NURBS曲面G1/G2光滑拼接方法
A Practical Method to Construct G1/G2 Continuous NURBS Patches
Abstract
非均匀有理B样条(NURBS)因其优越的性能而在几何造型中被广泛应用。单片NURBS曲面具有较好的参数与几何连续的性质,而在实际造型系统中,经常需要将不同的曲面片加以拼合。笔者利用G连续的充分条件及B样条基函数的导数性质,构造了具有q阶公共边界的NURBS曲面之间实现G1(切平面连续)与G2(高斯曲率连续)光滑拼接的实用算法。即根据一个已知的NURBS曲面片,通过调整边界附近的部分控制点及权因子,以达到光滑拼接的目的。 Non-Uniform Rational B-Splines (NURBS) provide a powerful tool in Geometric modeling and have been widely used. Although it is continuous in one single NURBS, in modeling system It is always needed to adjoin two different patches to gether. With the sufficient condition of geometric continuous and the properties of the derivative of the base function of B-Splines, this paper provides a practi cal method to make the adjacent NURBS patches G\ (tangent surface) and G2(Gauss curative) continuous. That is: For a given patch we modify the control points and the relative weights of another to make the two patches G1/G2 continuous.