/* -*- 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