An integer coordinate rectangle. More...

#include <Box.h>

Public Types
enum	EdgeHandlingEnum { EXPAND, SHRINK }

typedef Point2I	Point

typedef Extent2I	Extent

typedef int	Element

Public Member Functions
	Box2I () noexcept
	Construct an empty box. More...

	Box2I (Point2I const &minimum, Point2I const &maximum, bool invert=true)
	Construct a box from its minimum and maximum points. More...

	Box2I (Point2I const &corner, Extent2I const &dimensions, bool invert=true)
	Construct a box from one corner and dimensions. More...

	Box2I (Box2D const &other, EdgeHandlingEnum edgeHandling=EXPAND)
	Construct an integer box from a floating-point box. More...

	Box2I (Box2I const &) noexcept=default
	Standard copy constructor. More...

	Box2I (Box2I &&) noexcept=default

	~Box2I () noexcept=default

void	swap (Box2I &other) noexcept

Box2I &	operator= (Box2I const &) noexcept=default
	Standard assignment operator. More...

Box2I &	operator= (Box2I &&) noexcept=default

ndarray::View< boost::fusion::vector2< ndarray::index::Range, ndarray::index::Range > >	getSlices () const
	Return slices to extract the box's region from an ndarray::Array. More...

bool	isEmpty () const noexcept
	Return true if the box contains no points. More...

bool	contains (Point2I const &point) const noexcept
	Return true if the box contains the point. More...

bool	contains (Box2I const &other) const noexcept
	Return true if all points contained by other are also contained by this. More...

bool	overlaps (Box2I const &other) const noexcept
	Return true if any points in other are also in this. More...

void	grow (int buffer)
	Increase the size of the box by the given buffer amount in all directions. More...

void	grow (Extent2I const &buffer)
	Increase the size of the box by the given buffer amount in each direction. More...

void	shift (Extent2I const &offset)
	Shift the position of the box by the given offset. More...

void	flipLR (int xExtent)
	Flip a bounding box about the y-axis given a parent box of extent (xExtent). More...

void	flipTB (int yExtent)
	Flip a bounding box about the x-axis given a parent box of extent (yExtent). More...

void	include (Point2I const &point)
	Expand this to ensure that this->contains(point). More...

void	include (Box2I const &other)
	Expand this to ensure that this->contains(other). More...

void	clip (Box2I const &other) noexcept
	Shrink this to ensure that `other.contains(*this)`. More...

bool	operator== (Box2I const &other) const noexcept
	Compare two boxes for equality. More...

bool	operator!= (Box2I const &other) const noexcept
	Compare two boxes for equality. More...

std::size_t	hash_value () const noexcept
	Return a hash of this object. More...

std::vector< Point2I >	getCorners () const
	Get the corner points. More...

std::string	toString () const

Min/Max Accessors
Return the minimum and maximum coordinates of the box (inclusive).
Point2I const	getMin () const noexcept

int	getMinX () const noexcept

int	getMinY () const noexcept

Point2I const	getMax () const noexcept

int	getMaxX () const noexcept

int	getMaxY () const noexcept

Begin/End Accessors
Return STL-style begin (inclusive) and end (exclusive) coordinates for the box.
Point2I const	getBegin () const noexcept

int	getBeginX () const noexcept

int	getBeginY () const noexcept

Point2I const	getEnd () const noexcept

int	getEndX () const noexcept

int	getEndY () const noexcept

Size Accessors
Return the size of the box in pixels.
Extent2I const	getDimensions () const noexcept

int	getWidth () const noexcept

int	getHeight () const noexcept

int	getArea () const

Center Accessors
Return the center coordinate of the box.
Point2D const	getCenter () const noexcept

double	getCenterX () const noexcept

double	getCenterY () const noexcept

Static Public Member Functions
static Box2I	makeCenteredBox (Point2D const &center, Extent const &size)
	Create a box centered as closely as possible on a particular point. More...

Detailed Description

An integer coordinate rectangle.

Box2I is an inclusive box that represents a rectangular region of pixels. A box never has negative dimensions; the empty box is defined to have zero-size dimensions, and is treated as though it does not have a well-defined position (regardless of the return value of getMin() or getMax() for an empty box).

Examples:: image2.cc, and maskedImage2.cc.

Definition at line 54 of file Box.h.

Member Typedef Documentation

◆ Element

typedef int lsst::geom::Box2I::Element

Definition at line 58 of file Box.h.

◆ Extent

typedef Extent2I lsst::geom::Box2I::Extent

Definition at line 57 of file Box.h.

◆ Point

typedef Point2I lsst::geom::Box2I::Point

Definition at line 56 of file Box.h.

Member Enumeration Documentation

◆ EdgeHandlingEnum

enum lsst::geom::Box2I::EdgeHandlingEnum

Enumerator
EXPAND
SHRINK

Definition at line 60 of file Box.h.

60 { EXPAND, SHRINK };

lsst::geom::Box2I::EXPAND

Definition: Box.h:60

lsst::geom::Box2I::SHRINK

Definition: Box.h:60

Constructor & Destructor Documentation

◆ Box2I() [1/6]

lsst::geom::Box2I::Box2I ( )

inlinenoexcept

Construct an empty box.

Definition at line 63 of file Box.h.

63 : _minimum(0), _dimensions(0) {}

◆ Box2I() [2/6]

lsst::geom::Box2I::Box2I	(	Point2I const &	minimum,
		Point2I const &	maximum,
		bool	invert = `true`
	)

Construct a box from its minimum and maximum points.

Parameters

[in]	minimum	Minimum (lower left) coordinate (inclusive).
[in]	maximum	Maximum (upper right) coordinate (inclusive).
[in]	invert	If true (default), swap the minimum and maximum coordinates if minimum > maximum instead of creating an empty box.

Definition at line 31 of file Box.cc.

         : _minimum(minimum), _dimensions(maximum - minimum) {
     for (int n = 0; n < 2; ++n) {
         if (_dimensions[n] < 0) {
             if (invert) {
                 _minimum[n] += _dimensions[n];
                 _dimensions[n] = -_dimensions[n];
             } else {
                 *this = Box2I();
                 return;
             }
         }
     }
     _dimensions += Extent2I(1);
 }

◆ Box2I() [3/6]

lsst::geom::Box2I::Box2I	(	Point2I const &	corner,
		Extent2I const &	dimensions,
		bool	invert = `true`
	)

Construct a box from one corner and dimensions.

Parameters

[in]	corner	Reference coordinate. This is the lower left corner if both dimensions are positive, but a right corner or upper corner if the corresponding dimension is negative and `invert` is set.
[in]	dimensions	Box dimensions. If either dimension coordinate is 0, the box will be empty.
[in]	invert	If true (default), invert any negative dimensions instead of creating an empty box.

Exceptions

lsst::pex::exceptions::OverflowError Thrown if the maximum Point2I would overflow.

Definition at line 47 of file Box.cc.

         : _minimum(corner), _dimensions(dimensions) {
     for (int n = 0; n < 2; ++n) {
         if (_dimensions[n] == 0) {
             *this = Box2I();
             return;
         } else if (_dimensions[n] < 0) {
             if (invert) {
                 _minimum[n] += (_dimensions[n] + 1);
                 _dimensions[n] = -_dimensions[n];
             } else {
                 *this = Box2I();
                 return;
             }
         }
     }
     if (!isEmpty() && any(getMin().gt(getMax()))) {
         throw LSST_EXCEPT(pex::exceptions::OverflowError,
                           "Box dimensions too large; integer overflow detected.");
     }
 }

◆ Box2I() [4/6]

lsst::geom::Box2I::Box2I	(	Box2D const &	other,
		EdgeHandlingEnum	edgeHandling = `EXPAND`
	)

explicit

Construct an integer box from a floating-point box.

Floating-point to integer box conversion is based on the concept that a pixel is not an infinitesimal point but rather a square of unit size centered on integer-valued coordinates. Converting a floating-point box to an integer box thus requires a choice on how to handle pixels which are only partially contained by the input floating-point box.

Parameters

[in]	other	A floating-point box to convert.
[in]	edgeHandling	If EXPAND, the integer box will contain any pixels that overlap the floating-point box. If SHRINK, the integer box will contain only pixels completely contained by the floating-point box.

Exceptions

lsst::pex::exceptions::InvalidParameterError Thrown if other is not finite.

Definition at line 69 of file Box.cc.

                                                               : _minimum(), _dimensions() {
     if (other.isEmpty()) {
         *this = Box2I();
         return;
     }
     if (!std::isfinite(other.getMinX()) || !std::isfinite(other.getMinY()) ||
         !std::isfinite(other.getMaxX()) || !std::isfinite(other.getMaxY())) {
         throw LSST_EXCEPT(pex::exceptions::InvalidParameterError, "Cannot convert non-finite Box2D to Box2I");
     }
     Point2D fpMin(other.getMin() + Extent2D(0.5));
     Point2D fpMax(other.getMax() - Extent2D(0.5));
     switch (edgeHandling) {
         case EXPAND:
             for (int n = 0; n < 2; ++n) {
                 _minimum[n] = static_cast<int>(std::floor(fpMin[n]));
                 _dimensions[n] = static_cast<int>(std::ceil(fpMax[n])) + 1 - _minimum[n];
             }
             break;
         case SHRINK:
             for (int n = 0; n < 2; ++n) {
                 _minimum[n] = static_cast<int>(std::ceil(fpMin[n]));
                 _dimensions[n] = static_cast<int>(std::floor(fpMax[n])) + 1 - _minimum[n];
             }
             break;
     }
 }

◆ Box2I() [5/6]

lsst::geom::Box2I::Box2I ( Box2I const & )

defaultnoexcept

Standard copy constructor.

◆ Box2I() [6/6]

lsst::geom::Box2I::Box2I ( Box2I && )

defaultnoexcept

◆ ~Box2I()

lsst::geom::Box2I::~Box2I ( )

defaultnoexcept

Member Function Documentation

◆ clip()

void lsst::geom::Box2I::clip ( Box2I const & other )

noexcept

Shrink this to ensure that other.contains(*this).

In particular, if other and this box do not overlap this box will become empty.

Parameters

other the box that must contain this one

Definition at line 194 of file Box.cc.

                                             {
     if (isEmpty()) return;
     if (other.isEmpty()) {
         *this = Box2I();
         return;
     }
     Point2I maximum(getMax());
     Point2I const& otherMin = other.getMin();
     Point2I const otherMax = other.getMax();
     for (int n = 0; n < 2; ++n) {
         if (otherMin[n] > _minimum[n]) {
             _minimum[n] = otherMin[n];
         }
         if (otherMax[n] < maximum[n]) {
             maximum[n] = otherMax[n];
         }
     }
     if (any(maximum.lt(_minimum))) {
         *this = Box2I();
         return;
     }
     _dimensions = Extent2I(1) + maximum - _minimum;
 }

◆ contains() [1/2]

bool lsst::geom::Box2I::contains ( Point2I const & point ) const

noexcept

Return true if the box contains the point.

Definition at line 117 of file Box.cc.

                                                         {
     return all(point.ge(this->getMin())) && all(point.le(this->getMax()));
 }

◆ contains() [2/2]

bool lsst::geom::Box2I::contains ( Box2I const & other ) const

noexcept

Return true if all points contained by other are also contained by this.

An empty box is contained by every other box, including other empty boxes.

Definition at line 121 of file Box.cc.

                                                       {
     return other.isEmpty() ||
            (all(other.getMin().ge(this->getMin())) && all(other.getMax().le(this->getMax())));
 }

◆ flipLR()

void lsst::geom::Box2I::flipLR ( int xExtent )

Flip a bounding box about the y-axis given a parent box of extent (xExtent).

Definition at line 143 of file Box.cc.

                               {
     if (isEmpty()) return;  // should we throw an exception here instead of a no-op?
     // Apply flip about y-axis assumine parent coordinate system
     _minimum[0] = xextent - (_minimum[0] + _dimensions[0]);
     // _dimensions should remain unchanged
 }

◆ flipTB()

void lsst::geom::Box2I::flipTB ( int yExtent )

Flip a bounding box about the x-axis given a parent box of extent (yExtent).

Definition at line 150 of file Box.cc.

                               {
     if (isEmpty()) return;  // should we throw an exception here instead of a no-op?
     // Apply flip about y-axis assumine parent coordinate system
     _minimum[1] = yextent - (_minimum[1] + _dimensions[1]);
     // _dimensions should remain unchanged
 }

◆ getArea()

int lsst::geom::Box2I::getArea ( ) const

inline

Definition at line 176 of file Box.h.

176 { return getWidth() * getHeight(); }

lsst::geom::Box2I::getHeight

int getHeight() const noexcept

Definition: Box.h:175

lsst::geom::Box2I::getWidth

int getWidth() const noexcept

Definition: Box.h:174

◆ getBegin()

Point2I const lsst::geom::Box2I::getBegin ( ) const

inlinenoexcept

Definition at line 158 of file Box.h.

158 { return _minimum; }

◆ getBeginX()

int lsst::geom::Box2I::getBeginX ( ) const

inlinenoexcept

Definition at line 159 of file Box.h.

159 { return _minimum.getX(); }

◆ getBeginY()

int lsst::geom::Box2I::getBeginY ( ) const

inlinenoexcept

Definition at line 160 of file Box.h.

160 { return _minimum.getY(); }

◆ getCenter()

Point2D const lsst::geom::Box2I::getCenter ( ) const

noexcept

Definition at line 96 of file Box.cc.

                                               {
     return Box2D(*this).getCenter();
 }

◆ getCenterX()

double lsst::geom::Box2I::getCenterX ( ) const

inlinenoexcept

Definition at line 186 of file Box.h.

186 { return this->getCenter().getX(); }

lsst::geom::Box2I::getCenter

Point2D const getCenter() const noexcept

Definition: Box.cc:96

◆ getCenterY()

double lsst::geom::Box2I::getCenterY ( ) const

inlinenoexcept

Definition at line 187 of file Box.h.

187 { return this->getCenter().getY(); }

lsst::geom::Box2I::getCenter

Point2D const getCenter() const noexcept

Definition: Box.cc:96

◆ getCorners()

std::vector< Point2I > lsst::geom::Box2I::getCorners ( ) const

Get the corner points.

The order is counterclockise, starting from the lower left corner, i.e.: (minX, minY), (maxX, maxY), (maxX, maxX), (minX, maxY)

Definition at line 231 of file Box.cc.

                                            {
     std::vector<Point2I> retVec;
     retVec.push_back(getMin());
     retVec.push_back(Point2I(getMaxX(), getMinY()));
     retVec.push_back(getMax());
     retVec.push_back(Point2I(getMinX(), getMaxY()));
     return retVec;
 }

◆ getDimensions()

Extent2I const lsst::geom::Box2I::getDimensions ( ) const

inlinenoexcept

Definition at line 173 of file Box.h.

173 { return _dimensions; }

◆ getEnd()

Point2I const lsst::geom::Box2I::getEnd ( ) const

inlinenoexcept

Definition at line 162 of file Box.h.

162 { return _minimum + _dimensions; }

◆ getEndX()

int lsst::geom::Box2I::getEndX ( ) const

inlinenoexcept

Definition at line 163 of file Box.h.

163 { return _minimum.getX() + _dimensions.getX(); }

◆ getEndY()

int lsst::geom::Box2I::getEndY ( ) const

inlinenoexcept

Definition at line 164 of file Box.h.

164 { return _minimum.getY() + _dimensions.getY(); }

◆ getHeight()

int lsst::geom::Box2I::getHeight ( ) const

inlinenoexcept

Definition at line 175 of file Box.h.

175 { return _dimensions.getY(); }

◆ getMax()

Point2I const lsst::geom::Box2I::getMax ( ) const

inlinenoexcept

Definition at line 147 of file Box.h.

147 { return _minimum + _dimensions - Extent2I(1); }

lsst::geom::Extent2I

Extent< int, 2 > Extent2I

Definition: Extent.h:397

◆ getMaxX()

int lsst::geom::Box2I::getMaxX ( ) const

inlinenoexcept

Definition at line 148 of file Box.h.

148 { return _minimum.getX() + _dimensions.getX() - 1; }

◆ getMaxY()

int lsst::geom::Box2I::getMaxY ( ) const

inlinenoexcept

Definition at line 149 of file Box.h.

149 { return _minimum.getY() + _dimensions.getY() - 1; }

◆ getMin()

Point2I const lsst::geom::Box2I::getMin ( ) const

inlinenoexcept

Definition at line 143 of file Box.h.

143 { return _minimum; }

◆ getMinX()

int lsst::geom::Box2I::getMinX ( ) const

inlinenoexcept

Definition at line 144 of file Box.h.

144 { return _minimum.getX(); }

◆ getMinY()

int lsst::geom::Box2I::getMinY ( ) const

inlinenoexcept

Definition at line 145 of file Box.h.

145 { return _minimum.getY(); }

◆ getSlices()

ndarray::View< boost::fusion::vector2< ndarray::index::Range, ndarray::index::Range > > lsst::geom::Box2I::getSlices ( ) const

Return slices to extract the box's region from an ndarray::Array.

Definition at line 112 of file Box.cc.

               {
     return ndarray::view(getBeginY(), getEndY())(getBeginX(), getEndX());
 }

◆ getWidth()

int lsst::geom::Box2I::getWidth ( ) const

inlinenoexcept

Definition at line 174 of file Box.h.

174 { return _dimensions.getX(); }

◆ grow() [1/2]

void lsst::geom::Box2I::grow ( int buffer )

inline

Increase the size of the box by the given buffer amount in all directions.

If a negative buffer is passed and the final size of the box is less than or equal to zero, the box will be made empty.

Definition at line 219 of file Box.h.

219 { grow(Extent2I(buffer)); }

lsst::geom::Box2I::grow

void grow(int buffer)

Increase the size of the box by the given buffer amount in all directions.

Definition: Box.h:219

lsst::geom::Extent2I

Extent< int, 2 > Extent2I

Definition: Extent.h:397

◆ grow() [2/2]

void lsst::geom::Box2I::grow ( Extent2I const & buffer )

Increase the size of the box by the given buffer amount in each direction.

If a negative buffer is passed and the final size of the box is less than or equal to zero, the box will be made empty.

Definition at line 131 of file Box.cc.

                                        {
     if (isEmpty()) return;  // should we throw an exception here instead of a no-op?
     _minimum -= buffer;
     _dimensions += buffer * 2;
     if (any(_dimensions.le(0))) *this = Box2I();
 }

◆ hash_value()

std::size_t lsst::geom::Box2I::hash_value ( ) const

noexcept

Return a hash of this object.

Definition at line 226 of file Box.cc.

                                            {
     // Completely arbitrary seed
     return utils::hashCombine(17, _minimum, _dimensions);
 }

◆ include() [1/2]

void lsst::geom::Box2I::include ( Point2I const & point )

Expand this to ensure that this->contains(point).

Definition at line 157 of file Box.cc.

                                         {
     if (isEmpty()) {
         _minimum = point;
         _dimensions = Extent2I(1);
         return;
     }
     Point2I maximum(getMax());
     for (int n = 0; n < 2; ++n) {
         if (point[n] < _minimum[n]) {
             _minimum[n] = point[n];
         } else if (point[n] > maximum[n]) {
             maximum[n] = point[n];
         }
     }
     _dimensions = Extent2I(1) + maximum - _minimum;
 }

◆ include() [2/2]

void lsst::geom::Box2I::include ( Box2I const & other )

Expand this to ensure that this->contains(other).

Definition at line 174 of file Box.cc.

                                       {
     if (other.isEmpty()) return;
     if (this->isEmpty()) {
         *this = other;
         return;
     }
     Point2I maximum(getMax());
     Point2I const& otherMin = other.getMin();
     Point2I const otherMax = other.getMax();
     for (int n = 0; n < 2; ++n) {
         if (otherMin[n] < _minimum[n]) {
             _minimum[n] = otherMin[n];
         }
         if (otherMax[n] > maximum[n]) {
             maximum[n] = otherMax[n];
         }
     }
     _dimensions = Extent2I(1) + maximum - _minimum;
 }

◆ isEmpty()

bool lsst::geom::Box2I::isEmpty ( ) const

inlinenoexcept

Return true if the box contains no points.

Definition at line 194 of file Box.h.

194 { return _dimensions.getX() == 0 && _dimensions.getY() == 0; }

◆ makeCenteredBox()

Box2I lsst::geom::Box2I::makeCenteredBox	(	Point2D const &	center,
		Box2I::Extent const &	size
	)

static

Create a box centered as closely as possible on a particular point.

Parameters

center	The desired center of the box.
size	The desired width and height (in that order) of the box.

Returns: if size is positive, a box with size size; otherwise, an empty box. If the returned box is not empty, its center shall be within half a pixel of center in either dimension.

Exceptions

lsst::pex::exceptions::OverflowError	Thrown if the resulting box would overflow.
lsst::pex::exceptions::InvalidParameterError	Thrown if `center` is not finite.

Definition at line 100 of file Box.cc.

                                                                            {
     if (!std::isfinite(center[0]) || !std::isfinite(center[1])) {
         throw LSST_EXCEPT(pex::exceptions::InvalidParameterError, "Cannot make Box2I with non-finite center");
     }
 
     lsst::geom::Point2D corner(center);
     corner.shift(-0.5 * lsst::geom::Extent2D(size));
     // compensate for Box2I's coordinate conventions (where max = min + size - 1)
     corner.shift(lsst::geom::Extent2D(0.5, 0.5));
     return lsst::geom::Box2I(lsst::geom::Point2I(corner), size, false);
 }

◆ operator!=()

bool lsst::geom::Box2I::operator!= ( Box2I const & other ) const

noexcept

Compare two boxes for equality.

All empty boxes are equal.

Definition at line 222 of file Box.cc.

                                                         {
     return other._minimum != this->_minimum || other._dimensions != this->_dimensions;
 }

◆ operator=() [1/2]

Box2I& lsst::geom::Box2I::operator= ( Box2I const & )

defaultnoexcept

Standard assignment operator.

◆ operator=() [2/2]

Box2I& lsst::geom::Box2I::operator= ( Box2I && )

defaultnoexcept

◆ operator==()

bool lsst::geom::Box2I::operator== ( Box2I const & other ) const

noexcept

Compare two boxes for equality.

All empty boxes are equal.

Definition at line 218 of file Box.cc.

                                                         {
     return other._minimum == this->_minimum && other._dimensions == this->_dimensions;
 }

◆ overlaps()

bool lsst::geom::Box2I::overlaps ( Box2I const & other ) const

noexcept

Return true if any points in other are also in this.

Any overlap operation involving an empty box returns false.

Definition at line 126 of file Box.cc.

                                                       {
     return !(other.isEmpty() || this->isEmpty() || any(other.getMax().lt(this->getMin())) ||
              any(other.getMin().gt(this->getMax())));
 }

◆ shift()

void lsst::geom::Box2I::shift ( Extent2I const & offset )

Shift the position of the box by the given offset.

Definition at line 138 of file Box.cc.

                                         {
     if (isEmpty()) return;  // should we throw an exception here instead of a no-op?
     _minimum += offset;
 }

◆ swap()

void lsst::geom::Box2I::swap ( Box2I & other )

inlinenoexcept

Definition at line 128 of file Box.h.

                                      {
         _minimum.swap(other._minimum);
         _dimensions.swap(other._dimensions);
     }

◆ toString()

std::string lsst::geom::Box2I::toString ( ) const

inline

Definition at line 277 of file Box.h.

                                {
         return (boost::format("Box2I(%s,%s)") % _minimum.toString() % _dimensions.toString()).str();
     }

The documentation for this class was generated from the following files:

/j/snowflake/release/lsstsw/stack/Linux64/geom/18.1.0/include/lsst/geom/Box.h
/j/snowflake/release/lsstsw/stack/Linux64/geom/18.1.0/src/Box.cc

Public Types

Public Member Functions

Static Public Member Functions

Detailed Description

Member Typedef Documentation

◆ Element

◆ Extent

◆ Point

Member Enumeration Documentation

◆ EdgeHandlingEnum

Constructor & Destructor Documentation

◆ Box2I() [1/6]

◆ Box2I() [2/6]

◆ Box2I() [3/6]

◆ Box2I() [4/6]

◆ Box2I() [5/6]

◆ Box2I() [6/6]

◆ ~Box2I()

Member Function Documentation

◆ clip()

◆ contains() [1/2]

◆ contains() [2/2]

◆ flipLR()

◆ flipTB()

◆ getArea()

◆ getBegin()

◆ getBeginX()

◆ getBeginY()

◆ getCenter()

◆ getCenterX()

◆ getCenterY()

◆ getCorners()

◆ getDimensions()

◆ getEnd()

◆ getEndX()

◆ getEndY()

◆ getHeight()

◆ getMax()

◆ getMaxX()

◆ getMaxY()

◆ getMin()

◆ getMinX()

◆ getMinY()

◆ getSlices()

◆ getWidth()

◆ grow() [1/2]

◆ grow() [2/2]

◆ hash_value()

◆ include() [1/2]

◆ include() [2/2]

◆ isEmpty()

◆ makeCenteredBox()

◆ operator!=()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ operator==()

◆ overlaps()

◆ shift()

◆ swap()

◆ toString()