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subdive a square

Posted by Alex Zhou on March 24, 2005 at 14:42:32:

I am a newbie in subdivision. I am wondering some issues on subdividing a square (surface) by Catmull-Clark scheme. For the first step, the boundary rules need to be used for generating new edge points and vertex points since all four edges are boundary edges. By applying the boundary rules, finally, the surface boundary will become a cubic bspline curve.

My question is:
Is the final surface a standard bi-cubic B-spline surface?

If yes, can we say the bi-cubic B-spline surface is only controlled by the four origin square vertices, and what will be the mathematical expression like?

If no, does it mean that it’s composed by some standard bspline patches and surrounding boundary patches? If so, is there any special for the boundary patches and how can we exactly evaluate these patches as did in J.Stam’s paper? Or could you point out some references for discussion on the boundary issues.

I read several papers and notes; however, I haven’t found the answer yet. Please forgive my ignorance, and your reply will be appreciated very much.


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