Discrete Laplace operators: No free lunch

Wardetzky, Max; Mathur, Saurabh; Kaelberer, Felix; Grinspun, Eitan

Discrete Laplace operators: No free lunch

Files

033-037.pdf (616.62 KB)

Date

2007

Authors

Wardetzky, Max
Mathur, Saurabh
Kaelberer, Felix
Grinspun, Eitan

Publisher

The Eurographics Association

Abstract

Discrete Laplace operators are ubiquitous in applications spanning geometric modeling to simulation. For robustness and efficiency, many applications require discrete operators that retain key structural properties inherent to the continuous setting. Building on the smooth setting, we present a set of natural properties for discrete Laplace operators for triangular surface meshes. We prove an important theoretical limitation: discrete Laplacians cannot satisfy all natural properties; retroactively, this explains the diversity of existing discrete Laplace operators. Finally, we present a family of operators that includes and extends well-known and widely-used operators.

        @inproceedings{:10.2312/SGP/SGP07/033-037
,
booktitle = {Geometry Processing
},
editor = {Alexander Belyaev and Michael Garland
},
title = {{Discrete Laplace operators: No free lunch
}},
author = {Wardetzky, Max and 
Mathur, Saurabh and 
Kaelberer, Felix and 
Grinspun, Eitan
},
year = {2007
},
publisher = {The Eurographics Association
},
ISSN = {1727-8384
},
ISBN = {978-3-905673-46-3
},
DOI = {/10.2312/SGP/SGP07/033-037
}
}