Article

Free access

Bounds on the size of tetrahedralizations

Authors:

Bernard Chazelle,

Nadia ShourabouraAuthors Info & Claims

SCG '94: Proceedings of the tenth annual symposium on Computational geometry

Pages 231 - 239

https://doi.org/10.1145/177424.177975

Published: 10 June 1994 Publication History

PDF eReader

References

[1]

Aronov, B., Sharir, M. Triangles in space or building (and analyzing) castles in the air, Combinatorica, 10 (1990), 137-173.

Crossref

Google Scholar

[2]

Aronov, B., Sharir, M. The Union of convex polyhedra in three dimensions, Proc. 34th Annu. IEEE Sympos. Found. Comput. Sci. (1993), 518-527.

Digital Library

Google Scholar

[3]

Aronov, B., Sharir, M. Castles in the air revisited, Proc. 8th Annu. ACM Sympos. Comput. Geom. (1992), 146-156.

Digital Library

Google Scholar

[4]

Bajaj, C.L., Dey, T.K. Convex Decompositions of Polyhedra and Robustness, SIAM Journal on Computing 21 (1992), 339-364.

Digital Library

Google Scholar

[5]

Bern, M. Compatible tetrahedralizations, Proc. 9th Annu. ACM Sympos. Comput. Geom. (1993), 281- 288.

Digital Library

Google Scholar

[6]

Chazelle, B. Convex partitions of polyhedra: a lower bound and worst-case optimal algorithm, SiAM Journal on Computing, 13 (1984), 488-507.

Digital Library

Google Scholar

[7]

Chazelle, B. An optimal algorithm for intersecting three-dimensional convex polyhedra, SIAM Journal on Computing, 21 (1992), 671-696.

Digital Library

Google Scholar

[8]

Chazelle, B., Palios, L. Triangulating a nonconvex polytope, Discrete and Computational Geometry, 5 (199o), 5os-5

Google Scholar

[9]

Dey, T.K. Triangulation and CSG representation of polyhedra with arbitrary genus, Proc. 7th Annu. ACM Sympos. Comput. Geom. (1991), 364-372.

Digital Library

Google Scholar

[10]

Dobkin, D.P., Kirkpatrick, D.G. Fast detection of polyhedral intersection, Theoret. Comput. Sci. 27 (1983), 241-253.

Crossref

Google Scholar

[11]

Dobkin, D.P., Laszlo, M.J. Primiiives for the manipulation of three-dimensional subdivisions, Algorithmica, 4 (1989), 3-32.

Crossref

Google Scholar

[12]

Martin, A. A simple primal algorithm for intersecting 3-polyhedra in linear time, Tech. Report 91-16, July 1991.

Digital Library

Google Scholar

[13]

Mehlhorn, K. Data Structures and Algorithms 3: Multidimensional Searching and Computational Geometry, Springer-Verlag, Heidelberg, Germany, 1984.

Digital Library

Google Scholar

[14]

Mulmuley, K. Computational Geometry: An Introduction Through Randomized Algoriihms, Prentice-Hall, 1994.

Google Scholar

[15]

Pellegrini, M. Building convex space partitions induced by pairwise interior-disjoint simplices, ICSI TR-93-039, Aug. 1993.

Google Scholar

[16]

Ruppert, J., Seidel, R. On the difficul;ly of triangulating three-dimensional non-convex polyhedra, Discrete and Computational Geometry, 7 (1992), 227-253.

Digital Library

Google Scholar

[17]

SchSnhardt, E. Uber die Zerlegung von Dreieckspolyedern in Telraeder, Math. Annalen, 98 (1928), 309-312.

Crossref

Google Scholar

Cited By

View all

Mackerle J(2001)2D and 3D finite element meshing and remeshingEngineering Computations10.1108/EUM000000000649518:8(1108-1197)Online publication date: 1-Dec-2001
https://doi.org/10.1108/EUM0000000006495
Wang CYang B(2000)Tetrahedralization of Two Nested Convex PolyhedraComputing and Combinatorics10.1007/3-540-44968-X_29(291-298)Online publication date: 21-Jul-2000
https://doi.org/10.1007/3-540-44968-X_29
Eppstein DWhitesides S(1996)Linear complexity hexahedral mesh generationProceedings of the twelfth annual symposium on Computational geometry10.1145/237218.237237(58-67)Online publication date: 1-May-1996
https://dl.acm.org/doi/10.1145/237218.237237
Show More Cited By

Index Terms

Bounds on the size of tetrahedralizations
1. Information systems
  1. Information storage systems
    1. Record storage systems
      1. Record storage alternatives
        Linked lists
2. Theory of computation
  1. Randomness, geometry and discrete structures
    1. Computational geometry

Recommendations

Compatible tetrahedralizations
SCG '93: Proceedings of the ninth annual symposium on Computational geometry

We give some special-case tetrahedralization algorithms. We first consider the problem of finding a tetrahedralization compatible with a fixed triangulation of the boundary of a polyhedron. We then adapt our solution to the related problem of compatibly ...
Incrementally constructing and updating constrained Delaunay tetrahedralizations with finite-precision coordinates

Constrained Delaunay tetrahedralizations (CDTs) are valuable for discretizing three-dimensional domains with constraints such as edges and polygons. But they are difficult to generate and maintain robustly when finite-precision coordinates yield ...
Some Bounds on the Size of Codes

We present some upper bounds on the size of nonlinear codes and their restriction to systematic codes and linear codes. These bounds are independent of other known theoretical bounds, e.g., the Griesmer bound, the Johnson bound, the Plotkin bound, and ...

Comments

Information & Contributors

Information

Published In

SCG '94: Proceedings of the tenth annual symposium on Computational geometry

June 1994

400 pages

ISBN:0897916484

DOI:10.1145/177424

Chairman:
Kurt Mehlhorn
U.S. Army Research Office

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 10 June 1994

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Qualifiers

Article

Conference

SCG94

Sponsor:

SCG94: Tenth Symposium on Computational Geometry

June 6 - 8, 1994

New York, Stony Brook, USA

Acceptance Rates

Overall Acceptance Rate 625 of 1,685 submissions, 37%

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

6
Total Citations
View Citations
272
Total Downloads

Downloads (Last 12 months)24
Downloads (Last 6 weeks)2

Reflects downloads up to 26 Jul 2024

Other Metrics

View Author Metrics

Citations

Cited By

View all

Mackerle J(2001)2D and 3D finite element meshing and remeshingEngineering Computations10.1108/EUM000000000649518:8(1108-1197)Online publication date: 1-Dec-2001
https://doi.org/10.1108/EUM0000000006495
Wang CYang B(2000)Tetrahedralization of Two Nested Convex PolyhedraComputing and Combinatorics10.1007/3-540-44968-X_29(291-298)Online publication date: 21-Jul-2000
https://doi.org/10.1007/3-540-44968-X_29
Eppstein DWhitesides S(1996)Linear complexity hexahedral mesh generationProceedings of the twelfth annual symposium on Computational geometry10.1145/237218.237237(58-67)Online publication date: 1-May-1996
https://dl.acm.org/doi/10.1145/237218.237237
Chazelle BDobkin DShouraboura NTal ASnoeyink J(1995)Strategies for polyhedral surface decompositionProceedings of the eleventh annual symposium on Computational geometry10.1145/220279.220311(297-305)Online publication date: 1-Sep-1995
https://dl.acm.org/doi/10.1145/220279.220311
Agarwal PAronov BSuri SSnoeyink J(1995)Stabbing triangulations by lines in 3DProceedings of the eleventh annual symposium on Computational geometry10.1145/220279.220308(267-276)Online publication date: 1-Sep-1995
https://dl.acm.org/doi/10.1145/220279.220308
Chazelle BLeighton FGoodrich M(1994)Computational geometryProceedings of the twenty-sixth annual ACM symposium on Theory of Computing10.1145/195058.195110(75-94)Online publication date: 23-May-1994
https://dl.acm.org/doi/10.1145/195058.195110

View Options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Cited By

Index Terms

Recommendations

Compatible tetrahedralizations

Incrementally constructing and updating constrained Delaunay tetrahedralizations with finite-precision coordinates

Some Bounds on the Size of Codes