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

Published

October 10, 2018

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.

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

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 October 13, 2025)