrix()
a[1][0] = 2
a[0][3] = -5
b = multiply_matrix(a, inverse(a))
print(b)
print()
print(
"Is there any difference between the inverse of the transpose of a matrix, and the transpose of the inverse?"
)
c = inverse(transpose(a))
d = transpose(inverse(a))
print(c)
print(d)
print()
print(
"Remember how multiplying the identity matrix by a tuple gives you the tuple, unchanged?"
)
t = tuple_4d(5, 4, 3, 1)
i = identity_matrix()
c = multiply_tuple(i, t)
print(c)
print()
print(
"Now, try changing any single element of the identity matrix to a different number, and then multiplying it by a tuple. What happens to the tuple?"
)
i[1][1] = 2
i[2][2] = 3
c = multiply_tuple(i, t)
print(c)
def main():
c = Canvas(500, 500)
p = point(0, 0, 1)
translate = translation(250, 0, 250)
scale = scaling(100, 0, 100)
for h in range(12):
r = rotation_y(h * pi / 6)
transform = multiply_matrix(translate, multiply_matrix(scale, r))
p2 = multiply_tuple(transform, p)
print(f"position ({p2[0]}, {p2[1]}, {p2[2]})")
c.set_pixel(round(p2[0]), c.height - round(p2[2]),
color(0.0, 1.0, 0.0))
with open('clock.ppm', 'w') as out_file:
out_file.write(c.to_ppm())
def step_impl(context):
context.p4 = multiply_tuple(context.C, context.p3)
def step_impl(context):
context.p3 = multiply_tuple(context.B, context.p2)
def step_impl(context):
context.p2 = multiply_tuple(context.full_quarter, context.p)
def step_impl(context, x, y, z):
actual = multiply_tuple(context.full_quarter, context.p)
expected = point(x, y, z)
assert_tuple(actual, expected)
def step_impl(context):
actual = multiply_tuple(context.inv, context.p)
expected = point(0, sqrt(2) / 2, -sqrt(2) / 2)
def step_impl(context):
actual = multiply_tuple(context.half_quarter, context.p)
expected = point(-sqrt(2) / 2, sqrt(2) / 2, 0)
assert_tuple(actual, expected)
def step_impl(context):
actual = multiply_tuple(context.transform, context.v)
expected = context.v
assert actual == expected, "%r is not %r" % (actual, expected)
def step_impl(context, x, y, z):
actual = multiply_tuple(context.transform, context.p)
expected = point(x, y, z)
assert_tuple(actual, expected)
def world_to_object(self, point):
if self.parent:
point = self.parent.world_to_object(point)
return multiply_tuple(self.__inverse_transform, point)
def pattern_at_shape(self, shape, point):
""""""
shape_point = shape.world_to_object(point)
pattern_point = multiply_tuple(self.__inverse_transform, shape_point)
return self.pattern_at(pattern_point)
def step_impl(context):
assert multiply_tuple(context.a, context.b) == tuple_4d(18, 24, 33, 1)
def step_impl(context):
assert multiply_tuple(identity_matrix(), context.a) == context.a
def step_impl(context, x, y, z):
actual = multiply_tuple(context.transform, context.v)
expected = vector(x, y, z)
assert actual == expected, "%r is not %r" % (actual, expected)