Research on Reconstruction of Complicated Curved Surface Based on Extended Approximating Method

To implement reconstruction of complicated curved surface, a mathematical model based on extended approximating method and its corresponding algorithms are given. In this model, the reconstructed curved surface satisfies all the scattered interpolation points. Coordinate information of points both in interior and external region is used to realize minimized least-square approximation errors. Changes between internal and external interpolation regions are continuous and reconstruction of curved surface is of higher precision, therefore the best fitting curved surface is obtained. The practical example approves that the proposed method has higher accuracy and makes surface shape contain properties of partial controllability, variation reduction, and convex hull.