Abstract
In previous paper, geometric models including cell complex chains (object models), and abstract cell complex chains (formal data models) were proposed as a base for unification of different models in CAE databases. In this paper, their basic operations are defined theoretically. The basic operations of the geometric models are organized by dividing into operations on figures (subsets in an Euclidean space), on cell complexes, on cell complex chains, and mappings between them. The basic operations of abstract cell complex chains are defined by formalizing the restricted operations of cell complex chains. The relationship between these mathematical models (geometric models and formal data models), physical entities and internal models in CAE systems are discussed, and an implementation method of systems based on these mathematical models is described.
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