Triangulations in CGAL

Computational Geometry: Theory and Applications

Volumn 22, Issue 1-3, 2002, Pages 5-19

  Boissonnat, Jean Daniel ^a   Devillers, Olivier ^a   Pion, Sylvain ^a   Teillaud, Monique ^a   Yvinec, Mariette ^a  

^a INRIA   (France)

Author keywords

Delaunay triangulation; Implementation; Triangulation

Indexed keywords

EID: 31244436344     PISSN: 09257721     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0925-7721(01)00054-2     Document Type: Article

References (42)

1. F. Aurenhammer, Voronoi diagrams: A survey of a fundamental geometric data structure, ACM Comput. Surv. 23 (3) (1991) 34505.
2. B. Barber, Qhull, http://www.geom.umn.edu/locate/qhull, Version 2.3.
3. C.B. Barber, O.P. Dobkin, H. Huhdanpaa, The quickhull algorithm for convex hulls, ACM Trans. Math. Softw. 22 (4) (1996) 469-483.
4. M. Bern, D. Eppstein, Mesh generation and optimal triangulation, in: D.-Z. Du, F.K. Hwang (Eds.), Computing in Euclidean Geometry, Lecture Notes Series on Computing, Vol. 1, World Scientific, Singapore, 1992, pp. 23-90.
5. Y. Bertrand, J.-F. Dufourd, Algebraic specification of a SD-modeler based on hypermaps, CVGIP: Graph. Models Image Process. 56 (1994) 29-60.
6. J.-D. Boissonnat, M. Yvinec, Algorithmic Geometry, Cambridge University Press, UK, 1998. Translated by Hervé Brönnimann.
7. E. Brisson, Representing geometric structures in d dimensions: Topology and order, Discrete Comput. Geom. 9 (1993) 387-426.
8. H. Brönnimann, C. Burnikel, S. Pion, Interval arithmetic yields efficient dynamic filters for computational geometry, in: Proc. 14th Annual ACM Symp. Comput. Geom., 1998, pp. 165-174.
9. D. Cazier, J.-F. Dufourd, A formal specification of geometric refinements, Visual Computer 15 (1999) 279-301.
10. M. de Berg, M. van Kreveld, M. Overmars, O. Schwarzkopf, Computational Geometry: Algorithms and Applications, Springer-Verlag, Berlin, 1997.
11. M. de Berg, R. van Oostrum, M. Overmars, Simple traversal of a subdivision without extra storage, in: Proc. 12th Annual ACM Symp. Comput. Geom., 1996, pp. C5-C6.
12. O. Devillers, The Delaunay hierarchy, http://www-sop.inria.fr/prisme/logiciel/del-hierarchyJ.
13. O. Devillers, Improved incremental randomized Delaunay triangulation, in: Proc. 14th Annual ACM Symp. Comput. Geom., 1998, pp. 106-115.
14. O. Devillers, G. Liotta, P.P. Preparata, R. Tamassia, Checking the convexity of poly topes and the planarity of subdivisions, Comput. Geom. Theory Appl. 11 (1998) 187-208.
15. O. Devillers, S. Pion, M. Teillaud, Walking in a triangulation, in: Proc. 17th Annual ACM Symp. Comput. Geom., 2001.
16. O. Devillers, S. Pion, M. Teillaud, Walking in a triangulation, Rapport de recherche 4120, INRIA, 2001.
17. R.A. Dvvyer, A simple divide-and-conquer algorithm for computing Delaunay triangulations in O(/i log log) expected time, in: Proc. 2nd Annual ACM Symp. Comput. Geom., 1986, pp. 276-284.
18. R.A. Dwyer, A faster divide-and-conquer algorithm for constructing Delaunay triangulations, Algorithmica 2 (1987) 137-151.
19. H. Edelsbrunner, R. Seidel, Voronoi diagrams and arrangements, Discrete Comput. Geom. 1 (1986) 25-14.
20. H. Edelsbrunner, T.S. Tan, An upper bound for conforming Delaunay triangulations, Discrete Comput. Geom. 10 (2) (1993) 197-213.
21. A. Fabri, G.-J. Giezeman, L. Kettner, S. Schirra, S. Schönherr, On the design of CGAL, the Computational Geometry Algorithms Library, Research Report 3407, INRIA, 1998.
22. E. Flato, D. Halperin, I. Hanniel, O. Nechushtan, The design and implementation of planar maps in CGAL, in: Abstracts 15th European Workshop Comput. Geom., INRIA, Sophia-Antipolis, 1999, pp. 169-172.
23. E.G. Flekk0y, P.V. Coveney, G. De Fabritis, Foundations of dissipative particle dynamics, Phys. Rev. E 62 (2000)2140.
24. P.-L. George, H. Borouchaki, Triangulation de Delaunay et maillage. Applications aux éléments finis, Hermes, Paris, France, 1997.
25. T. Granlund, GMP, The GNU Multiple Precision Arithmetic Library, 2.0.2 edition, 1996. http://www.swox. com/gmpJ.
26. L.J. Guibas, J. Stolfi, Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams, ACM Trans. Graph. 4 (2) (1985) 74-123.
27. F. Hoffmann, K. Kriegel, C. Wenk, A geometric approach to protein identification in 2D electrophoretic gel images, in: Abstracts 15th European Workshop Comput. Geom., INRIA, Sophia-Antipolis, 1999, pp. 173-174.
28. L. Kettner, Using generic programming for designing a data structure for polyhedral surfaces, Comput. Geom. Theory and Appl. 13 (1999) 65-90.
29. LEDA, http://www.mpi-sb.mpg.de/LEDA/, Version 4.0.
30. P. Lienhardt, N-dimensional generalized combinatorial maps and cellular quasi-manifolds, Internat. J. Comput. Geom. Appl. 4 (3) (1994) 275-324
31. D. Lischinski, Graphics Gems IV, ftp://wuarchive.wustl.edu/graphics/graphics/books/graphics-gemsJ.
32. E.P. Mücke, I. Saias, B. Zhu, Fast randomized point location without preprocessing in two- and three-dimensional Delaunay triangulations, in: Proc. 12th Annual ACM Symp. Comput. Geom., 1996, pp. 274-283.
33. K. Mulmuley, Randomized multidimensional search trees: Dynamic sampling, in: Proc. 7th Annual ACM Symp. Comput. Geom., 1991, pp. 121-131.
34. M. Murphy, D.M. Mount, C.W. Gable, A point-placement strategy for conforming Delaunay tetrahedralization, in: Proc. 11th ACM-SIAM Symp. Discrete Algorithms, 2000, pp. 67-74.
35. S. Pion, De la géométrie algorithmique au calcul géométrique, Thèse de Doctorat en Sciences, Université de Nice-Sophia Antipolis, France, 1999.
36. S. Pion, Interval arithmetic: An efficient implementation and an application to computational geometry, in: Workshop on Applications of Interval Analysis to Systems and Control, 1999, pp. 99-110.
37. E. Schönhardt, Über die Zerlegung von Dreieckspolyedern in Tetraeder, Mathematische Annalen 98 (1928) 309-312.
38. J.R. Shewchuk, Triangle: Engineering a 2D quality mesh generator and Delaunay triangulator, in: M.C. Lin, D. Manocha (Eds.), Applied Computational Geometry: Towards Geometric Engineering, First ACM Workshop on Applied Computational Geometry, Lecture Notes in Computer Science, Vol. 1148, Springer, Berlin, 1996, pp. 203-222.
39. J.R. Shewchuk, Triangle. A two-dimensional quality mesh generator and Delaunay triangulator, http://www. cs.cmu.edu/~quake/triangle.html, Version 1.3.
40. J.R. Shewchuk, Robust adaptive floating-point geometric predicates, in: Proc. 12th Annual ACM Symp. Comput. Geom., 1996, pp. 141-150.
41. J.R. Shewchuk, A condition guaranteeing the existence of higher-dimensional constrained Delaunay triangulations, in: Proc. 14th Annual ACM Symp. Comput. Geom., 1998, pp. 76-85.
42. R.C. Veltkamp, Generic programming in CGAL, the Computational Geometry Algorithms Library, in: Proceedings of the 6th Eurographics Workshop on Programming Paradigms in Graphics, Budapest, Hungary, 1997, pp. 127-138.