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
