$\Phi$-functions for complex 2D-objects

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.