This is not yet an answer to the n-sided polygon question,
but something more fundametal on bicubic patches.
I studied the math involved again over the last few days
and reached some conclusions.
1) you can stich bicubic patches seemlessly together.
  you can follow the rule of thumb on having controlpoints
  in one plane (though it is somewhat more subtle than
  that). I can even explain it, but that would
  make a very long post, with some math in it.
  If anybody is interested, he/she must point out what is
  the right way (e.g. newsgroup) to publish that.
  I withdraw hereby my former claim that you can not have
  continues normals along the entire length of the edge.
  I apologize for causing confusion. I mixed up control
  points and actual surface points when I was thinking about
  it before. The math for bicubic patches is relatively simple
  but sometimes tricky (especially when you expect the wrong
  answer :( ).
2) I (and probably others) have been fooled by the way
  POV-Ray renders these patches. For the moment I think
  that there is something wrong with the normals.

Attached are two images. Both of four patches stitched together.
The wide angle picture suggests that there are kinks (cracks, bends?)
in the surface on the left going upwards crossing the middle and
on top going from left to right. I also included a lot of markers
where the surface should be, and it is precisely there.
In the closeup view of the green line you can clearly see that
the shadows have sometimes little to do with the curvature of
the surface.

Can anybody with access to the source explain the shape of the
shadows, or point out where I am wrong?

	Andrel

Rune wrote:
> andrel wrote:
> 
>>Rune wrote:
>>
>>>There is no way to create smooth n-sided
>>>bicubic patches from 4-sided bicubic patches.
>>
>>I take that as a challenge.
> 
> 
> Sounds good to me. I'm skeptical, but if you do succeed, I'd be
> interested in the result.
> 
> Rune
> --
> 3D images and anims, include files, tutorials and more:
> rune|vision:  http://runevision.com **updated Dec 30**
> POV-Ray Ring: http://webring.povray.co.uk
> 
>

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