Efficient representation and computation of geometric uncertainty: the linear parametric model
نویسندگان
چکیده
This paper describes the Linear Parametric Model of Geometric Uncertainty (LPMGU). The model, based on our previous work on shape and position uncertainties, 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 LPMGU 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.
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