RhodeCode

/* -*- C++ -*-

 *

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

 *

 * 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.

 *

 */

///\file

///\brief Some basic non inline function and static global data.

#include<lemon/tolerance.h>

#include<lemon/bits/invalid.h>

namespace lemon {

  float Tolerance<float>::def_epsilon = 1e-4;

  double Tolerance<double>::def_epsilon = 1e-10;

  long double Tolerance<long double>::def_epsilon = 1e-14;

#ifndef LEMON_ONLY_TEMPLATES

  const Invalid INVALID = Invalid();

#endif

} //namespace lemon

/* -*- C++ -*-

 *

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

 *

 * 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_BITS_INVALID_H

#define LEMON_BITS_INVALID_H

///\file

///\brief Definition of INVALID.

namespace lemon {

  /// \brief Dummy type to make it easier to create invalid iterators.

  ///

  /// See \ref INVALID for the usage.

  struct Invalid {

  public:

    bool operator==(Invalid) { return true;  }

    bool operator!=(Invalid) { return false; }

    bool operator< (Invalid) { return false; }

  };

  /// \brief Invalid iterators.

  ///

  /// \ref Invalid is a global type that converts to each iterator

  /// in such a way that the value of the target iterator will be invalid.

  //Some people didn't like this:

  //const Invalid &INVALID = *(Invalid *)0;

#ifdef LEMON_ONLY_TEMPLATES

  const Invalid INVALID = Invalid();

#else

  extern const Invalid INVALID;

#endif

} //namespace lemon

#endif

/* -*- C++ -*-

 *

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

 *

 * 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.

 *

 */

// This file contains a modified version of the enable_if library from BOOST.

// See the appropriate copyright notice below.

// Boost enable_if library

// Copyright 2003 � The Trustees of Indiana University.

// Use, modification, and distribution is subject to the Boost Software

// License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at

// http://www.boost.org/LICENSE_1_0.txt)

//    Authors: Jaakko J�rvi (jajarvi at osl.iu.edu)

//             Jeremiah Willcock (jewillco at osl.iu.edu)

//             Andrew Lumsdaine (lums at osl.iu.edu)

#ifndef LEMON_BITS_UTILITY_H

#define LEMON_BITS_UTILITY_H

///\file

///\brief Miscellaneous basic utilities

///

///\todo Please rethink the organisation of the basic files like this.

///E.g. this file might be merged with invalid.h.

namespace lemon

{

  /// Basic type for defining "tags". A "YES" condition for \c enable_if.

  /// Basic type for defining "tags". A "YES" condition for \c enable_if.

  ///

  ///\sa False

  ///

  /// \todo This should go to a separate "basic_types.h" (or something)

  /// file.

  struct True {

    ///\e

    static const bool value = true;

  };

  /// Basic type for defining "tags". A "NO" condition for \c enable_if.

  /// Basic type for defining "tags". A "NO" condition for \c enable_if.

  ///

  ///\sa True

  struct False {

    ///\e

    static const bool value = false;

  };

  struct InvalidType {

  };

  template <typename T>

  struct Wrap {

    const T &value;

    Wrap(const T &t) : value(t) {}

  };

  /**************** dummy class to avoid ambiguity ****************/

  template<int T> struct dummy { dummy(int) {} };

  /**************** enable_if from BOOST ****************/

  template <typename Type, typename T = void>

  struct exists {

    typedef T type;

  };

  template <bool B, class T = void>

  struct enable_if_c {

    typedef T type;

  };

  template <class T>

  struct enable_if_c<false, T> {};

  template <class Cond, class T = void> 

  struct enable_if : public enable_if_c<Cond::value, T> {};

  template <bool B, class T>

  struct lazy_enable_if_c {

    typedef typename T::type type;

  };

  template <class T>

  struct lazy_enable_if_c<false, T> {};

  template <class Cond, class T> 

  struct lazy_enable_if : public lazy_enable_if_c<Cond::value, T> {};

  template <bool B, class T = void>

  struct disable_if_c {

    typedef T type;

  };

  template <class T>

  struct disable_if_c<true, T> {};

  template <class Cond, class T = void> 

  struct disable_if : public disable_if_c<Cond::value, T> {};

  template <bool B, class T>

  struct lazy_disable_if_c {

    typedef typename T::type type;

  };

  template <class T>

  struct lazy_disable_if_c<true, T> {};

  template <class Cond, class T> 

  struct lazy_disable_if : public lazy_disable_if_c<Cond::value, T> {};

} // namespace lemon

#endif

/* -*- C++ -*-

 *

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

 *

 * 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.

 *

 */

// This file contains a modified version of the concept checking

// utility from BOOST.

// See the appropriate copyright notice below.

// (C) Copyright Jeremy Siek 2000.

// Distributed under the Boost Software License, Version 1.0. (See

// accompanying file LICENSE_1_0.txt or copy at

// http://www.boost.org/LICENSE_1_0.txt)

//

// Revision History:

//   05 May   2001: Workarounds for HP aCC from Thomas Matelich. (Jeremy Siek)

//   02 April 2001: Removed limits header altogether. (Jeremy Siek)

//   01 April 2001: Modified to use new <boost/limits.hpp> header. (JMaddock)

//

// See http://www.boost.org/libs/concept_check for documentation.

#ifndef LEMON_CONCEPT_CHECKS_H

#define LEMON_CONCEPT_CHECKS_H

namespace lemon {

  /*

    "inline" is used for ignore_unused_variable_warning()

    and function_requires() to make sure there is no

    overtarget with g++.

  */

  template <class T> inline void ignore_unused_variable_warning(const T&) { }

  template <class Concept>

  inline void function_requires()

  {

#if !defined(NDEBUG)

    void (Concept::*x)() = & Concept::constraints;

    ignore_unused_variable_warning(x);

#endif

  }

  template <typename Concept, typename Type>

  inline void checkConcept() {

#if !defined(NDEBUG)

    typedef typename Concept::template Constraints<Type> ConceptCheck;

    void (ConceptCheck::*x)() = & ConceptCheck::constraints;

    ignore_unused_variable_warning(x);

#endif

  }

#define BOOST_CLASS_REQUIRE(type_var, ns, concept) \

  typedef void (ns::concept <type_var>::* func##type_var##concept)(); \

  template <func##type_var##concept Tp1_> \

  struct concept_checking_##type_var##concept { }; \

  typedef concept_checking_##type_var##concept< \

    BOOST_FPTR ns::concept<type_var>::constraints> \

    concept_checking_typedef_##type_var##concept

#define BOOST_CLASS_REQUIRE2(type_var1, type_var2, ns, concept) \

  typedef void (ns::concept <type_var1,type_var2>::* \

     func##type_var1##type_var2##concept)(); \

  template <func##type_var1##type_var2##concept Tp1_> \

  struct concept_checking_##type_var1##type_var2##concept { }; \

  typedef concept_checking_##type_var1##type_var2##concept< \

    BOOST_FPTR ns::concept<type_var1,type_var2>::constraints> \

    concept_checking_typedef_##type_var1##type_var2##concept

#define BOOST_CLASS_REQUIRE3(tv1, tv2, tv3, ns, concept) \

  typedef void (ns::concept <tv1,tv2,tv3>::* \

     func##tv1##tv2##tv3##concept)(); \

  template <func##tv1##tv2##tv3##concept Tp1_> \

  struct concept_checking_##tv1##tv2##tv3##concept { }; \

  typedef concept_checking_##tv1##tv2##tv3##concept< \

    BOOST_FPTR ns::concept<tv1,tv2,tv3>::constraints> \

    concept_checking_typedef_##tv1##tv2##tv3##concept

#define BOOST_CLASS_REQUIRE4(tv1, tv2, tv3, tv4, ns, concept) \

  typedef void (ns::concept <tv1,tv2,tv3,tv4>::* \

     func##tv1##tv2##tv3##tv4##concept)(); \

  template <func##tv1##tv2##tv3##tv4##concept Tp1_> \

  struct concept_checking_##tv1##tv2##tv3##tv4##concept { }; \

  typedef concept_checking_##tv1##tv2##tv3##tv4##concept< \

    BOOST_FPTR ns::concept<tv1,tv2,tv3,tv4>::constraints> \

    concept_checking_typedef_##tv1##tv2##tv3##tv4##concept

} // namespace lemon

#endif // LEMON_CONCEPT_CHECKS_H

/* -*- C++ -*-

 *

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

 *

 * 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_CONCEPT_MAPS_H

#define LEMON_CONCEPT_MAPS_H

#include <lemon/bits/utility.h>

#include <lemon/concept_check.h>

///\ingroup concept

///\file

///\brief Map concepts checking classes for testing and documenting.

namespace lemon {

  namespace concepts {

    /// \addtogroup concept

    /// @{

    /// Readable map concept

    /// Readable map concept.

    ///

    template<typename K, typename T>

    class ReadMap

    {

    public:

      /// The key type of the map.

      typedef K Key;    

      /// The value type of the map. (The type of objects associated with the keys).

      typedef T Value;

      /// Returns the value associated with a key.

      /// \bug Value shouldn't need to be default constructible.

      ///

      Value operator[](const Key &) const {return Value();}

      template<typename _ReadMap>

      struct Constraints {

	void constraints() {

	  Value val = m[key];

	  val = m[key];

	  typename _ReadMap::Value own_val = m[own_key]; 

	  own_val = m[own_key]; 

	  ignore_unused_variable_warning(val);

	  ignore_unused_variable_warning(own_val);

	  ignore_unused_variable_warning(key);

	}

	Key& key;

	typename _ReadMap::Key& own_key;

	_ReadMap& m;

      };

    };

    /// Writable map concept

    /// Writable map concept.

    ///

    template<typename K, typename T>

    class WriteMap

    {

    public:

      /// The key type of the map.

      typedef K Key;    

      /// The value type of the map. (The type of objects associated with the keys).

      typedef T Value;

      /// Sets the value associated with a key.

      void set(const Key &,const Value &) {}

      ///Default constructor

      WriteMap() {}

      template <typename _WriteMap>

      struct Constraints {

	void constraints() {

	  // No constraints for constructor.

	  m.set(key, val);

	  m.set(own_key, own_val);

	  ignore_unused_variable_warning(key);

	  ignore_unused_variable_warning(val);

	  ignore_unused_variable_warning(own_key);

	  ignore_unused_variable_warning(own_val);

	}

	Value& val;

	typename _WriteMap::Value own_val;

	Key& key;

	typename _WriteMap::Key& own_key;

	_WriteMap& m;

      };

    };

    /// Read/Writable map concept

    /// Read/writable map concept.

    ///

    template<typename K, typename T>

    class ReadWriteMap : public ReadMap<K,T>,

			 public WriteMap<K,T>

    {

    public:

      /// The key type of the map.

      typedef K Key;    

      /// The value type of the map. (The type of objects associated with the keys).

      typedef T Value;

      /// Returns the value associated with a key.

      Value operator[](const Key &) const {return Value();}

      /// Sets the value associated with a key.

      void set(const Key & ,const Value &) {}

      template<typename _ReadWriteMap>

      struct Constraints {

	void constraints() {

	  checkConcept<ReadMap<K, T>, _ReadWriteMap >();

	  checkConcept<WriteMap<K, T>, _ReadWriteMap >();

	}

      };

    };

    /// Dereferable map concept

    /// Dereferable map concept.

    ///

    template<typename K, typename T, typename R, typename CR>

    class ReferenceMap : public ReadWriteMap<K,T>

    {

    public:

      /// Tag for reference maps.

      typedef True ReferenceMapTag;

      /// The key type of the map.

      typedef K Key;    

      /// The value type of the map. (The type of objects associated with the keys).

      typedef T Value;

      /// The reference type of the map.

      typedef R Reference;

      /// The const reference type of the map.

      typedef CR ConstReference;

    protected:

      Value tmp;

    public:

      ///Returns a reference to the value associated to a key.

      Reference operator[](const Key &) { return tmp; }

      ///Returns a const reference to the value associated to a key.

      ConstReference operator[](const Key &) const { return tmp; }

      /// Sets the value associated with a key.

      void set(const Key &k,const Value &t) { operator[](k)=t; }

      /// \todo Rethink this concept. 

      template<typename _ReferenceMap>

      struct ReferenceMapConcept {

	void constraints() {

	  checkConcept<ReadWriteMap, _ReferenceMap >();

	  m[key] = val;

	  val  = m[key];

	  m[key] = ref;

	  ref = m[key];

	  m[own_key] = own_val;

	  own_val  = m[own_key];

	  m[own_key] = own_ref;

	  own_ref = m[own_key];	  	  

	}

	typename _ReferenceMap::Key& own_key;

	typename _ReferenceMap::Value& own_val;

	typename _ReferenceMap::Reference& own_ref;

	Key& key;

	Value& val;

	Reference& ref;

	_ReferenceMap& m;

      };

    };

    // @}

  } //namespace concepts

} //namespace lemon

#endif // LEMON_CONCEPT_MAPS_H

/* -*- C++ -*-

 *

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

 *

 * 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 <lemon/bits/utility.h>

///\ingroup misc

///\file

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

///

/// The class \ref lemon::dim2::Point "dim2::Point" implements

///a two dimensional vector with the usual

/// operations.

///

/// The class \ref lemon::dim2::BoundingBox "dim2::BoundingBox"

/// can be used to determine

/// the rectangular bounding box of a set of

/// \ref lemon::dim2::Point "dim2::Point"'s.

namespace lemon {

  ///Tools for handling two dimensional coordinates

  ///This namespace is a storage of several

  ///tools for handling two dimensional coordinates

  namespace dim2 {

  /// \addtogroup misc

  /// @{

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

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

  ///with the usual vector

  /// operators.

  ///

  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) { }

      ///The dimension of the vector.

      ///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 u

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

        x += u.x;

        y += u.y;

        return *this;

      }

      ///Decrement the left hand side by 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 plainvector from a stream

  ///Read a plainvector 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 plainvector to a stream

  ///Write a plainvector 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);

  }

  /// A class to calculate or store the bounding box of plainvectors.

  /// A class to calculate or store the bounding box of plainvectors.

  ///

    template<typename T>

    class BoundingBox {

      Point<T> bottom_left, top_right;

      bool _empty;

    public:

      ///Default constructor: creates an empty bounding box

      BoundingBox() { _empty = true; }

      ///Construct an instance from one point

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

      ///Construct an instance from two points

      ///Construct an instance 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.

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

      {

	bottom_left=a;

	top_right=b;

	_empty = false;

      }

      ///Construct an instance from four numbers

      ///Construct an instance 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. 

      BoundingBox(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 bounding box is empty.

      ///Return \c true if the bounding 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 bounding box are not defined. 

      bool empty() const {

        return _empty;

      }

      ///Make the BoundingBox empty

      void clear() {

        _empty=1;

      }

      ///Give back the bottom left corner

      ///Give back the bottom left corner.

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

      Point<T> bottomLeft() const {

        return bottom_left;

      }

      ///Set the bottom left corner

      ///Set the bottom left corner.

      ///It should only be used for non-empty box.

      void bottomLeft(Point<T> p) {

	bottom_left = p;

      }

      ///Give back the top right corner

      ///Give back the top right corner.

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

      Point<T> topRight() const {

        return top_right;

      }

      ///Set the top right corner

      ///Set the top right corner.

      ///It should only be used for non-empty box.

      void topRight(Point<T> p) {

	top_right = p;

      }

      ///Give back the bottom right corner

      ///Give back the bottom right corner.

      ///If the bounding 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

      ///Set the bottom right corner.

      ///It should only be used for non-empty box.

      void bottomRight(Point<T> p) {

	top_right.x = p.x;

	bottom_left.y = p.y;

      }

      ///Give back the top left corner

      ///Give back the top left corner.

      ///If the bounding 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

      ///Set the top left corner.

      ///It should only be used for non-empty box.

      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 bounding 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.

      ///It should only be used for non-empty box.

      void bottom(T t) {

	bottom_left.y = t;

      }

      ///Give back the top of the box

      ///Give back the top of the box.

      ///If the bounding 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.

      ///It should only be used for non-empty box.

      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 bounding 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.

      ///It should only be used for non-empty box.

      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 bounding 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.

      ///It should only be used for non-empty box.

      void right(T t) {

	top_right.x = t;

      }

      ///Give back the height of the box

      ///Give back the height of the box.

      ///If the bounding 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 bounding 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 a bounding 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 a bounding box with a point

      ///Increments a bounding box with a point.

      ///

      BoundingBox& 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 a bounding box to contain another bounding box

      ///Increments a bounding box to contain another bounding box.

      ///

      BoundingBox& add(const BoundingBox &u){

        if ( !u.empty() ){

          this->add(u.bottomLeft());

	  this->add(u.topRight());

        }

        return *this;

      }

      ///Intersection of two bounding boxes

      ///Intersection of two bounding boxes.

      ///

      BoundingBox operator&(const BoundingBox& u) const {

        BoundingBox b;

        if (this->_empty || u._empty) {

	  b._empty = true;

	} else {

	  b.bottom_left.x = std::max(this->bottom_left.x,u.bottom_left.x);

	  b.bottom_left.y = std::max(this->bottom_left.y,u.bottom_left.y);

	  b.top_right.x = std::min(this->top_right.x,u.top_right.x);

	  b.top_right.y = std::min(this->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 Boundingbox

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

  ///\ingroup maps