Shakarji, C.
and Srinivasan, V.
(2018),
Optimality Conditions for Constrained Least Squares Fitting of Circles, Cylinders, and Spheres to Establish Datums, ASME Journal of Computing and Information Science in Engineering, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=926749
(Accessed April 20, 2024)
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Optimality Conditions for Constrained Least Squares Fitting of Circles, Cylinders, and Spheres to Establish Datums
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Abstract
This paper addresses the combinatorial characterizations of the optimality conditions for constrained least squares fitting of circles, cylinders, and spheres to a set of input points. It is shown that the necessary condition for optimization requires contacting at least two input points. It is also shown that there exist cases where the optimal condition is achieved while contacting only two input points. These problems arise in digital manufacturing, where one is confronted with the task of processing a (potentially large) number of points with three- dimensional coordinates to establish datums on manufactured parts. The optimality conditions reported in this paper provide the necessary conditions to verify if a candidate solution is feasible, and to design new algorithms to compute globally optimal solutions.Citation
ASME Journal of Computing and Information Science in Engineering
Pub Type
Journals
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Keywords
circle, constrained least-squares, coordinate metrology, curve fitting, cylinder, datum, dimensional metrology, fitting, geometric dimensioning and tolerancing, least-squares, optimization, sphere, standards, surface fitting
Citation
Created October 10, 2018, Updated October 2, 2019