transformations.py 文件源码

def orthogonalization_matrix(lengths, angles):
    """Return orthogonalization matrix for crystallographic cell coordinates.

    Angles are expected in degrees.

    The de-orthogonalization matrix is the inverse.

    >>> O = orthogonalization_matrix((10., 10., 10.), (90., 90., 90.))
    >>> numpy.allclose(O[:3, :3], numpy.identity(3, float) * 10)
    True
    >>> O = orthogonalization_matrix([9.8, 12.0, 15.5], [87.2, 80.7, 69.7])
    >>> numpy.allclose(numpy.sum(O), 43.063229)
    True

    """
    a, b, c = lengths
    angles = numpy.radians(angles)
    sina, sinb, _ = numpy.sin(angles)
    cosa, cosb, cosg = numpy.cos(angles)
    co = (cosa * cosb - cosg) / (sina * sinb)
    return numpy.array((
        ( a*sinb*math.sqrt(1.0-co*co),  0.0,    0.0, 0.0),
        (-a*sinb*co,                    b*sina, 0.0, 0.0),
        ( a*cosb,                       b*cosa, c,   0.0),
        ( 0.0,                          0.0,    0.0, 1.0)),
        dtype=numpy.float64)