// -*- c++ -*-

 #ifndef HUGO_XY_H

 #define HUGO_XY_H

 #include <iostream>

 namespace hugo {

 ///\file

 ///\brief A simple two dimensional vector and a bounding box implementation 

 ///

 /// The class \ref hugo::xy "xy" implements

 ///a two dimensional vector with the usual

 /// operations.

 ///

 /// The class \ref hugo::BoundingBox "BoundingBox" can be used to determine

 /// the rectangular bounding box a set of \ref hugo::xy "xy"'s.

 /** \brief

 2 dimensional vector (plainvector) implementation

 */

   template<typename T>

     class xy {

     public:

       T x,y;     

       ///Default constructor: both coordinates become 0

       xy() : x(0), y(0) {}

       ///Constructing the instance from coordinates

       xy(T a, T b) : x(a), y(a) { }

       ///Gives back the square of the norm of the vector

       T normSquare(){

 	return x*x+y*y;

       };

       ///Increments the left hand side by u

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

 	x += u.x;

 	y += u.y;

 	return *this;

       };

       ///Decrements the left hand side by u

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

 	x -= u.x;

 	y -= u.y;

 	return *this;

       };

       ///Multiplying the left hand side with a scalar

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

 	x *= u;

 	y *= u;

 	return *this;

       };

       ///Dividing the left hand side by a scalar

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

 	x /= u;

 	y /= u;

 	return *this;

       };

       ///Returns the scalar product of two vectors

       T operator *(const xy<T>& u){

 	return x*u.x+y*u.y;

       };

       ///Returns the sum of two vectors

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

 	xy<T> b=*this;

 	return b+=u;

       };

       ///Returns the difference of two vectors

       xy<T> operator-(const xy<T> &u) const {

 	xy<T> b=*this;

 	return b-=u;

       };

       ///Returns a vector multiplied by a scalar

       xy<T> operator*(const T &u) const {

 	xy<T> b=*this;

 	return b*=u;

       };

       ///Returns a vector divided by a scalar

       xy<T> operator/(const T &u) const {

 	xy<T> b=*this;

 	return b/=u;

       };

       ///Testing equality

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

 	return (x==u.x) && (y==u.y);

       };

       ///Testing inequality

       bool operator!=(xy u){

 	return  (x!=u.x) || (y!=u.y);

       };

     };

   ///Reading a plainvector from a stream

   template<typename T>

   inline

   std::istream& operator>>(std::istream &is, xy<T> &z)

   {

     is >> z.x >> z.y;

     return is;

   }

   ///Outputting a plainvector to a stream

   template<typename T>

   inline

   std::ostream& operator<<(std::ostream &os, xy<T> z)

   {

     os << "(" << z.x << ", " << z.y << ")";

     return os;

   }

   /** \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

 } //namespace hugo

 #endif //HUGO_XY_H