一种任意曲线曲率中心、半径及Frenet标架的图解算法

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

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.