An optimal-time algorithm for shortest paths on a convex polytope in three dimensions

Proceedings of the Annual Symposium on Computational Geometry

Volumn 2006, Issue , 2006, Pages 30-39

  Schreiber, Yevgeny ^a   Sharir, Micha ^a,b  

^a TEL AVIV UNIVERSITY   (Israel)

^b NEW YORK UNIVERSITY   (United States)

Author keywords

Continuous Dijkstra; Geodesics; Polytope Surface; Shortest Path; Shortest Path Map; Unfolding; Wavefront

Indexed keywords

ALGORITHMS; DATA ACQUISITION; GRAPHIC METHODS; QUERY LANGUAGES; THREE DIMENSIONAL;

POLYTOPE SURFACE; SHORTEST PATH MAP; VORONOI DIAGRAM;

COMPUTATIONAL GEOMETRY;

EID: 33748060967     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1137856.1137862     Document Type: Conference Paper

References (27)

1. P. K. Agarwal, S. Har-Peled, M. Sharir, and K. R. Varadarajan, Approximate shortest paths on a convex polytope in three dimensions, J. ACM 44:567-584, 1997.
2. L. Aleksandrov, A. Maheshwari, and J.-R. Sack, An improved approximation algorithm for computing geometric shortest paths, 14th FCT, Lecture Notes Comput. Sci. 2751:246-257, 2003.
3. B. Aronov and J. O'Rourke, Nonoverlap of the star unfolding, Discrete Comput. Geom., 8:219-250, 1992.
4. J. Chen and Y. Han, Shortest paths on a polyhedron, Part I: Computing shortest paths, Internat. J. Comput. Geom. Appl. 6:127-144, 1996.
5. J. Chen and Y. Han, Shortest paths on a polyhedron, Part II: Storing shortest paths, Tech. Rept. 161-90, Comput. Sci. Dept., Univ. Kentucky, Lexington, KY, February 1990.
6. J. R. Driscoll, D. D. Sleator, and R. E. Tarjan, Fully persistent lists with catenation, J. ACM 41(5):943-949, 1994.
7. S. Har-Peled, Approximate shortest paths and geodesic diameters on convex polytopes in three dimensions, Discrete Comput. Geom., 21:216-231, 1999.
8. S. Har-Peled, Constructing approximate shortest path maps in three dimensions, SIAM J. Comput., 28(4):1182-1197, 1999.
9. J. Hershberger and S. Suri, An optimal algorithm for Euclidean shortest paths in the plane, in Proc. 34th IEEE Sympos. Found. Comput. Sci., 508-517, 1993.
10. J. Hershberger and S. Suri, An optimal algorithm for Euclidean shortest paths in the plane, Manuscript, Washington University, 1995.
11. J. Hershberger and S. Suri, An optimal algorithm for Euclidean shortest paths in the plane, SIAM J. Comput. 28(6):2215-2256, 1999.
12. S. Kapoor, Efficient computation of geodesic shortest paths, in Proc. 32nd Annu. ACM Sympos. Theory Comput., New York, NY, USA: ACM Press, 770-779, 1999.
13. J. S. B. Mitchell, Shortest paths and networks, in J. E. Goodman and J. ORourke, editors, Handbook of Discrete and Computational Geometry (2nd Edition), chapter 27, 607-641, North-Holland, Chapman & Hall/CRC, Boca Raton, FL, 2004.
14. J. S. B. Mitchell, D. M. Mount, and C. H. Papadimitriou, The discrete geodesic problem, SIAM J. Comput. 16:647-668, 1987.
15. D. M. Mount, On finding shortest paths on convex polyhedra, Tech. Rept., Computer Sience Dept., Univ. Maryland, College Park, October 1984.
16. D. M. Mount, Storing the subdivision of a polyhedral surface, Discrete Comput. Geom., 2:153-174, 1987.
17. J. O'Rourke, Computational geometry column 35, Internat. J. Comput. Geom. Appl., 9:513-515, 1999;
18. also in SIGACT News, 30(2):31-32, (1999) Issue 111.
19. J. O'Rourke, Folding and unfolding in computational geometry, in Lecture Notes Comput, Sci., Vol. 1763, J. Akiyama, M. Kano, M. Urabe, editors, Springer-Verlag, Berlin, 2000, pp. 258-266.
20. J. O'Rourke, S. Suri, and H. Booth, Shortest path on polyhedral surfaces, Manuscript, The Johns Hopkins Univ., Baltimore, MD,1984.
21. R. P. Paul, Robot Manipulators: Mathematics, Programming, and Control, MIT Press, Cambridge, Massachusetts, 1981.
22. Y. Schreiber and M. Sharir, An optimal-time algorithm for shortest paths on a convex polytope in three dimensions, http://www.tau.ac.il/~syevgeny/ ShortestPath.ps.
23. M. Sharir, On shortest paths amidst convex polyhedra, SIAM J. Comput. 16:561-572, 1987.
24. M. Sharir and A. Schorr, On shortest paths in polyhedral spaces, SIAM J. Comput. 15:193-215, 1986.
25. K. R. Varadarajan and P.K. Agarwal, Approximating shortest paths on a nonconvex polyhedron, in Proc. 38th Annu. IEEE Sympos. Found. Comput. Sci., 182-191, 1997.
26. E. W. Weisstein, Riemann Surface, Math World - A Wolfram Web Resource, http://mathworld.wolfram.com/RiemannSurface.html.
27. E. W. Weisstein, Unfolding, MathWorld - A Wolfram Web Resource, http://mathworld.wolfram.com/Unfolding.html.