polygon_area.h

// Description: Area of a polygon
// Documentation: area.txt

#ifndef PASTELGEOMETRY_POLYGON_AREA_H
#define PASTELGEOMETRY_POLYGON_AREA_H

#include "pastel/geometry/shape/polygon.h"

namespace Pastel
{

    //! Computes the signed area of a simple polygon.
    /*!
   Time complexity: linear
   */
    template <typename Real>
    Real signedArea(const Polygon<Real, 2>& polygon)
    {
        integer n = polygon.size();

        if (n < 3)
        {
            return 0;
        }

        // This formula is essentially
        // an application of Green's theorem.

        Real result =
            polygon[0].x() *
            (polygon[1].y() - polygon[n - 1].y());

        for (integer i = 1;i < n - 1;++i)
        {
            result +=
                polygon[i].x() *
                (polygon[i + 1].y() - polygon[i - 1].y());
        }

        result +=
            polygon[n - 1].x() *
            (polygon[0].y() - polygon[n - 2].y());

        return result / 2;
    }

}

#endif