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

Tom 29 / 2002

Y. Stoyan, J. Terno, M. Gil, T. Romanova, G. Scheithauer 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
    National Ukrainian Academy of Sciences
    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
    National Ukrainian Academy of Sciences
    2/10 Pozharsky St.
    Kharkov, 61046, Ukraine
  • T. RomanovaInstitute for Problems in Machinery
    National Ukrainian Academy of Sciences
    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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