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Encyclopedia of Algorithms pp 1269–1272Cite as

Meshing Piecewise Smooth Complexes

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  • First Online:

  • 63 Accesses

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...

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Recommended Reading

  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 337–346

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  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 477–494

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  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 1096–1105

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  4. Cheng S-W, Dey TK, Shewchuk JR (2012) Delaunay mesh generation. CRC, Boca Raton

    MATH  Google Scholar 

  5. Dey TK, Levine JA (2009) Delaunay meshing of piecewise smooth complexes without expensive predicates. Algorithms 2(4):1327–1349

    Article  MathSciNet  Google Scholar 

  6. Edelsbrunner H, Shah N (1997) Triangulating topological spaces. Int J Comput Geom Appl 7:365–378

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, The Ohio State University, 43210, Columbus, OH, USA

    Tamal Krishna Dey

Authors
  1. Tamal Krishna Dey
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Corresponding author

Correspondence to Tamal Krishna Dey .

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, USA

    Ming-Yang Kao

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© 2016 Springer Science+Business Media New York

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Dey, T.K. (2016). Meshing Piecewise Smooth Complexes. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_718

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