text: // Boost.Geometry (aka GGL, Generic Geometry Library)
  
  // Copyright (c) 2007-2011 Barend Gehrels, Amsterdam, the Netherlands.
  // Copyright (c) 2008-2011 Bruno Lalande, Paris, France.
  // Copyright (c) 2009-2011 Mateusz Loskot, London, UK.
  
  // Use, modification and distribution is subject to the Boost Software License,
  // Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
  // http://www.boost.org/LICENSE_1_0.txt)
  //
  // Custom Triangle Example
  
  #include <iostream>
  
  #include <boost/array.hpp>
  
  #include <boost/geometry/algorithms/area.hpp>
  #include <boost/geometry/algorithms/centroid.hpp>
  #include <boost/geometry/geometries/point_xy.hpp>
  #include <boost/geometry/geometries/register/ring.hpp>
  #include <boost/geometry/strategies/strategies.hpp>
  #include <boost/geometry/util/write_dsv.hpp>
  
  
  struct triangle : public boost::array<boost::geometry::model::d2::point_xy<double>, 4>
  {
      inline void close()
      {
          (*this)[3] = (*this)[0];
      }
  };
  
  
  // Register triangle as a ring
  BOOST_GEOMETRY_REGISTER_RING(triangle)
  
  
  // Specializations of algorithms, where useful. If not specialized the default ones
  // (for linear rings) will be used for triangle. Which is OK as long as the triangle
  // is closed, that means, has 4 points (the last one being the first).
  namespace boost { namespace geometry {
  
  template<>
  inline double area<triangle>(const triangle& t)
  {
      /*         C
                / \
               /   \
              A-----B
  
             ((Bx - Ax) * (Cy - Ay)) - ((Cx - Ax) * (By - Ay))
             -------------------------------------------------
                                     2
      */
  
      return 0.5 * ((t[1].x() - t[0].x()) * (t[2].y() - t[0].y())
                  - (t[2].x() - t[0].x()) * (t[1].y() - t[0].y()));
  }
  
  }} // namespace boost::geometry
  
  int main()
  {
      triangle t;
  
      t[0].x(0);
      t[0].y(0);
      t[1].x(5);
      t[1].y(0);
      t[2].x(2.5);
      t[2].y(2.5);
  
      t.close();
  
      std::cout << "Triangle: " << boost::geometry::dsv(t) << std::endl;
      std::cout << "Area: " << boost::geometry::area(t) << std::endl;
  
      boost::geometry::model::d2::point_xy<double> c;
      boost::geometry::centroid(t, c);
      std::cout << "Centroid: " << boost::geometry::dsv(c) << std::endl;
  
      return 0;
  }
  