基于几何方法的曲率单调Bézier曲线的一个充分必要准则

A Sufficient and Necessary Criterion for Curvature Monotone Bézier Curves

摘要: 曲率在曲线光顺性方面起着重要作用,针对Bézier曲线的光顺问题,给出并证明了一类具有曲率单调变化的任意次数Bézier曲线.首先基于一种有效的几何设计准则,通过缩放和旋转Bézier曲线的前一条控制边得到邻接的后一条控制边;然后依次得到所有控制边及Bézier曲线控制多边形.实验在Windows系统下采用C++语言实现,通过实例验证了该方法的有效性并给出这类曲线的几何特性.

Abstract: In this paper,we present and prove a sufficient and necessary condition for the monotone curvature of a class of Bézier curves.The point is to repeatedly scale and rotate the previous control edge of Bézier curves to obtain the latter control edge.Several examples are given to show the application of the proposed method.