def step_impl(context):
expected = Matrix(4, 4)
for e_row in range(4):
for e_col in range(4):
expected.matrix[e_row][e_col] = float(context.table[e_row][e_col])
result = context.B
assert expected == result, 'The expected matrix does not match what was given.'
def step_impl(context, row, column, rows, columns):
expected = Matrix(rows, columns)
for e_row in range(rows):
for e_col in range(columns):
expected.matrix[e_row][e_col] = float(context.table[e_row][e_col])
result = context.M.submatrix(row, column)
assert expected == result, 'The expected submatrix was not found with the calculated result.'
def step_impl(context):
expected = Matrix(4, 4)
for row in range(4):
for column in range(4):
expected.matrix[row][column] = float(context.table[row][column])
result = context.A.transpose()
assert expected == result, 'The transpose of Matrix A does not match the expected result.'
def step_impl(context):
expected = Matrix(4, 4)
for row in range(4):
for column in range(4):
expected.matrix[row][column] = float(context.table[row][column])
result = context.A * context.B
assert expected == result, 'The multiplication of A * B does not match the expected result.'
def step_impl(context):
expected = Matrix(4, 4)
for e_row in range(4):
for e_col in range(4):
expected.matrix[e_row][e_col] = float(context.table[e_row][e_col])
result = context.M.inverse()
assert expected == result, 'The expected matrix is does not match the given inverse.'
def hexagon_edge():
edge = Cylinder()
edge.minimum = 0
edge.maximum = 1
edge.transform = Matrix.translation(0, 0, -1) * \
Matrix.rotation_y(-30) * \
Matrix.rotation_z(-90) * \
Matrix.scaling(0.25, 1, 0.25)
return edge
def step_impl(context, col, row):
expected = Matrix(col, row)
i = j = 0
for row in context.table:
for col in row:
expected._matrix[i][j] = float(col)
j += 1
i += 1
j = 0
assert expected == context.t, f't != {expected._matrix}'
def question_one():
print('1. What happens when you invert the identity matrix?')
print('You get this:')
m = Matrix.identity_matrix().submatrix(3, 3)
m = m.inverse()
for row in m.matrix:
print(row)
print('The Identity matrix again :)\n')
def hexagon():
hex = Group()
for n in range(6):
side = hexagon_side()
side.transform = Matrix.rotation_y(n * 60)
hex.add_child(side)
return hex
def question_two():
print('2. What do you get when you multiply a matrix by its inverse?')
m = Matrix(3, 3)
m._matrix = [[1, 2, 3],
[20, 5, 6],
[7, 8, 11]]
print('We have the following matrix:')
for row in m.matrix:
print(row)
print('\nThe inverse matrix is the following:')
i = m.inverse()
for row in i.matrix:
print(row)
print('\nThe product of the matrix with it\'s inverse is the following:')
p = i * m
for row in p.matrix:
print(row)
def default_world():
world = World()
world.light = PointLight(point(-10, 10, -10), Color(1, 1, 1))
s1 = Sphere()
s1.material.color = Color(0.8, 1.0, 0.6)
s1.material.diffuse = 0.7
s1.material.specular = 0.2
world.objects.append(s1)
s2 = Sphere()
s2.transform = Matrix.scaling(0.5, 0.5, 0.5)
world.objects.append(s2)
return world
def ch9():
# Step 1
floor = Plane()
floor.transform = Matrix.scaling(10, 0.01, 10)
floor.material = Material()
floor.material.color = Color(1, 0.9, 0.9)
floor.material.specular = 0
floor.material.pattern = StripePattern(Color(1, 0, 0), Color(0, 0, 1))
# Middle biggest sphere
middle = Sphere()
middle.transform = Matrix.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
middle.material.pattern = RingPattern(Color(1, 0, 1), Color(1, 1, 1))
middle.material.pattern.transform = Matrix.scaling(0.25, 0.5, 0.25)
# Smaller right sphere
right = Sphere()
right.transform = Matrix.translation(1.5, 0.5, -0.5) * Matrix.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
right.material.reflective = 1.0
# Left yellow sphere
left = Sphere()
left.transform = Matrix.translation(-1.5, 0.33, -0.75) * Matrix.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.light = PointLight(point(-10, 10, -10), Color(1, 1, 1))
world.objects.extend([floor, middle, right, left])
camera = Camera(100, 50, 60)
# camera = Camera(500, 250, 60)
camera.transform = view_transform(point(0, 1.5, -5),
point(0, 1, 0),
vector(0, 1, 0))
canvas = camera.render(world)
with open('ch9.ppm', 'w') as fp:
fp.write(canvas.to_ppm())
def __init__(self, hsize, vsize, field_of_view):
self.hsize = hsize
self.vsize = vsize
self.field_of_view = field_of_view
self.transform = Matrix.identity_matrix()
# Calculate pixel size, pixel width, pixel height
self.fov_radians = math.radians(field_of_view)
half_view = math.tan(self.fov_radians / 2)
aspect = hsize / 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 step_impl(context, x, y, z):
context.B = Matrix.scaling(x, y, z)
def step_impl(context, x, y, z):
context.C = Matrix.translation(x, y, z)
def step_impl(context, xy, xz, yx, yz, zx, zy):
context.transform = Matrix.shearing(xy, xz, yx, yz, zx, zy)
def step_impl(context, degrees):
context.A = Matrix.rotation_x(degrees)
def step_impl(context, degrees):
context.half_quarter = Matrix.rotation_y(degrees)
def step_impl(context, degrees, x, y, z):
context.c.transform = Matrix.rotation_y(degrees) * Matrix.translation(
x, y, z)
def ch7():
# Step 1
floor = Sphere()
floor.transform = Matrix.scaling(10, 0.01, 10)
floor.material = Material()
floor.material.color = Color(1, 0.9, 0.9)
floor.material.specular = 0
# Step 2
left_wall = Sphere()
left_wall.transform = Matrix.translation(0, 0, 5) * Matrix.rotation_y(-45) * \
Matrix.rotation_x(90) * Matrix.scaling(10, 0.01, 10)
left_wall.material = floor.material
# Step 3
right_wall = Sphere()
right_wall.transform = Matrix.translation(0, 0, 5) * Matrix.rotation_y(45) * \
Matrix.rotation_x(90) * Matrix.scaling(10, 0.01, 10)
right_wall.material = floor.material
# Step 4
middle = Sphere()
middle.transform = Matrix.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
# Step 5
right = Sphere()
right.transform = Matrix.translation(1.5, 0.5, -0.5) * Matrix.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
# Step 6
left = Sphere()
left.transform = Matrix.translation(-1.5, 0.33, -0.75) * Matrix.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.light = PointLight(point(-10, 10, -10), Color(1, 1, 1))
world.objects.extend([floor, left_wall, right_wall, middle, right, left])
camera = Camera(100, 50, 60)
# camera = Camera(500, 250, 60)
camera.transform = view_transform(point(0, 1.5, -5), point(0, 1, 0),
vector(0, 1, 0))
canvas = camera.render(world)
with open('ch8.ppm', 'w') as fp:
fp.write(canvas.to_ppm())
def step_impl(context, x, y, z):
context.transform = Matrix.scaling(x, y, z)
def step_impl(context, x, y, z):
context.pattern.transform = Matrix.translation(x, y, z)
def step_impl(context, x, y, z):
expected = Matrix.translation(x, y, z)
result = context.pattern.transform
assert expected == result, f'pattern.transform != {expected}'
def step_impl(context):
assert context.t == Matrix.identity_matrix(), 't != identity_matrix'
def hexagon_corner():
corner = Sphere()
corner.transform = Matrix.translation(0, 0, -1) * \
Matrix.scaling(0.25, 0.25, 0.25)
return corner
def step_impl(context, degrees):
context.full_quarter = Matrix.rotation_z(degrees)
def step_impl(context, x, y, z):
expected = Matrix.scaling(x, y, z)
assert expected == context.t, f't != {expected}'
# Can probably have this done internally in the Canvas class, but left
# it here for simplicity and it doesn't hide how the conversion is done.
def convert_position_to_canvas(canvas: Canvas, world_position: Vec3):
"""Converts the position from world to canvas. This is done by subtracting
the z world position from the canvas height, the other positions are left alone."""
return point(
round(world_position.x + (canvas.width / 2)), round(world_position.y),
round((canvas.height - (canvas.height / 2) - world_position.z)))
if __name__ == '__main__':
width = 400
height = 400
canvas = Canvas(width, height)
hour_rotation = 360 / 12
hour_rotation_matrix = Matrix.rotation_y(hour_rotation)
radius = (3 / 8) * canvas.width
print(f'Radius: {radius}')
position = point(0, 0, 1) * radius
for i in range(12):
canvas_point = convert_position_to_canvas(canvas, position)
print(f'Position:{position}\nCanvas:{canvas_point}')
canvas.write_pixel(canvas_point.x, canvas_point.z, Color(1, 1, 1))
position = hour_rotation_matrix * position
with open('clock2.ppm', 'w') as fp:
fp.write(canvas.to_ppm())
def __init__(self, parent=None):
# Converts itself from shape -> world space
self.transform = Matrix.identity_matrix()
self.material = Material()
self.parent = parent
self.id = id(self)
def step_impl(context, x, y, z):
expected = Matrix.translation(x, y, z)
assert expected == context.t, f't != {expected}'