On Riemann sums and integrals for association operations in ISO Geometrical Product Specifications standards

Abstract Recent ISO Geometrical Product Specifications (GPS) standards have introduced multiple ways to define geometrical deviations in design and manufacturing. These definitions depend on an association operation, which fits an ideal-form surface to a nonideal-form feature. This paper describes new mathematical and computational challenges that stem from these recent developments and provides a unification of different points of view using classical definitions of Riemann sums and integration. It also provides important practical means to define association operations for verification using digital technologies.