等距曲面的NURBS放样插值方法

Creating Offset Surface by the Method of NURBS Lofted Interpolation

本文给出了等距曲面的一种 NU RBS放样插值生成方法 .该方法主要是在原始 NU RBS曲面上取得一个能较好反映曲面特征的型值点阵 ,再将这个型值点阵按某种算法沿法矢方向外推 ,从而得到原始曲面的等距曲面上的型值点阵 .然后 ,再用 NU RBS放样插值曲面来逼近等距曲面 .本文给出的算法几何意义明显、易于编程实现 ,且得到的等距曲面其 u向和 v向参数曲线仍是 NURBS曲线 ,且具有 C2 连续性 .最后 ,给出了一个实例 .

In this paper, a method to create offset surface by using NURBS lofted interpolation surface is introduced. The idea of the method is to get a position points array which can reflects the properities of the origin surface, the position points array will be offsetted at the normal vector direction by using an algorithm. Then the position points array on the original surface's offset surface is gotten. The offset surface will be approximated by the NURBS lofted interpolation surface. The algorithm has obvious geometric meaning and is easily to be realized by programming. The u,v parametric curves of the offset surface are still NURBS curves, and have C 2 continutity. At last, a practical example is given.