(left, right, bottom, top, near, far, perspective=False)
return numpy.array(M)
Return matrix to obtain normalized device coordinates from frustum.

    The frustum bounds are axis-aligned along x (left, right),
    y (bottom, top) and z (near, far).

    Normalized device coordinates are in range [-1, 1] if coordinates are
    inside the frustum.

    If perspective is True the frustum is a truncated pyramid with the
    perspective point at origin and direction along z axis, otherwise an
    orthographic canonical view volume (a box).

    Homogeneous coordinates transformed by the perspective clip matrix
    need to be dehomogenized (divided by w coordinate).

    >>> frustum = numpy.random.rand(6)
    >>> frustum[1] += frustum[0]
    >>> frustum[3] += frustum[2]
    >>> frustum[5] += frustum[4]
    >>> M = clip_matrix(perspective=False, *frustum)
    >>> numpy.dot(M, [frustum[0], frustum[2], frustum[4], 1])
    array([-1., -1., -1.,  1.])
    >>> numpy.dot(M, [frustum[1], frustum[3], frustum[5], 1])
    array([ 1.,  1.,  1.,  1.])
    >>> M = clip_matrix(perspective=True, *frustum)
    >>> v = numpy.dot(M, [frustum[0], frustum[2], frustum[4], 1])
    >>> v / v[3]
    array([-1., -1., -1.,  1.])
    >>> v = numpy.dot(M, [frustum[1], frustum[3], frustum[4], 1])
    >>> v / v[3]
    array([ 1.,  1., -1.,  1.])
Return matrix to obtain normalized device coordinates from frustum.
Return matrix to obtain normalized device coordinates from frustum .
def clip_matrix(left, right, bottom, top, near, far, perspective=False):
    """Return matrix to obtain normalized device coordinates from frustum.

    The frustum bounds are axis-aligned along x (left, right),
    y (bottom, top) and z (near, far).

    Normalized device coordinates are in range [-1, 1] if coordinates are
    inside the frustum.

    If perspective is True the frustum is a truncated pyramid with the
    perspective point at origin and direction along z axis, otherwise an
    orthographic canonical view volume (a box).

    Homogeneous coordinates transformed by the perspective clip matrix
    need to be dehomogenized (divided by w coordinate).

    >>> frustum = numpy.random.rand(6)
    >>> frustum[1] += frustum[0]
    >>> frustum[3] += frustum[2]
    >>> frustum[5] += frustum[4]
    >>> M = clip_matrix(perspective=False, *frustum)
    >>> numpy.dot(M, [frustum[0], frustum[2], frustum[4], 1])
    array([-1., -1., -1.,  1.])
    >>> numpy.dot(M, [frustum[1], frustum[3], frustum[5], 1])
    array([ 1.,  1.,  1.,  1.])
    >>> M = clip_matrix(perspective=True, *frustum)
    >>> v = numpy.dot(M, [frustum[0], frustum[2], frustum[4], 1])
    >>> v / v[3]
    array([-1., -1., -1.,  1.])
    >>> v = numpy.dot(M, [frustum[1], frustum[3], frustum[4], 1])
    >>> v / v[3]
    array([ 1.,  1., -1.,  1.])

    """
    if left >= right or bottom >= top or near >= far:
        raise ValueError('invalid frustum')
    if perspective:
        if near <= _EPS:
            raise ValueError('invalid frustum: near <= 0')
        t = 2.0 * near
        M = [[t/(left-right), 0.0, (right+left)/(right-left), 0.0],
             [0.0, t/(bottom-top), (top+bottom)/(top-bottom), 0.0],
             [0.0, 0.0, (far+near)/(near-far), t*far/(far-near)],
             [0.0, 0.0, -1.0, 0.0]]
    else:
        M = [[2.0/(right-left), 0.0, 0.0, (right+left)/(left-right)],
             [0.0, 2.0/(top-bottom), 0.0, (top+bottom)/(bottom-top)],
             [0.0, 0.0, 2.0/(far-near), (far+near)/(near-far)],
             [0.0, 0.0, 0.0, 1.0]]
    return numpy.array(M)
def clip_matrix ( left , right , bottom , top , near , far , perspective = False ) : if left >= right or bottom >= top or near >= far : raise ValueError ( 'invalid frustum' ) if perspective : if near <= _EPS : raise ValueError ( 'invalid frustum: near <= 0' ) t = 2.0 * near M = [ [ t / ( left - right ) , 0.0 , ( right + left ) / ( right - left ) , 0.0 ] , [ 0.0 , t / ( bottom - top ) , ( top + bottom ) / ( top - bottom ) , 0.0 ] , [ 0.0 , 0.0 , ( far + near ) / ( near - far ) , t * far / ( far - near ) ] , [ 0.0 , 0.0 , - 1.0 , 0.0 ] ] else : M = [ [ 2.0 / ( right - left ) , 0.0 , 0.0 , ( right + left ) / ( left - right ) ] , [ 0.0 , 2.0 / ( top - bottom ) , 0.0 , ( top + bottom ) / ( bottom - top ) ] , [ 0.0 , 0.0 , 2.0 / ( far - near ) , ( far + near ) / ( near - far ) ] , [ 0.0 , 0.0 , 0.0 , 1.0 ] ] return numpy . array ( M )