Computational metrology of the circle

Fitting a circle to a set of data points arranged in a circular pattern is a common problem in many fields of science and engineering. Specific applications in metrology include center position and circularity measurements. The fitting criteria usually depends on the application and varies with the statistical error model. Chebyshev fits, also known as minmax or least L-infinity fits, are of particular interest in metrology where they quantify the form error in addition to yielding an allegedly more objective position assessment. The paper offers further empirical evidence to support this conjecture. The Chebyshev circular fit problem can be solved using common computational geometry tools but the computational complexity of the algorithm is prohibitive for real-time applications. A substitute heuristic marching algorithm was developed and implemented. After a comprehensive state of the art review, the paper presents the marching algorithm and evaluates its convergence properties for full and partial circular data sets. A comparative study of convergence rate and accuracy is presented with respect to exhaustive computational geometry solutions and other fitting criteria.