#include "polygon.h"

#include <cmath>
#include <algorithm>
#include <sstream>

Polygon::Polygon (double n_, double len_):
    n (n_),
    len (len_)
{
}

double Polygon::bounding_box_area () const
{
    double alpha = 2 * M_PI / n;
    double radius = len / (2 * std::sin (alpha / 2));

    double alpha_i = 0.5 * (alpha - M_PI);    
    double min_x = std::cos (alpha_i);
    double max_x = min_x;
    double min_y = std::sin (alpha_i);
    double max_y = min_y;

    for (unsigned int i = 1; i != n; ++i)
    {
        alpha_i += alpha;
        
        double x = std::cos (alpha_i);
        double y = std::sin (alpha_i);

        min_x = std::min (min_x, x);
        max_x = std::max (max_x, x);

        min_y = std::min (min_y, y);
        max_y = std::max (max_y, y);
    }   

    return ((max_x - min_x) * radius) * ((max_y - min_y) * radius);
}

std::string Polygon::str () const
{
    std::stringstream buf;
    buf << n << "-szog (oldalhossz: " << len << ")";
    return buf.str ();
}