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Diagonals: Part II

Feature Column Archive

5. References

Aggarwal, A., The art gallery theorem: its variations, applications and algorithmic aspects, Ph.D. Thesis, Johns Hopkins University, Baltimore, 1984.

Aggarwal, A., and S. Suri, Computing the longest diagonal of a simple polygon, Inform. Process. Lett., 35 (1990) 13-18.

Bjorling-Sachs, I., Tight bound for edge guards in rectilinear monotone polygons, DIMACS Tech. Report, 93-12, Rutgers University, 1993.

Chazelle, B., Computational geometry and convexity, Ph. D. Thesis, Yale University, New Haven, 1980.

Chazelle, B., Triangulating a simple polygon in linear time, Disc. Comput. Geom., 6 (1991) 485-524.

Chazelle, B. and D. Dobkin, Optimal convex decompositions, In Computational Geometry, (G. Toussaint, ed.), Elsevier, North Holland, Amsterdam, 1985, p. 63-133.

Chin, W-P. and S. Ntafos, Shortest watchman routes in simple polygons, Discrete Comput. Geom., 6 (1991) 9-31.

Chvátal, V., A combinatorial theorem in plane geometry, JCT (B), 18 (1975) 39-41.

Czyzowicz, J. and E. Rivera-Campo, J. Urrutia, J. Zaks, Illuminating and guarding segments in the plane, Discr. Math., 137 (1995) 147-153.

De Berg, M. and M. van Kreveld, M. Overmans, O. Schwarzkopf, Polygon Triangulation: Guarding an Art Gallery, Chapter 3, in Computational Geometry: Algorithms and Applications, 2nd. rev. ed., Springer-Verlag, Berlin, 2000.

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Estivill-Castro, V. and J. O'Rourke, J. Urrutia, D. Xu, Illumination of polygons with vertex floodlights, Inform. Process. Lett., 56 (1995) 9-13.

Fejes-Tóth, L., Illumination of convex disks, Acta Math. Acad. Sci. Hungar., 29 (1977) 355-360.

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Computational Geometry, 23 (2000) 73-110.

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Gewali, L., Placing guards inside orthogonal polygons, Inform. Sci., 88 (1996) 1-14.

Gewali, L. and S. Ntafos, Cover grids and orthogonal polygons with periscope guards, Comput. Geom., 2 (1993) 309-334.

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Greene, D., The decomposition of polygons into convex parts, In Advances in Computing Research, Vol. I., F. Preparata, (ed.),, JAI Press, Connecticut, 1983, p. 235-259.

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Gyõri, A short proof of the rectilinear art gallery theorem, SIAM J. Algebraic Discrete Methods, 7 (1986) 452-454.

Hershberger, J. and S. Suri, Finding a shortest diagonal of a simple polygon in linear time, Comput. Geom., 7 (1997) 149-160.

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Shermer, T., Recent results in art galleries, Proc. IEEE, 80 (1992) 1384-1399.

Tóth, C., Illuminating both sides of line segments, in Discrete and Computational Geometry, J. Akiyama, M. Kano, and M. Urabe (eds.), Lecture Notes in Computer Science, 2098, Springer-Verlag, New York, 370-380.

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Urrutia, J., Art Gallery and Illumination Problems, in Handbook on Computational Geometry, J. Sac, and J. Urrutia, (eds.), Elsevier Science Publishers, Amsterdam, 2000, p. 973-1027.

Urrutia, J., Sixth proof of the orthogonal art gallery theorem (unpublished manuscript).

Valtr, P., Guarding galleries where no point sees a small area, Israel J. Math., 104 (1998) 1-16.

Viswanathan, S., Tight bounds for the number of edge guards for spiral polygons, J. Geom., 51 (1994) 178-186.

Zalik, B. and G. Clapworthy, A universal trapezoidation algorithm for planar polygons, Computers & Graphs, 23 (1999) 353-363.

Zalik, B. and A. Jezernik, K. Zalik, Polygon trapezoidation by sets of open trapezoids, Computers & Graphics, 27 (2003) 791-800.

Note:

The Association for Computing Machines via its special interest groups for Graphics and Algorithms and Computation Theory sponsors an annual meeting on Computational Geometry. The proceedings of this conference has been published every year since the first conference was held in 1985. Papers in these volumes can be accessed via the ACM Portal.

Those who can access JSTOR can find some of the papers mentioned above there. For those with access, the American Mathematical Society's MathSciNet can be used to get additional bibliographic information and reviews of some these materials.


  1. Introduction
  2. Orthogonal Polygons
  3. Guarding orthogonal art galleries
  4. Entering new territory
  5. References