Sort points by angle from given axis?

Question

How can I sort an array of points/vectors by counter-clockwise increasing angle from a given axis vector?

For example:

Answer 1

If S is an array of PointF, and mid is the PointF in the centre:

S = S.OrderBy(s => -Math.Atan2((s.Y - mid.Y), (s.X - mid.X))).ToArray();

will sort the list in order of rotation around mid, starting at the point closest to (-inf,0) and go ccw (clockwise if you leave out the negative sign before Math).

Answer 2

#include <iostream>
#include <cmath>
#include <algorithm>

using namespace std;

struct Point {
    static double base_angle;
    static void set_base_angle(double angle){
        base_angle = angle;
    }
    double x;
    double y;
    Point(double x, double y):x(x),y(y){}
    double Angle(Point o = Point(0.0, 0.0)){
        double dx = x - o.x;
        double dy = y - o.y;
        double r = sqrt(dx * dx + dy * dy);
        double angle = atan2(dy , dx);
        angle -= base_angle;
        if(angle < 0) angle += M_PI * 2;
        return angle;
    }
};
double Point::base_angle = 0;

ostream& operator<<(ostream& os, Point& p){
    return os << "Point(" << p.x << "," << p.y << ")";
}

bool comp(Point a, Point b){
    return a.Angle() < b.Angle();
}

int main(){
    Point p[] = { Point(-4., -4.), Point(-6., 3.), Point(2., -4.), Point(1., 5.) };
    Point::set_base_angle(p[0].Angle());
    sort(p, p + 4, comp);
    Point::set_base_angle(0.0);
    for(int i = 0;i< 4;++i){
        cout << p[i] << " angle:" << p[i].Angle() << endl;
    }
}

DEMO

Point(-4,-4) angle:3.92699
Point(2,-4) angle:5.17604
Point(1,5) angle:1.3734
Point(-6,3) angle:2.67795