一种修改NURBS曲线形状的新方法

曲线曲面的形状修改是计算机几何造型过程中的重要部分．文章提出了一种修改NURBS曲线的新方法，使得修改后的曲线在多个参数点处满足用户给定的几何约束(如点约束、切矢约束)，首先引入了一些新的概念如：局部曲线、总曲线、多余约束和多余曲线等．对于每个参数点分别计算出一系列满足该点处几何约束的局部曲线，并由此构造了总曲线．接着插值一条满足多余约束的多余曲线．最后运用构造Coons曲面的思想，计算出最终的修改曲线，它等于总曲线减去多余曲线．同时我们发现两种现存的修改NURBS曲线的方法是一样的．实例表明此方法适用于CAD软件系统。

New Method to Modify NURBS Curves

Shape modification of curves or surfaces is an important process in computer geometric modeling. This paper presents a new method to modify NURBS curves so that their shapes satisfy specified geometric constraints such as points and tangent vectors at more than one selected parametric points. The main idea of this method is given as follows: Firstly, some new conceptions are introduced, such as local curve, total curve, redundant constraints and redundant curve etc. For every parametric point, after computing a set of local curves that satisfy constraints at those parametric points respectively, one total curve consisting of those local curves is constructed. Subsequently, one redundant curve satisfying the redundant constraints is interpolated. Finally, applying the idea of constructing Coons surface, the modified curve that equals to the redundant curve subtracted from the total curve is obtained. Meanwhile, as a byproduct, authors find two existing methods are actually the same one. Examples show that the proposed approach is applicable for CAD systems.