def from_axis_and_angle(cls, axis, angle, point=[0, 0, 0]):
"""Calculates a ``Rotation`` from a rotation axis and an angle and an optional point of rotation.
The rotation is based on the right hand rule, i.e. anti-clockwise if the
axis of rotation points towards the observer.
Parameters
----------
axis : list of float
Three numbers that represent the axis of rotation.
angle : float
The rotation angle in radians.
point : :class:`Point` or list of float
A point to perform a rotation around an origin other than [0, 0, 0].
Examples
--------
>>> axis1 = normalize_vector([-0.043, -0.254, 0.617])
>>> angle1 = 0.1
>>> R = Rotation.from_axis_and_angle(axis1, angle1)
>>> axis2, angle2 = R.axis_and_angle
>>> allclose(axis1, axis2)
True
>>> allclose([angle1], [angle2])
True
Notes
-----
The rotation is based on the right hand rule, i.e. anti-clockwise
if the axis of rotation points towards the observer.
"""
R = cls()
R.matrix = matrix_from_axis_and_angle(axis, angle, point=point)
return R
def test_axis_and_angle_from_matrix():
axis1 = normalize_vector([-0.043, -0.254, 0.617])
angle1 = 0.1
R = matrix_from_axis_and_angle(axis1, angle1)
axis2, angle2 = axis_and_angle_from_matrix(R)
assert allclose(axis1, axis2)
assert allclose([angle1], [angle2])
def from_axis_and_angle(cls, axis, angle, point=[0, 0, 0]):
"""Calculates a ``Rotation`` from a rotation axis and an angle and \
an optional point of rotation.
Note:
The rotation is based on the right hand rule, i.e. anti-clockwise
if the axis of rotation points towards the observer.
Args:
axis (:obj:`list` of :obj:`float`): Three numbers that represent
the axis of rotation
angle (:obj:`float`): The rotation angle in radians.
point (:obj:`list` of :obj:`float`, optional): A point to
perform a rotation around an origin other than [0, 0, 0].
Example:
>>> axis1 = normalize_vector([-0.043, -0.254, 0.617])
>>> angle1 = 0.1
>>> R = Rotation.from_axis_and_angle(axis1, angle1)
>>> axis2, angle2 = R.axis_and_angle
>>> allclose(axis1, axis2)
True
>>> allclose([angle1], [angle2])
True
"""
M = matrix_from_axis_and_angle(axis, angle, point)
return cls(M)
def test_matrix_from_axis_angle_vector():
axis1 = normalize_vector([-0.043, -0.254, 0.617])
angle1 = 0.1
R = matrix_from_axis_and_angle(axis1, angle1)
r = [[0.9950248278789664, -0.09200371122722178, -0.03822183963195913, 0.0],
[0.09224781823368366, 0.9957251324831573, 0.004669108322156158, 0.0],
[
0.037628871037522216, -0.008171760019527692, 0.9992583701939277,
0.0
], [0.0, 0.0, 0.0, 1.0]]
assert np.allclose(R, r)
def rotate_points(points, angle, axis=None, origin=None):
"""Rotates points around an arbitrary axis in 3D.
Parameters
----------
points : list of point
A list of points.
angle : float
The angle of rotation in radians.
axis : vector, optional
The rotation axis.
Default is ``[0.0, 0.0, 1.0]``
origin : point, optional
The origin of the rotation axis.
Default is ``[0.0, 0.0, 0.0]``.
Returns
-------
list of point
The rotated points
Examples
--------
>>>
Notes
-----
For more info, see [1]_.
References
----------
.. [1] Wikipedia. *Rotation matrix*.
Available at: https://en.wikipedia.org/wiki/Rotation_matrix.
"""
if axis is None:
axis = [0.0, 0.0, 1.0]
if origin is None:
origin = [0.0, 0.0, 0.0]
R = matrix_from_axis_and_angle(axis, angle, origin)
points = transform_points(points, R)
return points
def from_axis_and_angle(cls, axis, angle, point=[0, 0, 0]):
"""Construct a rotation transformation from a rotation axis and an angle and an optional point of rotation.
The rotation is based on the right hand rule, i.e. anti-clockwise if the
axis of rotation points towards the observer.
Parameters
----------
axis : [float, float, float] | :class:`compas.geometry.Vector`
Three numbers that represent the axis of rotation.
angle : float
The rotation angle in radians.
point : [float, float, float] | :class:`compas.geometry.Point`
A point to perform a rotation around an origin other than [0, 0, 0].
Returns
-------
:class:`compas.geometry.Rotation`
Notes
-----
The rotation is based on the right hand rule, i.e. anti-clockwise
if the axis of rotation points towards the observer.
Examples
--------
>>> axis1 = normalize_vector([-0.043, -0.254, 0.617])
>>> angle1 = 0.1
>>> R = Rotation.from_axis_and_angle(axis1, angle1)
>>> axis2, angle2 = R.axis_and_angle
>>> allclose(axis1, axis2)
True
>>> allclose([angle1], [angle2])
True
"""
R = cls()
R.matrix = matrix_from_axis_and_angle(axis, angle, point=point)
return R