Rotate

gistfile1.txt

import math
import numpy as np

def get_rotating_transform(u, v):
    """
    Given two unit vectors u, v,
    we compute the rotation R such that v = R @ u
    """
    assert np.isclose(np.linalg.norm(u), 1)
    assert np.isclose(np.linalg.norm(v), 1)
    n = np.cross(u, v)
    while np.allclose(n, 0): # u and v are on the same line -.-
        rand_dir = np.random.randn(3)
        n = np.cross(u, rand_dir)
    n /= np.linalg.norm(n)
    t = np.cross(n, u)
    T = np.stack([u, t, n], axis=1)
    alpha = math.atan2(v @ t, v @ u)
    R = np.array([
        [math.cos(alpha), -math.sin(alpha), 0],
        [math.sin(alpha), math.cos(alpha), 0],
        [0, 0, 1]
    ])
    transform = T @ R @ T.T
    assert np.allclose(v, transform @ u)
    return transform