平面点集凸包Graham算法的改进

本文提出了一种计算平面点集最小凸包的快速算法。该算法首先对平面点集进行扫描,查找到最左、最右、最上、最下4个方向上的极值点,以此构造出一个初始凸包,并删除初始凸包内部的所有点;然后把剩余点集分组,每组运用格雷厄姆(Graham)算法生成一个新的凸包;最后将所有子集凸包的顶点看作一个新的点集,再次运用Graham算法生成最终凸包。测试结果表明,改进后的算法可较大幅度地提高执行效率。

An improved Graham algorithm for determining the convex hull of planar points set

In this paper,an efficient algorithm for obtaining the minimum convex hull of planar point set was presented.By scanning the point set,the extreme points in four directions (the leftmost,the rightmost,the topmost and the bottommost) were found to construct the initial convex hull.Other points inside the initial convex hull were excluded during the following scanning.Then,the remaining points were divided into several groups and each group respectively generated its convex hull based on Graham Algorithm.At last,the final convex hull was acquired from the vertices of the generated sub-convex hulls by using Graham Algorithm.Test results showed that the presented algorithm could improve the implementing efficiency and have certain theoretical significance and practical value.