Solving CSG equations for checking equivalency between two different geometric models

Abstract

For two given parametric constructive solid geometry (CSG) models, the problem of determining their parameter domains in which the two models are equivalent is addressed. Here, two CSG models are equivalent if they represent the exact same region in R 3, although their constituent features and feature attributes may differ. In this paper, an approach for solving the problem in a limited scope is proposed, in which a CSG model is polyhedral, its parametric form is explicit and its feature orientations are fixed. The solution includes the equivalent parameter domain for each model and parameter mapping that associates these two models on their equivalent parameter domains. One application of this research is to identify the equivalent parameter domains of two parametric part models, respectively, in the design option space and in the capability envelope set of a parametric machining process in order to facilitate the interoperation between part design and process planning through the generated parameter mapping between these two different kinds of models.