Discrete quadratic curvature energies

Max Wardetzky, Miklós Bergou, David Harmon, Denis Zorin, Eitan Grinspun

Research output: Contribution to journalArticle

Abstract

We present a family of discrete isometric bending models (IBMs) for triangulated surfaces in 3-space. These models are derived from an axiomatic treatment of discrete Laplace operators, using these operators to obtain linear models for discrete mean curvature from which bending energies are assembled. Under the assumption of isometric surface deformations we show that these energies are quadratic in surface positions. The corresponding linear energy gradients and constant energy Hessians constitute an efficient model for computing bending forces and their derivatives, enabling fast time-integration of cloth dynamics with a two- to three-fold net speedup over existing nonlinear methods, and near-interactive rates for Willmore smoothing of large meshes.

Original languageEnglish (US)
Pages (from-to)499-518
Number of pages20
JournalComputer Aided Geometric Design
Volume24
Issue number8-9
DOIs
StatePublished - Nov 2007

Fingerprint

Curvature
Energy
Isometric
Discrete Curvature
Discrete Operators
Laplace Operator
Threefolds
Time Integration
Mean Curvature
Smoothing
Linear Model
Speedup
Mesh
Model
Gradient
Derivatives
Derivative
Computing
Operator

Keywords

  • Bending energy
  • Cloth simulation
  • Discrete Laplace operator
  • Discrete mean curvature
  • Non-conforming finite elements
  • Thin plates
  • Willmore flow

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Geometry and Topology
  • Modeling and Simulation

Cite this

Wardetzky, M., Bergou, M., Harmon, D., Zorin, D., & Grinspun, E. (2007). Discrete quadratic curvature energies. Computer Aided Geometric Design, 24(8-9), 499-518. https://doi.org/10.1016/j.cagd.2007.07.006

Discrete quadratic curvature energies. / Wardetzky, Max; Bergou, Miklós; Harmon, David; Zorin, Denis; Grinspun, Eitan.

In: Computer Aided Geometric Design, Vol. 24, No. 8-9, 11.2007, p. 499-518.

Research output: Contribution to journalArticle

Wardetzky, M, Bergou, M, Harmon, D, Zorin, D & Grinspun, E 2007, 'Discrete quadratic curvature energies', Computer Aided Geometric Design, vol. 24, no. 8-9, pp. 499-518. https://doi.org/10.1016/j.cagd.2007.07.006
Wardetzky, Max ; Bergou, Miklós ; Harmon, David ; Zorin, Denis ; Grinspun, Eitan. / Discrete quadratic curvature energies. In: Computer Aided Geometric Design. 2007 ; Vol. 24, No. 8-9. pp. 499-518.
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