/**
 * Defines an ellispoid, which is a basic interpretaion of the ball when it is
 * bouncing.
 **/

#include <cstddef>
#include <cmath>
#include "Implicit.hpp"
#include "common_structures.hpp"

const double PI = 3.141592653589793;

class Spheroid : public ImplicitSurface {
    public:
        Spheroid(Point& _center, size_t _p, size_t _q);
        void update_center_pos(Point& _center);
        void update_radius();
        void set_stiffness(size_t _stiffness);
        double operator() (double _x, double _y, double _z) {
            return (pow(_x - center.x, 2) / pow(q, 2)
                  + pow(_y - center.y, 2) / pow(q, 2)
                  + pow(_z - center.z, 2) / pow(p, 2) -1);
        }
    private:
        /**
         * p corresponds to the half-height of the ball,
         * q to the radius of the ball,
         * V is the volume. Extremely useful to have a constant volume in the
         * ball
        **/
        size_t stiffness;
        double p, q;
        double V;
        Point& center;
        void _compute_volume();
};