Counting triangle crossings and halving planes
Dey T, Edelsbrunner H. 1994. Counting triangle crossings and halving planes. Discrete & Computational Geometry. 12(1), 281–289.
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Journal Article
| Published
| English
Scopus indexed
Author
Dey, Tamal;
Edelsbrunner, HerbertISTA 
Abstract
Every collection of t≥2 n2 triangles with a total of n vertices in ℝ3 has Ω(t4/n6) crossing pairs. This implies that one of their edges meets Ω(t3/n6) of the triangles. From this it follows that n points in ℝ3 have only O(n8/3) halving planes.
Publishing Year
Date Published
1994-09-01
Journal Title
Discrete & Computational Geometry
Publisher
Springer
Acknowledgement
The research of H. Edelsbrunner was supported by the National Science Foundation under Grant CCR-8921421 and under an Alan T. Waterman award, Grant CCR-9118874. Any opinions, findings and conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect the view of the National Science Foundation.
Volume
12
Issue
1
Page
281 - 289
ISSN
IST-REx-ID
Cite this
Dey T, Edelsbrunner H. Counting triangle crossings and halving planes. Discrete & Computational Geometry. 1994;12(1):281-289. doi:10.1007/BF02574381
Dey, T., & Edelsbrunner, H. (1994). Counting triangle crossings and halving planes. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/BF02574381
Dey, Tamal, and Herbert Edelsbrunner. “Counting Triangle Crossings and Halving Planes.” Discrete & Computational Geometry. Springer, 1994. https://doi.org/10.1007/BF02574381.
T. Dey and H. Edelsbrunner, “Counting triangle crossings and halving planes,” Discrete & Computational Geometry, vol. 12, no. 1. Springer, pp. 281–289, 1994.
Dey T, Edelsbrunner H. 1994. Counting triangle crossings and halving planes. Discrete & Computational Geometry. 12(1), 281–289.
Dey, Tamal, and Herbert Edelsbrunner. “Counting Triangle Crossings and Halving Planes.” Discrete & Computational Geometry, vol. 12, no. 1, Springer, 1994, pp. 281–89, doi:10.1007/BF02574381.
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