/** \brief

      Implementation of a bounding box of plainvectors.

   */

   template<typename T>

     class BoundingBox {

       xy<T> bottom_left, top_right;

       bool _empty;

     public:

       ///Default constructor: an empty bounding box

       BoundingBox() { _empty = true; }

       ///Constructing the instance from one point

       BoundingBox(xy<T> a) { bottom_left=top_right=a; _empty = false; }

       ///Is there any point added

       bool empty() const {

 	return _empty;

       }

       ///Gives back the bottom left corner (if the bounding box is empty, then the return value is not defined) 

       xy<T> bottomLeft() const {

 	return bottom_left;

       };

       ///Gives back the top right corner (if the bounding box is empty, then the return value is not defined) 

       xy<T> topRight() const {

 	return top_right;

       };

       ///Checks whether a point is inside a bounding box

       bool inside(const xy<T>& u){

 	if (_empty)

 	  return false;

 	else{

 	  return ((u.x-bottom_left.x)*(top_right.x-u.x) >= 0 &&

 		  (u.y-bottom_left.y)*(top_right.y-u.y) >= 0 );

 	}

       }

       ///Increments a bounding box with a point

       BoundingBox& operator +=(const xy<T>& u){

 	if (_empty){

 	  bottom_left=top_right=u;

 	  _empty = false;

 	}

 	else{

 	  if (bottom_left.x > u.x) bottom_left.x = u.x;

 	  if (bottom_left.y > u.y) bottom_left.y = u.y;

 	  if (top_right.x < u.x) top_right.x = u.x;

 	  if (top_right.y < u.y) top_right.y = u.y;

 	}

 	return *this;

       };

       ///Sums a bounding box and a point

       BoundingBox operator +(const xy<T>& u){

 	BoundingBox b = *this;

 	return b += u;

       };

       ///Increments a bounding box with an other bounding box

       BoundingBox& operator +=(const BoundingBox &u){

 	if ( !u.empty() ){

 	  *this += u.bottomLeft();

 	  *this += u.topRight();

 	}

 	return *this;

       };

       ///Sums two bounding boxes

       BoundingBox operator +(const BoundingBox& u){

 	BoundingBox b = *this;

 	return b += u;

       };

     };//class Boundingbox