  Heterogeneous object modelling is an emerging area where geometric shapes are
considered in concert with their internal physically-based attributes. This
paper describes a novel theoretical and practical framework for modelling
volumetric heterogeneous objects on the basis of a novel unifying
functionally-based hybrid representation called HFRep. This new representation
allows for obtaining a continuous smooth distance field in Euclidean space and
preserves the advantages of the conventional representations based on scalar
fields of different kinds without their drawbacks. We systematically describe
the mathematical and algorithmic basics of HFRep. The steps of the basic
algorithm are presented in detail for both geometry and attributes. To solve
some problematic issues, we have suggested several practical solutions,
including a new algorithm for solving the eikonal equation on hierarchical
grids. Finally, we show the practicality of the approach by modelling several
representative heterogeneous objects, including those of a time-variant nature.
