Counting and cutting cycles of lines and rods in space
Chazelle B, Edelsbrunner H, Guibas L, Pollack R, Seidel R, Sharir M, Snoeyink J. 1992. Counting and cutting cycles of lines and rods in space. Computational Geometry: Theory and Applications. 1(6), 305–323.
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Author
Chazelle, Bernard;
Edelsbrunner, HerbertISTA 
;
Guibas, Leonidas;
Pollack, Richard;
Seidel, Raimund;
Sharir, Micha;
Snoeyink, Jack
;
Guibas, Leonidas;
Pollack, Richard;
Seidel, Raimund;
Sharir, Micha;
Snoeyink, JackAbstract
A number of rendering algorithms in computer graphics sort three-dimensional objects by depth and assume that there is no cycle that makes the sorting impossible. One way to resolve the problem caused by cycles is to cut the objects into smaller pieces. In this paper we address the problem of estimating how many such cuts arc always sufficient. We also consider a few related algorithmic and combinatorial geometry problems. For example, we demonstrate that n lines in space can be sorted in randomized expected time O(n4’st’), provided that they define no cycle. We also prove an 0(n7’4) upper bound on the number of points in space so that there are n lines with the property that for each point there are at least three noncoplanar lines that contain it.
Publishing Year
Date Published
1992-06-01
Journal Title
Computational Geometry: Theory and Applications
Publisher
Elsevier
Acknowledgement
* Bernard Chazelle wishes to acknowledge the National Science Foundation for supporting this research in part under Grant CCR-9002352. Herbert Edelsbrunner acknowledges the support of the National Science Foundation under grants CCR-8714565 and CCR-8921421. Richard Pollack was supported in part by NSF grant CCR-8901484, NSA grant MDA904-89-H-2030, and DIMACS, a Science and Technology Center under NSF grant STC88-09648. Raimund Seidel acknowledges support by NSF grant CCR-8809040. Mich Sharir was partially supported by the Office of Naval
Research under Grant N00014-87-K-0129, by the National Science Foundation under Grant CCR-89-01484, and by grants from the U.S.-Israeli Binational Science Foundation and the Fund for Basic Research administered by the Israeli Academy of Sciences.
Volume
1
Issue
6
Page
305 - 323
ISSN
IST-REx-ID
Cite this
Chazelle B, Edelsbrunner H, Guibas L, et al. Counting and cutting cycles of lines and rods in space. Computational Geometry: Theory and Applications. 1992;1(6):305-323. doi:10.1016/0925-7721(92)90009-H
Chazelle, B., Edelsbrunner, H., Guibas, L., Pollack, R., Seidel, R., Sharir, M., & Snoeyink, J. (1992). Counting and cutting cycles of lines and rods in space. Computational Geometry: Theory and Applications. Elsevier. https://doi.org/10.1016/0925-7721(92)90009-H
Chazelle, Bernard, Herbert Edelsbrunner, Leonidas Guibas, Richard Pollack, Raimund Seidel, Micha Sharir, and Jack Snoeyink. “Counting and Cutting Cycles of Lines and Rods in Space.” Computational Geometry: Theory and Applications. Elsevier, 1992. https://doi.org/10.1016/0925-7721(92)90009-H.
B. Chazelle et al., “Counting and cutting cycles of lines and rods in space,” Computational Geometry: Theory and Applications, vol. 1, no. 6. Elsevier, pp. 305–323, 1992.
Chazelle B, Edelsbrunner H, Guibas L, Pollack R, Seidel R, Sharir M, Snoeyink J. 1992. Counting and cutting cycles of lines and rods in space. Computational Geometry: Theory and Applications. 1(6), 305–323.
Chazelle, Bernard, et al. “Counting and Cutting Cycles of Lines and Rods in Space.” Computational Geometry: Theory and Applications, vol. 1, no. 6, Elsevier, 1992, pp. 305–23, doi:10.1016/0925-7721(92)90009-H.
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