球面NURBS曲线

给出球面NURBS曲线生成算法：用球面上测地线－劣大圆弧代替直接段，将欧氏空间R^3中的deBoor递推算法推广到球面上构造曲线。讨论了这种曲线的若干性质，有类似地欧氏空间中的性质，指出其不具有类似于欧氏空间中的NURBS曲线的分裂性质，给出球面NURBS曲线的插入节点算法，以及球面上等距三次B样条的曲线的插值方法。作为对曲线生成算法和性质以及插值方法的应用，文末给出了一些图形实例。

Spherical NURBS Curves

An algorithm is given to construct the spherical NURBS curves which extend the de Boor recursive one in R 3 to that on the sphere by replacing the geodesic distances for the lines and their geometric properties which are analogous to those in Euclidean spaces are discussed, such as the differential property, the local property and so on. It is also pointed out that these curves are devoid of analogous split property possessed by NURBS curves in Euclidean spaces. At the same time, this paper also gives a knot insertion algorithm for the spherical NURBS curves and a method of the cubic uniform B spline interpolation, which is C 1 continuous at points of the curve connections. As an application of the algorithm and the properties, some graphical examples are given.