Construction of a Φ-function for two convex polytopes

Abstract

The analytical description of Φ-functions for two convex polytopes is investigated. These Φ-functions can be used for mathematical modelling of packing problems in the three-dimensional space. Only translations of the polytopes are considered. The approach consists of two stages. First the 0-level surface of a Φ-function is constructed, and secondly, the surface is extended to get the Φ-function. The method for constructing the 0-level surface is described in detail.