Efficient representation and computation of geometric uncertainty: The linear parametric model

This paper describes the linear parametric geometric uncertainty model (LPGUM) for modeling part shape and position uncertainties. It describes the worst-case first-order approximations of the uncertainty zones of basic geometric entities. It is general and expressive, allows for parameter dependencies typical of tolerance specifications, and can be uniformly used to study a wide variety of basic geometric problems in tolerancing and metrology. We first present the LPGUM of a point and a line, and then describe the properties of their uncertainty zones and that of a mesh triangle in the plane and in space. We show that their geometric complexity is low-polynomial in the number of dependent parameters.