Discrete quadratic curvature energies

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 assemble...

Full description

Saved in:

Bibliographic Details
Published in:	Computer aided geometric design 2007-11, Vol.24 (8), p.499-518
Main Authors:	Wardetzky, Max, Bergou, Miklós, Harmon, David, Zorin, Denis, Grinspun, Eitan
Format:	Article
Language:	eng
Subjects:	Bending energy Cloth simulation Discrete Laplace operator Discrete mean curvature Non-conforming finite elements Thin plates Willmore flow
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Description
Summary:	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.
ISSN:	0167-8396 1879-2332