> You did not explain what your macro does, and it is a bit hard
> to follow without comments but here is what I think you are doing:
> Lets call the corners A,B, and C. You split the triangle in three 
> patches. One with corners: A, the middle of A and B, the middle
> of A and C, and the centerpoint. Then you compute the remaining
> points as functions of the originally given points. I can only
> assume that the math is correct ;)

This is a little off topic now, I think if we continue a discussion 
about bezier patches we should start a new thread.

Anyway, that's exactly what it does. I've found the algorithm in a 
paper, I think it was:
Hu Shi-Min.
Conversion of a triangular Bezier surface into three rectangular Bezier 
surfaces.
Computer Aided Geometric Design, vol 13, 1996, 219-226.

> For POV to render these without cracks, you also have to
> make sure that the division in triangles, as controlled by
> u_step and v_step is the same in the patches in the triangle
> and in the adjacent quad patches. This simply means that
> in the triangle they have to be one lower then outside.
> I think that it also forces a flatness of zero in the entire
> set of patches. You have to be certain that the edges of
> adjacent patches edges are split in the middle, so they
> have to have flatness=0 and therefore their neighbours
> also etc.

You're right, but this is POV-Ray specific.
I've only posted this to prove that it is possible to smoothly connect 
three bezier patches to a triangular patch.
My problem is that a cubic bezier triangle can't be connected smoothly 
to cubic bezier patches - what I'd need is a similar conversion 
algorithm for something like Zheng-Ball patches (J.J. Zheng, A.A. Ball. 
Control point surfaces over non-four-sided areas. Computer Aided 
Geometric Design, 14:807-821, 1977) - discussed in this thread: 
http://news.povray.org/povray.binaries.images/thread/%3C3ff791bf%40news.povray.org%3E/?mtop=160788&moff=20

All those papers have been available for free download on the internet 
once, but now they have disappered and the only way to get them these 
days is to pay $30 for each one at http://www.elsevier.com :-(

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