Minimum zone evaluation of the form errors of quadric surfaces

Quadric surfaces commonly exist in natural objects and artificial components. It is widely needed to evaluate the form quality of a measured data set, but the commonly used least squares method will lead to over-estimation and its results are not consistent with the definitions in ISO standards. In this paper a shape recognition approach is presented to determine the surface type and shape parameters from the general implicit quadratic function. Then a self-adaptive differential evolution algorithm is utilized to perform minimum zone evaluation for generic quadrics. The maximal orthogonal distance from the data points to the associated surface is taken as the target to be optimized. Finally experimental examples are presented to verify the developed algorithm.