COIN-OR::LEMON - Graph Library

source: lemon/lemon/dim2.h

Last change on this file was 1311:6aea07d5ca48, checked in by Alpar Juttner <alpar@…>, 5 years ago

Add missing include header and std:: namespace spec. (#487)

File size: 17.0 KB
Line 
1/* -*- mode: C++; indent-tabs-mode: nil; -*-
2 *
3 * This file is a part of LEMON, a generic C++ optimization library.
4 *
5 * Copyright (C) 2003-2009
6 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
7 * (Egervary Research Group on Combinatorial Optimization, EGRES).
8 *
9 * Permission to use, modify and distribute this software is granted
10 * provided that this copyright notice appears in all copies. For
11 * precise terms see the accompanying LICENSE file.
12 *
13 * This software is provided "AS IS" with no warranty of any kind,
14 * express or implied, and with no claim as to its suitability for any
15 * purpose.
16 *
17 */
18
19#ifndef LEMON_DIM2_H
20#define LEMON_DIM2_H
21
22#include <iostream>
23#include <algorithm>
24
25///\ingroup geomdat
26///\file
27///\brief A simple two dimensional vector and a bounding box implementation
28
29namespace lemon {
30
31  ///Tools for handling two dimensional coordinates
32
33  ///This namespace is a storage of several
34  ///tools for handling two dimensional coordinates
35  namespace dim2 {
36
37  /// \addtogroup geomdat
38  /// @{
39
40  /// Two dimensional vector (plain vector)
41
42  /// A simple two dimensional vector (plain vector) implementation
43  /// with the usual vector operations.
44  template<typename T>
45    class Point {
46
47    public:
48
49      typedef T Value;
50
51      ///First coordinate
52      T x;
53      ///Second coordinate
54      T y;
55
56      ///Default constructor
57      Point() {}
58
59      ///Construct an instance from coordinates
60      Point(T a, T b) : x(a), y(b) { }
61
62      ///Returns the dimension of the vector (i.e. returns 2).
63
64      ///The dimension of the vector.
65      ///This function always returns 2.
66      int size() const { return 2; }
67
68      ///Subscripting operator
69
70      ///\c p[0] is \c p.x and \c p[1] is \c p.y
71      ///
72      T& operator[](int idx) { return idx == 0 ? x : y; }
73
74      ///Const subscripting operator
75
76      ///\c p[0] is \c p.x and \c p[1] is \c p.y
77      ///
78      const T& operator[](int idx) const { return idx == 0 ? x : y; }
79
80      ///Conversion constructor
81      template<class TT> Point(const Point<TT> &p) : x(p.x), y(p.y) {}
82
83      ///Give back the square of the norm of the vector
84      T normSquare() const {
85        return x*x+y*y;
86      }
87
88      ///Increment the left hand side by \c u
89      Point<T>& operator +=(const Point<T>& u) {
90        x += u.x;
91        y += u.y;
92        return *this;
93      }
94
95      ///Decrement the left hand side by \c u
96      Point<T>& operator -=(const Point<T>& u) {
97        x -= u.x;
98        y -= u.y;
99        return *this;
100      }
101
102      ///Multiply the left hand side with a scalar
103      Point<T>& operator *=(const T &u) {
104        x *= u;
105        y *= u;
106        return *this;
107      }
108
109      ///Divide the left hand side by a scalar
110      Point<T>& operator /=(const T &u) {
111        x /= u;
112        y /= u;
113        return *this;
114      }
115
116      ///Return the scalar product of two vectors
117      T operator *(const Point<T>& u) const {
118        return x*u.x+y*u.y;
119      }
120
121      ///Return the sum of two vectors
122      Point<T> operator+(const Point<T> &u) const {
123        Point<T> b=*this;
124        return b+=u;
125      }
126
127      ///Return the negative of the vector
128      Point<T> operator-() const {
129        Point<T> b=*this;
130        b.x=-b.x; b.y=-b.y;
131        return b;
132      }
133
134      ///Return the difference of two vectors
135      Point<T> operator-(const Point<T> &u) const {
136        Point<T> b=*this;
137        return b-=u;
138      }
139
140      ///Return a vector multiplied by a scalar
141      Point<T> operator*(const T &u) const {
142        Point<T> b=*this;
143        return b*=u;
144      }
145
146      ///Return a vector divided by a scalar
147      Point<T> operator/(const T &u) const {
148        Point<T> b=*this;
149        return b/=u;
150      }
151
152      ///Test equality
153      bool operator==(const Point<T> &u) const {
154        return (x==u.x) && (y==u.y);
155      }
156
157      ///Test inequality
158      bool operator!=(Point u) const {
159        return  (x!=u.x) || (y!=u.y);
160      }
161
162    };
163
164  ///Return a Point
165
166  ///Return a Point.
167  ///\relates Point
168  template <typename T>
169  inline Point<T> makePoint(const T& x, const T& y) {
170    return Point<T>(x, y);
171  }
172
173  ///Return a vector multiplied by a scalar
174
175  ///Return a vector multiplied by a scalar.
176  ///\relates Point
177  template<typename T> Point<T> operator*(const T &u,const Point<T> &x) {
178    return x*u;
179  }
180
181  ///Read a plain vector from a stream
182
183  ///Read a plain vector from a stream.
184  ///\relates Point
185  ///
186  template<typename T>
187  inline std::istream& operator>>(std::istream &is, Point<T> &z) {
188    char c;
189    if (is >> c) {
190      if (c != '(') is.putback(c);
191    } else {
192      is.clear();
193    }
194    if (!(is >> z.x)) return is;
195    if (is >> c) {
196      if (c != ',') is.putback(c);
197    } else {
198      is.clear();
199    }
200    if (!(is >> z.y)) return is;
201    if (is >> c) {
202      if (c != ')') is.putback(c);
203    } else {
204      is.clear();
205    }
206    return is;
207  }
208
209  ///Write a plain vector to a stream
210
211  ///Write a plain vector to a stream.
212  ///\relates Point
213  ///
214  template<typename T>
215  inline std::ostream& operator<<(std::ostream &os, const Point<T>& z)
216  {
217    os << "(" << z.x << "," << z.y << ")";
218    return os;
219  }
220
221  ///Rotate by 90 degrees
222
223  ///Returns the parameter rotated by 90 degrees in positive direction.
224  ///\relates Point
225  ///
226  template<typename T>
227  inline Point<T> rot90(const Point<T> &z)
228  {
229    return Point<T>(-z.y,z.x);
230  }
231
232  ///Rotate by 180 degrees
233
234  ///Returns the parameter rotated by 180 degrees.
235  ///\relates Point
236  ///
237  template<typename T>
238  inline Point<T> rot180(const Point<T> &z)
239  {
240    return Point<T>(-z.x,-z.y);
241  }
242
243  ///Rotate by 270 degrees
244
245  ///Returns the parameter rotated by 90 degrees in negative direction.
246  ///\relates Point
247  ///
248  template<typename T>
249  inline Point<T> rot270(const Point<T> &z)
250  {
251    return Point<T>(z.y,-z.x);
252  }
253
254
255
256  /// Bounding box of plain vectors (points).
257
258  /// A class to calculate or store the bounding box of plain vectors
259  /// (\ref Point "points").
260  template<typename T>
261  class Box {
262      Point<T> _bottom_left, _top_right;
263      bool _empty;
264    public:
265
266      ///Default constructor: creates an empty box
267      Box() { _empty = true; }
268
269      ///Construct a box from one point
270      Box(Point<T> a) {
271        _bottom_left = _top_right = a;
272        _empty = false;
273      }
274
275      ///Construct a box from two points
276
277      ///Construct a box from two points.
278      ///\param a The bottom left corner.
279      ///\param b The top right corner.
280      ///\warning The coordinates of the bottom left corner must be no more
281      ///than those of the top right one.
282      Box(Point<T> a,Point<T> b)
283      {
284        _bottom_left = a;
285        _top_right = b;
286        _empty = false;
287      }
288
289      ///Construct a box from four numbers
290
291      ///Construct a box from four numbers.
292      ///\param l The left side of the box.
293      ///\param b The bottom of the box.
294      ///\param r The right side of the box.
295      ///\param t The top of the box.
296      ///\warning The left side must be no more than the right side and
297      ///bottom must be no more than the top.
298      Box(T l,T b,T r,T t)
299      {
300        _bottom_left=Point<T>(l,b);
301        _top_right=Point<T>(r,t);
302        _empty = false;
303      }
304
305      ///Return \c true if the box is empty.
306
307      ///Return \c true if the box is empty (i.e. return \c false
308      ///if at least one point was added to the box or the coordinates of
309      ///the box were set).
310      ///
311      ///The coordinates of an empty box are not defined.
312      bool empty() const {
313        return _empty;
314      }
315
316      ///Make the box empty
317      void clear() {
318        _empty = true;
319      }
320
321      ///Give back the bottom left corner of the box
322
323      ///Give back the bottom left corner of the box.
324      ///If the box is empty, then the return value is not defined.
325      Point<T> bottomLeft() const {
326        return _bottom_left;
327      }
328
329      ///Set the bottom left corner of the box
330
331      ///Set the bottom left corner of the box.
332      ///\pre The box must not be empty.
333      void bottomLeft(Point<T> p) {
334        _bottom_left = p;
335      }
336
337      ///Give back the top right corner of the box
338
339      ///Give back the top right corner of the box.
340      ///If the box is empty, then the return value is not defined.
341      Point<T> topRight() const {
342        return _top_right;
343      }
344
345      ///Set the top right corner of the box
346
347      ///Set the top right corner of the box.
348      ///\pre The box must not be empty.
349      void topRight(Point<T> p) {
350        _top_right = p;
351      }
352
353      ///Give back the bottom right corner of the box
354
355      ///Give back the bottom right corner of the box.
356      ///If the box is empty, then the return value is not defined.
357      Point<T> bottomRight() const {
358        return Point<T>(_top_right.x,_bottom_left.y);
359      }
360
361      ///Set the bottom right corner of the box
362
363      ///Set the bottom right corner of the box.
364      ///\pre The box must not be empty.
365      void bottomRight(Point<T> p) {
366        _top_right.x = p.x;
367        _bottom_left.y = p.y;
368      }
369
370      ///Give back the top left corner of the box
371
372      ///Give back the top left corner of the box.
373      ///If the box is empty, then the return value is not defined.
374      Point<T> topLeft() const {
375        return Point<T>(_bottom_left.x,_top_right.y);
376      }
377
378      ///Set the top left corner of the box
379
380      ///Set the top left corner of the box.
381      ///\pre The box must not be empty.
382      void topLeft(Point<T> p) {
383        _top_right.y = p.y;
384        _bottom_left.x = p.x;
385      }
386
387      ///Give back the bottom of the box
388
389      ///Give back the bottom of the box.
390      ///If the box is empty, then the return value is not defined.
391      T bottom() const {
392        return _bottom_left.y;
393      }
394
395      ///Set the bottom of the box
396
397      ///Set the bottom of the box.
398      ///\pre The box must not be empty.
399      void bottom(T t) {
400        _bottom_left.y = t;
401      }
402
403      ///Give back the top of the box
404
405      ///Give back the top of the box.
406      ///If the box is empty, then the return value is not defined.
407      T top() const {
408        return _top_right.y;
409      }
410
411      ///Set the top of the box
412
413      ///Set the top of the box.
414      ///\pre The box must not be empty.
415      void top(T t) {
416        _top_right.y = t;
417      }
418
419      ///Give back the left side of the box
420
421      ///Give back the left side of the box.
422      ///If the box is empty, then the return value is not defined.
423      T left() const {
424        return _bottom_left.x;
425      }
426
427      ///Set the left side of the box
428
429      ///Set the left side of the box.
430      ///\pre The box must not be empty.
431      void left(T t) {
432        _bottom_left.x = t;
433      }
434
435      /// Give back the right side of the box
436
437      /// Give back the right side of the box.
438      ///If the box is empty, then the return value is not defined.
439      T right() const {
440        return _top_right.x;
441      }
442
443      ///Set the right side of the box
444
445      ///Set the right side of the box.
446      ///\pre The box must not be empty.
447      void right(T t) {
448        _top_right.x = t;
449      }
450
451      ///Give back the height of the box
452
453      ///Give back the height of the box.
454      ///If the box is empty, then the return value is not defined.
455      T height() const {
456        return _top_right.y-_bottom_left.y;
457      }
458
459      ///Give back the width of the box
460
461      ///Give back the width of the box.
462      ///If the box is empty, then the return value is not defined.
463      T width() const {
464        return _top_right.x-_bottom_left.x;
465      }
466
467      ///Checks whether a point is inside the box
468      bool inside(const Point<T>& u) const {
469        if (_empty)
470          return false;
471        else {
472          return ( (u.x-_bottom_left.x)*(_top_right.x-u.x) >= 0 &&
473                   (u.y-_bottom_left.y)*(_top_right.y-u.y) >= 0 );
474        }
475      }
476
477      ///Increments the box with a point
478
479      ///Increments the box with a point.
480      ///
481      Box& add(const Point<T>& u){
482        if (_empty) {
483          _bottom_left = _top_right = u;
484          _empty = false;
485        }
486        else {
487          if (_bottom_left.x > u.x) _bottom_left.x = u.x;
488          if (_bottom_left.y > u.y) _bottom_left.y = u.y;
489          if (_top_right.x < u.x) _top_right.x = u.x;
490          if (_top_right.y < u.y) _top_right.y = u.y;
491        }
492        return *this;
493      }
494
495      ///Increments the box to contain another box
496
497      ///Increments the box to contain another box.
498      ///
499      Box& add(const Box &u){
500        if ( !u.empty() ){
501          add(u._bottom_left);
502          add(u._top_right);
503        }
504        return *this;
505      }
506
507      ///Intersection of two boxes
508
509      ///Intersection of two boxes.
510      ///
511      Box operator&(const Box& u) const {
512        Box b;
513        if (_empty || u._empty) {
514          b._empty = true;
515        } else {
516          b._bottom_left.x = std::max(_bottom_left.x, u._bottom_left.x);
517          b._bottom_left.y = std::max(_bottom_left.y, u._bottom_left.y);
518          b._top_right.x = std::min(_top_right.x, u._top_right.x);
519          b._top_right.y = std::min(_top_right.y, u._top_right.y);
520          b._empty = b._bottom_left.x > b._top_right.x ||
521                     b._bottom_left.y > b._top_right.y;
522        }
523        return b;
524      }
525
526  };//class Box
527
528
529  ///Read a box from a stream
530
531  ///Read a box from a stream.
532  ///\relates Box
533  template<typename T>
534  inline std::istream& operator>>(std::istream &is, Box<T>& b) {
535    char c;
536    Point<T> p;
537    if (is >> c) {
538      if (c != '(') is.putback(c);
539    } else {
540      is.clear();
541    }
542    if (!(is >> p)) return is;
543    b.bottomLeft(p);
544    if (is >> c) {
545      if (c != ',') is.putback(c);
546    } else {
547      is.clear();
548    }
549    if (!(is >> p)) return is;
550    b.topRight(p);
551    if (is >> c) {
552      if (c != ')') is.putback(c);
553    } else {
554      is.clear();
555    }
556    return is;
557  }
558
559  ///Write a box to a stream
560
561  ///Write a box to a stream.
562  ///\relates Box
563  template<typename T>
564  inline std::ostream& operator<<(std::ostream &os, const Box<T>& b)
565  {
566    os << "(" << b.bottomLeft() << "," << b.topRight() << ")";
567    return os;
568  }
569
570  ///Map of x-coordinates of a <tt>Point</tt>-map
571
572  ///Map of x-coordinates of a \ref Point "Point"-map.
573  ///
574  template<class M>
575  class XMap
576  {
577    M& _map;
578  public:
579
580    typedef typename M::Value::Value Value;
581    typedef typename M::Key Key;
582    ///\e
583    XMap(M& map) : _map(map) {}
584    Value operator[](Key k) const {return _map[k].x;}
585    void set(Key k,Value v) {_map.set(k,typename M::Value(v,_map[k].y));}
586  };
587
588  ///Returns an XMap class
589
590  ///This function just returns an XMap class.
591  ///\relates XMap
592  template<class M>
593  inline XMap<M> xMap(M &m)
594  {
595    return XMap<M>(m);
596  }
597
598  template<class M>
599  inline XMap<M> xMap(const M &m)
600  {
601    return XMap<M>(m);
602  }
603
604  ///Constant (read only) version of XMap
605
606  ///Constant (read only) version of XMap.
607  ///
608  template<class M>
609  class ConstXMap
610  {
611    const M& _map;
612  public:
613
614    typedef typename M::Value::Value Value;
615    typedef typename M::Key Key;
616    ///\e
617    ConstXMap(const M &map) : _map(map) {}
618    Value operator[](Key k) const {return _map[k].x;}
619  };
620
621  ///Returns a ConstXMap class
622
623  ///This function just returns a ConstXMap class.
624  ///\relates ConstXMap
625  template<class M>
626  inline ConstXMap<M> xMap(const M &m)
627  {
628    return ConstXMap<M>(m);
629  }
630
631  ///Map of y-coordinates of a <tt>Point</tt>-map
632
633  ///Map of y-coordinates of a \ref Point "Point"-map.
634  ///
635  template<class M>
636  class YMap
637  {
638    M& _map;
639  public:
640
641    typedef typename M::Value::Value Value;
642    typedef typename M::Key Key;
643    ///\e
644    YMap(M& map) : _map(map) {}
645    Value operator[](Key k) const {return _map[k].y;}
646    void set(Key k,Value v) {_map.set(k,typename M::Value(_map[k].x,v));}
647  };
648
649  ///Returns a YMap class
650
651  ///This function just returns a YMap class.
652  ///\relates YMap
653  template<class M>
654  inline YMap<M> yMap(M &m)
655  {
656    return YMap<M>(m);
657  }
658
659  template<class M>
660  inline YMap<M> yMap(const M &m)
661  {
662    return YMap<M>(m);
663  }
664
665  ///Constant (read only) version of YMap
666
667  ///Constant (read only) version of YMap.
668  ///
669  template<class M>
670  class ConstYMap
671  {
672    const M& _map;
673  public:
674
675    typedef typename M::Value::Value Value;
676    typedef typename M::Key Key;
677    ///\e
678    ConstYMap(const M &map) : _map(map) {}
679    Value operator[](Key k) const {return _map[k].y;}
680  };
681
682  ///Returns a ConstYMap class
683
684  ///This function just returns a ConstYMap class.
685  ///\relates ConstYMap
686  template<class M>
687  inline ConstYMap<M> yMap(const M &m)
688  {
689    return ConstYMap<M>(m);
690  }
691
692
693  ///\brief Map of the normSquare() of a <tt>Point</tt>-map
694  ///
695  ///Map of the \ref Point::normSquare() "normSquare()"
696  ///of a \ref Point "Point"-map.
697  template<class M>
698  class NormSquareMap
699  {
700    const M& _map;
701  public:
702
703    typedef typename M::Value::Value Value;
704    typedef typename M::Key Key;
705    ///\e
706    NormSquareMap(const M &map) : _map(map) {}
707    Value operator[](Key k) const {return _map[k].normSquare();}
708  };
709
710  ///Returns a NormSquareMap class
711
712  ///This function just returns a NormSquareMap class.
713  ///\relates NormSquareMap
714  template<class M>
715  inline NormSquareMap<M> normSquareMap(const M &m)
716  {
717    return NormSquareMap<M>(m);
718  }
719
720  /// @}
721
722  } //namespce dim2
723
724} //namespace lemon
725
726#endif //LEMON_DIM2_H
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