CS679 Project - Subdivision Surfaces

I implemented two subdivision schemes for closed surfaces. I chose Catmull and Clark's scheme [CC78], which is widely known as Catmull-Clark surfaces and was one of the first subdivision schemes, as well as Peters and Reif's scheme [PR97], which was developed recently. Both yield C¹ continuity in the limit. I extended Catmull-Clark surfaces with additional sharp subdivision rules (constant integer sharpness) proposed by DeRose et al. [DKT98] to allow the generation of sharp and semi-sharp creases.

My program allows to edit a closed surface and then subdivide it with either method. It has the following basic features:

• Display model (closed surface):
• As wireframe.
• Gouraud shaded.
• As wireframe and Gouraud shaded.
• Edit the model:
• Insert cube, divided cube, and pyramid.
• Move vertices.
• Move faces.
• Split faces individually.
• Subdivide surface using Catmull-Clark's subdivision scheme.

• Subdivide surface à la Jörg Peters.
• Add creases (new subdivision rules).
• Edit sharpness of creases.
• Comparison of a face-model, subdivided with both schemes.

As you can see in Figure 1 the Catmull-Clark subdivision scheme gives the nicer results. It also seems to converge faster than Peter's scheme. The drawback is that Catmull-Clark subdivision is more complicated to compute. On the other hand the crease extension proposed by DeRose et al. makes it a very powerful method to model curved surfaces.

I think there are two major drawbacks of subdivision surfaces. First it is hard to guess what the subdivided model will look like. Adding a new mode that allows you to edit the original model while the program shows you a subdivided model (2-3 steps should be enough) would probably solve this problem. Secondly there is no ``given'' parameterization of the surface, which makes texture mapping complicated.

References

CC78

E. Catmull and J. Clark. Recursively generated B-spline surfaces on arbitrary topological meshes. Computer-Aided Design, 10:350--355, September 1978.

DKT98

Tony DeRose, Michael Kass, and Tien Truong. Subdivision surfaces in character animation. In Michael Cohen, editor, SIGGRAPH 98 Conference Proceedings, Annual Conference Series, pages 85--94. ACM SIGGRAPH, Addison Wesley, July 1998.

PR97

 Jörg Peters and Ulrich Reif. The simplest subdivision scheme for smoothing polyhedra. ACM Transactions on Graphics, 16(4):420--431, October 1997. ISSN 0730-0301.