Techniques for Least-Squares Fitting of Curves and Surfaces to a Large Set of Points

Three techniques for dealing with adjustment problems characterized by a huge set of measurements, e.g., on the order of millions, and a relatively small number of parameters are described. The general least-squares method employs two main techniques: grouping the condition equations and sequential adjustments. To optimize the adjustment procedure, both main techniques have been enhanced by the addition of the direct calculation technique. The techniques are then specified for issues involving the least-squares fitting of curves and surfaces to large set of points. A numerical application of the main techniques was performed in the fitting of a triaxial ellipsoid to a large set of points. For both approaches, C programming language codes were created to carry out the fitting experiment. The numerical equivalence of the findings, as assessed in the ellipsoid fitting experiment, serves as one of the criteria for validating the methods.