Discrete Willmore Flow

Bobenko, Alexander I.; Schröder, Peter

Discrete Willmore Flow

Files

101-110.pdf (1.89 MB)

Date

2005

Authors

Bobenko, Alexander I.
Schröder, Peter

Publisher

The Eurographics Association

Abstract

The Willmore energy of a surface, R(H2 -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.

        @inproceedings{:10.2312/SGP/SGP05/101-110
,
booktitle = {Eurographics Symposium on Geometry Processing 2005
},
editor = {Mathieu Desbrun and Helmut Pottmann
},
title = {{Discrete Willmore Flow
}},
author = {Bobenko, Alexander I. and 
Schröder, Peter
},
year = {2005
},
publisher = {The Eurographics Association
},
ISSN = {1727-8384
},
ISBN = {3-905673-24-X
},
DOI = {/10.2312/SGP/SGP05/101-110
}
}