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Trimmed NURBS and subdivision

Posted by Jianbing Huang on January 19, 2005 at 00:38:13:

Considering the fact that NURBS has been the de-facto standard representation for 3D models for a long time, doesn't it make sense to think about the differences and relations between NURBS and subdivision? For example, what is the advantages/disadvantages of subdivision over NURBS and how the conversion can be done between them.

Subdivision representation seems to be much more compact than trimmed NURBS representation: no trimming is necessary, control vertices are shared across the trim boundaries, and uniform knot vector may be ignored assuming uniform subdivision scheme.

However, there seem to be some issues. For example, is the subdivision always more compact. It is possible that subdivision may not be so compact for some shapes like a plane face with 1000 holes. While this face can represented as a trimmed NURBS with 1000 trimming curves, the control mesh for such simple shape clearly needs to have thousands of vertices. Also, current method of representing crease edges by adjusting local subdivision rules seems to be ad-hoc, while non-uniform rules with weights would compromise the size advantage. Exact representation of quadric surfaces may be realized by adding a parameter in addition to uniform subdivision - is there any link between this parameter and nurss? Nice representation of crease edges and quadric surfaces is critical for the adoption of subdivision scheme in some application areas (such as CAD).

Can somebody point out relevant work that may help me to further my understanding here? Thanks.



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