Points and triangles in the plane and halving planes in space
Aronov B, Chazelle B, Edelsbrunner H, Guibas L, Sharir M, Wenger R. 1990. Points and triangles in the plane and halving planes in space. Proceedings of the 6th annual symposium on Computational geometry. SCG: Symposium on Computational Geometry, 112–115.
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Conference Paper
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| English
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Author
Aronov, Boris;
Chazelle, Bernard;
Edelsbrunner, HerbertISTA 
;
Guibas, Leonidas;
Sharir, Micha;
Wenger, Rephael
;
Guibas, Leonidas;
Sharir, Micha;
Wenger, RephaelAbstract
We prove that for any set S of n points in the plane and n3-α triangles spanned by the points of S there exists a point (not necessarily of S) contained in at least n3-3α/(512 log25 n) of the triangles. This implies that any set of n points in three - dimensional space defines at most 6.4n8/3 log5/3 n halving planes.
Publishing Year
Date Published
1990-01-01
Proceedings Title
Proceedings of the 6th annual symposium on Computational geometry
Publisher
ACM
Page
112 - 115
Conference
SCG: Symposium on Computational Geometry
Conference Location
Berkley, CA, United States
Conference Date
1990-06-07 – 1990-06-09
ISBN
IST-REx-ID
Cite this
Aronov B, Chazelle B, Edelsbrunner H, Guibas L, Sharir M, Wenger R. Points and triangles in the plane and halving planes in space. In: Proceedings of the 6th Annual Symposium on Computational Geometry. ACM; 1990:112-115. doi:10.1145/98524.98548
Aronov, B., Chazelle, B., Edelsbrunner, H., Guibas, L., Sharir, M., & Wenger, R. (1990). Points and triangles in the plane and halving planes in space. In Proceedings of the 6th annual symposium on Computational geometry (pp. 112–115). Berkley, CA, United States: ACM. https://doi.org/10.1145/98524.98548
Aronov, Boris, Bernard Chazelle, Herbert Edelsbrunner, Leonidas Guibas, Micha Sharir, and Rephael Wenger. “Points and Triangles in the Plane and Halving Planes in Space.” In Proceedings of the 6th Annual Symposium on Computational Geometry, 112–15. ACM, 1990. https://doi.org/10.1145/98524.98548.
B. Aronov, B. Chazelle, H. Edelsbrunner, L. Guibas, M. Sharir, and R. Wenger, “Points and triangles in the plane and halving planes in space,” in Proceedings of the 6th annual symposium on Computational geometry, Berkley, CA, United States, 1990, pp. 112–115.
Aronov B, Chazelle B, Edelsbrunner H, Guibas L, Sharir M, Wenger R. 1990. Points and triangles in the plane and halving planes in space. Proceedings of the 6th annual symposium on Computational geometry. SCG: Symposium on Computational Geometry, 112–115.
Aronov, Boris, et al. “Points and Triangles in the Plane and Halving Planes in Space.” Proceedings of the 6th Annual Symposium on Computational Geometry, ACM, 1990, pp. 112–15, doi:10.1145/98524.98548.
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