C++ Program to implement Gift Wrapping Algorithm in Two Dimensions

We shall develop a C++ program to implement Gift Wrapping Algorithm in two dimensions. The Gift Wrapping Algorithm is an algorithm for computing the convex hull of a given set of points.

Algorithm

Begin
   function convexHull() to find convex hull of a set of n points:
   There must be at least three points.
   Initialize the result.
   Find the leftmost point.
   Starting from leftmost point, keep moving counterclockwise
   until reach the start point again.
   Print the result.
End

Example Code

#include <iostream>
using namespace std;
#define INF 10000
struct P {
   int x;
   int y;
};
int orient(P a, P b, P c) {
   int v = (b.y - a.y) * (c.x - b.x) - (b.x - a.x) * (c.y - b.y);
   if (v == 0)
      return 0; // colinear
      return (v >0) ? 1 : 2; // clock or counterclock wise
}
void convexHull(P points[], int m) {
   if (m < 3)//at least three points required
      return;
   int n[m];
   for (int i = 0; i < m; i++)
      n[i] = -1;
      int l = 0;//initialize result.
   for (int i = 1; i < m; i++)
      if (points[i].x < points[l].x)
         l = i; //find left most point
         int p = l, q;
   do {
      q = (p + 1) % m;
      for (int i = 0; i < m; i++)
         if (orient(points[p], points[i], points[q]) == 2)
            q = i;
            n[p] = q;
            p = q;
   } while (p != l);
   for (int i = 0; i < m; i++) {
      if (n[i] != -1)
         cout << "(" << points[i].x << ", " << points[i].y << ")\n";
   }
}
int main() {
   P points[] = {{0, 4}, {2, 1}, {2, 3}, {4, 1}, {3, 0}, {1, 1}, {7, 6}};
   cout << "The points in the convex hull are: ";
   int n = sizeof(points) / sizeof(points[0]);
   convexHull(points, n);
   return 0;
}

Output

The points in the convex hull are: (0, 4)
(4, 1)
(3, 0)
(1, 1)
(7, 6)