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// vect.h -- Vector class with <<, mode state
#ifndef VECTOR_H_
#define VECTOR_H_
#include <iostream>
namespace VECTOR
{
    class Vector
    {
    public:
        enum Mode {RECT, POL};
    // RECT for rectangular, POL for Polar modes
    private:
        double x; // horizontal value
        double y; // vertical value
        double mag; // length of vector
        double ang; // direction of vector in degrees
        Mode mode; // RECT or POL
        // private methods for setting values
        void set_mag();
        void set_ang();
        void set_x();
        void set_y();
    public:
        Vector();
        Vector(double n1, double n2, Mode form = RECT);
        void reset(double n1, double n2, Mode form = RECT);
        ~Vector();
        double xval() const {return x;} // report x value
        double yval() const {return y;} // report y value
        double magval() const {return mag;} // report magnitude
        double angval() const {return ang;} // report angle
        void polar_mode(); // set mode to POL
        void rect_mode(); // set mode to RECT
        // operator overloading
        Vector operator+(const Vector & b) const;
        Vector operator-(const Vector & b) const;
        Vector operator-() const;
        Vector operator*(double n) const;
        // friends
        friend Vector operator*(double n, const Vector & a);
        friend std::ostream &
        operator<<(std::ostream & os, const Vector & v);
    };
} // end namespace VECTOR
#endif

// 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