```// Copyright (C) 2005  Davis E. King (davis@dlib.net)
#undef DLIB_RECTANGLe_ABSTRACT_
#ifdef DLIB_RECTANGLe_ABSTRACT_

#include "vector_abstract.h"
#include <iostream>
#include "../serialize.h"

namespace dlib
{

class rectangle
{
/*!
INITIAL VALUE
The initial value of this object is defined by its constructor.

WHAT THIS OBJECT REPRESENTS
This object represents a rectangular region inside a Cartesian
coordinate system.  The region is the rectangle with its top
left corner at position (left(),top()) and its bottom right corner
at (right(),bottom()).

Note that the origin of the coordinate system, i.e. (0,0), is located
at the upper left corner.  That is, points such as (1,1) or (3,5)
represent locations that are below and to the right of the origin.

Also note that rectangles where top() > bottom() or left() > right()
represent empty rectangles.
!*/

public:

rectangle (
const rectangle& rect
);
/*!
ensures
- #*this represents the same rectangle as rect
!*/

rectangle (
);
/*!
ensures
- #left() == 0
- #top() == 0
- #right() == -1
- #bottom() == -1
- #is_empty() == true
!*/

rectangle (
long left_,
long top_,
long right_,
long bottom_
);
/*!
ensures
- #left() == left_
- #top() == top_
- #right() == right_
- #bottom() == bottom_
!*/

rectangle (
unsigned long width_,
unsigned long height_
);
/*!
requires
- (width_ > 0 && height_ > 0) || (width_ == 0 && height_ == 0)
ensures
- #left() == 0
- #top() == 0
- #width() == width_
- #height() == height_
!*/

rectangle (
const point& p
);
/*!
ensures
- #left()   == p.x()
- #top()    == p.y()
- #right()  == p.x()
- #bottom() == p.y()
!*/

template <typename T>
rectangle (
const vector<T,2>& p1,
const vector<T,2>& p2
);
/*!
ensures
- #*this == rectangle(p1) + rectangle(p2)
!*/

long left (
) const;
/*!
ensures
- returns the x coordinate for the left side of this rectangle
!*/

long& left (
);
/*!
ensures
- returns a non-const reference to the x coordinate for the left side
of this rectangle
!*/

void set_left (
long left_
);
/*!
ensures
- #left() == left_
!*/

long top (
) const;
/*!
ensures
- returns the y coordinate for the top of this rectangle
!*/

long& top (
);
/*!
ensures
- returns a non-const reference to the y coordinate for the
top of this rectangle
!*/

void set_top (
long top_
);
/*!
ensures
- #top() == top_
!*/

long right (
) const;
/*!
ensures
- returns the x coordinate for the right side of this rectangle
!*/

long& right (
);
/*!
ensures
- returns a non-const reference to the x coordinate for the right
side of this rectangle
!*/

void set_right (
long right_
);
/*!
ensures
- #right() == right_
!*/

long bottom (
) const;
/*!
ensures
- returns the y coordinate for the bottom of this rectangle
!*/

long& bottom (
);
/*!
ensures
- returns a non-const reference to the y coordinate for the bottom
of this rectangle
!*/

void set_bottom (
long bottom_
);
/*!
ensures
- #bottom() == bottom_
!*/

const point tl_corner (
) const;
/*!
ensures
- returns point(left(), top())
(i.e. returns the top left corner point for this rectangle)
!*/

const point bl_corner (
) const;
/*!
ensures
- returns point(left(), bottom())
(i.e. returns the bottom left corner point for this rectangle)
!*/

const point tr_corner (
) const;
/*!
ensures
- returns point(right(), top())
(i.e. returns the top right corner point for this rectangle)
!*/

const point br_corner (
) const;
/*!
ensures
- returns point(right(), bottom())
(i.e. returns the bottom right corner point for this rectangle)
!*/

bool is_empty (
) const;
/*!
ensures
- if (top() > bottom() || left() > right()) then
- returns true
- else
- returns false
!*/

unsigned long width (
) const;
/*!
ensures
- if (is_empty()) then
- returns 0
- else
- returns the width of this rectangle.
(i.e. right() - left() + 1)
!*/

unsigned long height (
) const;
/*!
ensures
- if (is_empty()) then
- returns 0
- else
- returns the height of this rectangle.
(i.e. bottom() - top() + 1)
!*/

unsigned long area (
) const;
/*!
ensures
- returns width()*height()
!*/

rectangle operator + (
const rectangle& rhs
) const;
/*!
ensures
- if (rhs.is_empty() == false && this->is_empty() == false) then
- returns the smallest rectangle that contains both *this and
rhs.
- if (rhs.is_empty() == true && this->is_empty() == false) then
- returns *this
- if (rhs.is_empty() == false && this->is_empty() == true) then
- returns rhs
- if (rhs.is_empty() == true && this->is_empty() == true) then
- returns a rectangle that has is_empty() == true
!*/

rectangle intersect (
const rectangle& rhs
) const;
/*!
ensures
- if (there is a region of intersection between *this and rhs) then
- returns a rectangle that represents the intersection of *this
and rhs.
- else
- returns a rectangle where is_empty() == true
!*/

bool contains (
long x,
long y
) const;
/*!
ensures
- if (the point (x,y) is contained in this rectangle) then
- returns true
- else
- returns false
!*/

bool contains (
const point& p
) const;
/*!
ensures
- if (the point (p.x(),p.y()) is contained in this rectangle) then
- returns true
- else
- returns false
!*/

bool contains (
const rectangle& rect
) const;
/*!
ensures
- if (rect + *this == *this) then
- returns true
(i.e. returns true if *this contains the given rectangle)
- else
- returns false
!*/

rectangle& operator= (
const rectangle& rect
);
/*!
ensures
- #*this represents the same rectangle as rect
- returns #*this
!*/

rectangle& operator+= (
const rectangle& rect
);
/*!
ensures
- #*this == *this + rect
- returns #*this
!*/

bool operator== (
const rectangle& rect
) const;
/*!
ensures
- if (top() == rect.top() && left() == rect.left() &&
right() == rect.right() && bottom() == rect.bottom()) then
- returns true
- else
- returns false
!*/

bool operator!= (
const rectangle& rect
) const;
/*!
ensures
- returns !(*this == rect)
!*/

bool operator< (
const dlib::rectangle& a,
const dlib::rectangle& b
) const;
/*!
ensures
- Defines a total ordering over rectangles so they can be used in
associative containers.
!*/
};

// ----------------------------------------------------------------------------------------

void serialize (
const rectangle& item,
std::ostream& out
);
/*!
provides serialization support
!*/

void deserialize (
rectangle& item,
std::istream& in
);
/*!
provides deserialization support
!*/

std::ostream& operator<< (
std::ostream& out,
const rectangle& item
);
/*!
ensures
- writes item to out in the form "[(left, top) (right, bottom)]"
!*/

std::istream& operator>>(
std::istream& in,
rectangle& item
);
/*!
ensures
- reads a rectangle from the input stream in and stores it in #item.
The data in the input stream should be of the form [(left, top) (right, bottom)]
!*/

// ----------------------------------------------------------------------------------------

point center (
const dlib::rectangle& rect
);
/*!
ensures
- returns the center of the given rectangle
!*/

// ----------------------------------------------------------------------------------------

dlib::vector<double,2> dcenter (
const dlib::rectangle& rect
);
/*!
ensures
- returns the center of the given rectangle using a real valued vector.
!*/

// ----------------------------------------------------------------------------------------

inline const rectangle centered_rect (
const point& p,
unsigned long width,
unsigned long height
);
/*!
ensures
- returns a rectangle R such that:
- center(R) == p
- if (width == 0 || height == 0)
- R.width() == 0
- R.height() == 0
- else
- R.width() == width
- R.height() == height
- R.tl_corner() == point(p.x()-width/2, p.y()-height/2)
!*/

// ----------------------------------------------------------------------------------------

inline std::vector<rectangle> centered_rects (
const std::vector<point>& pts,
unsigned long width,
unsigned long height
);
/*!
ensures
- returns an array ARR where:
- #ARR.size() == pts.size()
- #ARR[i] == centered_rect(pts[i], width, height)
!*/

// ----------------------------------------------------------------------------------------

const rectangle centered_rect (
long x,
long y,
unsigned long width,
unsigned long height
);
/*!
ensures
- returns a rectangle R such that:
- center(R) == p
- if (width == 0 || height == 0)
- R.width() == 0
- R.height() == 0
- else
- R.width() == width
- R.height() == height
- R.tl_corner() == point(x-width/2, y-height/2)
!*/

// ----------------------------------------------------------------------------------------

inline const rectangle centered_rect (
const rectangle& rect,
unsigned long width,
unsigned long height
);
/*!
ensures
- returns centered_rect( (rect.tl_corner() + rect.br_corner())/2, width, height)
(i.e. returns a rectangle centered on rect but with the given width
and height)
!*/

// ----------------------------------------------------------------------------------------

inline rectangle set_rect_area (
const rectangle& rect,
unsigned long area
);
/*!
requires
- area > 0
ensures
- Returns a rectangle R such that:
- center(R) == center(rect)
- R has the same aspect ratio as rect.  If rect.area() == 0 then the
returned rect has a 1:1 aspect ratio.
- R.area() == area
!*/

// ----------------------------------------------------------------------------------------

inline rectangle set_aspect_ratio (
const rectangle& rect,
double ratio
);
/*!
requires
- ratio > 0
ensures
- This function reshapes the given rectangle so that it has the given aspect
ratio.  In particular, this means we return a rectangle R such that the
following equations are as true as possible:
- R.width()/R.height() == ratio
- R.area() == rect.area()
- center(rect) == center(R)
!*/

// ----------------------------------------------------------------------------------------

inline rectangle intersect (
const rectangle& a,
const rectangle& b
);
/*!
ensures
- returns a.intersect(b)
(i.e. returns a rectangle representing the intersection of a and b)
!*/

// ----------------------------------------------------------------------------------------

inline unsigned long area (
const rectangle& a
);
/*!
ensures
- returns a.area()
!*/

// ----------------------------------------------------------------------------------------

inline const rectangle shrink_rect (
const rectangle& rect,
long num
);
/*!
ensures
- returns rectangle(rect.left()+num, rect.top()+num, rect.right()-num, rect.bottom()-num)
(i.e. shrinks the given rectangle by shrinking its border by num)
!*/

// ----------------------------------------------------------------------------------------

inline const rectangle grow_rect (
const rectangle& rect,
long num
);
/*!
ensures
- return shrink_rect(rect, -num)
(i.e. grows the given rectangle by expanding its border by num)
!*/

// ----------------------------------------------------------------------------------------

inline const rectangle shrink_rect (
const rectangle& rect,
long width,
long height
);
/*!
ensures
- returns rectangle(rect.left()+width, rect.top()+height, rect.right()-width, rect.bottom()-height)
(i.e. shrinks the given rectangle by shrinking its left and right borders by width
and its top and bottom borders by height. )
!*/

// ----------------------------------------------------------------------------------------

inline const rectangle grow_rect (
const rectangle& rect,
long width,
long height
);
/*!
ensures
- return shrink_rect(rect, -width, -height)
(i.e. grows the given rectangle by expanding its border)
!*/

// ----------------------------------------------------------------------------------------

const rectangle scale_rect (
const rectangle& rect,
double scale
);
/*!
requires
- scale > 0
ensures
- return rectangle(rect.left() * scale, rect.top() * scale, rect.right() * scale, rect.bottom() * scale)
(i.e. resizes the given rectangle by multiplying all side coordinates with a scale factor)
!*/

// ----------------------------------------------------------------------------------------

const rectangle translate_rect (
const rectangle& rect,
const point& p
);
/*!
ensures
- returns a rectangle R such that:
- R.left()   == rect.left()   + p.x()
- R.right()  == rect.right()  + p.x()
- R.top()    == rect.top()    + p.y()
- R.bottom() == rect.bottom() + p.y()
!*/

// ----------------------------------------------------------------------------------------

const rectangle translate_rect (
const rectangle& rect,
long x,
long y
);
/*!
ensures
- returns a rectangle R such that:
- R.left()   == rect.left()   + x
- R.right()  == rect.right()  + x
- R.top()    == rect.top()    + y
- R.bottom() == rect.bottom() + y
!*/

// ----------------------------------------------------------------------------------------

const rectangle resize_rect (
const rectangle& rect,
unsigned long width,
unsigned long height
);
/*!
ensures
- returns a rectangle R such that:
- if (width == 0 || height == 0)
- R.width() == 0
- R.height() == 0
- else
- R.width() == width
- R.height() == height
- R.left() == rect.left()
- R.top() == rect.top()
!*/

// ----------------------------------------------------------------------------------------

const rectangle resize_rect_width (
const rectangle& rect,
unsigned long width
);
/*!
ensures
- returns a rectangle R such that:
- R.width() == width
- R.left() == rect.left()
- R.top() == rect.top()
- R.bottom() == rect.bottom()
!*/

// ----------------------------------------------------------------------------------------

const rectangle resize_rect_height (
const rectangle& rect,
unsigned long height
);
/*!
ensures
- returns a rectangle R such that:
- R.height() == height
- R.left() == rect.left()
- R.top() == rect.top()
- R.right() == rect.right()
!*/

// ----------------------------------------------------------------------------------------

const rectangle move_rect (
const rectangle& rect,
const point& p
);
/*!
ensures
- returns a rectangle R such that:
- R.width() == rect.width()
- R.height() == rect.height()
- R.left() == p.x()
- R.top() == p.y()
!*/

// ----------------------------------------------------------------------------------------

const rectangle move_rect (
const rectangle& rect,
long x,
long y
);
/*!
ensures
- returns a rectangle R such that:
- R.width() == rect.width()
- R.height() == rect.height()
- R.left() == x
- R.top() == y
!*/

// ----------------------------------------------------------------------------------------

template <typename T>
inline const dlib::vector<T,2> nearest_point (
const rectangle& rect,
const dlib::vector<T,2>& p
);
/*!
ensures
- if (rect.contains(p)) then
- returns p
- else
- returns the point in rect that is closest to p
!*/

// ----------------------------------------------------------------------------------------

inline size_t nearest_rect (
const std::vector<rectangle>& rects,
const point& p
);
/*!
requires
- rects.size() > 0
ensures
- returns the index of the rectangle that is closest to the point p.  In
particular, this function returns an IDX such that:
length(nearest_point(rects[IDX],p) - p)
is minimized.
!*/

// ----------------------------------------------------------------------------------------

inline long distance_to_rect_edge (
const rectangle& rect,
const point& p
);
/*!
ensures
- returns the Manhattan distance between the edge of rect and p.
!*/

// ----------------------------------------------------------------------------------------

template <typename T>
void clip_line_to_rectangle (
const rectangle& box,
dlib::vector<T,2>& p1,
dlib::vector<T,2>& p2
);
/*!
ensures
- clips the line segment that goes from points p1 to p2 so that it is entirely
within the given box.  In particular, we will have:
- box.contains(#p1) == true
- box.contains(#p2) == true
- The line segment #p1 to #p2 is entirely contained within the line segment
p1 to p2.  Moreover, #p1 to #p2 is the largest such line segment that
fits within the given box.
- If the line segment does not intersect the box then the result is some
arbitrary line segment inside the box.
!*/

// ----------------------------------------------------------------------------------------

template <
typename T
>
const rectangle get_rect (
const T& m
);
/*!
requires
- It must be possible to determine the number of "rows" and "columns" in m.
Either by calling num_rows(m) and num_columns(m) or by calling m.nr() and
m.nc() to obtain the number of rows and columns respectively.  Moreover,
these routines should return longs.
ensures
- returns rectangle(0, 0, num_columns(m)-1, num_rows(m)-1)
(i.e. assuming T represents some kind of rectangular grid, such as
the dlib::matrix or dlib::array2d objects, this function returns the
bounding rectangle for that gridded object.)
!*/

// ----------------------------------------------------------------------------------------

inline rectangle operator+ (
const rectangle& r,
const point& p
);
/*!
ensures
- returns r + rectangle(p)
(i.e. returns the rectangle that contains both r and p)
!*/

// ----------------------------------------------------------------------------------------

inline rectangle operator+ (
const point& p,
const rectangle& r
);
/*!
ensures
- returns r + rectangle(p)
(i.e. returns the rectangle that contains both r and p)
!*/

// ----------------------------------------------------------------------------------------

}

#endif // DLIB_RECTANGLe_ABSTRACT_

```