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. © 2006 Springer-Verlag Berlin/Heidelberg.
CITATION STYLE
Dillard, S. E., Natarajan, V., Weber, G. H., Pascucci, V., & Hamann, B. (2006). Tessellation of quadratic elements. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4288 LNCS, pp. 722–731). https://doi.org/10.1007/11940128_72
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