def get_angle_axis_matrix(u, v, default_rot_axis):
'''
returns a rotation matrix that will align u with v. If the angle of rotation is 0 then it
returns an identity matrix, if angle is 180 then it rotates about the default_rot_axis
otherwise this function returns a matrix corresponding to angle-axis rotation that is
implemented in GeomTransform.rotate
'''
u = GT.normalize(u)
v = GT.normalize(v)
axis_of_rotation = GT.normalize(np.cross(u, v))
cos_theta = np.dot(u, v)
# due to floating point error abs(u.v) can be > 1, in which case arccos will be nan
if -1. <= cos_theta <= 1.:
angle_deg = np.rad2deg(np.arccos(cos_theta))
else: # here it's either -1-eps or 1 + eps
angle_deg = 0. if cos_theta > 0. else 180.
M = np.eye(4)
if abs(angle_deg - 180.) < 1e-6:
M = GT.rotate(angle_deg, default_rot_axis)
axis_of_rotation = default_rot_axis
elif abs(angle_deg) > 1e-6 and abs(angle_deg - 180.) > 1e-6:
M = GT.rotate(angle_deg, axis_of_rotation)
return M, angle_deg, axis_of_rotation
