def rotate(self, angle, vector1, vector2, rot_point):
tnd = self.to_num_dimension
num = self.num_dimension + 1
rot_pos = tnd(rot_point).reshape(num - 1, 1)
matrix_translate = np.eye(num)
matrix_translate[0:num - 1, num - 1:num] = rot_pos * -1.
matrix_rot = rotation_from_angle_and_plane(angle, tnd(vector1, up=1),
tnd(vector2, up=1))
matrix_from_origin = matrix_rot.copy()
matrix_rot = np.dot(matrix_rot, matrix_translate)
matrix_translate[0:num - 1, num - 1:num] = rot_pos
matrix_rot = np.dot(matrix_translate, matrix_rot)
# print(matrix_rot)
for obj in self.objects:
obj.rotate(matrix_rot, matrix_from_origin)
def test_rotation_multiple_90():
for dim in range(2, 6):
image_1 = np.ones((6, ) * dim)
image_2 = np.zeros((6, ) * dim)
image_2[(slice(None, 3), ) * dim] = 1
center_1 = None
center_2 = (1, ) * dim
for image, center in zip((image_1, image_2), (center_1, center_2)):
v1 = np.zeros(dim)
v2 = np.zeros(dim)
v1[-2] = 1
v2[-1] = 1
for angle in (np.pi / 2 * x for x in range(1, 4)):
rotation = mgen.rotation_from_angle_and_plane(angle, v1, v2)
output = transform(image, rotation, (0, ) * dim, origin=center)
# need some atol here since we are comparing exactly to 0
np.testing.assert_allclose(output, image, atol=1e-10)
def test_rotation_nd(self):
for rand1 in np.random.uniform(-np.pi, np.pi, 100):
# Test 2D case
is_close(rotation_from_angle(rand1), rotation_from_angle_and_plane(rand1, (1,0), (0,1)))
# Test 3D case
is_close(rotation_around_z(rand1), rotation_from_angle_and_plane(rand1, (1,0,0), (0,1,0)))
# Test normalisation of first parameter
is_close(rotation_around_z(rand1), rotation_from_angle_and_plane(rand1, (2,0,0), (0,1,0)))
# Test normalisation of second parameter
is_close(rotation_around_z(rand1), rotation_from_angle_and_plane(rand1, (1,0,0), (0,2,0)))
# Test normalisation of both parameters
is_close(rotation_around_z(rand1), rotation_from_angle_and_plane(rand1, (2,0,0), (0,2,0)))
is_close(rotation_around_x(rand1), rotation_from_angle_and_plane(rand1, (0,1,0), (0,0,1)))
is_close(rotation_around_y(rand1), rotation_from_angle_and_plane(rand1, (0,0,1), (1,0,0)))
# Test generic properties of higher dimensional rotations
# create two perpendicular random vectors
dimension = random.randint(4,100)
v1 = np.random.uniform(-1., 1., dimension)
v1 = v1/np.linalg.norm(v1)
v2 = np.random.uniform(-1., 1., dimension)
v2 = v2/np.linalg.norm(v2)
v2 = v2 - v2.dot(v1)*v1
m = rotation_from_angle_and_plane(rand1, v1, v2)
m_inv = rotation_from_angle_and_plane(-rand1, v1, v2)
is_close(m.dot(m.T), np.eye(dimension))
self.assertAlmostEqual(np.linalg.det(m), 1.0)
is_close(m, m_inv.T)
with self.assertRaises(ValueError):
rotation_from_angle_and_plane(0., (1,0,0), (0,1,0,0))
with self.assertRaises(ValueError):
rotation_from_angle_and_plane(0., (1,0,0,0), (0,1,0))
with self.assertRaises(ValueError):
rotation_from_angle_and_plane(0., (1,0,0), (1,0,0))
with self.assertRaises(ValueError):
rotation_from_angle_and_plane(0., (0,0), (1,0))
with self.assertRaises(ValueError):
rotation_from_angle_and_plane(0., (1,0), (0,0))