曲线、曲面光顺拟合的关键是寻找与型值点相应的最优参数,然后即可按最小二乘法通过建立最佳拟合方程来求出控制顶点.现有的各种参数选取法,由于没有体现最优参数的几何特征,从而使得最终的拟合精度偏低和计算的时间复杂性偏大.为了提高曲线、曲面拟合精度和计算速度,提出了一种型值点参数最优化的算法,该算法先利用点到曲线、曲面的正交投影,结合参数坐标邻域的搜索来提高计算速度,然后在曲线、曲面的迭代过程中不断修正参数,最终产生具有明显几何意义的型值点参数,以达到最佳拟合效果.与Hoschek,Carlos以及Piegl等算法的拟合结果比较表明,该算法迭代次数减少了10%～90%,计算时间复杂度降低了20%～70%,计算精确度提高了40%左右.

The key point in smooth and fairing fitting of curves and surfaces is to search the optimal parameters of data points, and then construct an optimal fitting equation according to the least square method and get control points based on the equation. As existing techniques for choosing parameters do not embody the geometric characteristic of the optimal parameters, the fitting is either imprecise or of great cost. In order to improve fitting precision and computing speed, we offers an algorithm on optimizing the parameters of data points. By using the orthogonal projection of data points to corresponding curve or surface, and making a search for the neighborhood of the parametric coordinate computation is speed up and the parameters can be ceaselessly corrected with the iterative process of the curves and the surfaces, so that the resulting parameters will possess distinct geometrical meaning, and the optimal fitting effect can be obtained, Comparing with the algorithms of Hoschek, Carlos and Picgl in some examples, it is validated that this method can cut down iteration times about 10% - 90% , reduce time consumption around 20% -70% , or improve precision nearly 40%.