B-spline流形的几何结构  

The Geometric Structure of the B-Spline Manifolds

作　　者：李春辉[1] 孙华飞[1] 张士诚[1,2] 

机构地区：[1]北京理工大学理学院,北京100081 [2]徐州师范大学数学科学学院,江苏徐州221116

出　　处：《北京理工大学学报》2011年第1期113-116,共4页Transactions of Beijing Institute of Technology

基　　金：国家自然科学基金资助项目(10871218)

摘　　要：给出了由B-spline方程构成的B-spline流形的几何结构.通过B-spline流形的定义,得到B-spline流形是±1平坦的,同时,还给出了B-spline流形的曲率张量和二维B-spline流形的高斯曲率.给出算例,验证文中二维B-spline流形的高斯曲率.In the present paper, the geometric structure of the B-spline manifolds, which consists of all the B-spline functions, is given. From the definition of the B-spline manifolds of all the B- spline functions, it can be seen that the B-spline manifolds are ±1-flat. Moreover, the curvature tensor and the Gaussian curvature for two dimensional B-spline manifolds are obtained. At last, an example illustrates the validity of the Gaussian curvature obtained in this paper.

关 键 词：B—spline流形 曲率张量 高斯曲率 

分 类 号：O186[理学—数学]