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research-article

On Algorithms and Heuristics for Constrained Least-Squares Fitting of Circles and Spheres to Support Standards

[+] Author and Article Information
Craig Shakarji

ASME Member, Physical Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, MD 20899, U.S.A.
craig.shakarji@nist.gov

Vijay Srinivasan

ASME Fellow, Engineering Laboratory, National Institute of Standards and Technology, Gaithersburg, MD 20899, U.S.A.
vijay.srinivasan@nist.gov

1Corresponding author.

ASME doi:10.1115/1.4043226 History: Received September 14, 2018; Revised March 05, 2019

Abstract

Constrained least-squares fitting has gained considerable popularity among national and international standards committees as the default method for establishing datums on manufactured parts. This has resulted in the emergence of several interesting and urgent problems in computational coordinate metrology. Among them is the problem of fitting inscribing and circumscribing circles (in two-dimensions) and spheres (in three-dimensions) using constrained least-squares criterion to a set of points that are usually described as a 'point-cloud.' This paper builds on earlier theoretical work, and provides practical algorithms and heuristics to compute such circles and spheres. Representative codes that implement these algorithms and heuristics are also given to encourage industrial use and rapid adoption of the emerging standards.

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