Selection of the number of control points for spline surface approximation

Parametric spline surfaces represent an important surface type in the process of reverse engineering. Various surface fitting techniques are available for fitting of splines to sets of data points, here we consider a least squares fitting technique. A user input to this algorithm is the number of control points to be used for the fitting in the two parametric directions. Using a larger number of points, gives a more accurate fitted surface but also results in a surface with a number of undulations or surface wiggles which may not be desired. This paper is concerned with the optimal selection of the number of control points to be used for the least squares surface fitting of B spline surface patches. An optimal method based on multicriteria optimization is presented do decide on the number of control points to be used in the fitting