You're right and I'm aware of this problem. I've taken two different 
approaches to this problem for the next version of JPatch:

1)
Subdivide a 3-sided patch into 3 4-sided patches (like 5-sided patches 
will be subdivided into 5 4-sided patches). The new patches are formed by:

* computing the center of the patch.
* deCasteljau'ing the edges
* Connecting the center with the mid-points of each edge

This works more or less for 5-point patches (I still have some minor 
discontinuity problems, I think this is because the 5-point-patch is 
somehow "overconstrained" and it's not clear to me how to exactly 
compute the center-point - suggestions are appreciated :-)
This works too for 3-point patches which connect only to 4-point patches 
but causes hughe problems when two 3-point patches meet.

2)
sPatch places two corner-points (and their tangents) at the same 
position - this of course makes it impossible to calculate the surface 
normal of this corner - when triangulizing the patch two triangles will 
have bad normals resulting in visible artifacts (REYES is more robust 
because it will subdivide until the triangles are smaller than a pixel, 
but POV has problems when the u/v_steps setting is too low).
I tried to place this two corner points not on the same point but move 
one slightly away - this seems to work well (no more discontinuities or 
artifacts), but I'm not sure if it will make troubles with U/V mapping - 
I haven't implemented u/v mapping yet so I have to try it later...

Your approach with triangulizing natively and exporting the 
triangle-mesh is an option too - if you've got an implementation let me 
know, I can easily integrate it into JPatch...

I'll do some tests with bezier-triangles too, but these will also have 
to be exported as triangle-meshes...

-sascha

Breton Slivka wrote:
> Most of us are aware of the phenomenon when it comes to bezier patches, and 
> programs like spatch, which produce 3 point patches.
> 
> That is, they always have a wrinkle in one corner, because it's actually 
> two corners scrunched together.
> 
> Well, The situation need not be the case!
> 
> As I understand, internally, bezier patches are converted by triangles by 
> simply taking grid UV samples from the bicubic patch function.
> 
> suppose, the UV samples were altered, so that instead of taking a 13 by 13 
> grid of samples, or 17 by 17 grid of samples as is the case now, the 
> algorithem could detect when two points touch, and if that is the case, 
> start at the edge where the two points touch, For example, if edge*1 is 
> actually a point, start with one sample in V=0.5 when U=0, then two samples 
> at V=0 and V=1 when U=1/16, then 3 samples at V=0,0.5 and 1 when U=2/16 
> etc.... until U=16..
> 
> In the case of a 3 point patch, this should result in no wrinkles, as in 
> this diagram I've prepared http://zenpsycho.com/wrinkle.gif
> 
> Perhaps this could either be implemented as a patch in povray itself, or as 
> a feature of Jpatch, the promising new patch modeller written in java, 3 
> point patches could simply be exported as a triangle mesh, using my UV 
> sampling scheme. 
> 
> Discontinuities at the edges shouldn't be more of a problem than usual, 
> since each edge will have the same amount of samples as connecting 4 point 
> patches. 
> 
> I'd try and implement this stuff myself, but I'm afraid I'm not smart 
> enough or have the time, but I figured that there should be a solution to 
> this problem that I should share. 
> 
> anyways, thoughts? questions?

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