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Optimality Conditions for Constrained Least-Squares Fitting of Circles, Cylinders, and Spheres to Establish Datums

Published

Author(s)

Craig M. Shakarji, Vijay Srinivasan

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.
Proceedings Title
Proceedings of the ASME 2017 International Design Engineering Technical Conferences & Computers
and
Information in Engineering Conference
Conference Dates
August 6-9, 2017
Conference Location
Cleveland, OH
Conference Title
The ASME 2017 International Design Engineering Technical Conferences & Computers and
Information in
Engineering Conference

Keywords

circle, constrained least-squares, coordinate metrology, cylinder, datum, dimensional metrology, fitting, geometric dimensioning and tolerancing, least-squares, optimization, sphere, standards

Citation

Shakarji, C. and Srinivasan, V. (2017), Optimality Conditions for Constrained Least-Squares Fitting of Circles, Cylinders, and Spheres to Establish Datums, Proceedings of the ASME 2017 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, Cleveland, OH, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=924369 (Accessed April 22, 2024)
Created August 9, 2017, Updated September 29, 2017