The presented approach to discretization of functionally defined heterogeneous objects is oriented towards applications associated with numerical simulation procedures, for example, finite element analysis (FEA). Such applications impose specific constraints upon the resulting surface and volume meshes in terms of their topology and metric characteristics, exactness of the geometry approximation, and conformity with initial attributes. The function representation of the initial object is converted into the resulting cellular representation described by a simplicial complex. We consider in detail all phases of the discretization algorithm from initial surface polygonization to final tetrahedral mesh generation and its adaptation to special FEA needs. The initial object attributes are used at all steps both for controlling geometry and topology of the resulting object and for calculating new attributes for the resulting cellular representation.