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• 计算机图形学 • 上一篇    下一篇

带形状参数的 R-Coons 曲面

  

  1. 1. 淮北师范大学信息学院，安徽 淮北 235000；
    2. 中南大学数学与统计学院，湖南 长沙 410083
  • 出版日期:2019-04-30 发布日期:2019-05-10
  • 基金资助:
    国家自然科学基金项目(11771453)；安徽省自然科学研究项目(KJ2017A849)

R-Coons Surface with Shape Parameters

  1. 1. College of Information, Huaibei Normal University, Huaibei Anhui 235000, China; 
    2. School of Mathematics and Statistics, Central South University, Changsha Hunan 410083, China
  • Online:2019-04-30 Published:2019-05-10

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摘要： 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。

关键词: R-Hermite 基, R-Coons 曲面, 形状参数, 椭圆锥面

Abstract:  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.

Key words: R-Hermite basis, R-Coons surface, shape parameter, elliptical cone