Form Error Evaluation: An Iterative Reweighted Least Squares Algorithm*

Abstract

This paper establishes the equivalence between the solution to a linear Chebyshev approximation problem and that of a weighted least squares (WLS) problem with the weighting parameters being appropriately defined. On this basis, we present an algorithm for form error evaluation of geometric features. The algorithm is implemented as an iterative procedure. At each iteration, a WLS problem is solved and the weighting parameters are updated. The proposed algorithm is of general-purpose, it can be used to evaluate the exact minimum zone error of various geometric features including flatness, circularity, sphericity, cylindericity and spatial straightness. Numerical examples are presented to show the effectiveness and efficiency of the algorithm.