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Published June 2003 | public
Book Section - Chapter

Data-dependent fairing of subdivision surfaces

Abstract

In this paper we present a new algorithm for solving the data dependent fairing problem for subdivision surfaces, using Catmull-Clark surfaces as an example. Earlier approaches to subdivision surface fairing encountered problems with singularities in the parametrization of the surface. We address these issues through the use of the characteristic map parametrization, leading to well defined membrane and bending energies even at irregular vertices. Combining this approach with ideas from data-dependent energy operators we are able to express the associated nonlinear stiffness matrices for Catmull-Clark surfaces as linear combinations of precomputed energy matrices. This machinery also provides exact, inexpensive gradients and Hessians of the new energy operators. With these the nonlinear minimization problem can be solved in a stable and efficient way using Steihaug's Newton/CG trust-region method. We compare properties of linear and nonlinear methods through a number of examples and report on the performance of the algorithm.

Additional Information

© 2003 ACM. This work was supported in part by NSF (DMS 0220905, DMS 0138458, ACI 0219979) the DOE (W-7405-ENG-48/B341492), Intel, Alias|wavefront, nVidia, Pixar, and the Packard Foundation. Special thanks to Cici Koenig, Nathan Litke and Igor Guskov.

Additional details

Created:
August 19, 2023
Modified:
October 23, 2023