# Wydawnictwa / Czasopisma IMPAN / Applicationes Mathematicae / Wszystkie zeszyty

## Construction of a ${\mit \Phi}$-function for two convex polytopes

### Tom 29 / 2002

Applicationes Mathematicae 29 (2002), 199-218 MSC: 90B06, 90C11, 90C26. DOI: 10.4064/am29-2-6

#### Streszczenie

The analytical description of ${\mit \Phi }$-functions for two convex polytopes is investigated. These ${\mit \Phi }$-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 ${\mit \Phi }$-function is constructed, and secondly, the surface is extended to get the ${\mit \Phi }$-function. The method for constructing the 0-level surface is described in detail.

#### Autorzy

• Y. StoyanInstitute for Problems in Machinery
2/10 Pozharsky St.
Kharkov, 61046, Ukraine
e-mail
• J. TernoInstitute for Numerical Mathematics
Dresden University of Technology
01062 Dresden, Germany
• M. GilInstitute for Problems in Machinery
2/10 Pozharsky St.
Kharkov, 61046, Ukraine
• T. RomanovaInstitute for Problems in Machinery
2/10 Pozharsky St.
Kharkov, 61046, Ukraine
e-mail
• G. ScheithauerInstitute for Numerical Mathematics
Dresden University of Technology
01062 Dresden, Germany
e-mail

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