def rotate_points_xy(points, axis, angle, origin=None):
"""Rotates points around an arbitrary axis in 2D.
Parameters:
points (sequence of sequence of float): XY coordinates of the points.
axis (sequence of float): The rotation axis.
angle (float): the angle of rotation in radians.
origin (sequence of float): Optional. The origin of the rotation axis.
Default is ``[0.0, 0.0, 0.0]``.
Returns:
list: the rotated points
References:
https://en.wikipedia.org/wiki/Rotation_matrix
"""
if not origin:
origin = [0.0, 0.0]
# rotation matrix
x, y = normalize_vector_xy(axis)
cosa = cos(angle)
sina = sin(angle)
R = [[cosa, -sina], [sina, cosa]]
# translate points
points = translate_points_xy(points, scale_vector_xy(origin, -1.0))
# rotate points
points = [multiply_matrix_vector(R, point) for point in points]
# translate points back
points = translate_points_xy(points, origin)
return points
def rotate_points_xy(points, angle, origin=None):
"""Rotates points in the XY plane around the Z axis at a specific origin.
Parameters
----------
points : list of point
A list of points.
angle : float
The angle of rotation in radians.
origin : point, optional
The origin of the rotation axis.
Default is ``[0.0, 0.0, 0.0]``.
Returns
-------
list
The rotated points in the XY plane (Z=0).
Examples
--------
>>>
"""
if not origin:
origin = [0.0, 0.0, 0.0]
cosa = math.cos(angle)
sina = math.sin(angle)
R = [[cosa, -sina, 0.0], [sina, cosa, 0.0], [0.0, 0.0, 1.0]]
# translate points
points = translate_points_xy(points, scale_vector_xy(origin, -1.0))
# rotate points
points = [multiply_matrix_vector(R, point) for point in points]
# translate points back
points = translate_points_xy(points, origin)
return points