def test_rotate_point_x(self):
p = Point(0, 1, 0)
half_quarter = Transformations.rotation_x(math.pi / 4)
full_quarter = Transformations.rotation_x(math.pi / 2)
self.assertEqual(Matrix.multiply_tuple(half_quarter, p),
Point(0,
math.sqrt(2) / 2,
math.sqrt(2) / 2))
self.assertEqual(Matrix.multiply_tuple(full_quarter, p),
Point(0, 0, 1))
def test_rotate_point_x_inverse(self):
p = Point(0, 1, 0)
half_quarter = Transformations.rotation_x(math.pi / 4)
inv = Matrix.inverse(half_quarter)
self.assertEqual(Matrix.multiply_tuple(inv, p),
Point(0,
math.sqrt(2) / 2, -math.sqrt(2) / 2))
def test_chained_transformations(self):
p = Point(1, 0, 1)
a = Transformations.rotation_x(math.pi / 2)
b = Transformations.scaling(5, 5, 5)
c = Transformations.translation(10, 5, 7)
t = c.dot(b.dot(a))
self.assertEqual(Matrix.multiply_tuple(t, p), Point(15, 0, 7))
def test_tranforming_bounding_box(self):
box = Bounds(Point(-1, -1, -1), Point(1, 1, 1))
matrix = Transformations.rotation_x(math.pi / 4).dot(
Transformations.rotation_y(math.pi / 4))
box2 = box.transform(matrix)
self.assertEqual(box2.min, Point(-1.4142, -1.7071, -1.7071))
self.assertEqual(box2.max, Point(1.4142, 1.7071, 1.7071))
def test_individual_transformations(self):
p = Point(1, 0, 1)
a = Transformations.rotation_x(math.pi / 2)
b = Transformations.scaling(5, 5, 5)
c = Transformations.translation(10, 5, 7)
# rotate first
p2 = Matrix.multiply_tuple(a, p)
self.assertEqual(p2, Point(1, -1, 0))
# apply scaling
p3 = Matrix.multiply_tuple(b, p2)
self.assertEqual(p3, Point(5, -5, 0))
# apply translation
p4 = Matrix.multiply_tuple(c, p3)
self.assertEqual(p4, Point(15, 0, 7))
if __name__ == '__main__':
# The floor is an extremely flattened sphere with a matte texture
floor = Sphere()
floor.transform = Transformations.scaling(10, 0.1, 10)
floor.material = Material()
floor.material.color = Color(1, 0.9, 0.9)
floor.material.specular = 0
# The wall on the left has the same scale and color as the floor, but is also rotated and translated into place
left_wall = Sphere()
left_wall.transform = Transformations.translation(0, 0, 5)
left_wall.transform = left_wall.transform.dot(
Transformations.rotation_y(-math.pi / 4))
left_wall.transform = left_wall.transform.dot(
Transformations.rotation_x(math.pi / 2))
left_wall.transform = left_wall.transform.dot(
Transformations.scaling(10, 0.1, 10))
left_wall.material = floor.material
# The wall on the right is identical to the left wall, but is rotated the opposite direction in y
right_wall = Sphere()
right_wall.transform = Transformations.translation(0, 0, 5)
right_wall.transform = right_wall.transform.dot(
Transformations.rotation_y(math.pi / 4))
right_wall.transform = right_wall.transform.dot(
Transformations.rotation_x(math.pi / 2))
right_wall.transform = right_wall.transform.dot(
Transformations.scaling(10, 0.1, 10))
right_wall.material = floor.material