def rot33(magnitude, direction) -> numpy.float32:
"""Return the 3x3 matrix of float32 which rotates
by the given magnitude and direction.
"""
return matrix33.create_from_axis_rotation(AXIS.dot(
matrix33.create_from_z_rotation(direction)),
magnitude,
dtype=numpy.float32)
def rotated_z():
quat = quaternion.create_from_z_rotation( math.pi )
result = matrix33.create_from_quaternion( quat )
expected = matrix33.create_from_z_rotation( math.pi )
self.assertTrue(
numpy.allclose( result, expected ),
"Matrix33 from quaternion incorrect with PI rotation about Z"
)
def rotated_z():
mat = matrix33.create_from_z_rotation( math.pi )
vec = vector3.unit.x
result = matrix33.apply_to_vector( mat, vec )
expected = -vec
self.assertTrue(
numpy.allclose( result, expected ),
"Matrix33 apply_to_vector incorrect with rotation about Y"
)
def create_from_z_rotation( theta ):
"""Creates a matrix with the specified rotation about the Z axis.
:param float theta: The rotation, in radians, about the Z-axis.
:rtype: numpy.array
:return: A matrix with the shape (4,4) with the specified rotation about
the Z-axis.
.. seealso:: http://en.wikipedia.org/wiki/Rotation_matrix#In_three_dimensions
"""
mat = create_identity()
mat[ 0:3, 0:3 ] = matrix33.create_from_z_rotation( theta )
return mat
def test_apply_to_vector_rotated_z(self):
mat = matrix33.create_from_z_rotation(np.pi)
vec = vector3.unit.x
result = matrix33.apply_to_vector(mat, vec)
expected = -vec
self.assertTrue(np.allclose(result, expected))
def test_create_from_quaternion_rotated_z(self):
quat = quaternion.create_from_z_rotation(np.pi)
result = matrix33.create_from_quaternion(quat)
expected = matrix33.create_from_z_rotation(np.pi)
self.assertTrue(np.allclose(result, expected))
def test_create_from_z_rotation(self):
mat = matrix33.create_from_z_rotation(np.pi / 2.)
self.assertTrue(np.allclose(np.dot([1., 0., 0.], mat), [0., -1., 0.]))
self.assertTrue(np.allclose(np.dot([0., 1., 0.], mat), [1., 0., 0.]))
self.assertTrue(np.allclose(np.dot([0., 0., 1.], mat), [0., 0., 1.]))
def test_apply_to_vector_rotated_z(self):
mat = matrix33.create_from_z_rotation(np.pi)
vec = vector3.unit.x
result = matrix33.apply_to_vector(mat, vec)
expected = -vec
self.assertTrue(np.allclose(result, expected))
def test_create_from_quaternion_rotated_z(self):
quat = quaternion.create_from_z_rotation(np.pi)
result = matrix33.create_from_quaternion(quat)
expected = matrix33.create_from_z_rotation(np.pi)
self.assertTrue(np.allclose(result, expected))
def test_create_from_z_rotation(self):
mat = matrix33.create_from_z_rotation(np.pi / 2.)
self.assertTrue(np.allclose(np.dot([1.,0.,0.], mat), [0.,-1.,0.]))
self.assertTrue(np.allclose(np.dot([0.,1.,0.], mat), [1.,0.,0.]))
self.assertTrue(np.allclose(np.dot([0.,0.,1.], mat), [0.,0.,1.]))
