Sascha Ledinsky wrote:

>  > (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).
> 
(to be honest I did not know that the standard bezier triangles had
only 10 control points, so that explains my confusion)
IIRC the Zheng Ball triangles had 3 inner control points. That implied
that every edge had 4 neighbour control points in the triangle
(two inside and 2 at the other edges). The derivative perpendicular
to the edge was defined by these 4 control points, just as in quad
patches. connecting to quad patches was thus conceptively simple.
Therefore, I think that patches with 12 control points will be more
useful for POV users, and true bezier triangles are only of academic
interest. You already seem to have a bezier patch with 12 control
points and I assume(hope) that they have the same properties as
the Zheng Ball triangles. So for all practical purposes my question
is: why look further?
And (just to annoy Thorsten): can we get Zheng Ball triangles and
pentangles as primitives in the next version of POV?
> 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).
If you insist, you can always compute the real 3D coordinates of the
points you want to use as the control points of your three patches
and invert the bezier computation to get the actual control points
that are needed by POV.
> 
>> 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.
Ah, getting off-topic. Yes an interesting IP question. I downloaded
it also and at that time it was free to use and distribute. Now,
it appears that it is not anymore. Is my copy still free and free
to distribute or am I not allowed anymore to share it. Basically
the question is can you change the legal status of a document
later without consent and without informing the holder of that
document.
> 
> 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?
No, unless they have a subscription to the paper.
> Would it be legal to share such a paper within an open-source project 
> (i.e. not for commercial use)?
Ask a lawyer :)
I guess it is, as the paper is not a part of the project, only
secondary literature.
>  > 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...
I do not know either.
> 
> -sascha

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