# source:lemon/lemon/dim2.h@478:5a1e9fdcfd3a

Last change on this file since 478:5a1e9fdcfd3a was 463:88ed40ad0d4f, checked in by Alpar Juttner <alpar@…>, 12 years ago

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1/* -*- mode: C++; indent-tabs-mode: nil; -*-
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
24///\ingroup misc
25///\file
26///\brief A simple two dimensional vector and a bounding box implementation
27///
28/// The class \ref lemon::dim2::Point "dim2::Point" implements
29/// a two dimensional vector with the usual operations.
30///
31/// The class \ref lemon::dim2::Box "dim2::Box" can be used to determine
32/// the rectangular bounding box of a set of
33/// \ref lemon::dim2::Point "dim2::Point"'s.
34
35namespace lemon {
36
37  ///Tools for handling two dimensional coordinates
38
39  ///This namespace is a storage of several
40  ///tools for handling two dimensional coordinates
41  namespace dim2 {
42
44  /// @{
45
46  /// Two dimensional vector (plain vector)
47
48  /// A simple two dimensional vector (plain vector) implementation
49  /// with the usual vector operations.
50  template<typename T>
51    class Point {
52
53    public:
54
55      typedef T Value;
56
57      ///First coordinate
58      T x;
59      ///Second coordinate
60      T y;
61
62      ///Default constructor
63      Point() {}
64
65      ///Construct an instance from coordinates
66      Point(T a, T b) : x(a), y(b) { }
67
68      ///Returns the dimension of the vector (i.e. returns 2).
69
70      ///The dimension of the vector.
71      ///This function always returns 2.
72      int size() const { return 2; }
73
74      ///Subscripting operator
75
76      ///\c p[0] is \c p.x and \c p[1] is \c p.y
77      ///
78      T& operator[](int idx) { return idx == 0 ? x : y; }
79
80      ///Const subscripting operator
81
82      ///\c p[0] is \c p.x and \c p[1] is \c p.y
83      ///
84      const T& operator[](int idx) const { return idx == 0 ? x : y; }
85
86      ///Conversion constructor
87      template<class TT> Point(const Point<TT> &p) : x(p.x), y(p.y) {}
88
89      ///Give back the square of the norm of the vector
90      T normSquare() const {
91        return x*x+y*y;
92      }
93
94      ///Increment the left hand side by \c u
95      Point<T>& operator +=(const Point<T>& u) {
96        x += u.x;
97        y += u.y;
98        return *this;
99      }
100
101      ///Decrement the left hand side by \c u
102      Point<T>& operator -=(const Point<T>& u) {
103        x -= u.x;
104        y -= u.y;
105        return *this;
106      }
107
108      ///Multiply the left hand side with a scalar
109      Point<T>& operator *=(const T &u) {
110        x *= u;
111        y *= u;
112        return *this;
113      }
114
115      ///Divide the left hand side by a scalar
116      Point<T>& operator /=(const T &u) {
117        x /= u;
118        y /= u;
119        return *this;
120      }
121
122      ///Return the scalar product of two vectors
123      T operator *(const Point<T>& u) const {
124        return x*u.x+y*u.y;
125      }
126
127      ///Return the sum of two vectors
128      Point<T> operator+(const Point<T> &u) const {
129        Point<T> b=*this;
130        return b+=u;
131      }
132
133      ///Return the negative of the vector
134      Point<T> operator-() const {
135        Point<T> b=*this;
136        b.x=-b.x; b.y=-b.y;
137        return b;
138      }
139
140      ///Return the difference of two vectors
141      Point<T> operator-(const Point<T> &u) const {
142        Point<T> b=*this;
143        return b-=u;
144      }
145
146      ///Return a vector multiplied by a scalar
147      Point<T> operator*(const T &u) const {
148        Point<T> b=*this;
149        return b*=u;
150      }
151
152      ///Return a vector divided by a scalar
153      Point<T> operator/(const T &u) const {
154        Point<T> b=*this;
155        return b/=u;
156      }
157
158      ///Test equality
159      bool operator==(const Point<T> &u) const {
160        return (x==u.x) && (y==u.y);
161      }
162
163      ///Test inequality
164      bool operator!=(Point u) const {
165        return  (x!=u.x) || (y!=u.y);
166      }
167
168    };
169
170  ///Return a Point
171
172  ///Return a Point.
173  ///\relates Point
174  template <typename T>
175  inline Point<T> makePoint(const T& x, const T& y) {
176    return Point<T>(x, y);
177  }
178
179  ///Return a vector multiplied by a scalar
180
181  ///Return a vector multiplied by a scalar.
182  ///\relates Point
183  template<typename T> Point<T> operator*(const T &u,const Point<T> &x) {
184    return x*u;
185  }
186
187  ///Read a plain vector from a stream
188
189  ///Read a plain vector from a stream.
190  ///\relates Point
191  ///
192  template<typename T>
193  inline std::istream& operator>>(std::istream &is, Point<T> &z) {
194    char c;
195    if (is >> c) {
196      if (c != '(') is.putback(c);
197    } else {
198      is.clear();
199    }
200    if (!(is >> z.x)) return is;
201    if (is >> c) {
202      if (c != ',') is.putback(c);
203    } else {
204      is.clear();
205    }
206    if (!(is >> z.y)) return is;
207    if (is >> c) {
208      if (c != ')') is.putback(c);
209    } else {
210      is.clear();
211    }
212    return is;
213  }
214
215  ///Write a plain vector to a stream
216
217  ///Write a plain vector to a stream.
218  ///\relates Point
219  ///
220  template<typename T>
221  inline std::ostream& operator<<(std::ostream &os, const Point<T>& z)
222  {
223    os << "(" << z.x << "," << z.y << ")";
224    return os;
225  }
226
227  ///Rotate by 90 degrees
228
229  ///Returns the parameter rotated by 90 degrees in positive direction.
230  ///\relates Point
231  ///
232  template<typename T>
233  inline Point<T> rot90(const Point<T> &z)
234  {
235    return Point<T>(-z.y,z.x);
236  }
237
238  ///Rotate by 180 degrees
239
240  ///Returns the parameter rotated by 180 degrees.
241  ///\relates Point
242  ///
243  template<typename T>
244  inline Point<T> rot180(const Point<T> &z)
245  {
246    return Point<T>(-z.x,-z.y);
247  }
248
249  ///Rotate by 270 degrees
250
251  ///Returns the parameter rotated by 90 degrees in negative direction.
252  ///\relates Point
253  ///
254  template<typename T>
255  inline Point<T> rot270(const Point<T> &z)
256  {
257    return Point<T>(z.y,-z.x);
258  }
259
260
261
262  /// Bounding box of plain vectors (points).
263
264  /// A class to calculate or store the bounding box of plain vectors
265  /// (\ref Point "points").
266  template<typename T>
267  class Box {
268      Point<T> _bottom_left, _top_right;
269      bool _empty;
270    public:
271
272      ///Default constructor: creates an empty box
273      Box() { _empty = true; }
274
275      ///Construct a box from one point
276      Box(Point<T> a) {
277        _bottom_left = _top_right = a;
278        _empty = false;
279      }
280
281      ///Construct a box from two points
282
283      ///Construct a box from two points.
284      ///\param a The bottom left corner.
285      ///\param b The top right corner.
286      ///\warning The coordinates of the bottom left corner must be no more
287      ///than those of the top right one.
288      Box(Point<T> a,Point<T> b)
289      {
290        _bottom_left = a;
291        _top_right = b;
292        _empty = false;
293      }
294
295      ///Construct a box from four numbers
296
297      ///Construct a box from four numbers.
298      ///\param l The left side of the box.
299      ///\param b The bottom of the box.
300      ///\param r The right side of the box.
301      ///\param t The top of the box.
302      ///\warning The left side must be no more than the right side and
303      ///bottom must be no more than the top.
304      Box(T l,T b,T r,T t)
305      {
306        _bottom_left=Point<T>(l,b);
307        _top_right=Point<T>(r,t);
308        _empty = false;
309      }
310
311      ///Return \c true if the box is empty.
312
313      ///Return \c true if the box is empty (i.e. return \c false
314      ///if at least one point was added to the box or the coordinates of
315      ///the box were set).
316      ///
317      ///The coordinates of an empty box are not defined.
318      bool empty() const {
319        return _empty;
320      }
321
322      ///Make the box empty
323      void clear() {
324        _empty = true;
325      }
326
327      ///Give back the bottom left corner of the box
328
329      ///Give back the bottom left corner of the box.
330      ///If the box is empty, then the return value is not defined.
331      Point<T> bottomLeft() const {
332        return _bottom_left;
333      }
334
335      ///Set the bottom left corner of the box
336
337      ///Set the bottom left corner of the box.
338      ///\pre The box must not be empty.
339      void bottomLeft(Point<T> p) {
340        _bottom_left = p;
341      }
342
343      ///Give back the top right corner of the box
344
345      ///Give back the top right corner of the box.
346      ///If the box is empty, then the return value is not defined.
347      Point<T> topRight() const {
348        return _top_right;
349      }
350
351      ///Set the top right corner of the box
352
353      ///Set the top right corner of the box.
354      ///\pre The box must not be empty.
355      void topRight(Point<T> p) {
356        _top_right = p;
357      }
358
359      ///Give back the bottom right corner of the box
360
361      ///Give back the bottom right corner of the box.
362      ///If the box is empty, then the return value is not defined.
363      Point<T> bottomRight() const {
364        return Point<T>(_top_right.x,_bottom_left.y);
365      }
366
367      ///Set the bottom right corner of the box
368
369      ///Set the bottom right corner of the box.
370      ///\pre The box must not be empty.
371      void bottomRight(Point<T> p) {
372        _top_right.x = p.x;
373        _bottom_left.y = p.y;
374      }
375
376      ///Give back the top left corner of the box
377
378      ///Give back the top left corner of the box.
379      ///If the box is empty, then the return value is not defined.
380      Point<T> topLeft() const {
381        return Point<T>(_bottom_left.x,_top_right.y);
382      }
383
384      ///Set the top left corner of the box
385
386      ///Set the top left corner of the box.
387      ///\pre The box must not be empty.
388      void topLeft(Point<T> p) {
389        _top_right.y = p.y;
390        _bottom_left.x = p.x;
391      }
392
393      ///Give back the bottom of the box
394
395      ///Give back the bottom of the box.
396      ///If the box is empty, then the return value is not defined.
397      T bottom() const {
398        return _bottom_left.y;
399      }
400
401      ///Set the bottom of the box
402
403      ///Set the bottom of the box.
404      ///\pre The box must not be empty.
405      void bottom(T t) {
406        _bottom_left.y = t;
407      }
408
409      ///Give back the top of the box
410
411      ///Give back the top of the box.
412      ///If the box is empty, then the return value is not defined.
413      T top() const {
414        return _top_right.y;
415      }
416
417      ///Set the top of the box
418
419      ///Set the top of the box.
420      ///\pre The box must not be empty.
421      void top(T t) {
422        _top_right.y = t;
423      }
424
425      ///Give back the left side of the box
426
427      ///Give back the left side of the box.
428      ///If the box is empty, then the return value is not defined.
429      T left() const {
430        return _bottom_left.x;
431      }
432
433      ///Set the left side of the box
434
435      ///Set the left side of the box.
436      ///\pre The box must not be empty.
437      void left(T t) {
438        _bottom_left.x = t;
439      }
440
441      /// Give back the right side of the box
442
443      /// Give back the right side of the box.
444      ///If the box is empty, then the return value is not defined.
445      T right() const {
446        return _top_right.x;
447      }
448
449      ///Set the right side of the box
450
451      ///Set the right side of the box.
452      ///\pre The box must not be empty.
453      void right(T t) {
454        _top_right.x = t;
455      }
456
457      ///Give back the height of the box
458
459      ///Give back the height of the box.
460      ///If the box is empty, then the return value is not defined.
461      T height() const {
462        return _top_right.y-_bottom_left.y;
463      }
464
465      ///Give back the width of the box
466
467      ///Give back the width of the box.
468      ///If the box is empty, then the return value is not defined.
469      T width() const {
470        return _top_right.x-_bottom_left.x;
471      }
472
473      ///Checks whether a point is inside the box
474      bool inside(const Point<T>& u) const {
475        if (_empty)
476          return false;
477        else {
478          return ( (u.x-_bottom_left.x)*(_top_right.x-u.x) >= 0 &&
479                   (u.y-_bottom_left.y)*(_top_right.y-u.y) >= 0 );
480        }
481      }
482
483      ///Increments the box with a point
484
485      ///Increments the box with a point.
486      ///
488        if (_empty) {
489          _bottom_left = _top_right = u;
490          _empty = false;
491        }
492        else {
493          if (_bottom_left.x > u.x) _bottom_left.x = u.x;
494          if (_bottom_left.y > u.y) _bottom_left.y = u.y;
495          if (_top_right.x < u.x) _top_right.x = u.x;
496          if (_top_right.y < u.y) _top_right.y = u.y;
497        }
498        return *this;
499      }
500
501      ///Increments the box to contain another box
502
503      ///Increments the box to contain another box.
504      ///
506        if ( !u.empty() ){
509        }
510        return *this;
511      }
512
513      ///Intersection of two boxes
514
515      ///Intersection of two boxes.
516      ///
517      Box operator&(const Box& u) const {
518        Box b;
519        if (_empty || u._empty) {
520          b._empty = true;
521        } else {
522          b._bottom_left.x = std::max(_bottom_left.x, u._bottom_left.x);
523          b._bottom_left.y = std::max(_bottom_left.y, u._bottom_left.y);
524          b._top_right.x = std::min(_top_right.x, u._top_right.x);
525          b._top_right.y = std::min(_top_right.y, u._top_right.y);
526          b._empty = b._bottom_left.x > b._top_right.x ||
527                     b._bottom_left.y > b._top_right.y;
528        }
529        return b;
530      }
531
532  };//class Box
533
534
535  ///Read a box from a stream
536
537  ///Read a box from a stream.
538  ///\relates Box
539  template<typename T>
540  inline std::istream& operator>>(std::istream &is, Box<T>& b) {
541    char c;
542    Point<T> p;
543    if (is >> c) {
544      if (c != '(') is.putback(c);
545    } else {
546      is.clear();
547    }
548    if (!(is >> p)) return is;
549    b.bottomLeft(p);
550    if (is >> c) {
551      if (c != ',') is.putback(c);
552    } else {
553      is.clear();
554    }
555    if (!(is >> p)) return is;
556    b.topRight(p);
557    if (is >> c) {
558      if (c != ')') is.putback(c);
559    } else {
560      is.clear();
561    }
562    return is;
563  }
564
565  ///Write a box to a stream
566
567  ///Write a box to a stream.
568  ///\relates Box
569  template<typename T>
570  inline std::ostream& operator<<(std::ostream &os, const Box<T>& b)
571  {
572    os << "(" << b.bottomLeft() << "," << b.topRight() << ")";
573    return os;
574  }
575
576  ///Map of x-coordinates of a <tt>Point</tt>-map
577
578  ///Map of x-coordinates of a \ref Point "Point"-map.
579  ///
580  template<class M>
581  class XMap
582  {
583    M& _map;
584  public:
585
586    typedef typename M::Value::Value Value;
587    typedef typename M::Key Key;
588    ///\e
589    XMap(M& map) : _map(map) {}
590    Value operator[](Key k) const {return _map[k].x;}
591    void set(Key k,Value v) {_map.set(k,typename M::Value(v,_map[k].y));}
592  };
593
594  ///Returns an XMap class
595
596  ///This function just returns an XMap class.
597  ///\relates XMap
598  template<class M>
599  inline XMap<M> xMap(M &m)
600  {
601    return XMap<M>(m);
602  }
603
604  template<class M>
605  inline XMap<M> xMap(const M &m)
606  {
607    return XMap<M>(m);
608  }
609
610  ///Constant (read only) version of XMap
611
612  ///Constant (read only) version of XMap.
613  ///
614  template<class M>
615  class ConstXMap
616  {
617    const M& _map;
618  public:
619
620    typedef typename M::Value::Value Value;
621    typedef typename M::Key Key;
622    ///\e
623    ConstXMap(const M &map) : _map(map) {}
624    Value operator[](Key k) const {return _map[k].x;}
625  };
626
627  ///Returns a ConstXMap class
628
629  ///This function just returns a ConstXMap class.
630  ///\relates ConstXMap
631  template<class M>
632  inline ConstXMap<M> xMap(const M &m)
633  {
634    return ConstXMap<M>(m);
635  }
636
637  ///Map of y-coordinates of a <tt>Point</tt>-map
638
639  ///Map of y-coordinates of a \ref Point "Point"-map.
640  ///
641  template<class M>
642  class YMap
643  {
644    M& _map;
645  public:
646
647    typedef typename M::Value::Value Value;
648    typedef typename M::Key Key;
649    ///\e
650    YMap(M& map) : _map(map) {}
651    Value operator[](Key k) const {return _map[k].y;}
652    void set(Key k,Value v) {_map.set(k,typename M::Value(_map[k].x,v));}
653  };
654
655  ///Returns a YMap class
656
657  ///This function just returns a YMap class.
658  ///\relates YMap
659  template<class M>
660  inline YMap<M> yMap(M &m)
661  {
662    return YMap<M>(m);
663  }
664
665  template<class M>
666  inline YMap<M> yMap(const M &m)
667  {
668    return YMap<M>(m);
669  }
670
671  ///Constant (read only) version of YMap
672
673  ///Constant (read only) version of YMap.
674  ///
675  template<class M>
676  class ConstYMap
677  {
678    const M& _map;
679  public:
680
681    typedef typename M::Value::Value Value;
682    typedef typename M::Key Key;
683    ///\e
684    ConstYMap(const M &map) : _map(map) {}
685    Value operator[](Key k) const {return _map[k].y;}
686  };
687
688  ///Returns a ConstYMap class
689
690  ///This function just returns a ConstYMap class.
691  ///\relates ConstYMap
692  template<class M>
693  inline ConstYMap<M> yMap(const M &m)
694  {
695    return ConstYMap<M>(m);
696  }
697
698
699  ///\brief Map of the normSquare() of a <tt>Point</tt>-map
700  ///
701  ///Map of the \ref Point::normSquare() "normSquare()"
702  ///of a \ref Point "Point"-map.
703  template<class M>
704  class NormSquareMap
705  {
706    const M& _map;
707  public:
708
709    typedef typename M::Value::Value Value;
710    typedef typename M::Key Key;
711    ///\e
712    NormSquareMap(const M &map) : _map(map) {}
713    Value operator[](Key k) const {return _map[k].normSquare();}
714  };
715
716  ///Returns a NormSquareMap class
717
718  ///This function just returns a NormSquareMap class.
719  ///\relates NormSquareMap
720  template<class M>
721  inline NormSquareMap<M> normSquareMap(const M &m)
722  {
723    return NormSquareMap<M>(m);
724  }
725
726  /// @}
727
728  } //namespce dim2
729
730} //namespace lemon
731
732#endif //LEMON_DIM2_H
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