Tessellation of quadratic elements

Authors:
Scott E. Dillard;Vijay Natarajan;Gunther H. Weber;Valerio Pascucci;Bernd Hamann
Affiliations:
Department of Computer Science, University of California, Davis;Department of Computer Science, University of California, Davis;Department of Computer Science, University of California, Davis;Lawrence Livermore National Laboratory;Department of Computer Science, University of California, Davis
Venue:
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Year:
2006

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Abstract

Topology-based methods have been successfully used for the analysis and visualization of piecewise-linear functions defined on triangle meshes. This paper describes a mechanism for extending these methods to piecewise-quadratic functions defined on triangulations of surfaces. Each triangular patch is tessellated into monotone regions, so that existing algorithms for computing topological representations of piecewise-linear functions may be applied directly to piecewise-quadratic functions. In particular, the tessellation is used for computing the Reeb graph, which provides a succinct representation of level sets of the function.