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

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.