#ifndef _Vector_h
#define _Vector_h

#include <math.h>
#include <iostream>

using namespace std;

class Vector
{
    friend istream & operator >> (istream & is, Vector & v)
        {
            is >> v._x >> v._y >> v._phi;
            return is;
        }

    friend ostream & operator << (ostream & os, const Vector & v)
        {
            os << v._x << " " << v._y << " " << v._phi;
            return os;
        }

    friend Vector operator + (const Vector & v1, const Vector & v2)
        {
            Vector res(v1);
            res+=v2;
            return res;
        }

    friend Vector operator - (const Vector & v1, const Vector & v2)
        {
            Vector res(v1);
            res-=v2;
            return res;
        }

    friend Vector operator * (double c, const Vector & p)
        {
            Vector res=p;
            res*=c;
            return res;
        }

    friend Vector operator * (const Vector & p, double c)
        {
            return c*p;
        }

    friend double norm2d(const Vector & v)
        {
            return sqrt(v._x*v._x+v._y*v._y);
        }

    friend double scalprod2d(const Vector & v1, const Vector & v2)
        {
            return v1._x*v2._x + v1._y*v2._y;
        }

    friend double vecprod2d(const Vector & v1, const Vector & v2)
        {
            return v1._x*v2._y-v1._y*v2._x;
        }

public:

    explicit Vector(double x=0,double y=0,double phi=0): _x(x), _y(y), _phi(phi){};

    double & x() {return _x;}
    double x() const {return _x;}
    double & y() {return _y;}
    double y() const {return _y;}
    double & phi() {return _phi;}
    double phi() const {return _phi;}

    const Vector & operator += (const Vector & p)
        {
            _x+=p._x; _y+=p._y; _phi+=p._phi;
            return *this;
        }
    const Vector & operator -= (const Vector & p)
        {
            _x-=p._x; _y-=p._y; _phi-=p._phi;
            return *this;
        }

    const Vector & operator *= (double c)
        {
            _x*=c; _y*=c; _phi*=c;
            return *this;
        }

private:
    double _x,_y,_phi;
};

const Vector null(0,0,0);
#endif