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

Published

August 28, 2018

Author(s)

Craig M. Shakarji, Vijay Srinivasan

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.

Proceedings Title

Proceedings of the ASME 2018 International Design Engineering Technical Conferences and Computers and
Information in Engineering Conference

Conference Dates

August 26-29, 2018

Conference Location

Quebec, CA

Conference Title

ASME 2018 International Design Engineering Technical Conferences and Computers and Information in
Engineering Conference

Pub Type

Conferences

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Keywords

circle, circumscribed, constrained least squares, datum, inscribed, least squares, optimization, sphere

Citation

Shakarji, C. and Srinivasan, V. (2018), On Algorithms and Heuristics for Constrained Least-Squares Fitting of Circles and Spheres to Support Standards, Proceedings of the ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Quebec, CA, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=926634 (Accessed April 23, 2024)