Modified subdivision surfaces with continuous curvature

Adi Levin

To appear in the proceedings of SIGGRAPH 2006, acm Transactions On Graphics.


We present a modification to subdivision surfaces, which guarantees second-order smoothness everywhere in the surface, including extraordinary points. The idea is to blend the limit surface with a low degree polynomial defined over the characteristic map, in the vicinity of each extraordinary point. We demonstrate our method on Catmull-Clark surfaces, but a similar modification can be applied to other schemes as well. The proposed modification to Catmull-Clark is simple to implement and can be applied to quad meshes of arbitrary topological type, even when extraordinary vertices share edges.

Download paper (PDF version, 2.2Mb)

Copyright notice

Copyright ACM 2006. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version will be published in the SIGGRAPH proceedings, acm Transactions On Graphics, 2006, and will be available on-line via the ACM digital library.

Optimal blending

A development of the basic blending method that is presented in the paper. This short paper suggests a better way to compute the polynomial around each extraordinary vertex.