/* -*- mode: C++; indent-tabs-mode: nil; -*-

  *

  * This file is a part of LEMON, a generic C++ optimization library.

  *

  * Copyright (C) 2003-2009

  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport

  * (Egervary Research Group on Combinatorial Optimization, EGRES).

  *

  * Permission to use, modify and distribute this software is granted

  * provided that this copyright notice appears in all copies. For

  * precise terms see the accompanying LICENSE file.

  *

  * This software is provided "AS IS" with no warranty of any kind,

  * express or implied, and with no claim as to its suitability for any

  * purpose.

  *

  */

 #ifndef LEMON_DIM2_H

 #define LEMON_DIM2_H

 #include <iostream>

 #include <algorithm>

 ///\ingroup geomdat

 ///\file

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

 namespace lemon {

   ///Tools for handling two dimensional coordinates

   ///This namespace is a storage of several

   ///tools for handling two dimensional coordinates

   namespace dim2 {

   /// \addtogroup geomdat

   /// @{

   /// Two dimensional vector (plain vector)

   /// A simple two dimensional vector (plain vector) implementation

   /// with the usual vector operations.

   template<typename T>

     class Point {

     public:

       typedef T Value;

       ///First coordinate

       T x;

       ///Second coordinate

       T y;

       ///Default constructor

       Point() {}

       ///Construct an instance from coordinates

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

       ///Returns the dimension of the vector (i.e. returns 2).

       ///The dimension of the vector.

       ///This function always returns 2.

       int size() const { return 2; }

       ///Subscripting operator

       ///\c p[0] is \c p.x and \c p[1] is \c p.y

       ///

       T& operator[](int idx) { return idx == 0 ? x : y; }

       ///Const subscripting operator

       ///\c p[0] is \c p.x and \c p[1] is \c p.y

       ///

       const T& operator[](int idx) const { return idx == 0 ? x : y; }

       ///Conversion constructor

       template<class TT> Point(const Point<TT> &p) : x(p.x), y(p.y) {}

       ///Give back the square of the norm of the vector

       T normSquare() const {

         return x*x+y*y;

       }

       ///Increment the left hand side by \c u

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

         x += u.x;

         y += u.y;

         return *this;

       }

       ///Decrement the left hand side by \c u

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

         x -= u.x;

         y -= u.y;

         return *this;

       }

       ///Multiply the left hand side with a scalar

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

         x *= u;

         y *= u;

         return *this;

       }

       ///Divide the left hand side by a scalar

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

         x /= u;

         y /= u;

         return *this;

       }

       ///Return the scalar product of two vectors

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

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

       }

       ///Return the sum of two vectors

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

         Point<T> b=*this;

         return b+=u;

       }

       ///Return the negative of the vector

       Point<T> operator-() const {

         Point<T> b=*this;

         b.x=-b.x; b.y=-b.y;

         return b;

       }

       ///Return the difference of two vectors

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

         Point<T> b=*this;

         return b-=u;

       }

       ///Return a vector multiplied by a scalar

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

         Point<T> b=*this;

         return b*=u;

       }

       ///Return a vector divided by a scalar

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

         Point<T> b=*this;

         return b/=u;

       }

       ///Test equality

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

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

       }

       ///Test inequality

       bool operator!=(Point u) const {

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

       }

     };

   ///Return a Point

   ///Return a Point.

   ///\relates Point

   template <typename T>

   inline Point<T> makePoint(const T& x, const T& y) {

     return Point<T>(x, y);

   }

   ///Return a vector multiplied by a scalar

   ///Return a vector multiplied by a scalar.

   ///\relates Point

   template<typename T> Point<T> operator*(const T &u,const Point<T> &x) {

     return x*u;

   }

   ///Read a plain vector from a stream

   ///Read a plain vector from a stream.

   ///\relates Point

   ///

   template<typename T>

   inline std::istream& operator>>(std::istream &is, Point<T> &z) {

     char c;

     if (is >> c) {

       if (c != '(') is.putback(c);

     } else {

       is.clear();

     }

     if (!(is >> z.x)) return is;

     if (is >> c) {

       if (c != ',') is.putback(c);

     } else {

       is.clear();

     }

     if (!(is >> z.y)) return is;

     if (is >> c) {

       if (c != ')') is.putback(c);

     } else {

       is.clear();

     }

     return is;

   }

   ///Write a plain vector to a stream

   ///Write a plain vector to a stream.

   ///\relates Point

   ///

   template<typename T>

   inline std::ostream& operator<<(std::ostream &os, const Point<T>& z)

   {

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

     return os;

   }

   ///Rotate by 90 degrees

   ///Returns the parameter rotated by 90 degrees in positive direction.

   ///\relates Point

   ///

   template<typename T>

   inline Point<T> rot90(const Point<T> &z)

   {

     return Point<T>(-z.y,z.x);

   }

   ///Rotate by 180 degrees

   ///Returns the parameter rotated by 180 degrees.

   ///\relates Point

   ///

   template<typename T>

   inline Point<T> rot180(const Point<T> &z)

   {

     return Point<T>(-z.x,-z.y);

   }

   ///Rotate by 270 degrees

   ///Returns the parameter rotated by 90 degrees in negative direction.

   ///\relates Point

   ///

   template<typename T>

   inline Point<T> rot270(const Point<T> &z)

   {

     return Point<T>(z.y,-z.x);

   }

   /// Bounding box of plain vectors (points).

   /// A class to calculate or store the bounding box of plain vectors

   /// (\ref Point "points").

   template<typename T>

   class Box {

       Point<T> _bottom_left, _top_right;

       bool _empty;

     public:

       ///Default constructor: creates an empty box

       Box() { _empty = true; }

       ///Construct a box from one point

       Box(Point<T> a) {

         _bottom_left = _top_right = a;

         _empty = false;

       }

       ///Construct a box from two points

       ///Construct a box from two points.

       ///\param a The bottom left corner.

       ///\param b The top right corner.

       ///\warning The coordinates of the bottom left corner must be no more

       ///than those of the top right one.

       Box(Point<T> a,Point<T> b)

       {

         _bottom_left = a;

         _top_right = b;

         _empty = false;

       }

       ///Construct a box from four numbers

       ///Construct a box from four numbers.

       ///\param l The left side of the box.

       ///\param b The bottom of the box.

       ///\param r The right side of the box.

       ///\param t The top of the box.

       ///\warning The left side must be no more than the right side and

       ///bottom must be no more than the top.

       Box(T l,T b,T r,T t)

       {

         _bottom_left=Point<T>(l,b);

         _top_right=Point<T>(r,t);

         _empty = false;

       }

       ///Return \c true if the box is empty.

       ///Return \c true if the box is empty (i.e. return \c false

       ///if at least one point was added to the box or the coordinates of

       ///the box were set).

       ///

       ///The coordinates of an empty box are not defined.

       bool empty() const {

         return _empty;

       }

       ///Make the box empty

       void clear() {

         _empty = true;

       }

       ///Give back the bottom left corner of the box

       ///Give back the bottom left corner of the box.

       ///If the box is empty, then the return value is not defined.

       Point<T> bottomLeft() const {

         return _bottom_left;

       }

       ///Set the bottom left corner of the box

       ///Set the bottom left corner of the box.

       ///\pre The box must not be empty.

       void bottomLeft(Point<T> p) {

         _bottom_left = p;

       }

       ///Give back the top right corner of the box

       ///Give back the top right corner of the box.

       ///If the box is empty, then the return value is not defined.

       Point<T> topRight() const {

         return _top_right;

       }

       ///Set the top right corner of the box

       ///Set the top right corner of the box.

       ///\pre The box must not be empty.

       void topRight(Point<T> p) {

         _top_right = p;

       }

       ///Give back the bottom right corner of the box

       ///Give back the bottom right corner of the box.

       ///If the box is empty, then the return value is not defined.

       Point<T> bottomRight() const {

         return Point<T>(_top_right.x,_bottom_left.y);

       }

       ///Set the bottom right corner of the box

       ///Set the bottom right corner of the box.

       ///\pre The box must not be empty.

       void bottomRight(Point<T> p) {

         _top_right.x = p.x;

         _bottom_left.y = p.y;

       }

       ///Give back the top left corner of the box

       ///Give back the top left corner of the box.

       ///If the box is empty, then the return value is not defined.

       Point<T> topLeft() const {

         return Point<T>(_bottom_left.x,_top_right.y);

       }

       ///Set the top left corner of the box

       ///Set the top left corner of the box.

       ///\pre The box must not be empty.

       void topLeft(Point<T> p) {

         _top_right.y = p.y;

         _bottom_left.x = p.x;

       }

       ///Give back the bottom of the box

       ///Give back the bottom of the box.

       ///If the box is empty, then the return value is not defined.

       T bottom() const {

         return _bottom_left.y;

       }

       ///Set the bottom of the box

       ///Set the bottom of the box.

       ///\pre The box must not be empty.

       void bottom(T t) {

         _bottom_left.y = t;

       }

       ///Give back the top of the box

       ///Give back the top of the box.

       ///If the box is empty, then the return value is not defined.

       T top() const {

         return _top_right.y;

       }

       ///Set the top of the box

       ///Set the top of the box.

       ///\pre The box must not be empty.

       void top(T t) {

         _top_right.y = t;

       }

       ///Give back the left side of the box

       ///Give back the left side of the box.

       ///If the box is empty, then the return value is not defined.

       T left() const {

         return _bottom_left.x;

       }

       ///Set the left side of the box

       ///Set the left side of the box.

       ///\pre The box must not be empty.

       void left(T t) {

         _bottom_left.x = t;

       }

       /// Give back the right side of the box

       /// Give back the right side of the box.

       ///If the box is empty, then the return value is not defined.

       T right() const {

         return _top_right.x;

       }

       ///Set the right side of the box

       ///Set the right side of the box.

       ///\pre The box must not be empty.

       void right(T t) {

         _top_right.x = t;

       }

       ///Give back the height of the box

       ///Give back the height of the box.

       ///If the box is empty, then the return value is not defined.

       T height() const {

         return _top_right.y-_bottom_left.y;

       }

       ///Give back the width of the box

       ///Give back the width of the box.

       ///If the box is empty, then the return value is not defined.

       T width() const {

         return _top_right.x-_bottom_left.x;

       }

       ///Checks whether a point is inside the box

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

         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 the box with a point

       ///Increments the box with a point.

       ///

       Box& add(const Point<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;

       }

       ///Increments the box to contain another box

       ///Increments the box to contain another box.

       ///

       Box& add(const Box &u){

         if ( !u.empty() ){

           add(u._bottom_left);

           add(u._top_right);

         }

         return *this;

       }

       ///Intersection of two boxes

       ///Intersection of two boxes.

       ///

       Box operator&(const Box& u) const {

         Box b;

         if (_empty || u._empty) {

           b._empty = true;

         } else {

           b._bottom_left.x = std::max(_bottom_left.x, u._bottom_left.x);

           b._bottom_left.y = std::max(_bottom_left.y, u._bottom_left.y);

           b._top_right.x = std::min(_top_right.x, u._top_right.x);

           b._top_right.y = std::min(_top_right.y, u._top_right.y);

           b._empty = b._bottom_left.x > b._top_right.x ||

                      b._bottom_left.y > b._top_right.y;

         }

         return b;

       }

   };//class Box

   ///Read a box from a stream

   ///Read a box from a stream.

   ///\relates Box

   template<typename T>

   inline std::istream& operator>>(std::istream &is, Box<T>& b) {

     char c;

     Point<T> p;

     if (is >> c) {

       if (c != '(') is.putback(c);

     } else {

       is.clear();

     }

     if (!(is >> p)) return is;

     b.bottomLeft(p);

     if (is >> c) {

       if (c != ',') is.putback(c);

     } else {

       is.clear();

     }

     if (!(is >> p)) return is;

     b.topRight(p);

     if (is >> c) {

       if (c != ')') is.putback(c);

     } else {

       is.clear();

     }

     return is;

   }

   ///Write a box to a stream

   ///Write a box to a stream.

   ///\relates Box

   template<typename T>

   inline std::ostream& operator<<(std::ostream &os, const Box<T>& b)

   {

     os << "(" << b.bottomLeft() << "," << b.topRight() << ")";

     return os;

   }

   ///Map of x-coordinates of a <tt>Point</tt>-map

   ///Map of x-coordinates of a \ref Point "Point"-map.

   ///

   template<class M>

   class XMap

   {

     M& _map;

   public:

     typedef typename M::Value::Value Value;

     typedef typename M::Key Key;

     ///\e

     XMap(M& map) : _map(map) {}

     Value operator[](Key k) const {return _map[k].x;}

     void set(Key k,Value v) {_map.set(k,typename M::Value(v,_map[k].y));}

   };

   ///Returns an XMap class

   ///This function just returns an XMap class.

   ///\relates XMap

   template<class M>

   inline XMap<M> xMap(M &m)

   {

     return XMap<M>(m);

   }

   template<class M>

   inline XMap<M> xMap(const M &m)

   {

     return XMap<M>(m);

   }

   ///Constant (read only) version of XMap

   ///Constant (read only) version of XMap.

   ///

   template<class M>

   class ConstXMap

   {

     const M& _map;

   public:

     typedef typename M::Value::Value Value;

     typedef typename M::Key Key;

     ///\e

     ConstXMap(const M &map) : _map(map) {}

     Value operator[](Key k) const {return _map[k].x;}

   };

   ///Returns a ConstXMap class

   ///This function just returns a ConstXMap class.

   ///\relates ConstXMap

   template<class M>

   inline ConstXMap<M> xMap(const M &m)

   {

     return ConstXMap<M>(m);

   }

   ///Map of y-coordinates of a <tt>Point</tt>-map

   ///Map of y-coordinates of a \ref Point "Point"-map.

   ///

   template<class M>

   class YMap

   {

     M& _map;

   public:

     typedef typename M::Value::Value Value;

     typedef typename M::Key Key;

     ///\e

     YMap(M& map) : _map(map) {}

     Value operator[](Key k) const {return _map[k].y;}

     void set(Key k,Value v) {_map.set(k,typename M::Value(_map[k].x,v));}

   };

   ///Returns a YMap class

   ///This function just returns a YMap class.

   ///\relates YMap

   template<class M>

   inline YMap<M> yMap(M &m)

   {

     return YMap<M>(m);

   }

   template<class M>

   inline YMap<M> yMap(const M &m)

   {

     return YMap<M>(m);

   }

   ///Constant (read only) version of YMap

   ///Constant (read only) version of YMap.

   ///

   template<class M>

   class ConstYMap

   {

     const M& _map;

   public:

     typedef typename M::Value::Value Value;

     typedef typename M::Key Key;

     ///\e

     ConstYMap(const M &map) : _map(map) {}

     Value operator[](Key k) const {return _map[k].y;}

   };

   ///Returns a ConstYMap class

   ///This function just returns a ConstYMap class.

   ///\relates ConstYMap

   template<class M>

   inline ConstYMap<M> yMap(const M &m)

   {

     return ConstYMap<M>(m);

   }

   ///\brief Map of the normSquare() of a <tt>Point</tt>-map

   ///

   ///Map of the \ref Point::normSquare() "normSquare()"

   ///of a \ref Point "Point"-map.

   template<class M>

   class NormSquareMap

   {

     const M& _map;

   public:

     typedef typename M::Value::Value Value;

     typedef typename M::Key Key;

     ///\e

     NormSquareMap(const M &map) : _map(map) {}

     Value operator[](Key k) const {return _map[k].normSquare();}

   };

   ///Returns a NormSquareMap class

   ///This function just returns a NormSquareMap class.

   ///\relates NormSquareMap

   template<class M>

   inline NormSquareMap<M> normSquareMap(const M &m)

   {

     return NormSquareMap<M>(m);

   }

   /// @}

   } //namespce dim2

 } //namespace lemon

 #endif //LEMON_DIM2_H