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3D Conforming Delaunay Triangulation

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  • First Online:
Encyclopedia of Algorithms

  • 252 Accesses

Years and Authors of Summarized Original Work

  • 1998; Shewchuk

  • 2004; Cohen-Steiner, de Verdière, Yvinec

  • 2006; Cheng, Poon

  • 2012; Cheng, Dey, Shewchuk

Problem Definition

3D Conforming Delaunay Triangulation, Fig. 1
figure 44 figure 44

A PLC and its conforming Delaunay triangulation in (a) and (b). A sliver with negligible volume and edge lengths similar to its circumradius in (c).

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Recommended Reading

  1. Cheng S-W, Dey TK (2003) Quality meshing with weighted Delaunay refinement. SIAM J Comput 33(1):69–93

    Article  MathSciNet  MATH  Google Scholar 

  2. Cheng S-W, Poon S-H (2006) Three-dimensional Delaunay mesh generation. Discret Comput Geom 36(3):419–456; conference version in Proceedings of the ACM-SIAM symposium on discrete algorithms (2003)

    Google Scholar 

  3. Cheng S-W, Dey TK, Ramos EA, Ray T (2005) Quality meshing for polyhedra with small angles. Int J Comput Geom Appl 15(4):421–461; conference version in Proceedings of the annual symposium on computational geometry (2004)

    Google Scholar 

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

    MATH  Google Scholar 

  5. Cohen-Steiner D, de Verdière ÉC, Yvinec M (2004) Conforming Delaunay triangulation in 3D. Comput Geom Theory Appl 28(2–3):217–233

    Article  MATH  Google Scholar 

  6. Murphy M, Mount DM, Gable CW (2001) A point-placement strategy for conforming Delaunay tetrahedralization. Int J Comput Geom Appl 11(6):669–682

    Article  MathSciNet  MATH  Google Scholar 

  7. Pav SE, Walkington NJ (2004) Robust three-dimensional Delaunay refinement. In: Proceedings of the international meshing roundtable, Williamsburg, pp 145–156

    Google Scholar 

  8. Ruppert J (1995) A Delaunay refinement algorithm for quality 2-dimensional mesh generation. J. Algorithms 18(3):548–585

    Article  MathSciNet  MATH  Google Scholar 

  9. Shewchuk JR (1998) Tetrahedral mesh generation by Delaunay refinement. In: Proceedings of the annual symposium on computational geometry, Minneapolis, pp 86–95

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Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, Hong Kong University of Science and Technology, Hong Kong, China

    Siu-Wing Cheng

Authors
  1. Siu-Wing Cheng
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Corresponding author

Correspondence to Siu-Wing Cheng .

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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Cheng, SW. (2016). 3D Conforming Delaunay Triangulation. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_716

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