\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.8 - 3D Triangulations

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Bibliographic References

[1]

  Nina Amenta, Dominique Attali, and Olivier Devillers. Complexity of Delaunay triangulation for points on lower-dimensional polyhedra. In Proc. 18th ACM-SIAM Sympos. Discrete Algorithms, pages 1106–1113, 2007.

[2]

  Dominique Attali and Jean-Daniel Boissonnat. Complexity of the Delaunay triangulation of points on polyhedral surfaces. Discrete and Computational Geometry, 30(3):437–452, 2003.

[3]

  Dominique Attali, Jean-Daniel Boissonnat, and André Lieutier. Complexity of the Delaunay triangulation of points on surfaces: The smooth case. In Proc. 19th Annual Symposium on Computational Geometry, pages 237–246, 2003.

[4]

  Jean-Daniel Boissonnat and Mariette Yvinec. Algorithmic Geometry. Cambridge University Press, UK, 1998. Translated by Hervé Brönnimann.

[5]

  Jean-Daniel Boissonnat, Olivier Devillers, Monique Teillaud, and Mariette Yvinec. Triangulations in CGAL. In Proc. 16th Annu. ACM Sympos. Comput. Geom., pages 11–18, 2000.

[6]

  Jean-Daniel Boissonnat, Olivier Devillers, Sylvain Pion, Monique Teillaud, and Mariette Yvinec. Triangulations in CGAL. Comput. Geom. Theory Appl., 22:5–19, 2002.

[7]

  Olivier Devillers and Sylvain Pion. Efficient exact geometric predicates for Delaunay triangulations. In Proc. 5th Workshop Algorithm Eng. Exper., pages 37–44, 2003.

[8]

  Olivier Devillers and Monique Teillaud. Perturbations and vertex removal in a 3D Delaunay triangulation. In Proc. 14th ACM-SIAM Sympos. Discrete Algorithms (SODA), pages 313–319, 2003.

[9]

  Olivier Devillers and Monique Teillaud. Perturbations and vertex removal in Delaunay and regular 3D triangulations. Research Report 5968, INRIA, 2006. ttp://hal.inria.fr/inria-00090522.

[10]

  Olivier Devillers, Giuseppe Liotta, Franco P. Preparata, and Roberto Tamassia. Checking the convexity of polytopes and the planarity of subdivisions. Comput. Geom. Theory Appl., 11:187–208, 1998.

[11]

  Olivier Devillers, Sylvain Pion, and Monique Teillaud. Walking in a triangulation. Internat. J. Found. Comput. Sci., 13:181–199, 2002.

[12]

  Olivier Devillers. The Delaunay hierarchy. Internat. J. Found. Comput. Sci., 13:163–180, 2002.

[13]

  R. A. Dwyer. Higher-dimensional Voronoi diagrams in linear expected time. In Proc. 5th Annu. ACM Sympos. Comput. Geom., pages 326–333, 1989.

[14]

  H. Edelsbrunner and N. R. Shah. Incremental topological flipping works for regular triangulations. Algorithmica, 15:223–241, 1996.

[15]

  Jeff Erickson. Dense point sets have sparse Delaunay triangulations. In Proc. 13th ACM-SIAM Sympos. Discrete Algorithms (SODA), pages 125–134, 2002.

[16]

  Lutz Kettner, Kurt Mehlhorn, Sylvain Pion, Stefan Schirra, and Chee Yap. Classroom examples of robustness problems in geometric computations. Computational Geometry: Theory and Applications, 40(1):61–78, 2008.

[17]

  Yuanxin Liu and Jack Snoeyink. A comparison of five implementations of 3D Delaunay tessellation. In János Pach Jacob E. Goodman and Emo Welzl, editors, Combinatorial and Computational Geometry, pages 439–458. MSRI Publications, 2005.

[18]

  Kurt Mehlhorn, Stefan Näher, Thomas Schilz, Stefan Schirra, Michael Seel, Raimund Seidel, and Christian Uhrig. Checking geometric programs or verification of geometric structures. In Proc. 12th Annu. ACM Sympos. Comput. Geom., pages 159–165, 1996.

[19]

  Jonathan R. Shewchuk. A condition guaranteeing the existence of higher-dimensional constrained Delaunay triangulations. In Proc. 14th Annu. ACM Sympos. Comput. Geom., pages 76–85, 1998.

[20]

  Monique Teillaud. Three dimensional triangulations in CGAL. In Abstracts 15th European Workshop Comput. Geom., pages 175–178. INRIA Sophia-Antipolis, 1999.