David Avis, Prosenjit Bose, Thomas C. Shermer, Jack Snoeyink, Godfried Toussaint, Binhai Zhu  Home/Search
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Abstract: Let K be a convex polytope in R d , let h(x) be the hyperplane consisting of all points with first coordinate equal to x, and let A(x) be the area (or volume, if d ? 3) of the section K " h(x). Using the Brunn-Minkowski inequality, we show that A(x) is a strictly unimodal function and give an algorithm to determine a hyperplane that achieves the maximum. Our algorithm runs in linear time, if the facial lattice of K is given. 1 Introduction A function f : R ! R is said to be unimodal if it... (Update)
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...of the cross section of R and h(t) that is, #(t) vol d 1 (R # h(t) Because R is convex, the function # is unimodal. Avis et al. [1] prove this for convex polytopes using the Brunn Minkowski theorem, but the proof holds verbatim for arbitrary convex sets. Let t # be a...
...contact with v 2 Figure 1: Two convex polygons with Omega Gamma1 8 nm 2 n 2 m) distinct placements. Following Avis et al. [4], we can now apply the BrunnMinkowski theorem [13] which states that the square root of the function that describes the area of intersection of PPQ...
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BibTeX entry: (Update)
D. Avis, P. Bose, T. Shermer, J. Snoeyink, G. Toussaint, and B. Zhu. On the sectional area of convex polytopes. In Communication at the 12th Annu. ACM Sympos. Comput. Geom., page C, 1996. http://citeseer.nj.nec.com/article/avis96sectional.html More
@inproceedings{ avis96sectional,
author = "David Avis and Prosenjit Bose and Godfried T. Toussaint and Thomas C. Shermer and Binhai Zhu and Jack Snoeyink",
title = "On the Sectional Area of Convex Polytopes",
booktitle = "Symposium on Computational Geometry",
pages = "C-11-C-12",
year = "1996",
url = "citeseer.nj.nec.com/article/avis96sectional.html" }
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