Meshing of Surfaces

Jean-Daniel Boissonnat (1) , David Cohen-Steiner (1) , Bernard Mourrain (2) , Guenter Rote (3) , Gert Vegter (4)

1 GEOMETRICA - Geometric computing
2 GALAAD - Geometry, algebra, algorithms
3 Institute of Computer Science
4 Bernoulli Institute for Mathematics and Computer Science and Artificial Intelligence

Meshing algorithms can be roughly characterized as (i) continuation-based methods, that grow a mesh following the surface, and (ii) mesh-based methods, which build some sort of three-dimensional scaffolding around the surface. Although continuation-based methods are often used in practice, it is not easy to achieve correctness guarantees for them. Thus, all algorithms discussed in this paper fall into the second category. There are three types of adaptive “grid structures” which are used: axis-aligned cubes, vertical planes, and the Voronoi diagram. The algorithms use different algorithmic strategies and a variety of conditions to ensure topological correctness.

Keywords: Computational geometry; mesh generation; surface approximation

Domains: Computational Geometry [cs.CG]

Jean-Daniel Boissonnat, David Cohen-Steiner, Bernard Mourrain, Guenter Rote, Gert Vegter. Meshing of Surfaces. Effective Computational Geometry for Curves and Surfaces, Springer, pp.181-230, 2007, Mathematics and Visualization. ⟨hal-00488274⟩