给定主曲率函数的旋转曲面设计  

Design of rotation surface with given principal curvature function

作　　者：张先波[1] 杨文颖[1] 宋来忠[1] 彭刚[2] 

机构地区：[1]三峡大学理学院,湖北宜昌443002 [2]三峡大学土木水电学院,湖北宜昌443002

出　　处：《计算机工程与设计》2009年第4期1030-1032,1035,共4页Computer Engineering and Design

基　　金：国家自然科学基金项目(50679039);湖北省教育厅自然科学重点科研基金项目(D200613009)

摘　　要：旋转曲面的设计在CAD/CAM及CAGD中有重要作用。由于给定主曲率函数的嵌入旋转曲面存在性已得到较好证明,故使得曲面的设计成为可能。给出了一种给定主曲率函数的嵌入旋转曲面的设计算法,该算法通过求解一个二阶微分方程,并适当选取初始条件,得到旋转曲面的位置矢量,从而做出了符合要求的旋转曲面。实例表明,该算法是可行的,且易于编程实现,为旋转曲面的工程设计与曲面造型提供了一个新方法。The design of rotation surfaces is an important subject in CAD/CAM and CAGD. Since the existence of embedded rotation surface with given principal curvature function is well proofed, the design and modeling of the surface becomes possible. An algorithm for design of embedded rotationsurfaces with given principal curvature function is presented. The position vector of the rotation surface is obtained by solving a second-order differential equation with proper initial condition, so we can get the rotation surface which satisfied the conditions. Some practical examples are given to indicate the algorithm is feasible and is carried out easily. A new method for engineering design and surface modeling of rotation surface is presented.

关 键 词：旋转曲面 主曲率 嵌入 位置矢量 工程设计 曲面造型 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]