A Measure of Non-convexity in the Plane and the Minkowski Sum

被引：2

作者：

Karasev, R. N. ^{[1
]}

机构：

[1] Moscow Inst Phys & Technol, Dept Math, Dolgoprudnyi 141700, Russia

来源：

DISCRETE & COMPUTATIONAL GEOMETRY | 2010年 / 44卷 / 03期

关键词：

Minkowski sum; Weak convexity; NO-FIT POLYGON;

D O I：

10.1007/s00454-010-9258-z

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

In this paper a measure of non-convexity for a simple polygonal region in the plane is introduced. It is proved that for "not far from convex" regions this measure does not decrease under the Minkowski sum operation, and guarantees that the Minkowski sum has no "holes".

引用

页码：608 / 621

页数：14

共 5 条

[1]

AGARWAL PK, 2000, LECT NOTES COMPUTER, V1897, P20

[2] The irregular cutting-stock problem - a new procedure for deriving the no-fit polygon [J].

Bennell, JA ;

Dowsland, KA ;

Dowsland, WB .

COMPUTERS & OPERATIONS RESEARCH, 2001, 28 (03) :271-287

[3] Complete and robust no-fit polygon generation for the irregular stock cutting problem [J].

Burke, E. K. ;

Hellier, R. S. R. ;

Kendall, G. ;

Whitwell, G. .

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 2007, 179 (01) :27-49

[4] Weak convexity in the senses of Vial and Efimov-Stechkin [J].

Ivanov, GE .

IZVESTIYA MATHEMATICS, 2005, 69 (06) :1113-1135

[5]

PANSU P, 2001, METRIC STRUCTURES RI, P393

← 1 →