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Parallel Delaunay triangulation in E3: make it simple

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Abstract

The randomized incremental insertion algorithm of Delaunay triangulation in E3 is very popular due to its simplicity and stability. This paper describes a new parallel algorithm based on this approach. The goals of the proposed parallel solution are not only to make it efficient but also to make it simple. The algorithm is intended for computer architectures with several processors and shared memory. Several versions of the proposed method were tested on workstations with up to eight processors and on datasets of up to 200000 points with favorable results.

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References

  1. Aurenhammer F (1991) Voronoi diagrams: a survey of a fundamental geometric data structure. ACM Comput Surv 23(3):345–405

    Article  Google Scholar 

  2. De Berg M, van Kreveld M, Overmars M, Schwarzkopf O (1997) Computational geometry: algorithms and applications. Springer, Berlin Heidelberg New York

    Google Scholar 

  3. Borland Delphi v. 5.0 (1999) Online help

  4. Chrisochoides N, Sukup F (1996) Task parallel implementation of the Bowyer–Watson algorithm. In: Proceedings of the 5th international conference on numerical grid generation in computational fluid dynamic and related fields, Mississippi State University, Mississippi State, MS, April 1996

  5. Chrisochoides N, Nave D (1999) Simultaneous mesh generation and partitioning for Delaunay meshes. In: Proceedings of the 8th international meshing roundtable, South Lake Tahoe, CA, October 1999, pp 55–66

  6. Cignoni P, Montani C, Perego R, Scopigno R (1993) Parallel 3D Delaunay triangulation. Computer Graphics Forum 12(3), NCC Blackwell, 1993, pp C129–C142

  7. Cignoni P, Montani C, Scopigno R (1998) DeWall: a fast divide and conquer Delaunay triangulation algorithm in Ed. Comput Aided Des 30(5):333–341

    Article  Google Scholar 

  8. Edelsbrunner H, Guoy D (2001) Sink insertion for mesh improvement. In: Proceedings of the 17th annual ACM symposium on computational geometry, Tufts University, Medford, MA, 3–5 July 2001, pp 115–123

  9. Erickson J (2001) Nice point sets can have nasty Delaunay triangulations. In: Proceedings of the 17th annual ACM symposium on computational geometry, Tufts University, Medford, MA, 3–5 July 2001, pp 96–105

  10. Facello MA (1995) Implementation of a randomized algorithm for Delaunay and regular triangulations in three dimensions. Comput Aided Geom Des 12:349–370

    Article  MathSciNet  Google Scholar 

  11. Fang TP, Piegl LA (1995) Delaunay triangulation in three dimensions. IEEE Comput Graph Appl 9:62–69

    Article  Google Scholar 

  12. Golias NA, Dutton RW (1997) Delaunay triangulation and 3D adaptive mesh generation. Finite Elem Anal Des 25:331–341

    Article  Google Scholar 

  13. Guibas LJ, Knuth DE, Sharir M (1992) Randomized incremental construction of Delaunay and Voronoi diagrams. Algorithmica 7:381–413

    Article  MathSciNet  Google Scholar 

  14. Hardwick JC (1997) Implementation and Evaluation Of An Efficient parallel Delaunay triangulation algorithm. In: Proceedings of the 9th annual symposium on parallel algorithms and architectures, Newport, RI, 22–25 June 1997, pp 22–25

  15. Joe B (1991a) Construction of three-dimensional Delaunay triangulations using local transformations. Comput Aided Geom Des 8:123–142

    Article  MathSciNet  Google Scholar 

  16. Joe B (1991b) Delaunay versus max-min solid angle triangulations for 3D mesh generation. Int J Numer Meth Eng 31:987–997

    Article  Google Scholar 

  17. Kolingerová I, Kohout J (2000) Pessimistic threaded Delaunay triangulation by randomized incremental insertion. In: Proceedings of Graphicon 2000, Moscow, pp 76–83

  18. Kolingerová I, Kohout J (2002) Optimistic parallel Delaunay triangulation. Vis Comput 18:511–529

    Article  Google Scholar 

  19. Maur P (2002) Delaunay triangulation in 3D. Technical Report, Departmen.of Computer Science and Engineering, University of West Bohemia, Pilsen, Czech Republic

  20. MVE – Modular Visualization Environment. Available at: http://herakles.zcu.cz/research/mveruntime/index.php

  21. Rajan VT (1994) Optimality of the Delaunay triangulation in Rd, Discrete Comput Geom 12:189–202

  22. Shewchuk JR (2000) Stabbing Delaunay tetrahedralizations. Available at: http://www.cs.berkeley.edu/∼jrs/stab.html

  23. Shewchuk JR (1996) Robust adaptive floating-point geometric predicates In: Proceedings of the 12th annual symposium on computational geometry, Philadelphia, 24–26 May 1996, pp 141–150

  24. Siu-Wing C, Dey TK, Edelsbrunner H, Facello MA, Shang-Hua T (1999) Sliver excudation. In: Proceedings of the 15th annual symposium on computational geometry, Miami Beach, FL, 13–16 June 1999, pp 1–13

  25. http://www.graphics.stanford.edu/data/3Dscanrep/

  26. Teng YA, Sullivan F, Beichl I, Puppo E (1993) A data-parallel algorithm for three-dimensional Delaunay triangulation and its implementation. In: Proceedings of the 1993 ACM/IEEE conference on Supercomputing, Portland, OR, pp 112–121

  27. Watson DF (1981) Computing the n-dimensional Delaunay tesselation with application to Voronoi polytopes. Comput J 24(2):167–172

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Centre of Computer Graphics and Data Visualization, Department of Computer Science and Engineering, University of West Bohemia, Univerzitní 8, 306 14, Plzen, Czech Republic

    Josef Kohout & Ivana Kolingerová

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  1. Josef Kohout
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  2. Ivana Kolingerová
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Correspondence to Josef Kohout.

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Kohout, J., Kolingerová, I. Parallel Delaunay triangulation in E3: make it simple. Vis Comput 19, 532–548 (2003). https://doi.org/10.1007/s00371-003-0219-x

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  • DOI: https://doi.org/10.1007/s00371-003-0219-x

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