Exact Evaluation of Catmull-Clark Subdivision Surfaces at Arbitrary Parameter Values

AbstractIn this paper we disprove the belief widespread within the computer graphics community that Catmull-Clark subdivision surfaces cannot be evaluated directly without explicitly subdividing. We show that the surface and all its derivatives can be evaluated in terms of a set of eigenbasis functions which depend only on the subdivision scheme and we derive analytical expressions for these basis functions. In particular, on the regular part of the control mesh where Catmull-Clark surfaces are bi-cubic B-splines, the eigenbasis is equal to the power basis. Also, our technique is both easy to implement and efficient. We have used our implementation to compute high quality curvature plots of subdivision surfaces. The cost of our evaluation scheme is comparable to that of a bi-cubic spline. Therefore, our method allows many algorithms developedfor parametric surfaces to be applied to Catmull-Clark subdivision surfaces. This makes subdivision surfaces an even more attractive tool for free-form surface modeling.

Download publication

Related Resources

See what’s new.



Considering Multiscale Scenes to Elucidate Problems Encumbering 3D Intellection and Navigation

Virtual 3D environments have become pervasive tools in a number of…



Toward Better Surface Tracking for Fluid Simulation



Geppetto: Enabling Semantic Design of Expressive Robot Behaviors

Expressive robots are useful in many contexts, from industrial to…



TinkerCell: modular CAD tool for Synthetic Biology

An ideal CAD application for engineering biological systems would…

Get in touch

Something pique your interest? Get in touch if you’d like to learn more about Autodesk Research, our projects, people, and potential collaboration opportunities.

Contact us