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Data-dependent fairing of subdivision surfaces

Friedel, Ilja and Mullen, Patrick and Schröder, Peter (2003) Data-dependent fairing of subdivision surfaces. In: SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications. ACM , New York, NY, pp. 185-195. ISBN 1-58113-706-0.

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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.

Item Type:Book Section
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URLURL TypeDescription
Schröder, Peter0000-0002-0323-7674
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.
Funding AgencyGrant Number
Department of Energy (DOE)W-7405-ENG-48/B341492
David and Lucile Packard FoundationUNSPECIFIED
Subject Keywords:Algorithms, Theory, Performance, Geometric Modeling, CAD, Fairing, Bicubic B-Splines, Subdivision Surfaces, Catmull-Clark, Thinplate Energy, Nonlinear Minimization
Classification Code:I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Curve, surface, solid, and ob- ject representations. G.1.6 [Numerical Analysis]: Optimization— Unconstrained optimization
Record Number:CaltechAUTHORS:20161024-173523014
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Official Citation:Ilja Friedel, Patrick Mullen, and Peter Schröder. 2003. Data-dependent fairing of subdivision surfaces. In Proceedings of the eighth ACM symposium on Solid modeling and applications (SM '03). ACM, New York, NY, USA, 185-195. DOI=
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:71426
Deposited On:25 Oct 2016 16:56
Last Modified:11 Nov 2021 04:44

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