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$Phi $-functions for complex 2D-objects
Authors:Yurij?Stoyan,Guntram?Scheithauer  author-information"  >  author-information__contact u-icon-before"  >  mailto:scheit@math.tu-dresden.de"   title="  scheit@math.tu-dresden.de"   itemprop="  email"   data-track="  click"   data-track-action="  Email author"   data-track-label="  "  >Email author,Nikolay?Gil,Tatiana?Romanova
Affiliation:(1) Institute of Problems in Machinery, National Academy of Science, 310064 Kharkov, Ukraina;(2) Institute for Numerical Mathematics, Dresden University of Technology, 01069 Dresden, Germany
Abstract:Within two-dimensional cutting and packing problems with irregular shaped objects, the concept of $Phi $-functions has been proven to be very helpful for several solution approaches. In order to construct such $Phi $-functions a previous work, in which so-called primary objects are considered, is continued. Now $Phi $-functions are constructed for pairs of objects which can be represented as a finite combination (union, intersection, complement) of primary objects which allows the handling of arbitrary shaped objects by appropriate approximations of sufficient accuracy.Received: October 2002, Revised: October 2003, AMS classification: 65K05, 90C26, 90B06All correspondence to: Guntram Scheithauer
Keywords:Cutting and packing  mathematical modelling  optimization  2D placement problems
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