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.
2024
Optimal Design of Vehicle Dynamics Using Gradient-Based, Mixed-Fidelity Multidisciplinary OptimizationThis research showcases a multidisciplinary approach to optimize a…
2023
Revolutionizing Water Management – Part TwoExploring RL techniques for water distribution, part two…
1993
The Design and Evaluation of Marking MenusThis research focuses on the use of hand drawn marks as a…
2017
Annotation Graphs: A Graph-Based Visualization for Meta-Analysis of Data based on User-Authored AnnotationsUser-authored annotations of data can support analysts in the activity…
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