文献类型：期刊文献

中文题名：一种任意曲线曲率中心、半径及Frenet标架的图解算法

英文题名：A Graphical Algorithm for Computing the Center,Radius of Curvature and Frenet Frame on Any Curves

作者：郑鹏飞[1,2];刘青[2];赵菊娣[1];林大钧[1];安琦[1]

机构：[1]华东理工大学机械与动力工程学院,上海200237;[2]义乌工商职业技术学院,浙江义乌322000

年份：2016

卷号：42

期号：4

起止页码：593

中文期刊名：东华大学学报（自然科学版）

外文期刊名：Journal of Donghua University(Natural Science)

收录：CSTPCD;;北大核心:【北大核心2014】；CSCD:【CSCD2015_2016】；

基金：浙江省教育厅科研资助项目(Y201432394)

语种：中文

中文关键词：曲率中心;曲率半径;Frenet标架;图解

外文关键词：curvature center ; curvature radius; Frenet frame; graphics

摘要：通过分析现有曲线曲率中心、曲率半径的求解方法,与微分几何中Frenet标架的定义及求解方法,提出了一种基于离散点分段构建平面曲线逼近空间任意曲线的方法,并以此建立以两中垂面与密切平面求交的方式求解曲线曲率中心和Frenet标架的图解及解析模型.所给出的求解任意曲线曲率中心、曲率半径及Frenet标架的图解算法简便可行,试验证明,该算法稳定可靠,适应性广.
A method of approximating space curve based on planar curves constructed by discrete points is proposed through analyzing the existing methods of computing the curvature center and curvature radius of curves and the definition and solving method of Frenet frame in differential geometry. A graphical model and mathematical model for computing the curvature center of the curve and Frenet frame are constructed by computing the intersection of two vertical planes and osculating plane. The graphical computing algorithm for computing the curvature center of curves and Frenet frame presented is simple and feasible. It is proved that this algorithm is stable and reliable, and the adaptability of this algorithm is extensive.