Thread: How to write points in this algorithm

Hi all!

I have found Andrew's monotone convex hull algorithm implemented on the net:
Algorithm Implementation/Geometry/Convex hull/Monotone chain - Wikibooks, open books for an open world

This is perfect for me, but I have an irritating problem... I just can't figure out how to use the stuct Point. Here's the implementation:

Code:

// Implementation of Andrew's monotone chain 2D convex hull algorithm.
// Asymptotic complexity: O(n log n).
// Practical performance: 0.5-1.0 seconds for n=1000000 on a 1GHz machine.
#include <algorithm>
#include <vector>
using namespace std;
 
typedef int coord_t;         // coordinate type
typedef long long coord2_t;  // must be big enough to hold 2*max(|coordinate|)^2
 
struct Point {
        coord_t x, y;
 
        bool operator <(const Point &p) const {
                return x < p.x || (x == p.x && y < p.y);
        }
};
 
// 2D cross product of OA and OB vectors, i.e. z-component of their 3D cross product.
// Returns a positive value, if OAB makes a counter-clockwise turn,
// negative for clockwise turn, and zero if the points are collinear.
coord2_t cross(const Point &O, const Point &A, const Point &B)
{
        return (A.x - O.x) * (B.y - O.y) - (A.y - O.y) * (B.x - O.x);
}
 
// Returns a list of points on the convex hull in counter-clockwise order.
// Note: the last point in the returned list is the same as the first one.
vector<Point> convex_hull(vector<Point> P)
{
        int n = P.size(), k = 0;
        vector<Point> H(2*n);
 
        // Sort points lexicographically
        sort(P.begin(), P.end());
 
        // Build lower hull
        for (int i = 0; i < n; i++) {
                while (k >= 2 && cross(H[k-2], H[k-1], P[i]) <= 0) k--;
                H[k++] = P[i];
        }
 
        // Build upper hull
        for (int i = n-2, t = k+1; i >= 0; i--) {
                while (k >= t && cross(H[k-2], H[k-1], P[i]) <= 0) k--;
                H[k++] = P[i];
        }
 
        H.resize(k);
        return H;
}

If i for example want to use the method cross(), then what do I write? This seems the most logical: cross(1.1, 3.9, 11.0), but this is read as doubles.

I don't want to use the cross method of cause, just to understand how Points are written, so I can supply the convex_hull method with a vector containing these Points.

Best regards
Jannick