lemon/dim2.h
changeset 8 a1b1d672f37a
child 15 062f361aa520
     1.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     1.2 +++ b/lemon/dim2.h	Thu Dec 20 16:11:56 2007 +0000
     1.3 @@ -0,0 +1,689 @@
     1.4 +/* -*- C++ -*-
     1.5 + *
     1.6 + * This file is a part of LEMON, a generic C++ optimization library
     1.7 + *
     1.8 + * Copyright (C) 2003-2007
     1.9 + * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
    1.10 + * (Egervary Research Group on Combinatorial Optimization, EGRES).
    1.11 + *
    1.12 + * Permission to use, modify and distribute this software is granted
    1.13 + * provided that this copyright notice appears in all copies. For
    1.14 + * precise terms see the accompanying LICENSE file.
    1.15 + *
    1.16 + * This software is provided "AS IS" with no warranty of any kind,
    1.17 + * express or implied, and with no claim as to its suitability for any
    1.18 + * purpose.
    1.19 + *
    1.20 + */
    1.21 +
    1.22 +#ifndef LEMON_DIM2_H
    1.23 +#define LEMON_DIM2_H
    1.24 +
    1.25 +#include <iostream>
    1.26 +#include <lemon/bits/utility.h>
    1.27 +
    1.28 +///\ingroup misc
    1.29 +///\file
    1.30 +///\brief A simple two dimensional vector and a bounding box implementation 
    1.31 +///
    1.32 +/// The class \ref lemon::dim2::Point "dim2::Point" implements
    1.33 +///a two dimensional vector with the usual
    1.34 +/// operations.
    1.35 +///
    1.36 +/// The class \ref lemon::dim2::BoundingBox "dim2::BoundingBox"
    1.37 +/// can be used to determine
    1.38 +/// the rectangular bounding box of a set of
    1.39 +/// \ref lemon::dim2::Point "dim2::Point"'s.
    1.40 +///
    1.41 +///\author Attila Bernath
    1.42 +
    1.43 +
    1.44 +namespace lemon {
    1.45 +
    1.46 +  ///Tools for handling two dimensional coordinates
    1.47 +
    1.48 +  ///This namespace is a storage of several
    1.49 +  ///tools for handling two dimensional coordinates
    1.50 +  namespace dim2 {
    1.51 +
    1.52 +  /// \addtogroup misc
    1.53 +  /// @{
    1.54 +
    1.55 +  /// A simple two dimensional vector (plainvector) implementation
    1.56 +
    1.57 +  /// A simple two dimensional vector (plainvector) implementation
    1.58 +  ///with the usual vector
    1.59 +  /// operators.
    1.60 +  ///
    1.61 +  template<typename T>
    1.62 +    class Point {
    1.63 +
    1.64 +    public:
    1.65 +
    1.66 +      typedef T Value;
    1.67 +
    1.68 +      ///First co-ordinate
    1.69 +      T x;
    1.70 +      ///Second co-ordinate
    1.71 +      T y;     
    1.72 +      
    1.73 +      ///Default constructor
    1.74 +      Point() {}
    1.75 +
    1.76 +      ///Construct an instance from coordinates
    1.77 +      Point(T a, T b) : x(a), y(b) { }
    1.78 +
    1.79 +      ///The dimension of the vector.
    1.80 +
    1.81 +      ///This class give back always 2.
    1.82 +      ///
    1.83 +      int size() const { return 2; }
    1.84 +
    1.85 +      ///Subscripting operator
    1.86 +
    1.87 +      ///\c p[0] is \c p.x and \c p[1] is \c p.y
    1.88 +      ///
    1.89 +      T& operator[](int idx) { return idx == 0 ? x : y; }
    1.90 +
    1.91 +      ///Const subscripting operator
    1.92 +
    1.93 +      ///\c p[0] is \c p.x and \c p[1] is \c p.y
    1.94 +      ///
    1.95 +      const T& operator[](int idx) const { return idx == 0 ? x : y; }
    1.96 +
    1.97 +      ///Conversion constructor
    1.98 +      template<class TT> Point(const Point<TT> &p) : x(p.x), y(p.y) {}
    1.99 +
   1.100 +      ///Give back the square of the norm of the vector
   1.101 +      T normSquare() const {
   1.102 +        return x*x+y*y;
   1.103 +      }
   1.104 +  
   1.105 +      ///Increment the left hand side by u
   1.106 +      Point<T>& operator +=(const Point<T>& u) {
   1.107 +        x += u.x;
   1.108 +        y += u.y;
   1.109 +        return *this;
   1.110 +      }
   1.111 +  
   1.112 +      ///Decrement the left hand side by u
   1.113 +      Point<T>& operator -=(const Point<T>& u) {
   1.114 +        x -= u.x;
   1.115 +        y -= u.y;
   1.116 +        return *this;
   1.117 +      }
   1.118 +
   1.119 +      ///Multiply the left hand side with a scalar
   1.120 +      Point<T>& operator *=(const T &u) {
   1.121 +        x *= u;
   1.122 +        y *= u;
   1.123 +        return *this;
   1.124 +      }
   1.125 +
   1.126 +      ///Divide the left hand side by a scalar
   1.127 +      Point<T>& operator /=(const T &u) {
   1.128 +        x /= u;
   1.129 +        y /= u;
   1.130 +        return *this;
   1.131 +      }
   1.132 +  
   1.133 +      ///Return the scalar product of two vectors
   1.134 +      T operator *(const Point<T>& u) const {
   1.135 +        return x*u.x+y*u.y;
   1.136 +      }
   1.137 +  
   1.138 +      ///Return the sum of two vectors
   1.139 +      Point<T> operator+(const Point<T> &u) const {
   1.140 +        Point<T> b=*this;
   1.141 +        return b+=u;
   1.142 +      }
   1.143 +
   1.144 +      ///Return the neg of the vectors
   1.145 +      Point<T> operator-() const {
   1.146 +        Point<T> b=*this;
   1.147 +        b.x=-b.x; b.y=-b.y;
   1.148 +        return b;
   1.149 +      }
   1.150 +
   1.151 +      ///Return the difference of two vectors
   1.152 +      Point<T> operator-(const Point<T> &u) const {
   1.153 +        Point<T> b=*this;
   1.154 +        return b-=u;
   1.155 +      }
   1.156 +
   1.157 +      ///Return a vector multiplied by a scalar
   1.158 +      Point<T> operator*(const T &u) const {
   1.159 +        Point<T> b=*this;
   1.160 +        return b*=u;
   1.161 +      }
   1.162 +
   1.163 +      ///Return a vector divided by a scalar
   1.164 +      Point<T> operator/(const T &u) const {
   1.165 +        Point<T> b=*this;
   1.166 +        return b/=u;
   1.167 +      }
   1.168 +
   1.169 +      ///Test equality
   1.170 +      bool operator==(const Point<T> &u) const {
   1.171 +        return (x==u.x) && (y==u.y);
   1.172 +      }
   1.173 +
   1.174 +      ///Test inequality
   1.175 +      bool operator!=(Point u) const {
   1.176 +        return  (x!=u.x) || (y!=u.y);
   1.177 +      }
   1.178 +
   1.179 +    };
   1.180 +
   1.181 +  ///Return an Point 
   1.182 +
   1.183 +  ///Return an Point
   1.184 +  ///\relates Point
   1.185 +  template <typename T>
   1.186 +  inline Point<T> makePoint(const T& x, const T& y) {
   1.187 +    return Point<T>(x, y);
   1.188 +  }
   1.189 +
   1.190 +  ///Return a vector multiplied by a scalar
   1.191 +
   1.192 +  ///Return a vector multiplied by a scalar
   1.193 +  ///\relates Point
   1.194 +  template<typename T> Point<T> operator*(const T &u,const Point<T> &x) {
   1.195 +    return x*u;
   1.196 +  }
   1.197 +
   1.198 +  ///Read a plainvector from a stream
   1.199 +
   1.200 +  ///Read a plainvector from a stream
   1.201 +  ///\relates Point
   1.202 +  ///
   1.203 +  template<typename T>
   1.204 +  inline std::istream& operator>>(std::istream &is, Point<T> &z) {
   1.205 +    char c;
   1.206 +    if (is >> c) {
   1.207 +      if (c != '(') is.putback(c);
   1.208 +    } else {
   1.209 +      is.clear();
   1.210 +    }
   1.211 +    if (!(is >> z.x)) return is;
   1.212 +    if (is >> c) {
   1.213 +      if (c != ',') is.putback(c);
   1.214 +    } else {
   1.215 +      is.clear();
   1.216 +    }
   1.217 +    if (!(is >> z.y)) return is;
   1.218 +    if (is >> c) {
   1.219 +      if (c != ')') is.putback(c);
   1.220 +    } else {
   1.221 +      is.clear();
   1.222 +    }
   1.223 +    return is;
   1.224 +  }
   1.225 +
   1.226 +  ///Write a plainvector to a stream
   1.227 +
   1.228 +  ///Write a plainvector to a stream
   1.229 +  ///\relates Point
   1.230 +  ///
   1.231 +  template<typename T>
   1.232 +  inline std::ostream& operator<<(std::ostream &os, const Point<T>& z)
   1.233 +  {
   1.234 +    os << "(" << z.x << ", " << z.y << ")";
   1.235 +    return os;
   1.236 +  }
   1.237 +
   1.238 +  ///Rotate by 90 degrees
   1.239 +
   1.240 +  ///Returns its parameter rotated by 90 degrees in positive direction.
   1.241 +  ///\relates Point
   1.242 +  ///
   1.243 +  template<typename T>
   1.244 +  inline Point<T> rot90(const Point<T> &z)
   1.245 +  {
   1.246 +    return Point<T>(-z.y,z.x);
   1.247 +  }
   1.248 +
   1.249 +  ///Rotate by 180 degrees
   1.250 +
   1.251 +  ///Returns its parameter rotated by 180 degrees.
   1.252 +  ///\relates Point
   1.253 +  ///
   1.254 +  template<typename T>
   1.255 +  inline Point<T> rot180(const Point<T> &z)
   1.256 +  {
   1.257 +    return Point<T>(-z.x,-z.y);
   1.258 +  }
   1.259 +
   1.260 +  ///Rotate by 270 degrees
   1.261 +
   1.262 +  ///Returns its parameter rotated by 90 degrees in negative direction.
   1.263 +  ///\relates Point
   1.264 +  ///
   1.265 +  template<typename T>
   1.266 +  inline Point<T> rot270(const Point<T> &z)
   1.267 +  {
   1.268 +    return Point<T>(z.y,-z.x);
   1.269 +  }
   1.270 +
   1.271 +  
   1.272 +
   1.273 +  /// A class to calculate or store the bounding box of plainvectors.
   1.274 +
   1.275 +  /// A class to calculate or store the bounding box of plainvectors.
   1.276 +  ///
   1.277 +  ///\author Attila Bernath
   1.278 +    template<typename T>
   1.279 +    class BoundingBox {
   1.280 +      Point<T> bottom_left, top_right;
   1.281 +      bool _empty;
   1.282 +    public:
   1.283 +      
   1.284 +      ///Default constructor: creates an empty bounding box
   1.285 +      BoundingBox() { _empty = true; }
   1.286 +
   1.287 +      ///Construct an instance from one point
   1.288 +      BoundingBox(Point<T> a) { bottom_left=top_right=a; _empty = false; }
   1.289 +      
   1.290 +      ///Construct an instance from two points
   1.291 +      
   1.292 +      ///Construct an instance from two points
   1.293 +      ///\warning The coordinates of the bottom-left corner must be no more
   1.294 +      ///than those of the top-right one
   1.295 +      BoundingBox(Point<T> a,Point<T> b)
   1.296 +      {
   1.297 +	bottom_left=a;
   1.298 +	top_right=b;
   1.299 +	_empty = false;
   1.300 +      }
   1.301 +      
   1.302 +      ///Construct an instance from four numbers
   1.303 +
   1.304 +      ///Construct an instance from four numbers
   1.305 +      ///\warning The coordinates of the bottom-left corner must be no more
   1.306 +      ///than those of the top-right one
   1.307 +      BoundingBox(T l,T b,T r,T t)
   1.308 +      {
   1.309 +	bottom_left=Point<T>(l,b);
   1.310 +	top_right=Point<T>(r,t);
   1.311 +	_empty = false;
   1.312 +      }
   1.313 +      
   1.314 +      ///Were any points added?
   1.315 +      bool empty() const {
   1.316 +        return _empty;
   1.317 +      }
   1.318 +      
   1.319 +      ///Make the BoundingBox empty
   1.320 +      void clear() {
   1.321 +        _empty=1;
   1.322 +      }
   1.323 +
   1.324 +      ///Give back the bottom left corner
   1.325 +
   1.326 +      ///Give back the bottom left corner.
   1.327 +      ///If the bounding box is empty, then the return value is not defined.
   1.328 +      Point<T> bottomLeft() const {
   1.329 +        return bottom_left;
   1.330 +      }
   1.331 +
   1.332 +      ///Set the bottom left corner
   1.333 +
   1.334 +      ///Set the bottom left corner.
   1.335 +      ///It should only bee used for non-empty box.
   1.336 +      void bottomLeft(Point<T> p) {
   1.337 +	bottom_left = p;
   1.338 +      }
   1.339 +
   1.340 +      ///Give back the top right corner
   1.341 +
   1.342 +      ///Give back the top right corner.
   1.343 +      ///If the bounding box is empty, then the return value is not defined.
   1.344 +      Point<T> topRight() const {
   1.345 +        return top_right;
   1.346 +      }
   1.347 +
   1.348 +      ///Set the top right corner
   1.349 +
   1.350 +      ///Set the top right corner.
   1.351 +      ///It should only bee used for non-empty box.
   1.352 +      void topRight(Point<T> p) {
   1.353 +	top_right = p;
   1.354 +      }
   1.355 +
   1.356 +      ///Give back the bottom right corner
   1.357 +
   1.358 +      ///Give back the bottom right corner.
   1.359 +      ///If the bounding box is empty, then the return value is not defined.
   1.360 +      Point<T> bottomRight() const {
   1.361 +        return Point<T>(top_right.x,bottom_left.y);
   1.362 +      }
   1.363 +
   1.364 +      ///Set the bottom right corner
   1.365 +
   1.366 +      ///Set the bottom right corner.
   1.367 +      ///It should only bee used for non-empty box.
   1.368 +      void bottomRight(Point<T> p) {
   1.369 +	top_right.x = p.x;
   1.370 +	bottom_left.y = p.y;
   1.371 +      }
   1.372 + 
   1.373 +      ///Give back the top left corner
   1.374 +
   1.375 +      ///Give back the top left corner.
   1.376 +      ///If the bounding box is empty, then the return value is not defined.
   1.377 +      Point<T> topLeft() const {
   1.378 +        return Point<T>(bottom_left.x,top_right.y);
   1.379 +      }
   1.380 +
   1.381 +      ///Set the top left corner
   1.382 +
   1.383 +      ///Set the top left corner.
   1.384 +      ///It should only bee used for non-empty box.
   1.385 +      void topLeft(Point<T> p) {
   1.386 +	top_right.y = p.y;
   1.387 +	bottom_left.x = p.x;
   1.388 +      }
   1.389 +
   1.390 +      ///Give back the bottom of the box
   1.391 +
   1.392 +      ///Give back the bottom of the box.
   1.393 +      ///If the bounding box is empty, then the return value is not defined.
   1.394 +      T bottom() const {
   1.395 +        return bottom_left.y;
   1.396 +      }
   1.397 +
   1.398 +      ///Set the bottom of the box
   1.399 +
   1.400 +      ///Set the bottom of the box.
   1.401 +      ///It should only bee used for non-empty box.
   1.402 +      void bottom(T t) {
   1.403 +	bottom_left.y = t;
   1.404 +      }
   1.405 +
   1.406 +      ///Give back the top of the box
   1.407 +
   1.408 +      ///Give back the top of the box.
   1.409 +      ///If the bounding box is empty, then the return value is not defined.
   1.410 +      T top() const {
   1.411 +        return top_right.y;
   1.412 +      }
   1.413 +
   1.414 +      ///Set the top of the box
   1.415 +
   1.416 +      ///Set the top of the box.
   1.417 +      ///It should only bee used for non-empty box.
   1.418 +      void top(T t) {
   1.419 +	top_right.y = t;
   1.420 +      }
   1.421 +
   1.422 +      ///Give back the left side of the box
   1.423 +
   1.424 +      ///Give back the left side of the box.
   1.425 +      ///If the bounding box is empty, then the return value is not defined.
   1.426 +      T left() const {
   1.427 +        return bottom_left.x;
   1.428 +      }
   1.429 + 
   1.430 +      ///Set the left side of the box
   1.431 +
   1.432 +      ///Set the left side of the box.
   1.433 +      ///It should only bee used for non-empty box
   1.434 +      void left(T t) {
   1.435 +	bottom_left.x = t;
   1.436 +      }
   1.437 +
   1.438 +      /// Give back the right side of the box
   1.439 +
   1.440 +      /// Give back the right side of the box.
   1.441 +      ///If the bounding box is empty, then the return value is not defined.
   1.442 +      T right() const {
   1.443 +        return top_right.x;
   1.444 +      }
   1.445 +
   1.446 +      ///Set the right side of the box
   1.447 +
   1.448 +      ///Set the right side of the box.
   1.449 +      ///It should only bee used for non-empty box
   1.450 +      void right(T t) {
   1.451 +	top_right.x = t;
   1.452 +      }
   1.453 +
   1.454 +      ///Give back the height of the box
   1.455 +
   1.456 +      ///Give back the height of the box.
   1.457 +      ///If the bounding box is empty, then the return value is not defined.
   1.458 +      T height() const {
   1.459 +        return top_right.y-bottom_left.y;
   1.460 +      }
   1.461 +
   1.462 +      ///Give back the width of the box
   1.463 +
   1.464 +      ///Give back the width of the box.
   1.465 +      ///If the bounding box is empty, then the return value is not defined.
   1.466 +      T width() const {
   1.467 +        return top_right.x-bottom_left.x;
   1.468 +      }
   1.469 +
   1.470 +      ///Checks whether a point is inside a bounding box
   1.471 +      bool inside(const Point<T>& u){
   1.472 +        if (_empty)
   1.473 +          return false;
   1.474 +        else{
   1.475 +          return ((u.x-bottom_left.x)*(top_right.x-u.x) >= 0 &&
   1.476 +              (u.y-bottom_left.y)*(top_right.y-u.y) >= 0 );
   1.477 +        }
   1.478 +      }
   1.479 +  
   1.480 +      ///Increments a bounding box with a point
   1.481 +      BoundingBox& add(const Point<T>& u){
   1.482 +        if (_empty){
   1.483 +          bottom_left=top_right=u;
   1.484 +          _empty = false;
   1.485 +        }
   1.486 +        else{
   1.487 +          if (bottom_left.x > u.x) bottom_left.x = u.x;
   1.488 +          if (bottom_left.y > u.y) bottom_left.y = u.y;
   1.489 +          if (top_right.x < u.x) top_right.x = u.x;
   1.490 +          if (top_right.y < u.y) top_right.y = u.y;
   1.491 +        }
   1.492 +        return *this;
   1.493 +      }
   1.494 +    
   1.495 +      ///Increments a bounding to contain another bounding box
   1.496 +      BoundingBox& add(const BoundingBox &u){
   1.497 +        if ( !u.empty() ){
   1.498 +          this->add(u.bottomLeft());
   1.499 +	  this->add(u.topRight());
   1.500 +        }
   1.501 +        return *this;
   1.502 +      }
   1.503 +  
   1.504 +      ///Intersection of two bounding boxes
   1.505 +      BoundingBox operator &(const BoundingBox& u){
   1.506 +        BoundingBox b;
   1.507 +	b.bottom_left.x=std::max(this->bottom_left.x,u.bottom_left.x);
   1.508 +	b.bottom_left.y=std::max(this->bottom_left.y,u.bottom_left.y);
   1.509 +	b.top_right.x=std::min(this->top_right.x,u.top_right.x);
   1.510 +	b.top_right.y=std::min(this->top_right.y,u.top_right.y);
   1.511 +	b._empty = this->_empty || u._empty ||
   1.512 +	  b.bottom_left.x>top_right.x && b.bottom_left.y>top_right.y;
   1.513 +        return b;
   1.514 +      }
   1.515 +
   1.516 +    };//class Boundingbox
   1.517 +
   1.518 +
   1.519 +  ///Map of x-coordinates of a dim2::Point<>-map
   1.520 +
   1.521 +  ///\ingroup maps
   1.522 +  ///Map of x-coordinates of a dim2::Point<>-map
   1.523 +  ///
   1.524 +  template<class M>
   1.525 +  class XMap 
   1.526 +  {
   1.527 +    M& _map;
   1.528 +  public:
   1.529 +
   1.530 +    typedef typename M::Value::Value Value;
   1.531 +    typedef typename M::Key Key;
   1.532 +    ///\e
   1.533 +    XMap(M& map) : _map(map) {}
   1.534 +    Value operator[](Key k) const {return _map[k].x;}
   1.535 +    void set(Key k,Value v) {_map.set(k,typename M::Value(v,_map[k].y));}
   1.536 +  };
   1.537 +    
   1.538 +  ///Returns an \ref XMap class
   1.539 +
   1.540 +  ///This function just returns an \ref XMap class.
   1.541 +  ///
   1.542 +  ///\ingroup maps
   1.543 +  ///\relates XMap
   1.544 +  template<class M> 
   1.545 +  inline XMap<M> xMap(M &m) 
   1.546 +  {
   1.547 +    return XMap<M>(m);
   1.548 +  }
   1.549 +
   1.550 +  template<class M> 
   1.551 +  inline XMap<M> xMap(const M &m) 
   1.552 +  {
   1.553 +    return XMap<M>(m);
   1.554 +  }
   1.555 +
   1.556 +  ///Constant (read only) version of \ref XMap
   1.557 +
   1.558 +  ///\ingroup maps
   1.559 +  ///Constant (read only) version of \ref XMap
   1.560 +  ///
   1.561 +  template<class M>
   1.562 +  class ConstXMap 
   1.563 +  {
   1.564 +    const M& _map;
   1.565 +  public:
   1.566 +
   1.567 +    typedef typename M::Value::Value Value;
   1.568 +    typedef typename M::Key Key;
   1.569 +    ///\e
   1.570 +    ConstXMap(const M &map) : _map(map) {}
   1.571 +    Value operator[](Key k) const {return _map[k].x;}
   1.572 +  };
   1.573 +    
   1.574 +  ///Returns a \ref ConstXMap class
   1.575 +
   1.576 +  ///This function just returns an \ref ConstXMap class.
   1.577 +  ///
   1.578 +  ///\ingroup maps
   1.579 +  ///\relates ConstXMap
   1.580 +  template<class M> 
   1.581 +  inline ConstXMap<M> xMap(const M &m) 
   1.582 +  {
   1.583 +    return ConstXMap<M>(m);
   1.584 +  }
   1.585 +
   1.586 +  ///Map of y-coordinates of a dim2::Point<>-map
   1.587 +    
   1.588 +  ///\ingroup maps
   1.589 +  ///Map of y-coordinates of a dim2::Point<>-map
   1.590 +  ///
   1.591 +  template<class M>
   1.592 +  class YMap 
   1.593 +  {
   1.594 +    M& _map;
   1.595 +  public:
   1.596 +
   1.597 +    typedef typename M::Value::Value Value;
   1.598 +    typedef typename M::Key Key;
   1.599 +    ///\e
   1.600 +    YMap(M& map) : _map(map) {}
   1.601 +    Value operator[](Key k) const {return _map[k].y;}
   1.602 +    void set(Key k,Value v) {_map.set(k,typename M::Value(_map[k].x,v));}
   1.603 +  };
   1.604 +
   1.605 +  ///Returns an \ref YMap class
   1.606 +
   1.607 +  ///This function just returns an \ref YMap class.
   1.608 +  ///
   1.609 +  ///\ingroup maps
   1.610 +  ///\relates YMap
   1.611 +  template<class M> 
   1.612 +  inline YMap<M> yMap(M &m) 
   1.613 +  {
   1.614 +    return YMap<M>(m);
   1.615 +  }
   1.616 +
   1.617 +  template<class M> 
   1.618 +  inline YMap<M> yMap(const M &m) 
   1.619 +  {
   1.620 +    return YMap<M>(m);
   1.621 +  }
   1.622 +
   1.623 +  ///Constant (read only) version of \ref YMap
   1.624 +
   1.625 +  ///\ingroup maps
   1.626 +  ///Constant (read only) version of \ref YMap
   1.627 +  ///
   1.628 +  template<class M>
   1.629 +  class ConstYMap 
   1.630 +  {
   1.631 +    const M& _map;
   1.632 +  public:
   1.633 +
   1.634 +    typedef typename M::Value::Value Value;
   1.635 +    typedef typename M::Key Key;
   1.636 +    ///\e
   1.637 +    ConstYMap(const M &map) : _map(map) {}
   1.638 +    Value operator[](Key k) const {return _map[k].y;}
   1.639 +  };
   1.640 +    
   1.641 +  ///Returns a \ref ConstYMap class
   1.642 +
   1.643 +  ///This function just returns an \ref ConstYMap class.
   1.644 +  ///
   1.645 +  ///\ingroup maps
   1.646 +  ///\relates ConstYMap
   1.647 +  template<class M> 
   1.648 +  inline ConstYMap<M> yMap(const M &m) 
   1.649 +  {
   1.650 +    return ConstYMap<M>(m);
   1.651 +  }
   1.652 +
   1.653 +
   1.654 +    ///\brief Map of the \ref Point::normSquare() "normSquare()"
   1.655 +    ///of an \ref Point "Point"-map
   1.656 +    ///
   1.657 +    ///Map of the \ref Point::normSquare() "normSquare()"
   1.658 +    ///of an \ref Point "Point"-map
   1.659 +    ///\ingroup maps
   1.660 +    ///
   1.661 +  template<class M>
   1.662 +  class NormSquareMap 
   1.663 +  {
   1.664 +    const M& _map;
   1.665 +  public:
   1.666 +
   1.667 +    typedef typename M::Value::Value Value;
   1.668 +    typedef typename M::Key Key;
   1.669 +    ///\e
   1.670 +    NormSquareMap(const M &map) : _map(map) {}
   1.671 +    Value operator[](Key k) const {return _map[k].normSquare();}
   1.672 +  };
   1.673 +    
   1.674 +  ///Returns a \ref NormSquareMap class
   1.675 +
   1.676 +  ///This function just returns an \ref NormSquareMap class.
   1.677 +  ///
   1.678 +  ///\ingroup maps
   1.679 +  ///\relates NormSquareMap
   1.680 +  template<class M> 
   1.681 +  inline NormSquareMap<M> normSquareMap(const M &m) 
   1.682 +  {
   1.683 +    return NormSquareMap<M>(m);
   1.684 +  }
   1.685 +
   1.686 +  /// @}
   1.687 +
   1.688 +  } //namespce dim2
   1.689 +  
   1.690 +} //namespace lemon
   1.691 +
   1.692 +#endif //LEMON_DIM2_H