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 {
1.346 +      }
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 {
1.412 +      }
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 {
1.444 +      }
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 {
1.460 +      }
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 {
1.468 +      }
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() ){
1.500 +        }
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