Publication
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 publicationRelated Resources
See what’s new.
2018
Hybrid Finite Element-Geometric Forming Simulation of Composite MaterialsComputer simulations can extensively help engineers to gain a better…
2017
Simulating the Behavior of Building Occupants using Multi-agent Narratives: A Preliminary Study in a Generic Hospital WardIn architectural design it is of cardinal importance to anticipate how…
2006
Performing Incremental Bayesian Inference by Dynamic Model CountingThe ability to update the structure of a Bayesian network when new…
2009
Multimodal selection techniques for dense and occluded 3D virtual environmentsObject selection is a primary interaction technique which must be…
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