**Topology-guided tessellation of quadratic elements.**

**Scott E. Dillard, Vijay Natarajan, Gunther H. Weber, Valerio Pascucci, and Bernd Hamann.**

Invited paper in

*Intl. J. Computational Geometry and Applications*, 19(2), 2009, 195-211.

#### 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 piecewiselinear functions may be applied directly to the piecewise-quadratic function. In particular, the tessellation is used for computing the Reeb graph, a topological data structure that provides a succinct representation of level sets of the function.[PDF]

### Conference Version

Tessellation of quadratic elements.*Proc. Intl. Symp. Algorithms and Computation*, LNCS 4288, Springer-Verlag, 2006, 722-731.