On Verification of Interoperability of CAD Systems with a Focus on Invariant Properties

Abstract

Interoperability is the ability of a system to correctly interpret and function with another system’s components and products. In this paper, we propose a theoretical framework for the verification of (geometric) interoperability that would allow distinct CAD systems to interact with each other through a query-based data acquisition and exchange. In this regard, we establish a correspondence based on a topological equivalence and a geometric similarity between model instances authored by distinct systems. We generate shape equivalence classes by constructing proxy models, namely a point cloud and a union of balls, that serve as reference models in the property comparisons of models. The proxy models can be considered as identifiers of CAD models in property spaces, and they provide estimates for the models’ properties with accuracies that depend on model-specific data which is implicitly related to systems’ attributes. We note that the proxy model constructions and the property computations are completely carried out through a query-based approach, which allows us to liberate the model instances from their system-dependent representations. We show that the systems would interoperate in carrying out the tasks that solely depend on the shape properties that are invariant with a pre-computable accuracy and the model instances that belong to the same shape property equivalence class can be used interchangeably within the context of these tasks. We further show that our methodology can be used as a supplementary technique in the validation of model transfers and/or representation conversions.