Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

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

Published

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.
Citation
ASME Journal of Computing and Information Science in Engineering

Keywords

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

Citation

Shakarji, C. and Srinivasan, V. (2019), On Algorithms and Heuristics for Constrained Least-Squares Fitting of Circles and Spheres to Support Standards, ASME Journal of Computing and Information Science in Engineering (Accessed May 14, 2021)
Created September 1, 2019, Updated October 2, 2019