Article

Free access

Approximate shortest paths and geodesic diameters on convex polytopes in three dimensions

Author:

Sariel Har-PeledAuthors Info & Claims

SCG '97: Proceedings of the thirteenth annual symposium on Computational geometry

Pages 359 - 365

https://doi.org/10.1145/262839.263003

Published: 01 August 1997 Publication History

PDF eReader

References

[1]

P.K. Agarwal, B. Aronov, J. O'Rourke, and C. Schevon. Star unfolding of a polytope with applications. SIAM J. Comput., 1996, to appear.

Digital Library

Google Scholar

[2]

P.K. Agarwal, S. Har-Peled, M. Sha.dr, and K. R. Varadarajan. Approximate shortest paths on a convex polytope in three dimensions. Report CS- 1996-12, Dept. Comput. Sci., Duke Univ., Durham, NC, 1996.

Google Scholar

[3]

J. Chen and Y. Han. Shortest paths on a polyhedron; Part I: computing shortest paths. Int. J. Comput. Geom. # Appl., 6(2):127-144, 1996.

Google Scholar

[4]

K.L. Clarkson. Approximation algorithms for shortest path motion planning. In Proc. 19th Annu. A CM Sympos. Theory Comput., pages 56-65, 1987.

Digital Library

Google Scholar

[5]

J. Canny and J. H. Reif. New lower bound techniques for robot motion planning problems. In Proc. P.8th Annu. IEEE Sympoa. Found. Camput. Sci., pages 49-60, 1987.

Digital Library

Google Scholar

[6]

J. Choi, J. SeIlen, and C. K. Yap. Approximate Euclidean shortest path in 3-space. In Proc. l Oth Annu. A CM Sympaa. Camput. Geom., pages 41-48, 1994.

Digital Library

Google Scholar

[7]

D.P. Dobkin and D. G. Kirkpatrick. A llnear algorithm for determining the separation of convex polyhedra. J. Algorithma, 6:381-392, 1985.

Crossref

Google Scholar

[8]

D.P. Dobkin and D. G. Kirkpatrick. Determining the separation of preprocessed polyhedra - a unified approach. In Proc. 17th Internat. Colloq. Automata Lang. Program., volume 443 of Lecture Notes in Computer Science, pages 400-413. Springer-Verlag, 1990.

Digital Library

Google Scholar

[9]

S. Har-Peled. Constructing approximate shortest path maps in three dimensions, manuscript, 1997.

Google Scholar

[10]

J. Hershberger and S. Suri. Practical methods for approximating shortest paths on a convex polytope in IR3. In Proc. 6th A CM-SIAM Sympos. Discrete Algorithms, pages 447-456, 1995.

Digital Library

Google Scholar

[11]

J.S.B. Mitchell, D. M. Mount, and C. H. Papaclimitriou. The discrete geodesic problem. SIAM J. Comput., 16:647-668, 1987.

Digital Library

Google Scholar

[12]

C. H. Papadimitriou. An algorithm for shortest-path motion in three dimensions. Inform. Process. Lett., 20:259-263, 1985.

Crossref

Google Scholar

[13]

A.V. Pogorelov. Eztrinsic Geometry of Convez Surfaces, Volume 35 of Translations of Mathematical Monographs. American Mathematical Society, Providence, Rhode Island, 1973.

Google Scholar

[14]

J.H. Reif and J. A. Starer. A single-exponential upper bound for finding shortest paths in three dimensions. J. A CM, 41(5):1013-1019, 1994.

Digital Library

Google Scholar

[15]

M. Sharir. On shortest paths amidst convex polyhedra. SIAM J. Comput., 16:561-572, 1987.

Digital Library

Google Scholar

[16]

M. Sharir and A. Schorr. On shortest paths in polyhedral spaces. Siam J. Comput., 15:193- 215, 1986.

Digital Library

Google Scholar

[17]

K.R. Varadarajan and P.K. Agarwal. Approximating shortest paths on a polyhedron. manuscript, 1996.

Google Scholar

Cited By

View all

Wang XFang ZWu JXin SHe Y(2017)Discrete geodesic graph (DGG) for computing geodesic distances on polyhedral surfacesComputer Aided Geometric Design10.1016/j.cagd.2017.03.01052:C(262-284)Online publication date: 1-Mar-2017
https://dl.acm.org/doi/10.1016/j.cagd.2017.03.010
Liu Y(2013)Exact geodesic metric in 2-manifold triangle meshes using edge-based data structuresComputer-Aided Design10.1016/j.cad.2012.11.00545:3(695-704)Online publication date: 1-Mar-2013
https://dl.acm.org/doi/10.1016/j.cad.2012.11.005
Gudmundsson JLevcopoulos CNarasimhan GSmid M(2008)Approximate distance oracles for geometric spannersACM Transactions on Algorithms10.1145/1328911.13289214:1(1-34)Online publication date: 28-Mar-2008
https://dl.acm.org/doi/10.1145/1328911.1328921
Show More Cited By

Index Terms

Approximate shortest paths and geodesic diameters on convex polytopes in three dimensions
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Paths and connectivity problems
2. Theory of computation
  1. Randomness, geometry and discrete structures
    1. Computational geometry

Recommendations

Computing Approximate Shortest Paths on Convex Polytopes

The algorithms for computing a shortest path on a polyhedral surface are slow, complicated, and numerically unstable. We have developed and implemented a robust and efficient algorithm for computing approximate shortest paths on a convex polyhedral ...
Convex hulls of spheres and convex hulls of disjoint convex polytopes

Given a set @S of spheres in E^d, with d>=3 and d odd, having a constant number of m distinct radii @r"1,@r"2,...,@r"m, we show that the worst-case combinatorial complexity of the convex hull of @S is @Q(@__ __"1"=<"i"<>"j"=<"mn"in"j^@__ __^d^2^@__ __), ...
Approximating shortest paths on a convex polytope in three dimensions

Given a convex polytope P with n faces in ℝ³, points ∈ ∂P, and a parameter 0 < ϵ ≤ 1, we present an algorithm that constructs a path on ∂P from s to t whose length is at most (1 + ϵ)d_p(s, t), where d_p(s, t) is the length of the shortest path between s ...

Comments

Information & Contributors

Information

Published In

SCG '97: Proceedings of the thirteenth annual symposium on Computational geometry

August 1997

490 pages

ISBN:0897918789

DOI:10.1145/262839

Chairman:
Jean-Daniel Boissonnat
INRIA Sophia-Antipolis

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: 01 August 1997

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Qualifiers

Article

Conference

SoCG97

Sponsor:

SoCG97: 13th ACM Symposium on Computational Geometry

June 4 - 6, 1997

Nice, France

Acceptance Rates

SCG '97 Paper Acceptance Rate 75 of 199 submissions, 38%;

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

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

9
Total Citations
View Citations
350
Total Downloads

Downloads (Last 12 months)43
Downloads (Last 6 weeks)7

Reflects downloads up to 14 Jan 2025

Other Metrics

View Author Metrics

Citations

Cited By

View all

Wang XFang ZWu JXin SHe Y(2017)Discrete geodesic graph (DGG) for computing geodesic distances on polyhedral surfacesComputer Aided Geometric Design10.1016/j.cagd.2017.03.01052:C(262-284)Online publication date: 1-Mar-2017
https://dl.acm.org/doi/10.1016/j.cagd.2017.03.010
Liu Y(2013)Exact geodesic metric in 2-manifold triangle meshes using edge-based data structuresComputer-Aided Design10.1016/j.cad.2012.11.00545:3(695-704)Online publication date: 1-Mar-2013
https://dl.acm.org/doi/10.1016/j.cad.2012.11.005
Gudmundsson JLevcopoulos CNarasimhan GSmid M(2008)Approximate distance oracles for geometric spannersACM Transactions on Algorithms10.1145/1328911.13289214:1(1-34)Online publication date: 28-Mar-2008
https://dl.acm.org/doi/10.1145/1328911.1328921
Nikonorov YNikonorova Y(2007)The Intrinsic Diameter of the Surface of a ParallelepipedDiscrete & Computational Geometry10.1007/s00454-007-9037-740:4(504-527)Online publication date: 29-Sep-2007
https://doi.org/10.1007/s00454-007-9037-7
Kanai TSuzuki H(2001)Approximate shortest path on a polyhedral surface and its applicationsComputer-Aided Design10.1016/S0010-4485(01)00097-533:11(801-811)Online publication date: Sep-2001
https://doi.org/10.1016/S0010-4485(01)00097-5
Kanai TSuzuki H(2000)Approximate shortest path on a polyhedral surface based on selective refinement of the discrete graph and its applicationsProceedings Geometric Modeling and Processing 2000. Theory and Applications10.1109/GMAP.2000.838256(241-250)Online publication date: 2000
https://doi.org/10.1109/GMAP.2000.838256
Chiang YMitchell JTarjan RWarnow T(1999)Two-point Euclidean shortest path queries in the planeProceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms10.5555/314500.314560(215-224)Online publication date: 1-Jan-1999
https://dl.acm.org/doi/10.5555/314500.314560
Barequet GHar-Peled STarjan RWarnow T(1999)Efficiently approximating the minimum-volume bounding box of a point set in three dimensionsProceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms10.5555/314500.314536(82-91)Online publication date: 1-Jan-1999
https://dl.acm.org/doi/10.5555/314500.314536
Har-Peled SJanardan R(1998)Constructing approximate shortest path maps in three dimensionsProceedings of the fourteenth annual symposium on Computational geometry10.1145/276884.276927(383-391)Online publication date: 7-Jun-1998
https://dl.acm.org/doi/10.1145/276884.276927

View Options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

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

Computing Approximate Shortest Paths on Convex Polytopes

Convex hulls of spheres and convex hulls of disjoint convex polytopes

Approximating shortest paths on a convex polytope in three dimensions

Comments

Published In

Sponsors

Publisher

Publication History

Permissions

Check for updates

Qualifiers

Conference

Acceptance Rates

Other Metrics

Article Metrics

Other Metrics

Cited By

PDF

eReader

Login options

Full Access

References

Cited By

Index Terms

Recommendations

Computing Approximate Shortest Paths on Convex Polytopes

Convex hulls of spheres and convex hulls of disjoint convex polytopes

Approximating shortest paths on a convex polytope in three dimensions

Comments

Information

Published In

Sponsors

Publisher

Publication History

Permissions

Check for updates

Qualifiers

Conference

Acceptance Rates

Contributors

Other Metrics

Bibliometrics

Article Metrics

Other Metrics

Citations

Cited By

View options

PDF

eReader

Login options

Full Access

Figures

Other

Share

Share this Publication link

Share on social media

Affiliations