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Counting triangle crossings and halving planes

Discrete & Computational Geometry (1994) 12(1) 281-289
DOI: 10.1007/BF02574381
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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. © 1994 Springer-Verlag New York Inc.

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APA

Dey, T. K., & Edelsbrunner, H. (1994). Counting triangle crossings and halving planes. Discrete & Computational Geometry, 12(1), 281–289. https://doi.org/10.1007/BF02574381

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