An improved orthogonal distance fitting algorithm for B-spline curves and surfaces

An improved orthogonal distance fitting (ODF) algorithm is presented for B-spline curves and surfaces. Considering the necessity of foot-point calculation of this algorithm and the influence of moving control points on the point projection algorithm, we use the Taylor expansion to predict a correct adjustment for the initial values of point projection algorithm, which accelerates the foot-point calculation and results in an improvement of stability and efficiency of the fitting algorithm. By the numerical tests, we can find that our algorithm is more robust than that without initial value correction and performs better than both Gauss-Newton-based variable projection(VP) method and limited memory BFGS (L-BFGS) method with less time consumption and fewer convergence steps.