The Least Squares Surface Optimization Based on Orthogonal Function

It is always necessary to improve fitting order and increase surface control points with least squares method for surface fitting to meet the accuracy of surface reconstruction, however, with the increasing of control points, the surface smoothness and curvature continuity become worse. According to the inadequacy of the least squares method for surface fitting, the surface optimization algorithm based on orthogonal function is proposed in this paper, which can ensure both reconstruction accuracy and surface smoothness. 3x3 order surface and 36 control points are applied in surface fitting with the maximum error only 0.057mm in surface reconstruction, as well as the surface is G2 continuous. Experimental results show that the proposed optimization algorithm achieves the best matching of surface control points, surface curvature and reconstruction precision, and improves the quality of surface fitting.