Necessary conditions for boundary representation variance
Srinivas Raghothama, Vadim Shapiro · 1997
One of the key unsolved problems in parametric solid modeling is a robust update (regeneration) of the solid's boundary representation, given a specified change in solid's parameter values.The fundamental difficulty lies in determining the mapping between boundary representations for solids in the same parametric family, also known as "persistent naming."We formulate the notion of Boundary Representation (BR-)variance for solids in the same parametric family based on the assumption of continuity: small changes in solid's parameter values should result in small changes in solid's boundary rep reeentation, which may include local collapses of cells in boundary representations.We show that our formulation gives the necessary conditions that must be satisfied by any BR-variant mappings between boundary representations.These conditions are powerful enough to identify invalid updates in many practical situations and provide a formal criteria for the recently proposed heuristic approaches to the "persistent naming" problem. Motivation Ambiguity of parametric solid modeling