Rotation of 3D vector?

Question

I have two vectors as Python lists and an angle. E.g.:

v = [3,5,0] axis = [4,4,1] theta = 1.2 #radian 

What is the best/easiest way to get the resulting vector when rotating the v vector around the axis?

The rotation should appear to be counter clockwise for an observer to whom the axis vector is pointing. This is called the right hand rule

Answer 1

Using the Euler-Rodrigues formula:

import numpy as np import math  def rotation_matrix(axis, theta):     """     Return the rotation matrix associated with counterclockwise rotation about     the given axis by theta radians.     """     axis = np.asarray(axis)     axis = axis / math.sqrt(np.dot(axis, axis))     a = math.cos(theta / 2.0)     b, c, d = -axis * math.sin(theta / 2.0)     aa, bb, cc, dd = a * a, b * b, c * c, d * d     bc, ad, ac, ab, bd, cd = b * c, a * d, a * c, a * b, b * d, c * d     return np.array([[aa + bb - cc - dd, 2 * (bc + ad), 2 * (bd - ac)],                      [2 * (bc - ad), aa + cc - bb - dd, 2 * (cd + ab)],                      [2 * (bd + ac), 2 * (cd - ab), aa + dd - bb - cc]])  v = [3, 5, 0] axis = [4, 4, 1] theta = 1.2   print(np.dot(rotation_matrix(axis, theta), v))  # [ 2.74911638  4.77180932  1.91629719]