On Levels in Arrangements of Surfaces in Three Dimensions

被引：2

作者：

Chan, Timothy M. ^{[1
]}

机构：

[1] Univ Waterloo, Sch Comp Sci, Waterloo, ON N2L 3G1, Canada

来源：

DISCRETE & COMPUTATIONAL GEOMETRY | 2012年 / 48卷 / 01期

基金：

加拿大自然科学与工程研究理事会;

关键词：

k-Level; Arrangements; The k-set problem; K-SETS; HALVING PLANES; IMPROVED BOUNDS; TRIANGLES; SEGMENTS; CURVES;

D O I：

10.1007/s00454-012-9428-2

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

A favorite open problem in combinatorial geometry is to determine the worst-case complexity of a in an arrangement. Up to now, nontrivial upper bounds in three dimensions are known only for the linear cases of planes and triangles. We propose the first technique that can deal with more general surfaces in three dimensions. For example, in an arrangement of "pseudo-planes" or "pseudo-spherical patches" (where the main criterion is that each triple of surfaces has at most two common intersections), we prove that there are at most ( (2.997)) vertices at any given level.

引用

页码：1 / 18

页数：18

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