zoukankan      html  css  js  c++  java
  • Convex hull

    we start from the leftmost point (or point with minimum x coordinate value) and we keep wrapping points in counterclockwise direction. The big question is, given a point p as current point, how to find the next point in output? The idea is to use orientation() here. Next point is selected as the point that beats all other points at counterclockwise orientation, i.e., next point is q if for any other point r, we have “orientation(p, r, q) = counterclockwise”. Following is the detailed algorithm.

    1) Initialize p as leftmost point.
    2) Do following while we don’t come back to the first (or leftmost) point.
    …..a) The next point q is the point such that the triplet (p, q, r) is counterclockwise for any other point r.
    …..b) next[p] = q (Store q as next of p in the output convex hull).
    …..c) p = q (Set p as q for next iteration).

    import java.util.*;
     
    class Point
    {
        int x, y;
        Point(int x, int y){
            this.x=x;
            this.y=y;
        }
    }
     
    class GFG {
         
        // To find orientation of ordered triplet (p, q, r).
        // The function returns following values
        // 0 --> p, q and r are colinear
        // 1 --> Clockwise
        // 2 --> Counterclockwise
        public static int orientation(Point p, Point q, Point r)
        {
            int val = (q.y - p.y) * (r.x - q.x) -
                      (q.x - p.x) * (r.y - q.y);
          
            if (val == 0) return 0;  // collinear
            return (val > 0)? 1: 2; // clock or counterclock wise
        }
         
        // Prints convex hull of a set of n points.
        public static void convexHull(Point points[], int n)
        {
            // There must be at least 3 points
            if (n < 3) return;
          
            // Initialize Result
            Vector<Point> hull = new Vector<Point>();
          
            // Find the leftmost point
            int l = 0;
            for (int i = 1; i < n; i++)
                if (points[i].x < points[l].x)
                    l = i;
          
            // Start from leftmost point, keep moving 
            // counterclockwise until reach the start point
            // again. This loop runs O(h) times where h is
            // number of points in result or output.
            int p = l, q;
            do
            {
                // Add current point to result
                hull.add(points[p]);
          
                // Search for a point 'q' such that 
                // orientation(p, x, q) is counterclockwise 
                // for all points 'x'. The idea is to keep 
                // track of last visited most counterclock-
                // wise point in q. If any point 'i' is more 
                // counterclock-wise than q, then update q.
                q = (p + 1) % n;
                 
                for (int i = 0; i < n; i++)
                {
                   // If i is more counterclockwise than 
                   // current q, then update q
                   if (orientation(points[p], points[i], points[q])
                                                       == 2)
                       q = i;
                }
          
                // Now q is the most counterclockwise with
                // respect to p. Set p as q for next iteration, 
                // so that q is added to result 'hull'
                p = q;
          
            } while (p != l);  // While we don't come to first 
                               // point
          
            // Print Result
            for (Point temp : hull)
                System.out.println("(" + temp.x + ", " +
                                    temp.y + ")");
        }
         
        /* Driver program to test above function */
        public static void main(String[] args) 
        {
     
            Point points[] = new Point[7];
            points[0]=new Point(0, 3);
            points[1]=new Point(2, 3);
            points[2]=new Point(1, 1);
            points[3]=new Point(2, 1);
            points[4]=new Point(3, 0);
            points[5]=new Point(0, 0);
            points[6]=new Point(3, 3);
             
            int n = points.length;
            convexHull(points, n);
            
        }
    }
    

      

  • 相关阅读:
    boost库在windows下的编译和使用
    【转】VMware设置共享文件夹之后Ubuntu中看不到怎么办?
    ffmpeg常用命令
    虚函数和纯虚函数的作用与区别
    PJSIP UA分析
    PJSIP在windows(xp或者win7)下的编译,编译工具是vs2008,PJSIP版本2.3
    live555源码研究(十)------在编译过程中遇到的问题及解决方法
    live555源码研究(五)------DynamicRTSPServer类
    live555源码研究(四)------UserAuthenticationDatabase类
    web响应式图片设计实现
  • 原文地址:https://www.cnblogs.com/apanda009/p/7965365.html
Copyright © 2011-2022 走看看