基于平面曲线的旋转曲面主曲率半径图形处理  

The Graphic Treating on Principal Curvature Radius for Curved Surface of Revolution Based on Curvature Radius of Plane

作　　者：刘永骏[1] 林大钧[1] 

机构地区：[1]华东理工大学机械与动力工程学院,上海200237

出　　处：《东华大学学报（自然科学版）》2010年第4期397-401,共5页Journal of Donghua University(Natural Science)

摘　　要：曲面主曲率半径在许多工程问题中是一个非常重要的几何量,微分几何对此有专门的计算方法.以研究平面曲线曲率半径的方法对旋转曲面主曲率半径进行图形处理,避开建立曲面方程,求解曲面第一类、第二类基本量的常规运算方法,使问题既具有直观解,又具有定量解.该方法将主曲率半径的图解与数解相结合,简化了求解过程并使得问题具有可视化特点,可应用于一些涉及主曲率半径的实际工程问题.Principal curvature radius of the curved surface is a very important geometric value in a number of engineering problems, which have a special mathematic solution in differential geometry. The graphic processing of principal curvature radius for curved surface of revolution is studied based on treating principal curvature radius of plane curve, which avoid the establishment of curved surface equation and solving the two fundamental values of curved surface. This method integrates graphic solution with digital solution, which simplifies the solution process and makes the problem with visual characteristics. The graphic treating can be used in some practical engineering problems involving principal curvature radius.

关 键 词：旋转曲面 主曲率半径 微分几何 图形处理 

分 类 号：TB23[一般工业技术—工程设计测绘]