On the computation of 3d periodic triangulations

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On the computation of 3d periodic triangulations

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Annual Symposium on Computational Geometry archive
Proceedings of the twenty-fourth annual symposium on Computational geometry table of contents

College Park, MD, USA

SESSION: Video and multimedia presentations table of contents

Pages 222-223

Year of Publication: 2008

ISBN:978-1-60558-071-5

Authors

Manuel Caroli	INRIA, Sophia-Antipolis, France
Monique Teillaud	INRIA, Sophia-Antipolis, France

Sponsors

ACM: Association for Computing Machinery
SIGGRAPH: ACM Special Interest Group on Computer Graphics and Interactive Techniques
SIGACT: ACM Special Interest Group on Algorithms and Computation Theory

Publisher

ACM New York, NY, USA

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ABSTRACT

In this video, we first review the incremental algorithm to compute Delaunay triangulations in R³. Then we examine the case of the periodic space T³, focusing on the differences with R³.

REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	A. Bowyer. Computing Dirichlet tesselations. In Comput. J. 24:162--166, 1981.
	2	Mark de Berg , Otfried Cheong , Marc van Kreveld , Mark Overmars, Computational Geometry: Algorithms and Applications, Springer-Verlag TELOS, Santa Clara, CA, 2008
	3	Jean-Daniel Boissonnat , Mariette Yvinec, Algorithmic geometry, Cambridge University Press, New York, NY, 1998
	4	M. Caroli, N. Kruithof, and M. Teillaud. Decoupling the Cgal 3D triangulations from the underlying space. In Proc. Workshop on Algorithm Engineering and Experiments (ALENEX), p. 101--108, 2008.
	5	M. Caroli, N. Kruithof, and M. Teillaud. Triangulating the 3D periodic space. In Proc. 24th European Workshop on Computational Geometry (EuroCG), 2008.
	6	CGAL, Computational Geometry Algorithms Library. http://www.cgal.org.
	7	P. J. Green and R. R. Sibson. Computing Dirichlet tessellations in the plane. In Comput. J. 21:168--173, 1978.
	8	A. Hatcher. Algebraic topology. Cambridge University Press, 2002.
	9	Martin Held, VRONI: an engineering approach to the reliable and efficient computation of voronoi diagrams of points and line segments, Computational Geometry: Theory and Applications, v.18 n.2, p.95-123, March 2001 [doi>10.1016/S0925-7721(01)00003-7]
	10	libQGL Viewer. http://artis.imag.fr/Software/QGLViewer.
	11	S. Pion and M. Teillaud. 3D triangulations. In Cgal Editorial Board, editor, CGAL User and Reference Manual. 3.3 edition, 2007.
	12	Qhull. http://www.qhull.org.
	13	V. Robins. Betti number signatures of homogeneous Poisson point processes Physical Review E 74 (2006) 061107.
	14	G. Rote and G. Vegter. Computational topology: An introduction. In J.-D. Boissonnat and M. Teillaud, editors, Effective Computational Geometry for Curves and Surfaces, p. 277--312, Springer-Verlag, Mathematics and Visualization, 2006.
	15	Jonathan Richard Shewchuk, Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator, Selected papers from the Workshop on Applied Computational Geormetry, Towards Geometric Engineering, p.203-222, May 27-28, 1996
	16	W. P. Thurston. Three-dimensional geometry and topology. Princeton University Press, 1997.
	17	Afra J. Zomorodian , M. J. Ablowitz , S. H. Davis , E. J. Hinch , A. Iserles , J. Ockendon , P. J. Olver, Topology for Computing (Cambridge Monographs on Applied and Computational Mathematics), Cambridge University Press, New York, NY, 2005