// vect.cpp -- methods for the Vector class
#include <cmath>
#include "vect.h"   // includes <iostream>
using std::sqrt;
using std::sin;
using std::cos;
using std::atan;
using std::atan2;
using std::cout;

namespace VECTOR
{
    // compute degrees in one radian
    const double Rad_to_deg = 45.0 / atan(1.0);
    // should be about 57.2957795130823

    // private methods
    // calculates magnitude from x and y
    void Vector::set_mag()
    {
        mag = sqrt(x * x + y * y);
    }

    void Vector::set_ang()
    {
        if (x == 0.0 && y == 0.0)
            ang = 0.0;
        else
            ang = atan2(y, x);
    }

    // set x from polar coordinate
    void Vector::set_x()
    {
        x = mag * cos(ang);
    }

    // set y from polar coordinate
    void Vector::set_y()
    {
        y = mag * sin(ang);
    }

    // public methods
    Vector::Vector()             // default constructor
    {
        x = y = mag = ang = 0.0;
        mode = RECT;
    }

    // construct vector from rectangular coordinates if form is r
    // (the default) or else from polar coordinates if form is p
    Vector::Vector(double n1, double n2, Mode form)
    {
        mode = form;
        if (form == RECT)
         {
             x = n1;
             y = n2;
             set_mag();
             set_ang();
        }
        else if (form == POL)
        {
             mag = n1;
             ang = n2 / Rad_to_deg;
             set_x();
             set_y();
        }
        else
        {
             cout << "Incorrect 3rd argument to Vector() -- ";
             cout << "vector set to 0\n";
             x = y = mag = ang = 0.0;
             mode = RECT;
        }
    }

    // reset vector from rectangular coordinates if form is
    // RECT (the default) or else from polar coordinates if
    // form is POL
    void Vector:: reset(double n1, double n2, Mode form)
    {
        mode = form;
        if (form == RECT)
         {
             x = n1;
             y = n2;
             set_mag();
             set_ang();
        }
        else if (form == POL)
        {
             mag = n1;
             ang = n2 / Rad_to_deg;
             set_x();
             set_y();
        }
        else
        {
             cout << "Incorrect 3rd argument to Vector() -- ";
             cout << "vector set to 0\n";
             x = y = mag = ang = 0.0;
             mode = RECT;
        }
    }

    Vector::~Vector()    // destructor
    {
    }

    void Vector::polar_mode()    // set to polar mode
    {
        mode = POL;
    }

    void Vector::rect_mode()     // set to rectangular mode
    {
        mode = RECT;
    }

    // operator overloading
    // add two Vectors
    Vector Vector::operator+(const Vector & b) const
    {
        return Vector(x + b.x, y + b.y);
    }

    // subtract Vector b from a
    Vector Vector::operator-(const Vector & b) const
    {
        return Vector(x - b.x, y - b.y);
    }

    // reverse sign of Vector
    Vector Vector::operator-() const
    {
        return Vector(-x, -y);
    }

    // multiply vector by n
    Vector Vector::operator*(double n) const
    {
        return Vector(n * x, n * y);
    }

    // friend methods
    // multiply n by Vector a
    Vector operator*(double n, const Vector & a)
    {
        return a * n;
    }

    // display rectangular coordinates if mode is RECT,
    // else display polar coordinates if mode is POL
    std::ostream & operator<<(std::ostream & os, const Vector & v)
    {
        if (v.mode == Vector::RECT)
             os << "(x,y) = (" << v.x << ", " << v.y << ")";
        else if (v.mode == Vector::POL)
        {
             os << "(m,a) = (" << v.mag << ", "
                 << v.ang * Rad_to_deg << ")";
        }
        else
             os << "Vector object mode is invalid";
        return os; 
    }

}  // end namespace VECTOR