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 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 step_impl(context):
assert multiply_matrix(context.a, identity_matrix()) == context.a
def step_impl(context):
expected = matrix(4, 4)
for r in range(4):
for c in range(4):
expected[r][c] = float(context.table[r][c])
assert multiply_matrix(context.a, context.b) == expected
def step_impl(context):
context.c = multiply_matrix(context.m, context.b)
def step_impl(context):
actual = multiply_matrix(context.c, inverse(context.b))
expected = context.m
assert_matrix(actual, expected)
def step_impl(context):
context.transform = multiply_matrix(
context.C, multiply_matrix(context.B, context.full_quarter))
def step_assert_transformation_matrix_of_object_at_index(
context, index, tx, ty, tz, sx, sy, sz):
assert_matrix(
context.w.objects[index].transform(),
multiply_matrix(scaling(sx, sy, sz), translation(tx, ty, tz)))
def step_create_scaling_rotation_z_matrix_m(context):
context.m = multiply_matrix(scaling(1, 0.5, 1), rotation_z(pi / 5))
def render_scene_with_plane():
floor = Plane()
floor.set_transform(scaling(10, 0.01, 10))
# floor.set_transform(
# multiply_matrix(translation(0, 0.33, 0), scaling(10, 0.01, 10)))
floor.material = Material()
floor.material.color = color(1, 0.9, 0.9)
floor.material.specular = 0
# left_wall = Plane()
# left_wall.set_transform(
# multiply_matrix(
# translation(0, 0, 5),
# multiply_matrix(rotation_y(-pi / 4),
# multiply_matrix(rotation_x(pi / 2), scaling(10, 0.01, 10)))))
# left_wall.material = floor.material
# right_wall = Plane()
# right_wall.set_transform(
# multiply_matrix(
# translation(0, 0, 5),
# multiply_matrix(rotation_y(pi / 4),
# multiply_matrix(rotation_x(pi / 2), scaling(10, 0.01, 10)))))
middle = Sphere()
middle.set_transform(translation(-0.5, 1, 0.5))
middle.material = Material()
middle.material.pattern = StripePattern(color(0.6, 1.0, 0.6),
color(0.3, 0.6, 0.3))
middle.material.color = color(0.1, 1, 0.5)
middle.material.diffuse = 0.7
middle.material.specular = 0.3
middle.material.pattern.set_transform(
multiply_matrix(scaling(0.2, 0.2, 0.2), rotation_y(pi / 4)))
right = Sphere()
right.set_transform(
multiply_matrix(translation(1.5, 0.5, -0.5), scaling(0.5, 0.5, 0.5)))
right.material = Material()
right.material.color = color(0.5, 1, 0.1)
# right.material.diffuse = 0.7
right.material.diffuse = 0.2
right.material.specular = 0.3
right.material.reflective = 0.7
left = Sphere()
left.set_transform(
multiply_matrix(translation(-1.5, 0.33, -0.75),
scaling(0.33, 0.33, 0.33)))
left.material = Material()
left.material.color = color(1, 0.8, 0.1)
left.material.diffuse = 0.7
left.material.specular = 0.3
world = World()
world.add_light(PointLight(point(-10, 10, -10), color(1, 1, 1)))
world.objects.append(floor)
# world.objects.append(left_wall)
# world.objects.append(right_wall)
world.objects.append(middle)
world.objects.append(right)
world.objects.append(left)
camera = Camera(600, 500, pi / 3)
camera.set_transform(
view_transform(point(0, 1.5, -5), point(0, 1, 0), vector(0, 1, 0)))
# camera.set_transform(
# view_transform(point(0, 4, -1), point(0, 1, 0), vector(0, 1, 0)))
canvas = RayTracer().render(camera, world)
ppm = canvas.to_ppm()
outf = open('render_scene_with_plane.ppm', 'w')
outf.write(ppm)
def step_set_transform_of_c_to_transformation_matrix(context):
context.c.set_transform(
multiply_matrix(rotation_y(pi / 4), translation(0, -2, 5)))
def render_simple_scene():
floor = Sphere()
floor.set_transform(scaling(10, 0.01, 10))
floor.material = Material()
floor.material.color = color(1, 0.9, 0.9)
floor.material.specular = 0
left_wall = Sphere()
left_wall.set_transform(
multiply_matrix(
translation(0, 0, 5),
multiply_matrix(
rotation_y(-pi / 4),
multiply_matrix(rotation_x(pi / 2), scaling(10, 0.01, 10)))))
left_wall.material = floor.material
right_wall = Sphere()
right_wall.set_transform(
multiply_matrix(
translation(0, 0, 5),
multiply_matrix(
rotation_y(pi / 4),
multiply_matrix(rotation_x(pi / 2), scaling(10, 0.01, 10)))))
right_wall.material = floor.material
middle = Sphere()
middle.set_transform(translation(-0.5, 1, 0.5))
middle.material = Material()
middle.material.color = color(0.1, 1, 0.5)
middle.material.diffuse = 0.7
middle.material.specular = 0.3
right = Sphere()
right.set_transform(
multiply_matrix(translation(1.5, 0.5, -0.5), scaling(0.5, 0.5, 0.5)))
right.material = Material()
right.material.color = color(0.5, 1, 0.1)
right.material.diffuse = 0.7
right.material.specular = 0.3
left = Sphere()
left.set_transform(
multiply_matrix(translation(-1.5, 0.33, -0.75),
scaling(0.33, 0.33, 0.33)))
left.material = Material()
left.material.color = color(1, 0.8, 0.1)
left.material.diffuse = 0.7
left.material.specular = 0.3
world = World()
world.add_light(PointLight(point(-10, 10, -10), color(1, 1, 1)))
world.objects.append(floor)
world.objects.append(left_wall)
world.objects.append(right_wall)
world.objects.append(middle)
world.objects.append(right)
world.objects.append(left)
camera = Camera(600, 500, pi / 3)
camera.set_transform(
view_transform(point(0, 1.5, -5), point(0, 1, 0), vector(0, 1, 0)))
canvas = RayTracer().render(camera, world)
with open('render_simple_scene.ppm', 'w') as out_file:
out_file.write(canvas.to_ppm())