The paper considers a class of phi-functions for three-dimensional (3D) oriented phi-objects formed by a finite union of basic objects. We introduce truncated cones and spherical caps to extend a class of 3D basic objects, including spheres, parallelepipeds, circular cones and cylinders, as well as their complements. We construct phi-functions for extended class of basic 3D-objects and show a unified approach to derive phi-functions for oriented сomposed phi-objects. The Stoyan phi-function technique is employed as a powerful tool for analytical description of containment and non-overlapping constraints within the field of Packing and Cutting.

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