Convex Hull | Set 1

Posted 2021-01-10 lightwindy

Given a set of points in the plane. the convex hull of the set is the smallest convex polygon that contains all the points of it.

 

https://www.geeksforgeeks.org/convex-hull-set-1-jarviss-algorithm-or-wrapping/

Lin家

Java:

// Java program to find convex hull of a set of points. Refer  
// https://www.geeksforgeeks.org/orientation-3-ordered-points/ 
// for explanation of orientation() 
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); 
         
    } 
}