Packing convex homothetic polytopes into a cuboid

• Date: 2018
• Main Authors: Stoyan, Yu. G., Chugay, A. M.
• Format: Article
• Language: English; Ukrainian
• Published: Інститут енергетичних машин і систем ім. А. М. Підгорного Національної академії наук України 2018
• Subjects: packing; homothetic polytopes; rotations; optimization; phi-functions; UDC 519.85
• Online Access: https://journals.uran.ua/jme/article/view/135431
• Journal Title: Journal of Mechanical Engineering

This paper deals with the optimization problem of packing a given set of homothetical arbitrarily oriented convex polytopes without their overlapping in a linear parallelepiped of minimal volume. Phi-functions are proposed to be used as a constructive means of the mathematical modeling of a given pr...