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.

异构对象建模是一个新兴领域，在该领域中，几何形状被认为与其内部基于物理的属性相一致。本文介绍了一种新的理论和实践框架，该框架基于称为HFRep的基于功能的新型统一混合表示形式，对体积异构对象进行建模。该新表示允许在欧几里得空间中获得连续的平滑距离场，并保留了基于不同种类的标量场的常规表示的优点，而没有它们的缺点。我们系统地描述了HFRep的数学和算法基础。基本算法的步骤针对几何形状和属性进行了详细介绍。为了解决一些问题，我们提出了几种实用的解决方案，包括用于求解分层网格上的本征方程的新算法。最后，我们通过对几个代表性的异构对象（包括那些具有时变性质的对象）进行建模来展示该方法的实用性。