A Weighted Delaunay Triangulation Framework for Merging Triangulations in a Connectivity Oblivious Fashion

Silva, Luis F.; Scheidegger, Luiz F.; Etiene, Tiago; Comba, João L. D.; Nonato, Luis G.; Silva, Cláudio T.

A Weighted Delaunay Triangulation Framework for Merging Triangulations in a Connectivity Oblivious Fashion

Date

2014

Authors

Silva, Luis F.
Scheidegger, Luiz F.
Etiene, Tiago
Comba, João L. D.
Nonato, Luis G.
Silva, Cláudio T.

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

        @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
}
}