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.

Authors: L. Joskowicz, Y. Ostrovsky-Berman, Y. Myers
Year of publication: 2010
Journal: Precision Engineering, Volume 34, Issue 1, Pages 2-6

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