Covering a convex 3D polytope by a minimal number of congruent spheres

被引：6
|
作者：
Stoyan, Yu. G. [1 ]
Patsuk, V. M. [1 ]
机构：
[1] Natl Ukrainian Acad Sci, Inst Mech Engn Problems, UA-61046 Kharkov, Ukraine
来源：
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 2014年 / 91卷 / 09期
关键词：
covering; spheres; optimisation; mathematical modelling; GLOBAL OPTIMIZATION; PACKING PROBLEMS; NETWORKS; CIRCLES; SET;
D O I：
10.1080/00207160.2013.865726
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The problem of covering a convex 3D polytope by the minimal number of congruent spheres is reduced to a sequence of problems of minimising sphere radius when fixing the number of the spheres. We form a mathematical model of the problem using the Voronoi polytopes. Characteristics of the model are investigated. Extrema are attained at the vertices of the Voronoi polytopes constructed for sphere centres. To search for local minima, a modification of the Zoutendijk feasible directions method in a combination with random search is developed. Some numerical results for a cube and a non-regular octahedron are obtained.
引用
收藏
页码：2010 / 2020
页数：11
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