Working with Polar Coordinates

Problem

You want to represent and manipulate polar coordinates.

Solution

The complex template from the <complex> header provides functions for conversion to and from polar coordinates. Example 11-34 shows how you can use the complex template class to represent and manipulate polar coordinates.

Example 11-34. Using complex template class to represent polar coordinates

#include <complex>
#include <iostream>

using namespace std;

int main( )  {
  double rho = 3.0; // magnitude
  double theta = 3.141592 / 2; // angle
  complex<double> coord = polar(rho, theta);
  cout << "rho = " << abs(coord) << ", theta = " << arg(coord) << endl;
  coord += polar(4.0, 0.0);
  cout << "rho = " << abs(coord) << ", theta = " << arg(coord) << endl;
}

Example 11-34 produces the following output:

rho = 3, theta = 1.5708
rho = 5, theta = 0.643501

Discussion

There is a natural relationship between polar coordinates and complex numbers. Even though the two are somewhat interchangeable, it is generally not a good idea to use the same type to represent different concepts. Since using the complex template to represent polar coordinates is inelegant, I have provided a polar coordinate class that is more natural to use in Example 11-35.

Example 11-35. A polar coordinate class

#include <complex>
#include <iostream>

using namespace std;

template<class T>
struct BasicPolar
{
  public:
    typedef BasicPolar self;

    // constructors
    BasicPolar( ) : m( ) {  }
    BasicPolar(const self& x) : m(x.m) {  }
    BasicPolar(const T& rho, const T& theta) : m(polar(rho, theta)) { }

    // assignment operations
    self operator-( ) { return Polar(-m); }
    self& operator+=(const self& x) { m += x.m; return *this; }
    self& operator-=(const self& x) { m -= x.m; return *this; }
    self& operator*=(const self& x) { m *= x.m; return *this; }
    self& operator/=(const self& x) { m /= x.m; return *this; }
    operator complex<T>( ) const { return m; }

    // public member functions
    T rho( ) const { return abs(m); }
    T theta( ) const { return arg(m); }

    // binary operations
    friend self operator+(self x, const self& y) { return x += y; }
    friend self operator-(self x, const self& y) { return x -= y; }
    friend self operator*(self x, const self& y) { return x *= y; }
    friend self operator/(self x, const self& y) { return x /= y; }

    // comparison operators
    friend bool operator==(const self& x, const self& y) { return x.m == y.m; }
    friend bool operator!=(const self& x, const self& y) { return x.m != y.m; }
  private:
    complex<T> m;
};

typedef BasicPolar<double> Polar;

int main( )  {
  double rho = 3.0; // magnitude
  double theta = 3.141592 / 2; // angle
  Polar coord(rho, theta);
  cout << "rho = " << coord.rho( ) << ", theta = " << coord.theta( ) << endl;
  coord += Polar(4.0, 0.0);
  cout << "rho = " << coord.rho( ) << ", theta = " << coord.theta( ) << endl;
  system("pause");
}

In Example 11-35, I have defined the Polar type as a typedef'd specialization of the BasicPolar template. This way you can have a convenient default but you can still specialize the BasicPolar template using another numerical type if you prefer. This technique is used in the standard library with the string class being a specialization of the basic_string template.