Least Squares Fitting of Circles and Ellipses to Measured Data

Abstract

Fitting conic sections to data is an important problem with many applications. Often the data are obtained from a physical object using a coordinate measuring machine with a touch probe. The probe directions, relative to a particular frame of reference, are an important part of the problem, although conventional methods make no use of these. Here an approach is used for fitting circles and ellipses which takes account of the measurement design. Algorithms are developed, and some numerical results are given.