A comprehensive framework for modeling heterogeneous objects

Abstract

Many real objects are heterogeneous. They are composed of diverse materials, which are present in varying proportions. Materials inside the solid do not have to be uniformly distributed. So, methods capable of accurately model not only the boundary of the solid, but also the distribution of material in every single point of its interior, are needed. In this paper we propose a new framework for modeling heterogeneous objects. The framework is comprehensive as it characterizes precisely heterogeneous objects, defines an adequate mathematical model that captures the essence of such objects, and a computational representation to represent the modeled objects in a computer. Our framework is based on Béziér hyperpatches and solves the main problems of this mathematical tool. We have implemented it completely in order to check whether it is possible to precisely model real objects.