带形状参数的R-Coons曲面

为了解决传统 Coons 曲面不具备形状可调性，不能精确表示椭球面、椭圆锥面、 椭圆柱面等二次曲面的问题，在有理函数空间上构造了一组有理混合基函数，称之为 R-Hermite 基。首先分析了 R-Hermite 基的性质；其次基于 R-Hermite 基，利用张量积方法，构造了一种 新的带两个形状参数的有理 Coons 曲面，并称之为 R-Coons 曲面，R-Coons 曲面不仅具有传统 Coons 曲面的良好性质，还具备形状可调性；最后给出了曲面精确表示椭球面、椭圆锥面、椭 圆柱面的方法，并通过实例说明方法的有效性。

R-Coons Surface with Shape Parameters

 In order to solve the lack of shape adjustability of the traditional Coons surface and the inability to accurately represent ellipsoid, elliptical cone, and elliptical cylinder etc., a set of rational hybrid basis functions is constructed in rational space, which is named R-Hermite basis. Firstly, the properties of R-Hermite basis are illustrated. Secondly, based on the R-Hermite basis, a rational Coons surface with two shape parameters is constructed by using the tensor product method, and it is called R-Coons surface, which not only has the good properties of traditional Coons surface, but also has shape adjustability. Finally, the method that can accurately represent ellipsoid, elliptical cone and elliptical cylinder is given, and some examples are illustrated to prove the effectiveness of the method.