Consistent updates in dual representation systems

Abstract

Abstract Dual representation systems rely on a parametric model to create and to manipulate the boundary representation of a solid. Parametric and boundary representations remain consistent if they continue to model the same solid, after updates applied to the parametric model and/or to the boundary representation. We consider the problem of verifying the consistency between the boundary representation and the CSG representation that is a restricted case of parametric representation. We determine the necessary and sufficient conditions for consistency of the two representations, identify the required computational utilities, and describe two implemented and tested algorithms. Our algorithms rely on sign-invariant space decompositions and can be used to verify consistency of other representations, including parametric definitions such as feature attachments. They could also be used to verify consistency of boundary and parametric representations in different systems, or corresponding representations in integrated modeling environments.