geometry.py 文件源码

def basis(a):
    '''Returns two vectors u and v such that (a, u, v) is a direct ON basis.

    '''
    ez = np.array([0., 0., 1.], dtype = np.float64)

    if np.abs(np.dot(a, ez)) == 1.:
        u = np.dot(a, ez) * np.array([1., 0., 0.], dtype = np.float64)
        v = np.array([0., 1., 0.], dtype = np.float64)
        return u,v
    else:
        theta = np.arccos(np.dot(a, ez))

        u = ez/np.sin(theta) - a/np.tan(theta)
        v = np.cross(a, u)
        u = u/np.linalg.norm(u)
        v = v/np.linalg.norm(v)
        return u, v