Convex Hull | set 1

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 Jia

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);              } } 

　　

Convex Hull | set 1