Least squares fitting of parametric surfaces to measured data

Abstract

The problem is considered of fitting surfaces to measured data using the least squares norm, where it is assumed that a parameterization of the surface is available. Examples of practical applications include the product design and quality assurance of manufactured parts. There has been much recent algorithmic development based on conventional fitting ideas, mainly orthogonal distance regression. A different approach is taken here which explicitly takes account of the measurement process, and this is illustrated by some examples.