def rotated_y():
quat = quaternion.create_from_y_rotation( math.pi )
result = matrix33.create_from_quaternion( quat )
expected = matrix33.create_from_y_rotation( math.pi )
self.assertTrue(
numpy.allclose( result, expected ),
"Matrix33 from quaternion incorrect with PI rotation about Y"
)
def rotated_y():
mat = matrix33.create_from_y_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_y_rotation( theta ):
"""Creates a matrix with the specified rotation about the Y axis.
:param float theta: The rotation, in radians, about the Y-axis.
:rtype: numpy.array
:return: A matrix with the shape (4,4) with the specified rotation about
the Y-axis.
.. seealso:: http://en.wikipedia.org/wiki/Rotation_matrix#In_three_dimensions
"""
mat = create_identity()
mat[ 0:3, 0:3 ] = matrix33.create_from_y_rotation( theta )
return mat
def test_inverse(self):
m = matrix33.create_from_y_rotation(np.pi)
result = matrix33.inverse(m)
self.assertTrue(
np.allclose(result, matrix33.create_from_y_rotation(-np.pi)))
def test_apply_to_vector_rotated_y(self):
mat = matrix33.create_from_y_rotation(np.pi)
vec = vector3.unit.x
result = matrix33.apply_to_vector(mat, vec)
expected = -vec
self.assertTrue(np.allclose(result, expected))
def test_multiply_rotation(self):
m1 = matrix33.create_from_x_rotation(np.pi)
m2 = matrix33.create_from_y_rotation(np.pi / 2.0)
result = matrix33.multiply(m1, m2)
self.assertTrue(np.allclose(result, np.dot(m1, m2)))
def test_create_from_y_rotation(self):
mat = matrix33.create_from_y_rotation(np.pi / 2.)
self.assertTrue(np.allclose(np.dot([1., 0., 0.], mat), [0., 0., 1.]))
self.assertTrue(np.allclose(np.dot([0., 1., 0.], mat), [0., 1., 0.]))
self.assertTrue(np.allclose(np.dot([0., 0., 1.], mat), [-1., 0., 0.]))
def test_create_from_quaternion_rotated_y(self):
quat = quaternion.create_from_y_rotation(np.pi)
result = matrix33.create_from_quaternion(quat)
expected = matrix33.create_from_y_rotation(np.pi)
self.assertTrue(np.allclose(result, expected))
def test_inverse(self):
m = matrix33.create_from_y_rotation(np.pi)
result = matrix33.inverse(m)
self.assertTrue(np.allclose(result, matrix33.create_from_y_rotation(-np.pi)))
def test_multiply_rotation(self):
m1 = matrix33.create_from_x_rotation(np.pi)
m2 = matrix33.create_from_y_rotation(np.pi / 2.0)
result = matrix33.multiply(m1, m2)
self.assertTrue(np.allclose(result, np.dot(m1,m2)))
def test_apply_to_vector_rotated_y(self):
mat = matrix33.create_from_y_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_y(self):
quat = quaternion.create_from_y_rotation(np.pi)
result = matrix33.create_from_quaternion(quat)
expected = matrix33.create_from_y_rotation(np.pi)
self.assertTrue(np.allclose(result, expected))
def test_create_from_y_rotation(self):
mat = matrix33.create_from_y_rotation(np.pi / 2.)
self.assertTrue(np.allclose(np.dot([1.,0.,0.], mat), [0.,0.,1.]))
self.assertTrue(np.allclose(np.dot([0.,1.,0.], mat), [0.,1.,0.]))
self.assertTrue(np.allclose(np.dot([0.,0.,1.], mat), [-1.,0.,0.]))