Least squares fitting of parametric surfaces to measured data

Least-Squares Fitting of Data with B-Spline Surfaces

Least Squares Fitting of Data

This is the usual introduction to least squares fit by a line when the data represents measurements where the y–component is assumed to be functionally dependent on the x–component. Given a set of samples {(xi, yi)}i=1, determine A and B so that the line y = Ax + B best fits the samples in the sense that the sum of the squared errors between the yi and the line values Axi + B is minimized. Note...

Direct Least-Squares Fitting of Algebraic Surfaces

Least-Squares Fitting of Algebraic Spline Surfaces

We present an algorithm for fitting implicitly defined algebraic spline surfaces to given scattered data. By simultaneously approximating points and associated normal vectors, we obtain a method which is computationally simple, as the result is obtained by solving a system of linear equations. In addition, the result is geometrically invariant, as no artificial normalization is introduced. The ...

A Revisit to Least Squares Orthogonal Distance Fitting of Parametric Curves and Surfaces

Fitting of data points by parametric curves and surfaces is demanded in many scientific fields. In this paper we review and analyze existing least squares orthogonal distance fitting techniques in a general numerical optimization framework. Two new geometric variant methods (GTDM and CDM) are proposed. The geometric meanings of existing and modified optimization methods are also revealed.