Cellular-functional modeling of heterogeneous objects

Abstract

The paper presents an approach to modeling heterogeneous objects as multidimensional point sets with multiple attributes (hypervolumes). A theoretical framework is based on a hybrid model of hypervolumes combining a cellular representation and a constructive representation using real-valued functions. This model allows for independent but unifying representation of geometry and attributes, and makes it possible to represent dimensionally non-homogeneous entities and their cellular decompositions. Hypervolume model components such as objects, operations and relations are introduced and outlined. The framework's inherent multidimensionality allowing, in particular, to deal naturally with time dependence promises to model complex dynamic objects composed of different materials with constructive building of their geometry and attributes. Attributes given at each point can represent properties of arbitrary nature (material, photometric, physical, statistical, etc.). To demonstrate a particular application of the proposed framework, we present an example of multimaterial modeling -a multilayer geological structure with cavities and wells. Another example illustrating the treatment of attributes other than material distributions is concerned with time-dependent adaptive mesh generation where function representation is used to describe object geometry and density of elements in the cellular model of the mesh. The examples have been implemented by using a specialized modeling language and software tools being developed by the authors.

Modelling with implicit complexes

“…We have proposed the hybrid IC-based cellular-functional model of heterogeneous objects in [Adzhiev et al 2001]. For the description of an IC, it is necessary to specify its topology and its geometry.…”

“…To describe the non-geometric properties of a heterogeneous object, represented by an IC, we use the cellular-function model of the attributes introduced in [Adzhiev et al 2001]. In the hybrid model, the geometry and attributes are completely independent although they share the same modelling space.…”

“…Such objects can be heterogeneous from the point of view of their dimensionality and their internal structure. We have defined a hybrid model, called an Implicit Complex (IC) [Adzhiev et al 2001], based on the concepts of cellular spaces and CW-complexes. We have extended CW-complexes with the implicit description of cells and allowed more sophisticated relations, between the cells, to be defined.…”

Adaptive Meshing of 2D Heterogeneous Objects Using Material Quadtree

“…have been developed for manipulating heterogeneous objects [12], [21], [25], [27]. Numerous heterogeneous object representation schemes that can handle the geometry and material of a heterogeneous object have been introduced and some of them can be found in [1], [10], [12], [14][15], [25]. Using these schemes, the information of a heterogeneous object can be output for other downstream applications, such as FEA.…”