利用点列折线的保凸插值  

Convexity-Preserving Interpolation Using the Polygonal Line of Data Points

作　　者：章仁江[1] 阚敦芝 

机构地区：[1]浙江工商大学数学系,杭州310018

出　　处：《计算机辅助设计与图形学学报》2015年第7期1167-1171,共5页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(61170100);浙江工商大学研究生基金(3100XJ1514064)

摘　　要：为了克服现有保凸插值方法的弊端,提出一种基于点列内在属性的保凸插值方法.该方法引入广义点列凸性的概念,对于给定平面上的广义凸(凹)点列,根据点列所连成折线的运动方向在每两点间直接插入Bézier曲线的控制顶点;控制顶点由其凸性与所给点列凸性一致,以及相邻Bézier曲线光滑连接两条件获得;每段Bézier曲线的控制顶点由4个邻近的顶点确定,故曲线形状局部可调.实例结果表明,文中方法是有效的,也佐证了理论推导的正确性.In order to overcome the drawbacks of the existing methods, a convexity-preserving interpolation method based on the intrinsic properties of a set of convex data points is proposed. The method introduces the concept of the generalized convexity of data points. For a set of generalized convex data points, directly insert the control points of Bezier segment into every two data points according to the direction of the polyline produced by the data points; The control points are obtained by the condition of its convexity being the same as that of the data points, and by assuming the smooth connecting between two adjacent B6zier segments; The control points of every Bezier segment are only determined by 4 adjacent data points, thus the curve is local shape adjustable. Some examples show that the method is very efficient, and the theory derivation is also right.

关 键 词：保凸插值 几何连续 BÉZIER曲线 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]