def from_matrix(cls, matrix):
"""Construct a frame from a matrix.
Parameters
----------
matrix : :obj:`list` of :obj:`list` of :obj:`float`
The 4x4 transformation matrix in row-major order.
Returns
-------
Frame
The constructed frame.
Examples
--------
>>> from compas.geometry import Frame
>>> from compas.geometry import matrix_from_euler_angles
>>> ea1 = [0.5, 0.4, 0.8]
>>> M = matrix_from_euler_angles(ea1)
>>> f = Frame.from_matrix(M)
>>> ea2 = f.euler_angles()
>>> allclose(ea1, ea2)
True
"""
sc, sh, a, point, p = decompose_matrix(matrix)
R = matrix_from_euler_angles(a, static=True, axes='xyz')
xaxis, yaxis = basis_vectors_from_matrix(R)
return cls(point, xaxis, yaxis)
def from_euler_angles(cls,
euler_angles,
static=True,
axes='xyz',
point=[0, 0, 0]):
"""Construct a transformation from a rotation represented by Euler angles.
Parameters
----------
euler_angles : list of float
Three numbers that represent the angles of rotations about the defined axes.
static : bool, optional
If true the rotations are applied to a static frame.
If not, to a rotational.
Defaults to ``True``.
axes : str, optional
A 3 character string specifying the order of the axes.
Defaults to ``'xyz'``.
point : list of float, optional
The point of the frame.
Defaults to ``[0, 0, 0]``.
Returns
-------
:class:`compas.geometry.Transformation`
The constructed transformation.
"""
R = matrix_from_euler_angles(euler_angles, static, axes)
T = matrix_from_translation(point)
M = multiply_matrices(T, R)
return cls.from_matrix(M)
def __init__(self, matrix=None):
if matrix:
_, _, angles, _, _ = decompose_matrix(matrix)
check = matrix_from_euler_angles(angles)
if not allclose(flatten(matrix), flatten(check)):
raise ValueError('This is not a proper rotation matrix.')
super(Rotation, self).__init__(matrix=matrix)
def basis_vectors(self):
"""Returns the basis vectors from the ``Rotation`` component of the
``Transformation``.
"""
sc, sh, a, t, p = decompose_matrix(self.matrix)
R = matrix_from_euler_angles(a, static=True, axes='xyz')
xv, yv = basis_vectors_from_matrix(R)
return Vector(*xv), Vector(*yv)
def test_matrix_from_euler_angles():
ea1 = 1.4, 0.5, 2.3
args = True, 'xyz'
R = matrix_from_euler_angles(ea1, *args)
r = [[-0.5847122176808724, -0.4415273357486694, 0.6805624396639868, 0.0],
[0.6544178905170501, 0.23906322244658262, 0.7173464994301357, 0.0],
[-0.479425538604203, 0.8648134986574489, 0.14916020070358058, 0.0],
[0.0, 0.0, 0.0, 1.0]]
assert np.allclose(R, r)
def basis_vectors(self):
"""Returns the basis vectors from the ``Rotation`` component of the ``Transformation``.
"""
# this has to be here to avoid circular import
from compas.geometry.primitives import Vector
sc, sh, a, t, p = decompose_matrix(self.matrix)
R = matrix_from_euler_angles(a, static=True, axes='xyz')
xv, yv = basis_vectors_from_matrix(R)
return Vector(*xv), Vector(*yv)
def from_euler_angles(cls,
euler_angles,
static=True,
axes='xyz',
point=[0, 0, 0]):
"""Construct a frame from a rotation represented by Euler angles.
Parameters
----------
euler_angles : :obj:`list` of :obj:`float`
Three numbers that represent the angles of rotations about the defined axes.
static : :obj:`bool`, optional
If true the rotations are applied to a static frame.
If not, to a rotational.
Defaults to true.
axes : :obj:`str`, optional
A 3 character string specifying the order of the axes.
Defaults to 'xyz'.
point : :obj:`list` of :obj:`float`, optional
The point of the frame.
Defaults to [0, 0, 0].
Returns
-------
Frame
The constructed frame.
Examples
--------
>>> from compas.geometry import Frame
>>> ea1 = 1.4, 0.5, 2.3
>>> f = Frame.from_euler_angles(ea1, static = True, axes = 'xyz')
>>> ea2 = f.euler_angles(static = True, axes = 'xyz')
>>> allclose(ea1, ea2)
True
"""
R = matrix_from_euler_angles(euler_angles, static, axes)
xaxis, yaxis = basis_vectors_from_matrix(R)
return cls(point, xaxis, yaxis)
def from_euler_angles(cls, euler_angles, static=True, axes='xyz'):
"""Calculates a ``Rotation`` from Euler angles.
In 3D space any orientation can be achieved by composing three
elemental rotations, rotations about the axes (x,y,z) of a coordinate
system. A triple of Euler angles can be interpreted in 24 ways, which
depends on if the rotations are applied to a static (extrinsic) or
rotating (intrinsic) frame and the order of axes.
Parameters
----------
euler_angles: list of float
Three numbers that represent the angles of rotations about the
defined axes.
static: bool, optional
If true the rotations are applied to a static frame. If not, to a
rotational. Defaults to true.
axes: str, optional
A 3 character string specifying order of the axes. Defaults to 'xyz'.
Examples
--------
>>> ea1 = 1.4, 0.5, 2.3
>>> args = False, 'xyz'
>>> R1 = Rotation.from_euler_angles(ea1, *args)
>>> ea2 = R1.euler_angles(*args)
>>> allclose(ea1, ea2)
True
>>> alpha, beta, gamma = ea1
>>> xaxis, yaxis, zaxis = [1, 0, 0], [0, 1, 0], [0, 0, 1]
>>> Rx = Rotation.from_axis_and_angle(xaxis, alpha)
>>> Ry = Rotation.from_axis_and_angle(yaxis, beta)
>>> Rz = Rotation.from_axis_and_angle(zaxis, gamma)
>>> R2 = Rx * Ry * Rz
>>> R1 == R2
True
"""
R = cls()
R.matrix = matrix_from_euler_angles(euler_angles, static, axes)
return R
def test_euler_angles_from_matrix():
ea1 = 1.4, 0.5, 2.3
args = True, 'xyz'
R = matrix_from_euler_angles(ea1, *args)
ea2 = euler_angles_from_matrix(R, *args)
assert np.allclose(ea1, ea2)
if __name__ == '__main__':
f1 = Frame([1, 1, 1], [0.68, 0.68, 0.27], [-0.67, 0.73, -0.15])
R = Rotation.from_frame(f1)
f2 = Frame.from_rotation(R, point=f1.point)
print(f1 == f2)
print(f2)
f1 = Frame([1, 1, 1], [0.68, 0.68, 0.27], [-0.67, 0.73, -0.15])
T = Transformation.from_frame(f1)
f2 = Frame.from_transformation(T)
print(f1 == f2)
ea1 = [0.5, 0.4, 0.8]
M = matrix_from_euler_angles(ea1)
f = Frame.from_matrix(M)
ea2 = f.euler_angles()
print(allclose(ea1, ea2))
q1 = [0.945, -0.021, -0.125, 0.303]
f = Frame.from_quaternion(q1, point=[1., 1., 1.])
q2 = f.quaternion
print(allclose(q1, q2, tol=1e-03))
aav1 = [-0.043, -0.254, 0.617]
f = Frame.from_axis_angle_vector(aav1, point=[0, 0, 0])
aav2 = f.axis_angle_vector
print(allclose(aav1, aav2))
ea1 = 1.4, 0.5, 2.3
f1 = Frame([2, 2, 2], [0.12, 0.58, 0.81], [-0.80, 0.53, -0.26])
f2 = Frame([1, 1, 1], [0.68, 0.68, 0.27], [-0.67, 0.73, -0.15])
T = Transformation.from_frame_to_frame(f1, f2)
f1.transform(T)
print(f1 == f2)
f = Frame([1, 1, 1], [0.68, 0.68, 0.27], [-0.67, 0.73, -0.15])
T = Transformation.from_frame(f)
p = Point(0, 0, 0)
p.transform(T)
print(allclose(f.point, p))
f1 = Frame([1, 1, 1], [0.68, 0.68, 0.27], [-0.67, 0.73, -0.15])
T = Transformation.from_frame(f1)
points = [[1.0, 1.0, 1.0], [1.68, 1.68, 1.27], [0.33, 1.73, 0.85]]
points = transform_points(points, T)
trans1 = [1, 2, 3]
angle1 = [-2.142, 1.141, -0.142]
scale1 = [0.123, 2, 0.5]
T = matrix_from_translation(trans1)
R = matrix_from_euler_angles(angle1)
S = matrix_from_scale_factors(scale1)
M = multiply_matrices(multiply_matrices(T, R), S)
# M = compose_matrix(scale1, None, angle1, trans1, None)
scale2, shear2, angle2, trans2, persp2 = decompose_matrix(M)
print(allclose(scale1, scale2))
print(allclose(angle1, angle2))
print(allclose(trans1, trans2))
