C++ Cookbook

11.18. 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 ...