![Sample our Computer Science journals, sign in here to start your access, latest two full volumes FREE to you for 14 days]({"type":"image" , "src" : "/sda/5928/TOC-Subject-Sample-2021-Computer-Science.jpg"})
Abstract
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.
Acknowledgements
We would like to express our gratitude to Dr Csaba Mészáros for the special interior point solver BPMPD which we used for solving our problem. It provided very good results in runtime and solution quality. We also used a modified dual simplex method program written by our colleague Dr A.V. Pankratov and thank him for it as well as for consultations on its use.