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Discrete Willmore flow

Bobenko, Alexander I. and Schröder, Peter (2005) Discrete Willmore flow. In: SGP '05 Proceedings of the third Eurographics symposium on Geometry processing. Eurographics Association , Aire-la-Ville, Switzerland, Art. No. 101. ISBN 3-905673-24-X. https://resolver.caltech.edu/CaltechAUTHORS:20160725-115639350

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Abstract

The Willmore energy of a surface, ∫(H^2 -- K) dA, as a function of mean and Gaussian curvature, captures the deviation of a surface from (local) sphericity. As such this energy and its associated gradient flow play an important role in digital geometry processing, geometric modeling, and physical simulation. In this paper we consider a discrete Willmore energy and its flow. In contrast to traditional approaches it is not based on a finite element discretization, but rather on an ab initio discrete formulation which preserves the Möbius symmetries of the underlying continuous theory in the discrete setting. We derive the relevant gradient expressions including a linearization (approximation of the Hessian), which are required for non-linear numerical solvers. As examples we demonstrate the utility of our approach for surface restoration, n-sided hole filling, and non-shrinking surface smoothing.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://www.eg.org/EG/DL/WS/SGP/SGP05;internal&action=checkAccessForm.action?fullPaper=EG/DL/WS/SGP/SGP05/101-110.pdfPublisherPaper
http://dl.acm.org/citation.cfm?id=1281937&CFID=817961681&CFTOKEN=79729665OrganizationAbstract
ORCID:
AuthorORCID
Schröder, Peter0000-0002-0323-7674
Additional Information:© The Eurographics Association 2005. This work was supported in part by NSF (DMS-0220905, DMS-0138458, ACI-0219979), DFG (Research Group “Polyhedral Surfaces” and Research Center MATHEON “Mathematics for Key Technologies” Berlin), DOE (W-7405-ENG-48/B341492), nVidia, the Center for Integrated Multiscale Modeling and Simulation, Alias, and Pixar. Special thanks to Kevin Bauer, Oscar Bruno, Mathieu Desbrun, Ilja Friedel, Cici Koenig, Nathan Litke, and Fabio Rossi.
Funders:
Funding AgencyGrant Number
NSFDMS-0220905
NSFDMS-0138458
NSFACI-0219979
Deutsche Forschungsgemeinschaft (DFG)UNSPECIFIED
Department of Energy (DOE)W-7405-ENG-48/B341492
nVidiaUNSPECIFIED
Center for Integrated Multiscale Modeling and SimulationUNSPECIFIED
AliasUNSPECIFIED
PixarUNSPECIFIED
Subject Keywords:Geometric Flow; Discrete Differential Geometry; Willmore Energy; Variational Surface Modeling; Digital Geometry Processing
Classification Code:G.1.8 [Numerical Analysis]: Partial Differential Equa- tions; I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling; I.6.8 [Simulation and Model- ing]: Types of Simulation.
Record Number:CaltechAUTHORS:20160725-115639350
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20160725-115639350
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:69195
Collection:CaltechAUTHORS
Deposited By: Kristin Buxton
Deposited On:25 Jul 2016 21:04
Last Modified:09 Mar 2020 13:19

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