source:lemon-1.2/lemon/dim2.h@135:6e7aee618f03

Last change on this file since 135:6e7aee618f03 was 49:9a556af88710, checked in by Peter Kovacs <kpeter@…>, 13 years ago

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