Boundary representation deformation in parametric solid modeling

One of the major unsolved problems in parametric solid modeling is a robust update (regeneration) of the solid's boundary representation, given a spec ified change in the solid's parameter values. The fundamental difficulty li es in determining the mapping between boundary representations for solids i n the same parametric family. Several heuristic approaches have been propos ed for dealing with this problem, but the formal properties of such mapping s are not well understood. We propose a formal definition for boundary repr esentation (BR-)deformation for solids in the-same parametric family, based on the assumption of continuity: small changes in solid parameter values s hould result in small changes in the solid's boundary representation, which may include local collapses of cells in the boundary representation. The n ecessary conditions that must be satisfied by any BR-deforming mappings bet ween boundary representations are powerful enough to identify invalid updat es in many (but not all) practical situations, and the algorithms to check them are simple. Our formulation provides a formal criterion for the recent ly proposed heuristic approaches to "persistent naming," and explains the d ifficulties in devising sufficient tests for BR-deformation encountered in practice. Finally, our methods are also applicable to more general cellular models of pointsets and should be useful in developing universal standards in parametric modeling.