Line transversals to disjoint balls

被引：9
|
作者：
Borcea, Ciprian [1 ]
Goaoc, Xavier [2 ]
Petitjean, Sylvain [3 ]
机构：
[1] Rider Univ, Lawrenceville, NJ 08648 USA
[2] LORIA, INRIA Lorraine, Nancy, France
[3] LORIA, CNRS, Nancy, France
来源：
DISCRETE & COMPUTATIONAL GEOMETRY | 2008年 / 39卷 / 1-3期
关键词：
transversal; geometric permutation; convexity;
D O I：
10.1007/s00454-007-9016-z
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
We prove that the set of directions of lines intersecting three disjoint balls in R-3 in a given order is a strictly convex subset of S-2. We then generalize this result to n disjoint balls in R-d. As a consequence, we can improve upon several old and new results on line transversals to disjoint balls in arbitrary dimension, such as bounds on the number of connected components and Helly-type theorems.
引用
收藏
页码：158 / 173
页数：16
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