improved_logarithmic_spiral

  vector<Vector2D> centered_logarithmic_spiral(double r_min,
                           double r_max,
                           double alpha,
                           const Vector2D& center)
  {
    const double theta_max = log(r_max/r_min)/alpha;
    const vector<double> theta_list =
      arange(0,theta_max,2*M_PI*alpha/(1-0.5*alpha));

    vector<double> r_list(theta_list.size(),0);
    for(size_t i=0;i<r_list.size();++i)
      r_list.at(i) = r_min*exp(alpha*theta_list.at(i));

    vector<Vector2D> res(r_list.size());
    for(size_t i=0;i<res.size();++i)
      res[i] = center+r_list[i]*Vector2D(cos(theta_list.at(i)),
                     sin(theta_list.at(i)));
    return res;
  }