基于多结点样条的自由曲线最小误差逼近及其应用

多结点样条函数具有良好的局部性，而最小二乘法对数据拟合的全局性较好， 因此多结点样条函数最小二乘逼近的稳定性及数值精度都能得到有效的保证。该文综合两者的特点，实现了自由曲线离散数据最小逼近误差数学模型的建立。同时应用此数学模型于一些平面及空间（甚至一些带噪音的）自由曲线拟合上和几何造型骨骼化上，测试其对各种自由曲线的拟合效果，结果证明最小逼近效果明显。

Least Error Approximation and Its Application for Free-FormCurves Based on Multi-Knots Spline

Muti-knots spline has good locality and least square method has good global characteristics for data fitting. Therefore, the stability and numerical accuracy of least square method based on multi-knots spline approximation could be reached effectively. This paper combines the advantages of them and completes the model building of the free-form curves with least approximation error based on multi-knots spline. Meanwhile, this method is applied to the free-form-curve fitting of some plane and space (even with noise) data and Geometry Shape Skelectonization. The fitting results show that the least approximation effect is good.