Orthogonal Least Squares Estimation of Surface Parameters

The least squares fitting of geometric features to given points minimizes the squares sum of error-of-fit in predefined measures. By the geometric fitting, the error distances are defined with the orthogonal, or shortest, distances from the given points to the geometric feature to be fitted. For the geometric fitting of surfaces, robust algorithms are proposed which are based on the coordinate description of the corresponding point on the surface for the given point, where the connecting line of the two points is the shortest path from the given point to the surface. All necessary information for the iterative nonlinear least squares could be obtained from the derivatives of the coordinate transform equation and of the orthogonal contacting equations.