4-sided bezier patches alone simply don't work for irregular topology.
Therefore, the shapes that can be created with just 4-sides bezier
patches are very limited, which is a shame, since bezier patches are
otherwise very flexible and useful shapes...

I've wanted 3, 5 and 6-sided bezier patches for a looong time, and
occasionally tried to figure out a way to implement them (as a macro
generating a mesh, not as a patch.) However, it's not very easy to come
up with the right method, and I have not succeeded at that.

Then, when searching the net for the topic, I found this page:
http://zhengjj.freeyellow.com/html/publications.html

Now that's interesting! The publication "Control point surfaces over
non-four-sided surfaces" explain exactly how to implement 3, 5 and
6-sided bezier patches! Unfortunately I'm not able to comprehend all
those formulas that they use, and thus I won't be able to implement it
myself, neither as a patch nor as macros.

But it is my hope that someone else here will implement it, actually
preferably as macros. The thing is that I have plans to create a system
to make modeling with bezier patches easier, and for the features I'm
planning, I'd need the capability to modify how the patches work.

I hope that one of you great POVers with abilities to read and
understand scientific papers will create some macros based on the
above-mentioned papers. I'm aware that the syntax for an n-sided bezier
patch would be much more confusing (code-wise, visually) than that of a
4-sided bezier patch, but it doesn't matter so much, since it's my
intention to create macros that take care of calculating the control
points for the bezier patches.

Anybody up for the challenge?

By the way, note that this is very high on my wish-list. I would happily
give up features such as isosurfaces and photon mapping in exchange for
n-sided bicubic patches. That's because I'm into character design and
animation, but I know that many others have different priorities...

Rune
--
3D images and anims, include files, tutorials and more:
rune|vision:  http://runevision.com (updated July 12)
POV-Ray Ring: http://webring.povray.co.uk

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