Comparison Performance between Orthogonal Polynomial Functions and NURBS Algorithm to Rebuild Free-Form Surfaces

Abstract

In reverse engineering, rebuilding a surface more precisely requires more data to be handled. Such a large amount of data cannot be treated using a CAD/CAM system. This study applies orthogonal polynomial functions to rebuild a surface. Fewer data are used to rebuild a surface and the performance of smooth error is compared to that of the NURBS algorithm. The proposed numerical method efficiently derives the coefficients. It requires only specified data sets to calculate the coefficients of the orthogonal function. The desired data set is determined by Lagrange interpolation method and a least square method is presented to determine the exact coefficients from linear simultaneous equations. The results show that the approximation error obtained using orthogonal polynomial functions to rebuild a continuous free surface are lower than obtained when the NURBS method is used.