transformations.py 文件源码

def angle_between_vectors(v0, v1, directed=True, axis=0):
    """Return angle between vectors.

    If directed is False, the input vectors are interpreted as undirected axes,
    i.e. the maximum angle is pi/2.

    >>> a = angle_between_vectors([1, -2, 3], [-1, 2, -3])
    >>> numpy.allclose(a, math.pi)
    True
    >>> a = angle_between_vectors([1, -2, 3], [-1, 2, -3], directed=False)
    >>> numpy.allclose(a, 0)
    True
    >>> v0 = [[2, 0, 0, 2], [0, 2, 0, 2], [0, 0, 2, 2]]
    >>> v1 = [[3], [0], [0]]
    >>> a = angle_between_vectors(v0, v1)
    >>> numpy.allclose(a, [0, 1.5708, 1.5708, 0.95532])
    True
    >>> v0 = [[2, 0, 0], [2, 0, 0], [0, 2, 0], [2, 0, 0]]
    >>> v1 = [[0, 3, 0], [0, 0, 3], [0, 0, 3], [3, 3, 3]]
    >>> a = angle_between_vectors(v0, v1, axis=1)
    >>> numpy.allclose(a, [1.5708, 1.5708, 1.5708, 0.95532])
    True

    """
    v0 = numpy.array(v0, dtype=numpy.float64, copy=False)
    v1 = numpy.array(v1, dtype=numpy.float64, copy=False)
    dot = numpy.sum(v0 * v1, axis=axis)
    dot /= vector_norm(v0, axis=axis) * vector_norm(v1, axis=axis)
    return numpy.arccos(dot if directed else numpy.fabs(dot))