Box2 Class Reference

Axis aligned box in the plane. More...

#include <box.h>

Inheritance diagram for Box2:

Public Member Functions
	Box2 ()
	Empty.
	Box2 (const double &)
	Create a square box centered at the origin and of given half side length.
	Box2 (const double &, const double &)
	Create a box centered at the origin and of given dimensions.
	Box2 (const Vector2 &)
	Create a box from a single vertex.
	Box2 (const Vector2 &, const Vector2 &)
	Create a box.
	Box2 (const Vector2 &, const double &)
	Creates a box.
	Box2 (const Vector2 &, const double &, const double &)
	Create a box given a center point and its width, length, and height.
	Box2 (const Box &)
	Create a box in the plane given a box.
	Box2 (const Box2 &, const Box2 &)
	Create a box embedding two boxes.
	Box2 (const Box2 &, const Matrix2 &)
	Creates an axis aligned bounding box from a box and a transformation matrix.
	Box2 (const Box2 &, const Frame2 &)
	Creates an axis aligned bounding box from a box and a frame.
	Box2 (const QVector< Vector2 > &)
	Compute the bounding box of a set of points.
	Box2 (const QSize &)
	Create a box from a Qt size.
Vector2 &	operator[] (int)
	Returns either end vertex of the box.
Vector2	operator[] (int) const
	Overloaded.
Vector2	Size () const
	Compute the size (width and height) of a box.
double	Width () const
	Compute the width of a box.
double	Height () const
	Compute the height of a box.
Vector2	Diagonal () const
	Returns the diagonal of the box.
double	Radius () const
	Returns the radius of the box, i.e. the length of the half diagonal of the box.
double	Area () const
	Compute the surface area of a box.
double	Perimeter () const
	Compute the perimeter of the box.
Vector2	Center () const
	Returns the center of the box.
Vector2	Vertex (int) const
	Returns the k-th vertex of the box.
Vector2	Vertex (int, int, int, int) const
	Compute the coordinates of a grid aligned point.
Vector2	VertexUV (const Vector2 &) const
	Compute the coordinates of a point inside the box given uv coordinates.
Box2	Sub (int) const
	Computes the sub-box in the n-th quadrant.
double	R (const Vector2 &) const
	Compute the squared distance between the box and a point.
double	Signed (const Vector2 &) const
	Computes the signed distance between the box and a point.
double	R (const Box2 &) const
	Compute the squared Euclidean distance between two boxes.
void	Translate (const Vector2 &)
	Translates a box.
void	Scale (const Vector2 &)
	Scales a box.
void	Scale (const double &)
	Scales a box.
Box2	Translated (const Vector2 &) const
	Translated box.
Box2	Scaled (const double &) const
	Scales a box and return the scaled box.
Box2	Scaled (const Vector2 &) const
	Scales a box and return the scaled box.
Box2	Scaled (const QSize &) const
	Scales a box according to a Qt size.
Box2	ScaledTo (const double &) const
	Scale the box so that the largest side should equal the argument value.
Box2	ScaledCentered (const double &) const
	Scales a box while preserving its center.
Box2	Rotated (const double &) const
	Compute the box embedding the rotated box.
Box2	Rotated (const Matrix2 &) const
	Compute the box embedding the rotated box.
Box2	Centered () const
	Compute the box translated to origin.
void	SetCubic ()
	Creates the tightest embedding cube from an arbitrarilly shaped box.
void	SetInscribedCubic ()
	Creates the biggest cube inscribed in the box.
Box2	Cube () const
	Return the tightest embedding cube from an arbitrarilly shaped box.
void	Extend (const double &)
	Extend the limits of the box by a given distance.
void	Extend (const Vector2 &)
	Extend the limits of the box given a point.
Box2	Extended (const double &) const
	Extend the limits of the box by a given distance.
void	SetParallelepipedic (int, int &, int &)
	Inflates a box so that its dimensions should be a fraction of its maximum side length.
void	SetParallelepipedic (const double &, int &, int &)
	Creates a parallelepipedic box whose dimensions are integer multiples of a given input reference size.
bool	Inside (const Vector2 &) const
	Test if a point is inside the box.
bool	Inside (const Vector2 &, const double &) const
	Test if a point lies withing a given range of the box.
bool	Intersect (const Box2 &) const
	Check if the box intersects another box.
double	OverlapArea (const Box2 &) const
	Computes the overlapping area of two boxes.
Box2	Intersection (const Box2 &) const
	Computes the intersection between two boxes.
Box	ToBox (const double &, const double &) const
	Convert a planar Box2 to a Box.
int	Quadrant (const Vector2 &) const
	Computes quadrant index of a vertex with respect to the box center.
bool	Intersect (const Ray2 &, double &, double &) const
	Computes the intersection between a box and a ray.
bool	Intersect (const Ray2 &) const
	Computes the intersection between a box and a ray.
bool	Intersect (const Line2 &, double &, double &) const
	Computes the intersection between a box and a line.
bool	Intersect (const Segment2 &, double &, double &) const
	Compute the intersection between a box and a segment.
bool	Intersect (const Line2 &) const
	Check the intersection between a box and a line.
bool	Intersect (const Segment2 &) const
	Check the intersection between a box and a segment.
void	Draw (QGraphicsScene &, const QPen &=QPen(), const QBrush &=QBrush()) const
	Draw a rectangle.
Vector2	RandomInside (Random &=Random::R239) const
	Generate a random vector inside the box.
Vector2	RandomOn (Random &=Random::R239) const
	Generate a random vector on the perimeter of the box.
QRectF	GetQtRect () const
	Create the Qt rectangle.
QRect	TileRange (const Box2 &) const
	Compute the range of index for tiling the argument box so that it covers the box.
Box2	Tile (int, int) const
	Return the tiled the box using integer coordinates.
Box2	Tile (const QRect &) const
	Return the tiled the box using integer coordinates.
Segment2	GetSegment (const double &, bool=true) const
	Compute the horizontal or vertical segment dividing the box into u and 1-u parts.
QVector< Vector2 >	Poisson (const double &, int, Random &=Random::R239) const
	Compute a Poisson disc distribution inside a box.
QVector< Vector2 >	Poisson (const double &, int, const QVector< Vector2 > &, bool=true, Random &=Random::R239) const
	Compute a Poisson disc distribution inside a box.

Static Public Member Functions
static Box2	MinMax (const Vector2 &, const Vector2 &)
	Create a box from any two points.

Static Public Attributes
static const double	epsilon = 1.0e-5
	Epsilon value used to check intersections and some round off errors.
static const Box2	Infinity
	Huge bounding box, which should enclose any other.
static const Box2	Null
	Null box, equivalent to.
static const Box2	Unit
	Unit box, defined as.

Protected Attributes
Vector2	b = Vector2(1.0)
	Lower and upper vertexes of the box.

Friends
bool	operator== (const Box2 &a, const Box2 &b)
	Check if two boxes are (strictly) equal.
bool	operator!= (const Box2 &a, const Box2 &b)
	Check if two boxes are (strictly) different.
Box2	operator+ (const Box2 &a, const Box2 &b)
	Computes the Minkowski sum of two boxes.
Box2	operator* (const double &t, const Box2 &box)
	Scales a box by a scalar factor.
Box2	operator* (const Box2 &box, const double &t)
	Overloaded.
std::ostream &	operator<< (std::ostream &s, const Box2 &box)
	Overloaded.

Detailed Description

Axis aligned box in the plane.

See also

Box

Constructor & Destructor Documentation

Box2() [1/12]

Box2::Box2 ( const double & r )

inlineexplicit

Create a square box centered at the origin and of given half side length.

This is equivalent to:

Box2 box(Vector2(0.0),2.0);  // Simplified constructor Box2(2.0);

Parameters

r	Half side length.

Box2() [2/12]

Box2::Box2 ( const double & x, const double & y )

inlineexplicit

Create a box centered at the origin and of given dimensions.

This is equivalent to:

double width, height;
Box2 box(Vector2(-width/2.0,-height/2.0),Vector2(width/2.0,height/2.0);  // Simplified constructor Box2(width,height);

Parameters

x,y

Size.

Box2() [3/12]

Box2::Box2 ( const Vector2 & p )

inlineexplicit

Create a box from a single vertex.

Parameters

p

Point.

Box2() [4/12]

Box2::Box2 ( const Vector2 & a, const Vector2 & b )

inlineexplicit

Create a box.

Note that is possible to create a box using Vector as parameters as the compiler will call the constructor Vector2::Vector2(const Vector&).

Parameters

a,b

Points.

Box2() [5/12]

Box2::Box2 ( const Vector2 & c, const double & r )

inlineexplicit

Creates a box.

Parameters

c	Center.
r	Radius.

Box2() [6/12]

Box2::Box2 ( const Vector2 & c, const double & x, const double & y )

inlineexplicit

Create a box given a center point and its width, length, and height.

Parameters

c	center.
x,y	Width and height.

Box2() [7/12]

Box2::Box2 ( const Box & box )

inlineexplicit

Create a box in the plane given a box.

Parameters

box

The box.

Box2() [8/12]

Box2::Box2 ( const Box2 & x, const Box2 & y )

explicit

Create a box embedding two boxes.

Parameters

x,y	Argument boxes.

Box2() [9/12]

Box2::Box2 ( const Box2 & box, const Matrix2 & t )

explicit

Creates an axis aligned bounding box from a box and a transformation matrix.

Parameters

box	The box.
t	Transformation matrix.

Box2() [10/12]

Box2::Box2 ( const Box2 & box, const Frame2 & frame )

explicit

Creates an axis aligned bounding box from a box and a frame.

Parameters

box	The box.
frame	Transformation.

Box2() [11/12]

Box2::Box2 ( const QVector< Vector2 > & p )

explicit

Compute the bounding box of a set of points.

Parameters

p	Set of points (should not be empty).

Box2() [12/12]

Box2::Box2 ( const QSize & size )

explicit

Create a box from a Qt size.

Parameters

size

Size.

Member Function Documentation

Centered()

Box2 Box2::Centered

(

)

const

Compute the box translated to origin.

This is the same as:

Box centered=box;
centered.Translate(-box.Center());

Cube()

Box2 Box2::Cube

(

)

const

Return the tightest embedding cube from an arbitrarilly shaped box.

See also

SetSubic()

Draw()

void Box2::Draw	(	QGraphicsScene &	scene,
		const QPen &	pen = QPen(),
		const QBrush &	brush = QBrush() ) const

Draw a rectangle.

Parameters

scene	Graphics scene.
pen	The pen.
brush	The brush, should the box be filled.

Extend() [1/2]

void Box2::Extend

(

const double &

r

)

Extend the limits of the box by a given distance.

Note that this is the same as performing the Minkowski sum with a cubic box of size r.

Parameters

r

Range.

Extend() [2/2]

void Box2::Extend

(

const Vector2 &

p

)

Extend the limits of the box given a point.

If the point lies inside the box, the vertices of the box are unchanged.

Parameters

p

Point.

Extended()

Box2 Box2::Extended

(

const double &

r

)

const

Extend the limits of the box by a given distance.

Note that this is the same as performing the Minkowski sum with a cubic box of size r.

Parameters

r

Range.

GetSegment()

Segment2 Box2::GetSegment	(	const double &	u,
		bool	horizontal = true ) const

Compute the horizontal or vertical segment dividing the box into u and 1-u parts.

Parameters

u	Real.
horizontal	Boolean, set to true for horizontal split, false for vertical.

Height()

double Box2::Height ( ) const

inline

Compute the height of a box.

See also

Box2::Size()

Inside() [1/2]

bool Box2::Inside

(

const Vector2 &

p

)

const

Test if a point is inside the box.

Parameters

p

Point.

Inside() [2/2]

bool Box2::Inside	(	const Vector2 &	p,
		const double &	r ) const

Test if a point lies withing a given range of the box.

The following two pieces of code are almost equivalent:

bool a=Box2(1.0).Inside(Vector(1.5),1.0); // Do not modify the box and test range directly

In this case we modify the geometry:

Box2 box(1.0);
box.Extend(1.0); // We change the box geometry
// Note that we could have used a Minkowski sum: box=box+Box(1.0);
bool a=box.Inside(Vector(1.5));

Parameters

p	Point.
r	Range.

Intersect() [1/7]

bool Box2::Intersect ( const Box2 & box ) const

inline

Check if the box intersects another box.

Parameters

box	Argument box.

Intersect() [2/7]

bool Box2::Intersect

(

const Line2 &

l

)

const

Check the intersection between a box and a line.

This function is a convenience fuction for:

double a,b;
// Intersect with segment
return Intersect(l,a,b);

Parameters

l

The line.

Intersect() [3/7]

bool Box2::Intersect	(	const Line2 &	s,
		double &	tmin,
		double &	tmax ) const

Computes the intersection between a box and a line.

Sorted intersection depths are returned if intersection occurs.

Parameters

s	The line.
tmin,tmax	Intersection depths

Intersect() [4/7]

bool Box2::Intersect

(

const Ray2 &

ray

)

const

Computes the intersection between a box and a ray.

Parameters

ray

The ray.

Intersect() [5/7]

bool Box2::Intersect	(	const Ray2 &	ray,
		double &	tmin,
		double &	tmax ) const

Computes the intersection between a box and a ray.

Parameters

ray	The ray.
tmin,tmax	Intersection depths

Intersect() [6/7]

bool Box2::Intersect

(

const Segment2 &

s

)

const

Check the intersection between a box and a segment.

Parameters

s	The segment.

Intersect() [7/7]

bool Box2::Intersect	(	const Segment2 &	s,
		double &	tmin,
		double &	tmax ) const

Compute the intersection between a box and a segment.

Parameters

s	The line.
tmin,tmax	Intersection depths

See also

Box2::Intersect(const Line2&,double&,double&) const

Intersection()

Box2 Box2::Intersection

(

const Box2 &

x

)

const

Computes the intersection between two boxes.

Note that if the intersection is empty, the resulting box is invalid.

Parameters

x	Argument box.

MinMax()

Box2 Box2::MinMax ( const Vector2 & a, const Vector2 & b )

inlinestatic

Create a box from any two points.

Parameters

a,b

Points.

OverlapArea()

double Box2::OverlapArea ( const Box2 & box ) const

inline

Computes the overlapping area of two boxes.

This is a convenience function for the following code:

Box2 a,b;
double area=(a.Intersection(b)).Area();

See also

Box2::Intersection(const Box2&) const

Parameters

box

Poisson() [1/2]

QVector< Vector2 > Box2::Poisson	(	const double &	r,
		int	n,
		const QVector< Vector2 > &	s,
		bool	a = true,
		Random &	random = Random::R239 ) const

Compute a Poisson disc distribution inside a box.

This function uses a simple dart throwing algorithm.

See also

SphereTile

Parameters

r	Radius of the discs.
n	Number of candidate points.
s	Set of points.
a	Add set of points flag: set to true it the set points should be added to the sampling, set to false to define constraints (typically for borders).
random	Random number generator.

See also

Box2::Poisson(const double& , int , Random& )

Poisson() [2/2]

QVector< Vector2 > Box2::Poisson	(	const double &	r,
		int	n,
		Random &	random = Random::R239 ) const

Compute a Poisson disc distribution inside a box.

This function uses a simple dart throwing algorithm.

See also

SphereTile

Parameters

r	Radius of the discs.
n	Number of candidate points.
random	Random number generator.

Quadrant()

int Box2::Quadrant

(

const Vector2 &

p

)

const

Computes quadrant index of a vertex with respect to the box center.

See also

Vector2::Quadrant()

Parameters

p

Point.

R() [1/2]

double Box2::R

(

const Box2 &

y

)

const

Compute the squared Euclidean distance between two boxes.

This function computes the squared distance to avoid the computation of a square root.

Parameters

y

The box.

R() [2/2]

double Box2::R

(

const Vector2 &

p

)

const

Compute the squared distance between the box and a point.

Parameters

p

Point.

RandomInside()

Vector2 Box2::RandomInside

(

Random &

random = Random::R239

)

const

Generate a random vector inside the box.

Parameters

random

Random number generator.

RandomOn()

Vector2 Box2::RandomOn

(

Random &

random = Random::R239

)

const

Generate a random vector on the perimeter of the box.

Parameters

random

Random number generator.

Rotated() [1/2]

Box2 Box2::Rotated

(

const double &

a

)

const

Compute the box embedding the rotated box.

Parameters

a	Rotation angle.

Rotated() [2/2]

Box2 Box2::Rotated

(

const Matrix2 &

r

)

const

Compute the box embedding the rotated box.

Parameters

r	Rotation matrix.

Scale() [1/2]

void Box2::Scale

(

const double &

s

)

Scales a box.

Note that this function handles negative coefficients.

Parameters

s	Scaling factor.

Scale() [2/2]

void Box2::Scale

(

const Vector2 &

s

)

Scales a box.

Note that this function handles negative coefficients in the scaling vector.

Parameters

s	Scaling vector.

Scaled() [1/3]

Box2 Box2::Scaled

(

const double &

s

)

const

Scales a box and return the scaled box.

Parameters

s	Scaling factor.

See also

Box2::Scaled(const Vector2&)

Scaled() [2/3]

Box2 Box2::Scaled

(

const QSize &

s

)

const

Scales a box according to a Qt size.

This function preserves the width of the box, and scales its height according to the ratio.

Parameters

s

Size.

See also

Box2::Scaled

Scaled() [3/3]

Box2 Box2::Scaled

(

const Vector2 &

s

)

const

Scales a box and return the scaled box.

Parameters

s	Scaling vector.

See also

Box2::Scale

ScaledCentered()

Box2 Box2::ScaledCentered

(

const double &

s

)

const

Scales a box while preserving its center.

Parameters

s

Size.

See also

Box2::Scaled

ScaledTo()

Box2 Box2::ScaledTo

(

const double &

s

)

const

Scale the box so that the largest side should equal the argument value.

Parameters

s	Target largest size.

SetCubic()

void Box2::SetCubic

(

)

Creates the tightest embedding cube from an arbitrarilly shaped box.

This function creates a cube located at the same center point, and its side length equal to the maximum side of the argument box.

SetInscribedCubic()

void Box2::SetInscribedCubic

(

)

Creates the biggest cube inscribed in the box.

This function creates a cube located at the same center point, and its side length equal to the minimum side of the argument box.

See also

SetCubic()

SetParallelepipedic() [1/2]

void Box2::SetParallelepipedic	(	const double &	size,
		int &	x,
		int &	y )

Creates a parallelepipedic box whose dimensions are integer multiples of a given input reference size.

Parameters

size	Reference size, the dimension of the box will be a multiple of this size.
x,y	Two integers.

SetParallelepipedic() [2/2]

void Box2::SetParallelepipedic	(	int	n,
		int &	x,
		int &	y )

Inflates a box so that its dimensions should be a fraction of its maximum side length.

Parameters

n	Fraction.
x,y	Two integers.

Signed()

double Box2::Signed

(

const Vector2 &

p

)

const

Computes the signed distance between the box and a point.

Parameters

p

Point.

Sub()

Box2 Box2::Sub

(

int

n

)

const

Computes the sub-box in the n-th quadrant.

Parameters

n	Quadrant index.

Tile() [1/2]

Box2 Box2::Tile

(

const QRect &

r

)

const

Return the tiled the box using integer coordinates.

Parameters

r	Rectangle defining tiling coordinates.

See also

TileRange(const Box2&), Tile(int,int)

Tile() [2/2]

Box2 Box2::Tile	(	int	x,
		int	y ) const

Return the tiled the box using integer coordinates.

Parameters

x,y	Integer coordinates.

See also

TileRange(const Box2&), Tile(const QRect&)

TileRange()

QRect Box2::TileRange

(

const Box2 &

t

)

const

Compute the range of index for tiling the argument box so that it covers the box.

Parameters

t	Tiling box.

See also

Tile(const Box2&), Tile(const QRect&)

ToBox()

Box Box2::ToBox	(	const double &	a,
		const double &	b ) const

Convert a planar Box2 to a Box.

Parameters

a,b	Lower and upper coordinates (note that a should be smaller than b).

Translate()

void Box2::Translate

(

const Vector2 &

t

)

Translates a box.

Parameters

t	Translation vector.

Translated()

Box2 Box2::Translated

(

const Vector2 &

t

)

const

Translated box.

Parameters

t	Translation vector.

Vertex() [1/2]

Vector2 Box2::Vertex ( int k ) const

inline

Returns the k-th vertex of the box.

The returned vector is computed by analysing the first two bits of k as follows:

Vector2 vertex=Vector2((k&1)?b[0]:a[0],(k&2)?b[1]:a[1]);

Vertex() [2/2]

Vector2 Box2::Vertex	(	int	i,
		int	j,
		int	x,
		int	y ) const

Compute the coordinates of a grid aligned point.

This function computes the coordinates of a point inside the box as if the box was decomposed into a regular grid.

Parameters

i,j	Integer coordinates.
x,y	Virtual grid size.

VertexUV()

Vector2 Box2::VertexUV ( const Vector2 & uv ) const

inline

Compute the coordinates of a point inside the box given uv coordinates.

Parameters

uv	Coordinates.

Width()

double Box2::Width ( ) const

inline

Compute the width of a box.

See also

Box2::Size()

Friends And Related Symbol Documentation

operator!=

bool operator!= ( const Box2 & a, const Box2 & b )

friend

Check if two boxes are (strictly) different.

Parameters

a,b

Boxes.

operator*

Box2 operator* ( const double & t, const Box2 & box )

friend

Scales a box by a scalar factor.

Parameters

t	Scaling factor.
box	The box.

operator+

Box2 operator+ ( const Box2 & a, const Box2 & b )

friend

Computes the Minkowski sum of two boxes.

Parameters

a,b	Argument boxes.

operator<<

std::ostream & operator<< ( std::ostream & s, const Box2 & box )

friend

Overloaded.

Parameters

s	Stream.
box	The box.

operator==

bool operator== ( const Box2 & a, const Box2 & b )

friend

Check if two boxes are (strictly) equal.

Parameters

a,b

Boxes.

Member Data Documentation

Null

const Box2 Box2::Null

static

Null box, equivalent to.

Box2(Vector2(0.0)); 

Unit

const Box2 Box2::Unit

static

Unit box, defined as.

Box2(Vector2(0.0),Vector2(1.0));