Counting triangle crossings and halving planes

T. Dey, H. Edelsbrunner, Discrete & Computational Geometry 12 (1994) 281–289.

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Author
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
1994-12-01
Journal Title
Discrete & Computational Geometry
Acknowledgement
National Science Foundation under Grant CCR-8921421 and Alan T. Waterman award, Grant CCR-9118874.
Volume
12
Issue
1
Page
281 - 289
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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, 12(1), 281–289. https://doi.org/10.1007/BF02574381
Dey, Tamal, and Herbert Edelsbrunner. “Counting Triangle Crossings and Halving Planes.” Discrete & Computational Geometry 12, no. 1 (1994): 281–89. https://doi.org/10.1007/BF02574381.
T. Dey and H. Edelsbrunner, “Counting triangle crossings and halving planes,” Discrete & Computational Geometry, vol. 12, no. 1, 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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