Encyclopedia of Algorithms

Living Edition
| Editors: Ming-Yang Kao

Meshing Piecewise Smooth Complexes

  • Tamal Krishna Dey
Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-27848-8_718-1

Years and Authors of Summarized Original Work

2006; Boissonnat, Oudot

2007; Cheng, Dey, Ramos

2007: Cheng, Dey, Levine

2012; Cheng, Dey, Shewchuk

Problem Definition

The class of piecewise smooth complex (PSC) includes geometries that go beyond smooth surfaces. They contain polyhedra, smooth and non-smooth surfaces with or without boundaries, and more importantly non-manifolds. Thus, provable mesh generation algorithms for this domain extend the scope of mesh generation to a wide variety of domains. Just as in surface mesh generation, we are required to compute a set of points on the input complex and then connect them with a simplicial complex which is geometrically close and is topologically equivalent to the input. One challenge that makes this task harder is that the PSCs allow arbitrary small input angles, a notorious well-known hurdle for mesh generation.

A PSC is a set of cells, each being a smooth, connected manifold, possibly with boundary. The 0-cells, 1-cells, and 2-cells...

Keywords

Delaunay mesh Delaunay refinement Piecewise smooth complex Volume mesh Topology 
This is a preview of subscription content, log in to check access.

Recommended Reading

  1. 1.
    Boissonnat J-D, Oudot S (2006) Provably good sampling and meshing of Lipschitz surfaces. In: Proceedings of the 22nd annual symposium on computational geometry, Sedona, pp 337–346Google Scholar
  2. 2.
    Cheng S-W, Dey TK, Levine J (2007) A practical Delaunay meshing algorithm for a large class of domains. In: Proceedings of the 16th international meshing roundtable, Seattle, pp 477–494Google Scholar
  3. 3.
    Cheng S-W, Dey TK, Ramos EA (2007) Delaunay refinement for piecewise smooth complexes. In: Proceedings of the 18th annual ACM-SIAM symposium on discrete algorithms, New Orleans, pp 1096–1105Google Scholar
  4. 4.
    Cheng S-W, Dey TK, Shewchuk JR (2012) Delaunay mesh generation. CRC, Boca RatonGoogle Scholar
  5. 5.
    Dey TK, Levine JA (2009) Delaunay meshing of piecewise smooth complexes without expensive predicates. Algorithms 2(4):1327–1349CrossRefMathSciNetGoogle Scholar
  6. 6.
    Edelsbrunner H, Shah N (1997) Triangulating topological spaces. Int J Comput Geom Appl 7:365–378CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Computer Science and Engineering, The Ohio State UniversityColumbus, OHUSA