一种改进的B样条曲线曲面正交距离拟合算法

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

提出了一种改进的B样条曲线曲面拟合的正交距离算法.在此类算法中,需要求解点投影问题以得到数据点的垂足,考虑到控制顶点对投影的影响,利用泰勒展式对投影算法的初值进行修正,加快了求解点投影问题的速度,从而提高了拟合算法的稳定性和效率.数值实验表明,改进算法比修正前的方法更加稳定,与变量投影法及LBFGS算法相比,达到最优解的计算时间更短,迭代步数更少.

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 effi- ciency of the fitting algorithm. By the numerical tests, we can find that our algorithm is more robust than that with out 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.