Allocating vertex π-guards in simple polygons via pseudo-triangulations

Discrete and Computational Geometry

Volumn 33, Issue 2, 2005, Pages 345-364

  Speckmann, Bettina ^a   Tóth, Csaba D ^b  

^a EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

^b Santa Barbara   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 12944275457     PISSN: 01795376     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00454-004-1091-9     Document Type: Article

References (25)

1. P. K. Agarwal, J. Basch, L. J. Guibas, J. Hershberger, and L. Zhang, Deformable free space tilings for kinetic collision detection, in: Algorithmic and Computational Robotics: New Directions, Proc. 5th Workshop Algorithmic Found. Robotics (Hanover, NH, 2001), pp. 83-96.
2. V. Brumberg, S. Ramaswami, and D. Souvaine, Experimental results on upper bounds for vertex pi-lights, in: Abstr. 11th Ann. Fall Workshop Comput. Geom. (Brooklyn, NY, 2001).
3. B. Chazelle, Triangulating a simple polygon in linear time, Discrete Comput. Geom. 6(5) (1991), 485-524.
4. B. Chazelle, H. Edelsbrunner, M. Gringi, L. J. Guibas, J. Hershberger, M. Sharir, and J. Snoeyink, Ray shooting in polygons using geodesic triangulations, Algorithmica 12 (1994), 54-68.
5. V. Chvátal, A combinatorial theorem in plane geometry, J. Combin. Theory Sci: B 18 (1975), 39-41.
6. V. Estivill-Castro, J. O'Rourke, J. Urrutia, and D. Xu, Illumination of polygons with vertex guards, Inform. Process. Lett. 56 (1995), 9-13.
7. S. Fisk, A short proof of Chvátal's watchman theorem, J. Combin. Theory Ser. B 24 (1978), 374.
8. M. Goodrich and R. Tamassia, Dynamic ray shooting and shortest paths in planar subdivision via balanced geodesic triangulations, J. Algorithms 23 (1997), 51-73.
9. 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 (1987), 209-233.
10. J. Hershberger and J. Snoeyink, Computing minimum length paths of a given homotopy class, Comput. Geom. Theory Appl. 4 (1994), 63-97.
11. D. Kirkpatrick, J. Snoeyink, and B. Speckmann, Kinetic collision detection for simple polygons, Internat. J. Comput. Geom. Appl. 12 (2002), 3-27.
12. J. S. B. Mitchell and J. O'Rourke, Computational geometry column 42, SIGACT News 32(3) (2001), 63-72.
13. M. Pocchiola and G. Vegter, Pseudo-triangulations: theory and applications, in: Proc. 12th ACM Symp. Comput. Geom. (Philadelphia, PA, 1996), ACM Press, New York 1996, pp. 291-300.
14. M. Pocchiola and G. Vegter, Topologically sweeping visibility complexes via pseudo-triangulations, Discrete Comput. Geom. 16 (1996), 419-153.
15. J. O'Rourke, Art Gallery Theorems and Algorithms, The International Series of Monographs on Computer Science, Oxford University Press, New York, 1987.
16. J. O'Rourke, Vertex π-lights for monotone mountains, in: Proc. 9th Canadian Conf. Comput. Geom. (Kingston, ON, 1997), pp. 1-5.
17. J. O'Rourke, Open problems in the combinatorics of visibility and illumination, in: Advances in Discrete and Computational Geometry (B. Chazelle, J. E. Goodman, and R. Pollack, eds.), AMS, Providence, RI, 1998, 237-243.
18. J. O'Rourke, Computational geometry column 43, SIGACT News 33(1) (2002), 58-60.
19. I. Streinu, A combinatorial approach to planar non-colliding robot arm motion planning, in: Proc. 41st Symp. Found. Comput. Sci. (Redondo Beach, CA, 2000), IEEE Computer Society Press, Los Alamitos, CA 2000, pp. 443-453.
20. L. Szabó, Recent results on illumination problems, in: Intuitive Geometry, Bolyai Society Mathematical Studies 6, Bolyai Mathematical Society, Budapest, 1997, pp. 207-221.
21. Cs. D. Tóth, Art gallery problem with guards whose range of vision is 180°, Comput. Geom. Theory Appl. 17 (2000), 121-134.
22. Cs. D. Tóth, Illuminating polygons with π-floodlights, in: Proc. Internat. Conf. Comput. Sci. (San Francisco, CA, 2001), Part I, vol. 2073 of Lecture Notes in Computer Science, Springer-Verlag, Berlin, 2001, pp. 772-781.
23. G. T. Toussaint, Computing geodesic properties inside a simple polygon, Rev. Intell. Artific. 3 (1989), 9-42.
24. J. Urrutia, Art gallery and illumination problems, in: Handbook on Computational Geometry (J. R. Sack and J. Urrutia, eds.), Elsevier, Amsterdam, 2000, pp. 973-1027.
25. J. Urrutia, Personal communication, 2001.