// -*- 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