The problem with the code above is that the cartesian_vector class accesses private members of the point class. Since we have written both classes, we are happy to bend the rules, and so we make the cartesian_vector class a friend of the point class:

    class cartesian_vector; // forward decalartion 

    class point 
    { 
        double x; double y; 
    public: 
        point(double x, double y) : x(x), y(y){} 
        friend class cartesian_point; 
    };

Since the cartesian_vector class is declared after the point class, we have to provide a forward declaration that essentially tells the compiler that the name cartesian_vector is about to be used and it will be declared elsewhere. The important line starts with friend. This indicates that the code for the entire class, cartesian_vector, can have access to the private members (data and methods) of the point class.

You can also declare friend functions. For example, you could declare an operator such that a point object can be inserted into the cout object, so it can be printed to the console. You cannot change the ostream class, but you can define a global method:

    ostream& operator<<(ostream& stm, const point& pt) 
    { 
        stm << "(" << pt.x << "," << pt.y << ")"; 
        return stm; 
    }

This function accesses the private members of point so you have to make the function a friend of the point class with:

    friend ostream& operator<<(ostream&, const point&);

Such friend declarations have to be declared in the point class, but it is irrelevant whether it is put in the public or private section.