On Envelopes of Arrangements of Lines

Journal of Algorithms

Volumn 21, Issue 1, 1996, Pages 111-148

  Eu, D ^a   Guevremont E ^b   Toussaint, G T ^c  

^a INSTITUTE FOR RESEARCH IN IMMUNOLOGY AND CANCER   (Canada)

^b SIMON FRASER UNIVERSITY   (Canada)

^c MCGILL UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY;

GEOMETRICAL PROPERTIES; LINEAR TIME; POLYGON;

GRAPH THEORY;

EID: 0030375748     PISSN: 01966774     EISSN: None     Source Type: Journal    
DOI: 10.1006/jagm.1996.0040     Document Type: Article

References (22)

1. M. J. Atallah, Computing the convex hull of line intersections, J. Algorithms, 7 (1986), 285-288.
2. M. Bern, D. Eppstein, P. Plassman, and F. Yao, "Horizon theorems for lines and polygons, "DIMACS Series in Discrete Mathematics and Computer Science," No. 6, pp. 45-66, North-Holland, Amsterdam, 1991.
3. M. Blum, R. W. Floyd, V. R. Rivest, and R. E. Tarjan, Time bounds for selection, J. Comput. System Sci. 7, No. 4 (1973), 448-461.
4. M. Ben-Or, Lower bounds for algebraic computation trees, in "Proc. 15th ACM Sympos. on Theory of Comput., 1983," pp. 80-86.
5. Y. T. Ching and D. T. Lee, Finding the diameter of a set of lines, Pattern Recognition 18 (1985), 249-255.
6. R. Cole, J. Salowe, W. Steiger, and E. Szemerédi, An optimal-time algorithm for slope selection, SIAM J. Comput. 18, No. 4 (1989), 792-810.
7. L. Devroye and G. T. Toussaint, "Convex hulls for random lines, J. Algorithms 14 (1993), 381-394.
8. H. Edelsbrunner, "Algorithms in Combinatorial Geometry," Springer-Verlag, Berlin/New York, 1987.
9. H. ElGindy, D. Avis, and G. T. Toussaint, Applications of a two-dimensional hidden-line algorithm to other geometric problems, Computing 31 (1983), 191-202.
10. H. ElGindy and G. T. Toussaint, On geodesic properties of polygons relevant to linear time triangulation, Visual Comput. 5 (1989), 68-74.
11. R. Graham, An efficient algorithm for determining the convex hull of a planar set, Inform. Process. Lett. 1 (1972), 132-133.
12. A. Horn and R. A. Valentine, Some properties of L-sets in the plane, Duke Math. J. 16 (1949), 131-140.
13. M. Keil, A simple algorithm for determining the envelope of a set of lines, Inform. Process. Lett. 39 (1991), 121-124.
14. W. Lenhart, R. Pollack, J. R. Sack, R. Seidel, M. Sharir, S. Suri, G. T. Toussaint, S. Whitesides, and C. K. Yap, Computing the link diameter of a simple polygon, Discrete Comput. Geom. 3, No. 3 (1988), 281-293.
15. J. O'Rourke, "Art gallery theorems and algorithms," Oxford Univ. Press, Oxford, 1987.
16. J.-P. Roudneff, Arrangements of lines with a minimum number of triangles are simple, Discrete Comput. Geom. 3, No. 2 (1988), 97-102.
17. S. Suri, Computing the envelope of a set of lines, unpublished manuscript, Johns Hopkins Univ., 1985.
18. G. T. Toussaint and D. Avis, On a convex hull algorithm for polygons and its application to triangulation problems, Pattern Recognition 15, No. 1 (1982), 23-29.
19. G. T. Toussaint, A simple linear algorithm for intersecting convex polygons, Visual Comput. 1 (1985), 118-123.
20. G. T. Toussaint, "Computing morphological properties of arrangements of lines, in "Proc. Conf. Society for the Advancement of Materials Process Engineering, Tokyo, Japan, Dec. 11-14, 1991.
21. G. Vegter, "Computing the Bounded Region Determined by Finitely Many Lines in the Plane," Technical Report 87-03, Dept. of Mathematics and Computing Science, Rijkuniversiteit Groningen, 1987.
22. T. Zaslavsky, Facing up to arrangements: Face-count formulas for partitions of space by hyperplanes, Mem. Amer. Math. Soc. 154 (1975).