Convex Hull using Jarvis’ Algorithm or Wrapping

// C# program to find convex hull of a set of points. Refer 
// https://www.geeksforgeeks.org/orientation-3-ordered-points/
// for explanation of orientation()
using System;
using System.Collections.Generic; 
    
public class Point
{
    public int x, y;
    public Point(int x, int y)
    {
        this.x = x;
        this.y = y;
    }
}

public class GFG 
{
    
    // To find orientation of ordered triplet (p, q, r).
    // The function returns following values
    // 0 --> p, q and r are collinear
    // 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
        List<Point> hull = new List<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, q, x) 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
        foreach (Point temp in hull)
            Console.WriteLine("(" + temp.x + ", " +
                                temp.y + ")");
    }
    
    /* Driver code */
    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);
        
    }
}

// This code is contributed by Princi Singh