Hybrid Function Representation for Heterogeneous Objects

TL;DR

This paper introduces HFRep, a new hybrid function-based representation for modeling volumetric heterogeneous objects that combines the advantages of scalar fields with continuous smooth distance functions.

Contribution

It presents a novel theoretical framework and practical algorithms for modeling heterogeneous objects with internal attributes using HFRep, including solutions for eikonal equations on hierarchical grids.

Findings

Successfully models various heterogeneous objects including time-variant ones.

Provides a continuous smooth distance field for complex geometries.

Introduces practical algorithms for eikonal equation solving on hierarchical grids.

Abstract

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.