Summary: 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 [{\it Yu. G. Stoyan} et al., Appl. Math. 29, No. 2, 199--218 (2002;

Zbl 1053.90009)], 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.