ConvexHull.h

// Most of this code is by Amritya Yagni, as posted at
// https://www.geeksforgeeks.org/quickhull-algorithm-convex-hull/
// This code just lacks the driver.

#include <cmath>
#include <set>
#include <utility>
#include <iostream>
using namespace std;
#define iPair pair<float, float>
  
// Stores the result (points of convex hull)
set<iPair> hull;
  
  
// Returns the side of point p with respect to line
// joining points p1 and p2.
int findSide(iPair p1, iPair p2, iPair p)
{
    float val = (p.second - p1.second) * (p2.first - p1.first) -
              (p2.second - p1.second) * (p.first - p1.first);
  
    if (val > 0)
        return 1;
    if (val < 0)
        return -1;
    return 0;
}
  
// returns a value proportional to the distance
// between the point p and the line joining the
// points p1 and p2
float lineDist(iPair p1, iPair p2, iPair p)
{
    return abs ((p.second - p1.second) * (p2.first - p1.first) -
               (p2.second - p1.second) * (p.first - p1.first));
}
  
// End points of line L are p1 and p2.  side can have value
// 1 or -1 specifying each of the parts made by the line L
void quickHull(iPair a[], int n, iPair p1, iPair p2, int side)
{
    int ind = -1;
    float max_dist = 0;
  
    // finding the point with maximum distance
    // from L and also on the specified side of L.
    for (int i=0; i<n; i++)
    {
        float temp = lineDist(p1, p2, a[i]);
        if (findSide(p1, p2, a[i]) == side && temp > max_dist)
        {
            ind = i;
            max_dist = temp;
        }
    }
  
    // If no point is found, add the end points
    // of L to the convex hull.
    if (ind == -1)
    {
        hull.insert(p1);
        hull.insert(p2);
        return;
    }
  
    // Recur for the two parts divided by a[ind]
    quickHull(a, n, a[ind], p1, -findSide(a[ind], p1, p2));
    quickHull(a, n, a[ind], p2, -findSide(a[ind], p2, p1));
}
  
set<iPair> printHull(iPair a[], int n)
{   
    set<iPair> res;
    // a[i].second -> y-coordinate of the ith point
    if (n < 3)
    {
        cout << "Convex hull not possible\n";
        return res;
    }
  
    // Finding the point with minimum and
    // maximum x-coordinate
    int min_x = 0, max_x = 0;
    for (int i=1; i<n; i++)
    {
        if (a[i].first < a[min_x].first)
            min_x = i;
        if (a[i].first > a[max_x].first)
            max_x = i;
    }
  
    // Recursively find convex hull points on
    // one side of line joining a[min_x] and
    // a[max_x]
    quickHull(a, n, a[min_x], a[max_x], 1);
  
    // Recursively find convex hull points on
    // other side of line joining a[min_x] and
    // a[max_x]
    quickHull(a, n, a[min_x], a[max_x], -1);
  
    // cout << "The points in Convex Hull are:\n";
    while (!hull.empty())
    {
        res.insert(*(hull.begin()));
        // cout << "(" <<( *hull.begin()).first << ", "
        //      << (*hull.begin()).second << ") ";
        hull.erase(hull.begin());
    }
    return res;
}