A级贝塞尔曲线的交互式控制生成方法

摘要

在介绍A级贝塞尔曲线的定义和性质的基础上，探讨如何通过简单的交互式控制来生成平面和空间的A级贝塞尔曲线的理论基础和实现方法。通过解明A级贝塞尔曲线与对数螺线的关系，阐述用对数曲率/挠率图直观表示A级贝塞尔曲线曲率/挠率单调性的基本原因。最后总结上述工作并提出进一步的研究方向。%In this paper we first introduce the definition and properties of Class A Bézier curve,based on it,we then discuss the theoretical foundation and implementation method in regard to how to generate planar and spatial Class A Bézier curve by simple interactive control.Through unriddling the relationship of Class A Bézier curve and logarithmic spiral,we expound the basic reason of intuitively representing the curvature/torsion monotonicity of Class A Bézier curve with LCG/LTG.In end of the paper,we summarise above works and present further study direction.