Location: LEMON/LEMON-official/lemon/dim2.h

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kpeter (Peter Kovacs)
Small fixes in README.
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/* -*- C++ -*-
*
* This file is a part of LEMON, a generic C++ optimization library
*
* Copyright (C) 2003-2007
* 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 <lemon/bits/utility.h>
///\ingroup misc
///\file
///\brief A simple two dimensional vector and a bounding box implementation
///
/// The class \ref lemon::dim2::Point "dim2::Point" implements
///a two dimensional vector with the usual
/// operations.
///
/// The class \ref lemon::dim2::BoundingBox "dim2::BoundingBox"
/// can be used to determine
/// the rectangular bounding box of a set of
/// \ref lemon::dim2::Point "dim2::Point"'s.
namespace lemon {
///Tools for handling two dimensional coordinates
///This namespace is a storage of several
///tools for handling two dimensional coordinates
namespace dim2 {
/// \addtogroup misc
/// @{
/// A simple two dimensional vector (plainvector) implementation
/// A simple two dimensional vector (plainvector) implementation
///with the usual vector
/// operators.
///
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) { }
///The dimension of the vector.
///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 u
Point<T>& operator +=(const Point<T>& u) {
x += u.x;
y += u.y;
return *this;
}
///Decrement the left hand side by 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 plainvector from a stream
///Read a plainvector 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 plainvector to a stream
///Write a plainvector 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);
}
/// A class to calculate or store the bounding box of plainvectors.
/// A class to calculate or store the bounding box of plainvectors.
///
template<typename T>
class BoundingBox {
Point<T> bottom_left, top_right;
bool _empty;
public:
///Default constructor: creates an empty bounding box
BoundingBox() { _empty = true; }
///Construct an instance from one point
BoundingBox(Point<T> a) { bottom_left=top_right=a; _empty = false; }
///Construct an instance from two points
///Construct an instance 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.
BoundingBox(Point<T> a,Point<T> b)
{
bottom_left=a;
top_right=b;
_empty = false;
}
///Construct an instance from four numbers
///Construct an instance 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.
BoundingBox(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 bounding box is empty.
///Return \c true if the bounding 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 bounding box are not defined.
bool empty() const {
return _empty;
}
///Make the BoundingBox empty
void clear() {
_empty=1;
}
///Give back the bottom left corner
///Give back the bottom left corner.
///If the bounding box is empty, then the return value is not defined.
Point<T> bottomLeft() const {
return bottom_left;
}
///Set the bottom left corner
///Set the bottom left corner.
///It should only be used for non-empty box.
void bottomLeft(Point<T> p) {
bottom_left = p;
}
///Give back the top right corner
///Give back the top right corner.
///If the bounding box is empty, then the return value is not defined.
Point<T> topRight() const {
return top_right;
}
///Set the top right corner
///Set the top right corner.
///It should only be used for non-empty box.
void topRight(Point<T> p) {
top_right = p;
}
///Give back the bottom right corner
///Give back the bottom right corner.
///If the bounding 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
///Set the bottom right corner.
///It should only be used for non-empty box.
void bottomRight(Point<T> p) {
top_right.x = p.x;
bottom_left.y = p.y;
}
///Give back the top left corner
///Give back the top left corner.
///If the bounding 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
///Set the top left corner.
///It should only be used for non-empty box.
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 bounding 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.
///It should only be used for non-empty box.
void bottom(T t) {
bottom_left.y = t;
}
///Give back the top of the box
///Give back the top of the box.
///If the bounding 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.
///It should only be used for non-empty box.
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 bounding 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.
///It should only be used for non-empty box.
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 bounding 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.
///It should only be used for non-empty box.
void right(T t) {
top_right.x = t;
}
///Give back the height of the box
///Give back the height of the box.
///If the bounding 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 bounding 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 a bounding 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 a bounding box with a point
///Increments a bounding box with a point.
///
BoundingBox& 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 a bounding box to contain another bounding box
///Increments a bounding box to contain another bounding box.
///
BoundingBox& add(const BoundingBox &u){
if ( !u.empty() ){
this->add(u.bottomLeft());
this->add(u.topRight());
}
return *this;
}
///Intersection of two bounding boxes
///Intersection of two bounding boxes.
///
BoundingBox operator&(const BoundingBox& u) const {
BoundingBox b;
if (this->_empty || u._empty) {
b._empty = true;
} else {
b.bottom_left.x = std::max(this->bottom_left.x,u.bottom_left.x);
b.bottom_left.y = std::max(this->bottom_left.y,u.bottom_left.y);
b.top_right.x = std::min(this->top_right.x,u.top_right.x);
b.top_right.y = std::min(this->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 Boundingbox
///Map of x-coordinates of a \ref Point "Point"-map
///\ingroup maps
///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 \ref XMap class
///This function just returns an \ref XMap class.
///
///\ingroup maps
///\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 \ref XMap
///\ingroup maps
///Constant (read only) version of \ref 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 \ref ConstXMap class
///This function just returns a \ref ConstXMap class.
///
///\ingroup maps
///\relates ConstXMap
template<class M>
inline ConstXMap<M> xMap(const M &m)
{
return ConstXMap<M>(m);
}
///Map of y-coordinates of a \ref Point "Point"-map
///\ingroup maps
///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 \ref YMap class
///This function just returns a \ref YMap class.
///
///\ingroup maps
///\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 \ref YMap
///\ingroup maps
///Constant (read only) version of \ref 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 \ref ConstYMap class
///This function just returns a \ref ConstYMap class.
///
///\ingroup maps
///\relates ConstYMap
template<class M>
inline ConstYMap<M> yMap(const M &m)
{
return ConstYMap<M>(m);
}
///\brief Map of the \ref Point::normSquare() "normSquare()"
///of a \ref Point "Point"-map
///
///Map of the \ref Point::normSquare() "normSquare()"
///of a \ref Point "Point"-map.
///\ingroup maps
///
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 \ref NormSquareMap class
///This function just returns a \ref NormSquareMap class.
///
///\ingroup maps
///\relates NormSquareMap
template<class M>
inline NormSquareMap<M> normSquareMap(const M &m)
{
return NormSquareMap<M>(m);
}
/// @}
} //namespce dim2
} //namespace lemon
#endif //LEMON_DIM2_H