保广义凸的曲线插值方法  

Interpolation Curves with Generalized Convexity-Preserving

作　　者：江伟 章仁江[1] Jiang Wei;Zhang Renjiang(School of Statistics and Mathematics,Zhejiang Gongshang University,Hangzhou 310018)

机构地区：[1]浙江工商大学统计与数学学院,杭州310018

出　　处：《计算机辅助设计与图形学学报》2018年第9期1686-1691,共6页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(61772025)

摘　　要：为了寻求简易有效的保凸曲线插值,提出一种用分段Bézier曲线拼接的方法,可以构造一条光滑的插值曲线.对于给定的平面有序点列,根据有序点列所连成的折线的运动方向,确定曲线在每个插值点处的切向量;进而利用点列广义凸的概念,在每2个相邻点之间按设计的算法直接插入2个三次Bézier曲线的控制顶点,该4点确定一条三次Bézier曲线;从而得到通过这组点列的分段光滑Bézier插值曲线,整条曲线G1连续.每段曲线的中间2个控制顶点由4个相邻的顶点确定.该方法适用于一般有序点列的插值,并具有保凸性,曲线局部形状可调,算法简单和计算量少的特点.最后通过实例说明了文中方法的有效性及正确性.In order to find a simple and effective convex curve interpolation, this paper proposes a method of using piecewise Bezier curve to construct a smooth interpolation curve. For a given set of point sequence, according to the direction of the polyline produced by the data points, we determine the vector of the curve at the every interpolating point. And then by using the concept of generalized convexity point sequence, we obtain the control points of the piecewise Bezier curves of degree three between every two points in view of the design algorithm. This four points determine a Bezier curves of degree three. Thus, we construct the piecewise smooth Bezier curves which pass through the data points. The middle two control points of each piece curve are determined by four adjacent points. The present method is available for an arbitrary set of point sequence, and enjoys the following advantages： Convexity-preserving; Local shape adjustable; Do not need to solve a system of equations; Simple algorithm and less computation. In the end, it shows that the method is very efficient through some examples.

关 键 词：曲线插值 保广义凸性 BEZIER曲线 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]