Geodesic
Construction of a ${\mit \Phi}$-function for two convex polytopes
Y. Stoyan1 ; J. Terno2 ; M. Gil1 ; T. Romanova1 ; G. Scheithauer2
1 Institute for Problems in Machinery National Ukrainian Academy of Sciences 2/10 Pozharsky St. Kharkov, 61046, Ukraine
2 Institute for Numerical Mathematics Dresden University of Technology 01062 Dresden, Germany
Applicationes Mathematicae, Tome 29 (2002) no. 2, pp. 199-218.

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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.
DOI : 10.4064/am29-2-6
Keywords: analytical description mit phi functions convex polytopes investigated these mit phi functions mathematical modelling packing problems three dimensional space only translations polytopes considered approach consists stages first level surface mit phi function constructed secondly surface extended get mit phi function method constructing level surface described detail

Y. Stoyan 1 ; J. Terno 2 ; M. Gil 1 ; T. Romanova 1 ; G. Scheithauer 2

1 Institute for Problems in Machinery National Ukrainian Academy of Sciences 2/10 Pozharsky St. Kharkov, 61046, Ukraine
2 Institute for Numerical Mathematics Dresden University of Technology 01062 Dresden, Germany 
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Y. Stoyan; J. Terno; M. Gil; T. Romanova; G. Scheithauer. Construction of a ${\mit \Phi}$-function
  for two convex polytopes. Applicationes Mathematicae, Tome 29 (2002) no. 2, pp. 199-218. doi : 10.4064/am29-2-6. http://geodesic.mathdoc.fr/articles/10.4064/am29-2-6/

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