A Weighted Delaunay Triangulation Framework for Merging Triangulations in a Connectivity Oblivious Fashion
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Date
2014
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Journal ISSN
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Publisher
The Eurographics Association and John Wiley and Sons Ltd.
Abstract
Simplicial meshes are useful as discrete approximations of continuous spaces in numerical simulations. In some applications, however, meshes need to be modified over time. Mesh update operations are often expensive and brittle, making the simulations unstable. In this paper we propose a framework for updating simplicial meshes that undergo geometric and topological changes. Instead of explicitly maintaining connectivity information, we keep a collection of weights associated with mesh vertices, using a Weighted Delaunay Triangulation (WDT). These weights implicitly define mesh connectivity and allow direct merging of triangulations. We propose two formulations for computing the weights, and two techniques for merging triangulations, and finally illustrate our results with examples in two and three dimensions.Simplicial meshes are useful as discrete approximations of continuous spaces in numerical simulations. In some applications, however, meshes need to be modified over time. Mesh update operations are often expensive and brittle, making the simulations unstable. In this paper we propose a framework for updating simplicial meshes that undergo geometric and topological changes. Instead of explicitly maintaining connectivity information, we keep a collection of weights associated with mesh vertices, using a Weighted Delaunay Triangulation (WDT). These weights implicitly define mesh connectivity and allow direct merging of triangulations
Description
@article{10.1111:cgf.12274,
journal = {Computer Graphics Forum},
title = {{A Weighted Delaunay Triangulation Framework for Merging Triangulations in a Connectivity Oblivious Fashion}},
author = {Silva, Luis F. and Scheidegger, Luiz F. and Etiene, Tiago and Comba, João L. D. and Nonato, Luis G. and Silva, Cláudio T.},
year = {2014},
publisher = {The Eurographics Association and John Wiley and Sons Ltd.},
ISSN = {1467-8659},
DOI = {10.1111/cgf.12274}
}