openalea.phenomenal.calibration.transformations.clip_matrix

openalea.phenomenal.calibration.transformations.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.])