Hybrid function representation for heterogeneous objects

A. Tereshin, A. Pasko, O. Fryazinov, V. Adzhiev

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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.

Original languageEnglish
Article number101098
JournalGraphical Models
Publication statusPublished - Mar 2021


  • Distance fields
  • Eikonal solver
  • Function representation
  • Heterogeneous objects
  • Hybrid representation
  • Time-variant objects
  • Volumetric modelling


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