基于双域双向水平倾角最小化圈绕的凸壳新算法

本文依据同构化凸壳构造基本定理,提出效率更高的双域双向水平倾角最小化圈绕凸壳新算法.本新算法的同构化特点是:1)"初始顶点与双域生成"处理:找出给定二维点集S的最低点和最高点,即Y轴坐标值最小点(若有多个最小点,则只取最左的最小点)和Y轴坐标值最大点(若有多个最大点,则只取最左的最大点),作为凸壳(逆时针围绕的)A向初始顶点、(顺时针圈绕的)B向初始顶点;并以这两个初始顶点为端点的线段,把原二维点集划分为两个独立的子点集S右、S左.2)在S右内,进行双向"圈绕寻找下一新顶点"即凸壳A向、B向最新顶点寻找处理:分别过自己的最近新顶点,作X轴正向射线,并A向或B向找出当前点集内对该顶点正向射线(为始边的)倾角最小的点;删除对已得各顶点所构成的子凸壳内点,当所剩当前点集非空时继续作"2)"逐边圈绕,直到为空.3)同理,在子点集S左内,进行双向"圈绕寻找下一新顶点"即凸壳A向、B向最新顶点寻找处理.

A New Algorithm for Finding Convex Hull Based on Coiling with a Minimum Lever Pitch in Double Domain and Double Direction

According to the isomorphic fundamental theorem of the convex hull construction,a more efficient new algorithm to find a convex hull based on coiling with a minimum lever pitch in double domain and double direction is advanced.This new algorithm isomorphism characteristic is:1)"The generation of initial vertex and double domain":find out the bottommost point and the highest point on the convex hull S as the initial vertex of the convex hull,which has the minimum or the maximum coordinate value of the Y axis among all the points in given 2D point set(if the bottommost point is not only one,the bottommost and leftmost or the highest rightmost point should be selected).The line which take the two initial vertexes as end points divide the 2D point set into two absolute point set Sright Sleft.2)In the 2D point set Sright do the process of seeking the newest apex with double direction:passing the last new regressive vertex,make the vertex''s half line paralleled by X axis along positive direction,and find out the current vertexes with a minimum pitch to its vertex''s regressive half line(as the initial line)to be the newest vertex in coiling;Delete the sub-convex hull''s inner points.And loop from"2)"to coil with double direction side by side continuingly while the reminded point set is not empty.3)in the 2D point set Sleft do the similar process.