基于曲率单调变化的空间非均匀三次B样条曲线的构造方法

A Method of Designing Non-Uniform Cubic B-Spline Curve Based on Monotone Curvature

摘要: B样条曲线在目前CAD系统中得到广泛应用,针对B样条曲线的光顺问题,给出并证明了具有曲率单调变化的非均匀三次B样条曲线的构造方法.首先通过给定非均匀三次B样条曲线的中间控制边矢量及相关初始条件,然后计算初始和结尾控制边矢量,由此得到的非均匀三次B样条曲线具有单调变化的曲率.实验在Windows系统下基于VC++语言实现,相关实例验证了该构造方法的有效性及实用性.

Abstract: In this paper,we present and prove a method of designing non-uniform cubic B-spline curve with monotone curvature.For the new method,the first and final control edge are got by giving the intermediate control vector of the non-uniform cubic B-spline curve and the related initial conditions,the obtained non-uniform cubic B-spline curve has monotonically varying curvature.