B样条曲面在严格约束状态下的光顺拟合

提出一种新的B样条曲面造型方法:光顺地拟合空间型值点且同时严格地通过其中部分点.运用Lagrange乘子的条件极值法并引入光顺加权项，求出位置偏离和形状弯曲的最小二乘解，可以得到被称为B样条光顺准拟合的良好造型曲面.这一方法在包含门窗的交通工具外壳曲面设计、机械产品装配联接件制造中具有明显的实用价值.

Smooth Fitting of B-Spline Surfaces with Strict Interpolation Conditions

In this paper, the authors present a new B-spline surface modelling method which fairly fits 3D data points while at the same time strictly interpolates some of them. By using Lagrange multiplier's conditional extreme method, introducing fairness weights and finding the least squares solutions of position deviation and shape curvature, some B-spline fair quasi-fitting modelling surfaces can be obtained. This method obviously has some practical applications in designing outer shell surfaces of transportation tools with windows and gates, or in manufacturing assembled/joined parts of mechanical productions.