Optimal output-sensitive convex hull algorithms in two and three dimensions

Discrete and Computational Geometry

Volumn 16, Issue 4, 1996, Pages 361-368

  Chan, T M ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030490026     PISSN: 01795376     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02712873     Document Type: Article

References (26)

1. T. M. Chan. Output-sensitive results on convex hulls, extreme points, and related problems. Discrete Comput. Geom., this issue, pp. 369-387.
2. T. M. Chan, J. Snoeyink, and C.-K. Yap. Output-sensitive construction of polytopes in four dimensions and clipped Voronoi diagrams in three. Proc. 6th ACM-SIAM Symp. on Discrete Algorithms, pp. 282-291, 1995.
3. D. R. Chand and S. S. Kapur. An algorithm for convex polytopes. J. Assoc. Comput. Mach., 17:78-86, 1970.
4. B. Chazelle. An optimal algorithm for intersecting three-dimensional convex polyhedra. SIAM J. Comput., 21:671-696, 1992.
5. B. Chazelle and D. P. Dobkin. Intersection of convex objects in two and three dimensions. J. Assoc. Comput. Mach., 34:1-27, 1987.
6. B. Chazelle, H. Edelsbrunner, M. Grigni, L. Guibas, J. Hershberger, M. Sharir, and J. Snoeyink. Ray shooting in polygons using geodesic triangulations. Proc. 18th Internat. Colloq. on Automata, Languages, and Programming, pp. 661-673, Lecture Notes in Computer Science, vol. 510. Springer-Verlag, Berlin, 1991.
7. B. Chazelle and J. Matoušek. Derandomizing an output-sensitive convex hull algorithm in three dimensions. Comput. Geom. Theory Appl., 5:27-32, 1995.
8. K. L. Clarkson and P. W. Shor. Applications of random sampling in computational geometry, II. Discrete Comput. Geom., 4:387-421, 1989.
9. D. P. Dobkin and D. G. Kirkpatrick. Fast detection of polyhedral intersection. Theoret. Comput Sci., 27:241-253, 1983.
10. D. P. Dobkin and D. G. Kirkpatrick. Determining the separation of preprocessed polyhedra: a unified approach. Proc. 17th Internat. Colloq. on Automata, Languages, and Programming, pp. 440-413, Lecture Notes in Computer Science, vol. 443. Springer-Verlag, Berlin, 1990.
11. H. Edelsbrunner. Algorithms in Combinatorial Geometry. Springer-Verlag, Berlin, 1987.
12. H. Edelsbrunner and E. P. Mücke. Simulation of simplicity: A technique to cope with degenerate cases in geometric algorithms. ACM Trans. Graphics, 9:66-104, 1990.
13. 2 h) time algorithm for the three-dimensional convex hull problem. SIAM J. Comput., 20:259-277, 1991.
14. I. Emiris and J. Canny. An efficient approach to removing geometric degeneracies. Proc. 8th ACM Symp. on Computational Geometry, pp. 74-82, 1992.
15. R. L. Graham. An efficient algorithm for determining the convex hull of a finite planar set. Inform. Process Lett., 1:132-133, 1972.
16. S. Hart and M. Sharir. Nonlinearity of Davenport-Schinzel sequences and of generalized path compression schemes. Combinatorica, 6:151-177, 1986.
17. J. Hershberger. Finding the upper envelope of n line segments in O(n log n) time. Inform. Process. Lett., 33:169-174, 1989.
18. J. Hershberger and S. Suri. A pedestrian approach to ray shooting: shoot a ray, take a walk. Proc. 4th ACM-SIAM Symp. on Discrete Algorithms, pp. 54-63, 1993.
19. R. A. Jarvis. On the identification of the convex hull of a finite set of points in the plane. Inform. Process. Lett., 2:18-21, 1973.
20. D. G. Kirkpatrick and R. Seidel. The ultimate planar convex hull algorithm? SIAM J. Comput., 15:287-299, 1986.
21. K. Mulmuley. Computational Geometry: An Introduction Through Randomized Algorithms. Prentice-Hall, Englewood Cliffs, NJ, 1994.
22. J. O'Rourke, C.-B. Chien, T. Olson, and D. Naddor. A new linear algorithm for intersecting convex polygons. Comput. Graph. Image Process., 19:384-391, 1982.
23. J. O'Rourke. Computational Geometry in C. Cambridge University Press, Cambridge, 1994.
24. F. P. Preparata and S. J. Hong. Convex hulls of finite sets of points in two and three dimensions. Commun. ACM, 20:87-93, 1977.
25. F. P. Preparata and M. I. Shamos. Computational Geometry: An Introduction. Springer-Verlag, New York, 1985.
26. G. F. Swart. Finding the convex hull facet by facet. J. Algorithms, 6:17-48, 1985.