$\Phi $-functions for complex 2D-objects |
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Authors: | Yurij?Stoyan Email author" target="_blank">Guntram?ScheithauerEmail author Nikolay?Gil Tatiana?Romanova |
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Institution: | (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 |
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Abstract: | Within two-dimensional cutting and packing problems with irregular shaped objects, the concept of
-functions has been proven to be very helpful for several solution approaches. In order to construct such
-functions a previous work, in which so-called primary objects are considered, is continued. Now
-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 |
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Keywords: | Cutting and packing mathematical modelling optimization 2D placement problems |
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