On the boundary of the union of planar convex sets

被引：16

作者：

Pach, J ^{[1
]}

Sharir, M

机构：

[1] CUNY City Coll, Dept Comp Sci, New York, NY 10031 USA

[2] NYU, Courant Inst Math Sci, New York, NY 10012 USA

[3] Tel Aviv Univ, Sch Math Sci, IL-69978 Tel Aviv, Israel

[4] Hungarian Acad Sci, Budapest, Hungary

来源：

DISCRETE & COMPUTATIONAL GEOMETRY | 1999年 / 21卷 / 03期

关键词：

Alternative Proof; Planar Convex; Connected Piece;

D O I：

10.1007/PL00009424

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We give two alternative proofs leading to different generalizations of the following theorem of [1]. Given n convex sets in the plane, such that the boundaries of each pair of sets cross at most twice, then the boundary of their union consists of at most 6n - 12 arcs. (An arc is a connected piece of the boundary of one of the sets.) In the generalizations we allow pairs of boundaries to cross more than twice.

引用

页码：321 / 328

页数：8

共 5 条

[1]

[Anonymous], 1934, Fund. Math., V23, P135, DOI DOI 10.4064/FM-23-1-135-142

[2] ON THE UNION OF JORDAN REGIONS AND COLLISION-FREE TRANSLATIONAL MOTION AMIDST POLYGONAL OBSTACLES [J].