Name
Abstract | ||
|---|---|---|
We define a discrete Laplace–Beltrami operator for simplicial surfaces (Definition 16). It depends only on the intrinsic geometry of the surface and its edge weights are positive. Our Laplace operator is similar to the well known finite-elements Laplacian (the so called “cotan formula”) except that it is based on the intrinsic Delaunay triangulation of the simplicial surface. This leads to new definitions of discrete harmonic functions, discrete mean curvature, and discrete minimal surfaces. The definition of the discrete Laplace–Beltrami operator depends on the existence and uniqueness of Delaunay tessellations in piecewise flat surfaces. While the existence is known, we prove the uniqueness. Using Rippa’s Theorem we show that, as claimed, Musin’s harmonic index provides an optimality criterion for Delaunay triangulations, and this can be used to prove that the edge flipping algorithm terminates also in the setting of piecewise flat surfaces. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1007/s00454-007-9006-1 | Discrete and Computational Geometry |
Keywords | Field | DocType |
Laplace operator,Delaunay triangulation,Dirichlet energy,Simplicial surfaces,Discrete differential geometry | Topology,Combinatorics,Discrete differential geometry,Harmonic function,Laplace–Beltrami operator,Mathematical analysis,Constant-mean-curvature surface,Spectral shape analysis,Minimal surface,Mathematics,Delaunay triangulation,Laplace operator | Journal |
Volume | Issue | ISSN |
38 | 4 | Discrete Comput. Geom. 38:4 (2007) 740-756 |
Citations | PageRank | References |
54 | 2.52 | 9 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Alexander I. Bobenko | 1 | 182 | 17.20 |
| Boris A. Springborn | 2 | 54 | 3.20 |