Convex Hull+ Diện tích bao lồi

struct Point{
 long double x,y;
};
long double determind(ld x1,ld y1,ld x2, ld y2){
   long double res=(x1*y2)-(x2*y1);
   return res;
}

Point p0;

Point nextToTop(stack<Point> &S)
{
    Point p = S.top();
    S.pop();
    Point res = S.top();
    S.push(p);
    return res;
}


int swap(Point &p1, Point &p2)
{
    Point temp = p1;
    p1 = p2;
    p2 = temp;
}


int distSq(Point p1, Point p2)
{
    return (p1.x - p2.x)*(p1.x - p2.x) +
          (p1.y - p2.y)*(p1.y - p2.y);
}


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;
    return (val > 0)? 1: 2;
}


int compare(const void *vp1, const void *vp2)
{
   Point *p1 = (Point *)vp1;
   Point *p2 = (Point *)vp2;
   int o = orientation(p0, *p1, *p2);
   if (o == 0)
     return (distSq(p0, *p2) >= distSq(p0, *p1))? -1 : 1;

   return (o == 2)? -1: 1;
}

void convexHull(Point points[], long long n)
{
   int ymin = points[0].y, min = 0;
   for (int i = 1; i < n; i++)
   {
     int y = points[i].y;

     if ((y < ymin) || (ymin == y &&
         points[i].x < points[min].x))
        ymin = points[i].y, min = i;
   }

   swap(points[0], points[min]);


   p0 = points[0];
   qsort(&points[1], n-1, sizeof(Point), compare);


   int m = 1;
   for (int i=1; i<n; i++)
   {

       while (i < n-1 && orientation(p0, points[i],
                                    points[i+1]) == 0)
          i++;


       points[m] = points[i];
       m++;
   }


   if (m < 3) return;


   stack<Point> S;
   S.push(points[0]);
   S.push(points[1]);
   S.push(points[2]);

   for (int i = 3; i < m; i++)
   {

      while (orientation(nextToTop(S), S.top(), points[i]) != 2)
         S.pop();
      S.push(points[i]);
   }


   long double a,b;
   long long cnt=0;
   while (!S.empty())
   {
       Point p = S.top();
       a=p.x;b=p.y;

      luu1[cnt++]=make_pair(a,b);
       S.pop();
}

  long double res=0;
  luu1[cnt]=luu1[0];
  cnt++;
  for(int i=0;i<cnt;i++) res+=determind(luu1[i].first,luu1[i].second,luu1[i+1].first,luu1[i+1].second);

  res_ngoai=abs(res)/2;
}