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+/* -*- mode: C++; indent-tabs-mode: nil; -*-
+ *
+ * This file is a part of LEMON, a generic C++ optimization library.
+ *
+ * Copyright (C) 2003-2009
+ * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
+ * (Egervary Research Group on Combinatorial Optimization, EGRES).
+ *
+ * Permission to use, modify and distribute this software is granted
+ * provided that this copyright notice appears in all copies. For
+ * precise terms see the accompanying LICENSE file.
+ *
+ * This software is provided "AS IS" with no warranty of any kind,
+ * express or implied, and with no claim as to its suitability for any
+ * purpose.
+ *
+ */
+
+#ifndef LEMON_DIM2_H
+#define LEMON_DIM2_H
+
+#include <iostream>
+#include <algorithm>
+
+///\ingroup geomdat
+///\file
+///\brief A simple two dimensional vector and a bounding box implementation
+
+namespace lemon {
+
+ ///Tools for handling two dimensional coordinates
+
+ ///This namespace is a storage of several
+ ///tools for handling two dimensional coordinates
+ namespace dim2 {
+
+ /// \addtogroup geomdat
+ /// @{
+
+ /// Two dimensional vector (plain vector)
+
+ /// A simple two dimensional vector (plain vector) implementation
+ /// with the usual vector operations.
+ template<typename T>
+ class Point {
+
+ public:
+
+ typedef T Value;
+
+ ///First coordinate
+ T x;
+ ///Second coordinate
+ T y;
+
+ ///Default constructor
+ Point() {}
+
+ ///Construct an instance from coordinates
+ Point(T a, T b) : x(a), y(b) { }
+
+ ///Returns the dimension of the vector (i.e. returns 2).
+
+ ///The dimension of the vector.
+ ///This function always returns 2.
+ int size() const { return 2; }
+
+ ///Subscripting operator
+
+ ///\c p[0] is \c p.x and \c p[1] is \c p.y
+ ///
+ T& operator[](int idx) { return idx == 0 ? x : y; }
+
+ ///Const subscripting operator
+
+ ///\c p[0] is \c p.x and \c p[1] is \c p.y
+ ///
+ const T& operator[](int idx) const { return idx == 0 ? x : y; }
+
+ ///Conversion constructor
+ template<class TT> Point(const Point<TT> &p) : x(p.x), y(p.y) {}
+
+ ///Give back the square of the norm of the vector
+ T normSquare() const {
+ return x*x+y*y;
+ }
+
+ ///Increment the left hand side by \c u
+ Point<T>& operator +=(const Point<T>& u) {
+ x += u.x;
+ y += u.y;
+ return *this;
+ }
+
+ ///Decrement the left hand side by \c u
+ Point<T>& operator -=(const Point<T>& u) {
+ x -= u.x;
+ y -= u.y;
+ return *this;
+ }
+
+ ///Multiply the left hand side with a scalar
+ Point<T>& operator *=(const T &u) {
+ x *= u;
+ y *= u;
+ return *this;
+ }
+
+ ///Divide the left hand side by a scalar
+ Point<T>& operator /=(const T &u) {
+ x /= u;
+ y /= u;
+ return *this;
+ }
+
+ ///Return the scalar product of two vectors
+ T operator *(const Point<T>& u) const {
+ return x*u.x+y*u.y;
+ }
+
+ ///Return the sum of two vectors
+ Point<T> operator+(const Point<T> &u) const {
+ Point<T> b=*this;
+ return b+=u;
+ }
+
+ ///Return the negative of the vector
+ Point<T> operator-() const {
+ Point<T> b=*this;
+ b.x=-b.x; b.y=-b.y;
+ return b;
+ }
+
+ ///Return the difference of two vectors
+ Point<T> operator-(const Point<T> &u) const {
+ Point<T> b=*this;
+ return b-=u;
+ }
+
+ ///Return a vector multiplied by a scalar
+ Point<T> operator*(const T &u) const {
+ Point<T> b=*this;
+ return b*=u;
+ }
+
+ ///Return a vector divided by a scalar
+ Point<T> operator/(const T &u) const {
+ Point<T> b=*this;
+ return b/=u;
+ }
+
+ ///Test equality
+ bool operator==(const Point<T> &u) const {
+ return (x==u.x) && (y==u.y);
+ }
+
+ ///Test inequality
+ bool operator!=(Point u) const {
+ return (x!=u.x) || (y!=u.y);
+ }
+
+ };
+
+ ///Return a Point
+
+ ///Return a Point.
+ ///\relates Point
+ template <typename T>
+ inline Point<T> makePoint(const T& x, const T& y) {
+ return Point<T>(x, y);
+ }
+
+ ///Return a vector multiplied by a scalar
+
+ ///Return a vector multiplied by a scalar.
+ ///\relates Point
+ template<typename T> Point<T> operator*(const T &u,const Point<T> &x) {
+ return x*u;
+ }
+
+ ///Read a plain vector from a stream
+
+ ///Read a plain vector from a stream.
+ ///\relates Point
+ ///
+ template<typename T>
+ inline std::istream& operator>>(std::istream &is, Point<T> &z) {
+ char c;
+ if (is >> c) {
+ if (c != '(') is.putback(c);
+ } else {
+ is.clear();
+ }
+ if (!(is >> z.x)) return is;
+ if (is >> c) {
+ if (c != ',') is.putback(c);
+ } else {
+ is.clear();
+ }
+ if (!(is >> z.y)) return is;
+ if (is >> c) {
+ if (c != ')') is.putback(c);
+ } else {
+ is.clear();
+ }
+ return is;
+ }
+
+ ///Write a plain vector to a stream
+
+ ///Write a plain vector to a stream.
+ ///\relates Point
+ ///
+ template<typename T>
+ inline std::ostream& operator<<(std::ostream &os, const Point<T>& z)
+ {
+ os << "(" << z.x << "," << z.y << ")";
+ return os;
+ }
+
+ ///Rotate by 90 degrees
+
+ ///Returns the parameter rotated by 90 degrees in positive direction.
+ ///\relates Point
+ ///
+ template<typename T>
+ inline Point<T> rot90(const Point<T> &z)
+ {
+ return Point<T>(-z.y,z.x);
+ }
+
+ ///Rotate by 180 degrees
+
+ ///Returns the parameter rotated by 180 degrees.
+ ///\relates Point
+ ///
+ template<typename T>
+ inline Point<T> rot180(const Point<T> &z)
+ {
+ return Point<T>(-z.x,-z.y);
+ }
+
+ ///Rotate by 270 degrees
+
+ ///Returns the parameter rotated by 90 degrees in negative direction.
+ ///\relates Point
+ ///
+ template<typename T>
+ inline Point<T> rot270(const Point<T> &z)
+ {
+ return Point<T>(z.y,-z.x);
+ }
+
+
+
+ /// Bounding box of plain vectors (points).
+
+ /// A class to calculate or store the bounding box of plain vectors
+ /// (\ref Point "points").
+ template<typename T>
+ class Box {
+ Point<T> _bottom_left, _top_right;
+ bool _empty;
+ public:
+
+ ///Default constructor: creates an empty box
+ Box() { _empty = true; }
+
+ ///Construct a box from one point
+ Box(Point<T> a) {
+ _bottom_left = _top_right = a;
+ _empty = false;
+ }
+
+ ///Construct a box from two points
+
+ ///Construct a box from two points.
+ ///\param a The bottom left corner.
+ ///\param b The top right corner.
+ ///\warning The coordinates of the bottom left corner must be no more
+ ///than those of the top right one.
+ Box(Point<T> a,Point<T> b)
+ {
+ _bottom_left = a;
+ _top_right = b;
+ _empty = false;
+ }
+
+ ///Construct a box from four numbers
+
+ ///Construct a box from four numbers.
+ ///\param l The left side of the box.
+ ///\param b The bottom of the box.
+ ///\param r The right side of the box.
+ ///\param t The top of the box.
+ ///\warning The left side must be no more than the right side and
+ ///bottom must be no more than the top.
+ Box(T l,T b,T r,T t)
+ {
+ _bottom_left=Point<T>(l,b);
+ _top_right=Point<T>(r,t);
+ _empty = false;
+ }
+
+ ///Return \c true if the box is empty.
+
+ ///Return \c true if the box is empty (i.e. return \c false
+ ///if at least one point was added to the box or the coordinates of
+ ///the box were set).
+ ///
+ ///The coordinates of an empty box are not defined.
+ bool empty() const {
+ return _empty;
+ }
+
+ ///Make the box empty
+ void clear() {
+ _empty = true;
+ }
+
+ ///Give back the bottom left corner of the box
+
+ ///Give back the bottom left corner of the box.
+ ///If the box is empty, then the return value is not defined.
+ Point<T> bottomLeft() const {
+ return _bottom_left;
+ }
+
+ ///Set the bottom left corner of the box
+
+ ///Set the bottom left corner of the box.
+ ///\pre The box must not be empty.
+ void bottomLeft(Point<T> p) {
+ _bottom_left = p;
+ }
+
+ ///Give back the top right corner of the box
+
+ ///Give back the top right corner of the box.
+ ///If the box is empty, then the return value is not defined.
+ Point<T> topRight() const {
+ return _top_right;
+ }
+
+ ///Set the top right corner of the box
+
+ ///Set the top right corner of the box.
+ ///\pre The box must not be empty.
+ void topRight(Point<T> p) {
+ _top_right = p;
+ }
+
+ ///Give back the bottom right corner of the box
+
+ ///Give back the bottom right corner of the box.
+ ///If the box is empty, then the return value is not defined.
+ Point<T> bottomRight() const {
+ return Point<T>(_top_right.x,_bottom_left.y);
+ }
+
+ ///Set the bottom right corner of the box
+
+ ///Set the bottom right corner of the box.
+ ///\pre The box must not be empty.
+ void bottomRight(Point<T> p) {
+ _top_right.x = p.x;
+ _bottom_left.y = p.y;
+ }
+
+ ///Give back the top left corner of the box
+
+ ///Give back the top left corner of the box.
+ ///If the box is empty, then the return value is not defined.
+ Point<T> topLeft() const {
+ return Point<T>(_bottom_left.x,_top_right.y);
+ }
+
+ ///Set the top left corner of the box
+
+ ///Set the top left corner of the box.
+ ///\pre The box must not be empty.
+ void topLeft(Point<T> p) {
+ _top_right.y = p.y;
+ _bottom_left.x = p.x;
+ }
+
+ ///Give back the bottom of the box
+
+ ///Give back the bottom of the box.
+ ///If the box is empty, then the return value is not defined.
+ T bottom() const {
+ return _bottom_left.y;
+ }
+
+ ///Set the bottom of the box
+
+ ///Set the bottom of the box.
+ ///\pre The box must not be empty.
+ void bottom(T t) {
+ _bottom_left.y = t;
+ }
+
+ ///Give back the top of the box
+
+ ///Give back the top of the box.
+ ///If the box is empty, then the return value is not defined.
+ T top() const {
+ return _top_right.y;
+ }
+
+ ///Set the top of the box
+
+ ///Set the top of the box.
+ ///\pre The box must not be empty.
+ void top(T t) {
+ _top_right.y = t;
+ }
+
+ ///Give back the left side of the box
+
+ ///Give back the left side of the box.
+ ///If the box is empty, then the return value is not defined.
+ T left() const {
+ return _bottom_left.x;
+ }
+
+ ///Set the left side of the box
+
+ ///Set the left side of the box.
+ ///\pre The box must not be empty.
+ void left(T t) {
+ _bottom_left.x = t;
+ }
+
+ /// Give back the right side of the box
+
+ /// Give back the right side of the box.
+ ///If the box is empty, then the return value is not defined.
+ T right() const {
+ return _top_right.x;
+ }
+
+ ///Set the right side of the box
+
+ ///Set the right side of the box.
+ ///\pre The box must not be empty.
+ void right(T t) {
+ _top_right.x = t;
+ }
+
+ ///Give back the height of the box
+
+ ///Give back the height of the box.
+ ///If the box is empty, then the return value is not defined.
+ T height() const {
+ return _top_right.y-_bottom_left.y;
+ }
+
+ ///Give back the width of the box
+
+ ///Give back the width of the box.
+ ///If the box is empty, then the return value is not defined.
+ T width() const {
+ return _top_right.x-_bottom_left.x;
+ }
+
+ ///Checks whether a point is inside the box
+ bool inside(const Point<T>& u) const {
+ if (_empty)
+ return false;
+ else {
+ return ( (u.x-_bottom_left.x)*(_top_right.x-u.x) >= 0 &&
+ (u.y-_bottom_left.y)*(_top_right.y-u.y) >= 0 );
+ }
+ }
+
+ ///Increments the box with a point
+
+ ///Increments the box with a point.
+ ///
+ Box& add(const Point<T>& u){
+ if (_empty) {
+ _bottom_left = _top_right = u;
+ _empty = false;
+ }
+ else {
+ if (_bottom_left.x > u.x) _bottom_left.x = u.x;
+ if (_bottom_left.y > u.y) _bottom_left.y = u.y;
+ if (_top_right.x < u.x) _top_right.x = u.x;
+ if (_top_right.y < u.y) _top_right.y = u.y;
+ }
+ return *this;
+ }
+
+ ///Increments the box to contain another box
+
+ ///Increments the box to contain another box.
+ ///
+ Box& add(const Box &u){
+ if ( !u.empty() ){
+ add(u._bottom_left);
+ add(u._top_right);
+ }
+ return *this;
+ }
+
+ ///Intersection of two boxes
+
+ ///Intersection of two boxes.
+ ///
+ Box operator&(const Box& u) const {
+ Box b;
+ if (_empty || u._empty) {
+ b._empty = true;
+ } else {
+ b._bottom_left.x = std::max(_bottom_left.x, u._bottom_left.x);
+ b._bottom_left.y = std::max(_bottom_left.y, u._bottom_left.y);
+ b._top_right.x = std::min(_top_right.x, u._top_right.x);
+ b._top_right.y = std::min(_top_right.y, u._top_right.y);
+ b._empty = b._bottom_left.x > b._top_right.x ||
+ b._bottom_left.y > b._top_right.y;
+ }
+ return b;
+ }
+
+ };//class Box
+
+
+ ///Read a box from a stream
+
+ ///Read a box from a stream.
+ ///\relates Box
+ template<typename T>
+ inline std::istream& operator>>(std::istream &is, Box<T>& b) {
+ char c;
+ Point<T> p;
+ if (is >> c) {
+ if (c != '(') is.putback(c);
+ } else {
+ is.clear();
+ }
+ if (!(is >> p)) return is;
+ b.bottomLeft(p);
+ if (is >> c) {
+ if (c != ',') is.putback(c);
+ } else {
+ is.clear();
+ }
+ if (!(is >> p)) return is;
+ b.topRight(p);
+ if (is >> c) {
+ if (c != ')') is.putback(c);
+ } else {
+ is.clear();
+ }
+ return is;
+ }
+
+ ///Write a box to a stream
+
+ ///Write a box to a stream.
+ ///\relates Box
+ template<typename T>
+ inline std::ostream& operator<<(std::ostream &os, const Box<T>& b)
+ {
+ os << "(" << b.bottomLeft() << "," << b.topRight() << ")";
+ return os;
+ }
+
+ ///Map of x-coordinates of a <tt>Point</tt>-map
+
+ ///Map of x-coordinates of a \ref Point "Point"-map.
+ ///
+ template<class M>
+ class XMap
+ {
+ M& _map;
+ public:
+
+ typedef typename M::Value::Value Value;
+ typedef typename M::Key Key;
+ ///\e
+ XMap(M& map) : _map(map) {}
+ Value operator[](Key k) const {return _map[k].x;}
+ void set(Key k,Value v) {_map.set(k,typename M::Value(v,_map[k].y));}
+ };
+
+ ///Returns an XMap class
+
+ ///This function just returns an XMap class.
+ ///\relates XMap
+ template<class M>
+ inline XMap<M> xMap(M &m)
+ {
+ return XMap<M>(m);
+ }
+
+ template<class M>
+ inline XMap<M> xMap(const M &m)
+ {
+ return XMap<M>(m);
+ }
+
+ ///Constant (read only) version of XMap
+
+ ///Constant (read only) version of XMap.
+ ///
+ template<class M>
+ class ConstXMap
+ {
+ const M& _map;
+ public:
+
+ typedef typename M::Value::Value Value;
+ typedef typename M::Key Key;
+ ///\e
+ ConstXMap(const M &map) : _map(map) {}
+ Value operator[](Key k) const {return _map[k].x;}
+ };
+
+ ///Returns a ConstXMap class
+
+ ///This function just returns a ConstXMap class.
+ ///\relates ConstXMap
+ template<class M>
+ inline ConstXMap<M> xMap(const M &m)
+ {
+ return ConstXMap<M>(m);
+ }
+
+ ///Map of y-coordinates of a <tt>Point</tt>-map
+
+ ///Map of y-coordinates of a \ref Point "Point"-map.
+ ///
+ template<class M>
+ class YMap
+ {
+ M& _map;
+ public:
+
+ typedef typename M::Value::Value Value;
+ typedef typename M::Key Key;
+ ///\e
+ YMap(M& map) : _map(map) {}
+ Value operator[](Key k) const {return _map[k].y;}
+ void set(Key k,Value v) {_map.set(k,typename M::Value(_map[k].x,v));}
+ };
+
+ ///Returns a YMap class
+
+ ///This function just returns a YMap class.
+ ///\relates YMap
+ template<class M>
+ inline YMap<M> yMap(M &m)
+ {
+ return YMap<M>(m);
+ }
+
+ template<class M>
+ inline YMap<M> yMap(const M &m)
+ {
+ return YMap<M>(m);
+ }
+
+ ///Constant (read only) version of YMap
+
+ ///Constant (read only) version of YMap.
+ ///
+ template<class M>
+ class ConstYMap
+ {
+ const M& _map;
+ public:
+
+ typedef typename M::Value::Value Value;
+ typedef typename M::Key Key;
+ ///\e
+ ConstYMap(const M &map) : _map(map) {}
+ Value operator[](Key k) const {return _map[k].y;}
+ };
+
+ ///Returns a ConstYMap class
+
+ ///This function just returns a ConstYMap class.
+ ///\relates ConstYMap
+ template<class M>
+ inline ConstYMap<M> yMap(const M &m)
+ {
+ return ConstYMap<M>(m);
+ }
+
+
+ ///\brief Map of the normSquare() of a <tt>Point</tt>-map
+ ///
+ ///Map of the \ref Point::normSquare() "normSquare()"
+ ///of a \ref Point "Point"-map.
+ template<class M>
+ class NormSquareMap
+ {
+ const M& _map;
+ public:
+
+ typedef typename M::Value::Value Value;
+ typedef typename M::Key Key;
+ ///\e
+ NormSquareMap(const M &map) : _map(map) {}
+ Value operator[](Key k) const {return _map[k].normSquare();}
+ };
+
+ ///Returns a NormSquareMap class
+
+ ///This function just returns a NormSquareMap class.
+ ///\relates NormSquareMap
+ template<class M>
+ inline NormSquareMap<M> normSquareMap(const M &m)
+ {
+ return NormSquareMap<M>(m);
+ }
+
+ /// @}
+
+ } //namespce dim2
+
+} //namespace lemon
+
+#endif //LEMON_DIM2_H
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