Thinking about this a little more - and thinking back, it was a combination of
TOK's work and the question about the vibrating plate that combined to start me
investigating how to control a bicubic patch - or a network of them - such that
the surface could be made to intersect specifically designated points.

Going in the opposite direction:

(ignoring trace(), and approaching this a priori / ab initio)

Given that a Bezier patch can be interpreted as a Bezier spline in one dimension
whose control points slide along Bezier splines oriented in the other dimension,
and that this can be expressed as a parametiric equation, then

It ought to be possible to define a parametric {} object in POV-Ray based on a
set of control points and the basis functions of the Bezier splines.

Then, given a point <m, n> (or <u, v>) on the surface, one could place things ON
the surface of the patch.

This should also allow the generation of _any_ spline between the ordinate /
cardinal splines defined by the corners.  In theory one should be able to
simulate a patch by juxtaposing a series of splines from one side to the other
in either dimension.

I think that it also might be possible to define an isosurface {} in the same
way, and since there's a method for creating offset surfaces with isosurfaces,
then I'd be interested in seeing what's possible with a 3D rectangular mesh
skinned in Bezier patches and making a thickened hollow shell by that method.

Just some thoughts.



I also have a question that I have not answered for myself yet - is there a type
of spline that is coincident with a Bezier spline, but that contains / is
coincident with its own control points?

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