Geodesic Fréchet distance inside a simple polygon

Proceedings of the 25th International Symposium on Theoretical Aspects of Computer Science, STACS 2008

Volumn , Issue , 2008, Pages 193-204

  Cook IV, Atlas F ^a   Wenk, Carola ^a  

^a University of Texas at San Antonio   (United States)

Author keywords

Fr chet distance; Geodesic; Parametric search; Simple polygon

Indexed keywords

CURVE FITTING; GEOMETRY; OPTIMIZATION;

BOUNDING POLYGONS; DECISION PROBLEMS; GEODESIC; HAUSDORFF DISTANCE; OPTIMIZATION PROBLEMS; PARAMETRIC SEARCH; RANDOMIZED APPROACH; SIMPLE POLYGON;

GEODESY;

EID: 45749097808     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (26)

1. P. K. Agarwal and M. Sharir. Davenport-Schinzel sequences and their geometric applications. Technical Report Technical report DUKE-TR-1995-21, 1995.
2. P. K. Agarwal and M. Sharir. Efficient algorithms for geometric optimization. ACM Comput Surv., 30(4):412-458, 1998.
3. P. K. Agarwal, M. Sharir, and S. Toledo. Applications of parametric searching in geometric optimization. volume 17, pages 292-318, Duluth, MN, USA, 1994. Academic Press, Inc.
4. H. Alt and M. Godau. Computing the Fréchet distance between two polygonal curves. International Journal of Computational Geometry and Applications, 5:75-91, 1995.
5. H. Alt, C. Knauer, and C. Wenk. Comparison of distance measures for planar curves. Algorithmica, 38(1):45-58, 2003.
6. S. Bespamyatnikh and M. Segal. Selecting distances in arrangements of hyperplanes spanned by points. volume 2, pages 333-345, September 2004.
7. K. Buchin, M. Buchin, and C. Wenk. Computing the Fréchet distance between simple polygons in polynomial time. SoCG: 22nd Symposium on Computational Geometry, pages 80-87, 2006.
8. E. W. Chambers, É. C. de Verdière, J. Erickson, S. Lazard, F. Lazarus, and S. Thite. Walking your dog in the woods in polynomial time. 17th Fall Workshop on Computational Geometry, 2007.
9. R. Cole. Slowing down sorting networks to obtain faster sorting algorithms. J. ACM, 34(1):200-208, 1987.
10. A. F. Cook IV and C. Wenk. Geodesic Fréchet and Hausdorff distance inside a simple polygon. Technical Report CS-TR-2007-004, University of Texas at San Antonio, August 2007.
11. C. A. Duncan, A. Efrat, S. G. Kobourov, and C. Wenk. Drawing with fat edges. Int. J. Found. Comput. Sci., 17(5):1143-1164, 2006.
12. A. Efrat, L. J. Guibas, S. Har-Peled, J. S. B. Mitchell, and T. M. Murali. New similarity measures between polylines with applications to morphing and polygon sweeping. Discrete & Computational Geometry, 28(4):535-569, 2002.
13. L. J. Guibas and J. Hershberger. Optimal shortest path queries in a simple polygon. J. Comput. Syst. Sci., 39(2):126-152, 1989.
14. L. J. Guibas, J. Hershberger, D. Leven, M. Sharir, and R. E. Tarjan. Linear time algorithms for visibility and shortest path problems inside simple polygons, pages 1-13, 1986.
15. L. J. Guibas, J. Hershberger, D. Leven, M. Sharir, and R. E. Tarjan. Linear-time algorithms for visibility and shortest path problems inside triangulated simple polygons. Algorithmica, 2:209-233, 1987.
16. J. Hershberger. A new data structure for shortest path queries in a simple polygon. Inf. Process. Lett., 38(5):231-235, 1991.
17. J. Komlós, Y. Ma, and E. Szemerédi. Matching nuts and bolts in O(n log n) time. SODA: 7th ACM-SIAM Symposium on Discrete Algorithms, pages 232-241, 1996.
18. A. Maheshwari and J. Yi. On computing Fréchet distance of two paths on a convex polyhedron. EWCG 2005, pages 41-4, 2005.
19. J. S. B. Mitchell. Geometric shortest paths and network optimization. Handbook of Computational Geometry, 1998.
20. J. S. B. Mitchell, D. M. Mount, and C.H. Papadimitriou. The discrete geodesic problem. SIAM J. Comput., 16(4):647-668, 1987.
21. L. Palazzi and J. Snoeyink. Counting and reporting red/blue segment intersections. CVGIP: Graph. Models Image Process., 56(4):304-310, 1994.
22. E. Papadopoulou and D. T. Lee. A new approach for the geodesic Voronoi diagram of points in a simple polygon and other restricted polygonal domains. Algorithmica, 20(4):319-352, 1998.
23. G. Rote. Computing the Fréchet distance between piecewise smooth curves. Technical Report ECGTR-241108-01, May 2005.
24. N. Sarnak and R. E. Tarjan. Planar point location using persistent search trees. Commun. ACM, 29(7):669-679, 1986.
25. R. van Oostrum and R. C. Veltkamp. Parametric search made practical. SoCG: 18th Symposium on Computational Geometry, pages 1-9, 2002.
26. C. Wenk, R. Salas, and D. Pfoser. Addressing the need for map-matching speed: Localizing global curve-matching algorithms. 18th Int'l Conf. on Sci. and Statistical Database Mgmt (SSDBM), pages 379-388, 2006.