> (you may decide to go to povray.off-topic, I read that also)

it's not off-topic to povray.general, just off-topic to "Boned mesh file 
formats?" - anyway, we can continue it here until someone complains ;-)

>> My problem is that a cubic bezier triangle can't be connected smoothly 
>> to cubic bezier patches 
> 
> Sorry, you lost me there. Exactly what is your problem?

the "standard" rectangular (tensor product) patches in povray are 
bicubic, thus they have 16 controlpoints.

A "standard" cubic bezier triangle 
http://www.google.at/search?q=bezier+triangle has got 10 controlpoints 
(the outlines are cubic bezier curves, and there is one center-point). 
As far as I know, you can't smoothly connect such a triangle to 
rectangular (cubic) patches. I think (but I'm not sure) that it would be 
possible for bezier-triangles of order 4 (quartic) - (by degree 
elevating http://www.google.at/search?degree+elevation the outlines) 
bacause it has three inner controlpoints...

The only three- and five-sided patches I know of, which can be smootly 
connected to the rectangular ones are Hosaka/Kimura (M. Hosaka and F. 
Kimura. Non-four-sided patch expressions with control points. Computer 
Aided Geometric Design 1(1): 75-86, 1984.) for the cubic case, and 
Zheng/Ball for the general case (arbitrary degree).

Thus, I'm looking for a conversion scheme for such patches, similar to 
that one for "classical" bezier-triangles into "standard" rectangular 
patches (as in my macro).

> I am quite sure that I downloaded and printed that article then.
> The paper will be in a stack somewhere and I probably have the PDF on
> a backup disk.
> There is a new elsevier policy that allows the authors to have a PDF
> of their article for download at a page of their institution.

I have a zip archive with the zheng/ball publication (it was available 
for download on Mr. Zhengs webpage some time age), but I don't know if 
it is legal to share it.

It's a little bit beyond my math skills, so I'd be interested in reading 
the Hosaka/Kimura version, but I'Ve never found a download link :-/

Elsevier: I'm not a student, do you know if universities have (free) 
access to such material?
Would it be legal to share such a paper within an open-source project 
(i.e. not for commercial use)?

 > Perhaps there should be a tutorial
 > on advanced bezier techniques, but I do not have the time to write
 > that.

We could start with a discussion about "advanced bezier techniques" to 
share expirence and discuss all that scary math stuff ;-)
It could eventually become something like a tutrial with tips on using 
bezier patches in povray.
Not sure what the best platform would be - a thread in p.advanced-users?
Alternatively I could add a forum on my webpage's phpbb board 
http://www.jpatch.com/forum_frameset.html
or a wiki...

-sascha

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