Box Class Reference

An axis aligned box. More...

#include <box.h>

Inheritance diagram for Box:

Public Member Functions
	Box ()
	Empty.
	Box (const double &)
	Create a cube centered at the origin and of given half side length. More...
	Box (const Vector &)
	Create an empty box given one vertex. More...
	Box (const Vector &, const Vector &)
	Create a box given two opposite corners. More...
	Box (const Vector &, const double &)
	Create a box given a center point and the half side length. More...
	Box (const Vector &, const double &, const double &, const double &)
	Create a box given a center point and its width, length, and height. More...
	Box (const double &, const double &, const double &)
	Create a box given its sizes. More...
	Box (const Vector *, int)
	Creates the bounding box of a set of points. More...
	Box (const QVector< Vector > &)
	Creates the bounding box of a set of points. More...
	Box (const Box &, const Box &)
	Create a box embedding two boxes. More...
	Box (const Box &, const Frame &)
	Creates an axis aligned bounding box from a box and a frame. More...
	Box (const Box &, const FrameScaled &)
	Creates an axis aligned bounding box from a box and a frame. More...
	Box (const Box &, const Matrix &)
	Creates an axis aligned bounding box from a box and a transformation matrix. More...
	~Box ()
	Empty.
Vector &	operator[] (int)
	Returns either end vertex of the box.
Vector	operator[] (int) const
	Overloaded.
Vector	Center () const
	Returns the center of the box.
Vector	Vertex (int) const
	Returns the k-th vertex of the box. More...
Vector	Vertex (int, int, int, int, int, int) const
	Compute the coordinates of a grid aligned point. More...
Segment	Edge (int) const
	Compute the k-th edge segment of the box. More...
Plane	Face (int) const
	Compute the k-th plane of the box. More...
Vector	Size () const
	Compute the size (width, length and height) of a box. More...
Vector	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	R (const Vector &) const
	Computes the squared Euclidean distance between the box and a point. More...
double	Signed (const Vector &) const
	Computes the signed distance between the box and a point. More...
Vector	Normal (const Vector &) const
	Computes the normal vector between a point and a box. More...
double	R (const Box &) const
	Compute the squared Euclidean distance between two boxes. More...
double	RInfinity (const Box &) const
	Compute the maximum distance between two boxes. More...
int	Intersect (const Ray &) const
	Check the intersection between a box and a ray. More...
int	Intersect (const Ray &, double &, double &) const
	Computes the intersection between a box and a ray. More...
int	Intersect (const Ray &, double &) const
	Compute the first positive intersection between the box and a ray. More...
int	Intersect (const Ray &, double &, double &, Vector &, Vector &) const
	Compute the intersection between an axis aligned box and a ray. More...
int	Intersect (const Ray &, double &, Vector &) const
	Compute the first positive intersection between the box and a ray. More...
int	Intersect (const Vector &, const Vector &) const
	Check if a segment intersects an axis aligned box. More...
bool	Intersect (const Box &) const
	Check if the box intersects another box. More...
bool	Inside (const Box &) const
	Check if an argument box is inside the box. More...
bool	Inside (const Vector &) const
	Check if a point is inside the box. More...
Box	Intersection (const Box &) const
	Computes the intersection between two boxes. More...
int	Difference (const Box &, Box *) const
	Computes the difference between two boxes. More...
bool	Empty () const
	Check if a box is empty. More...
double	Volume () const
	Compute the volume of a box.
double	Area () const
	Compute the surface area of a box.
void	SetCubic ()
	Creates the tightest embedding cube from an arbitrarilly shaped box. More...
void	SetInscribedCubic ()
	Creates the biggest cube iscribed in the box. More...
Box	Cube () const
	Return the tightest embedding cube from an arbitrarilly shaped box. More...
void	Extend (const double &)
	Extend the limits of the box by a given distance. More...
Box	Extended (const double &) const
	Extend the limits of the box by a given distance. More...
void	Extend (const Vector &)
	Extend the limits of the box given a point. More...
void	SetParallelepipedic (const double &, int &, int &, int &)
	Creates a parallelepipedic box whose dimensions are integer multiples of a given input reference size. More...
void	SetParallelepipedic (int, int &, int &, int &)
	Inflates a box so that its dimensions should be a fraction of its maximum side length. More...
Box	Sub (int) const
	Computes the sub-box in the n-th octant. More...
int	Octant (const Vector &) const
	Compute the octant index of a vertex with respect to the box center. More...
void	Translate (const Vector &)
	Translates a box. More...
Box	Translated (const Vector &) const
	Translated box. More...
void	Scale (const double &)
	Scales a box. More...
void	Scale (const Vector &)
	Scales a box. More...
Box	Scaled (const Vector &) const
	Scales a box and return the scaled box. More...
Box	Offsetted (const Vector &) const
	Offets a box. More...
Box	Centered () const
	Compute the box translated to origin. More...
Box	Cut (const Vector &, const Vector &) const
	Compute the minimal box embedding the box cut by half space. More...
int	IntegerAxis () const
	Compute the axis which has the greater length.
Vector	RandomInside (Random &=Random::R239) const
	Generate a random vector inside the box. More...
Vector	RandomSurface (Random &=Random::R239) const
	Generate a random vector on the surface of the box. More...
QVector< Vector >	Poisson (const double &, int, Random &=Random::R239) const
	Compute a Poisson sphere distribution inside a box. More...

Static Public Attributes
static constexpr const double	epsilon = 1.0e-5
	Epsilon value used to check intersections and some round off errors and for ray intersection tests.
static const Box	Infinity
	Largest box. More...
static const Box	Null
	Null box, equivalent to: More...
static const Box	Unit
	Unit box.
static const int	edge [24]
	Edge vertex indexes.
static const Vector	normal [6]
	Face normals.

Protected Attributes
Vector	a
	Lower vertex.
Vector	b
	Upper vertex.

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

Detailed Description

An axis aligned box.

The class stores the opposite two corners as vectors. The center and the radius (diagonal vector) are computed on the fly by inline functions.

The vertices of a box can be obtained by the Box::Vertex() member function which returns one of the eight vertices of the box. The two opposite corners can be obtained faster as follows:

Box box(Vector(0.0,0.0,0.0),Vector(1.0,1.0,1.0)); // Unit box
Vector a=box[0]; // Lower vertex
Vector b=box[1]; // Opposite vertex

This class provides a set of useful functions, such as the intersection between a box and a ray. This class also implements the Minkowski sum of boxes by overloading some operators.

Note that some intersection methods involving boxes may be implemented in other classes, for instance Segment::Intersect(const Box&) const.

Constructor & Destructor Documentation

Box() [1/12]

Box::Box ( const double &  r )

explicit

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

This is equivalent to:

Box box(Vector(0.0),2.0);  // Simplified constructor Box(2.0);

Parameters

r	Half side length.

Box() [2/12]

Box::Box ( const Vector &  a )

explicit

Create an empty box given one vertex.

Parameters

a

Vertex.

Box() [3/12]

Box::Box ( const Vector &  a, const Vector &  b  )

explicit

Create a box given two opposite corners.

Note that this constructor does not check the coordinates of the two vectors. Therefore, the coordinates of a should be lower than those of b.

To create the axis aligned bounding box of two vectors a and b in the general case, one should use:

Box box(Vector::Min(a,b),Vector::Max(a,b));

Parameters

a,b	End vertices.

Box() [4/12]

Box::Box ( const Vector &  c, const double &  r  )

explicit

Create a box given a center point and the half side length.

Parameters

c	Center.
r	Half side length.

Box() [5/12]

Box::Box ( const Vector &  c, const double &  x, const double &  y, const double &  z  )

explicit

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

Parameters

c	center.
x,y,z	Width,length, and height.

Box() [6/12]

Box::Box ( const double &  x, const double &  y, const double &  z  )

explicit

Create a box given its sizes.

Parameters

x,y,z

Width,length, and height.

Box() [7/12]

Box::Box ( const Vector *  v, int  n  )

explicit

Creates the bounding box of a set of points.

Parameters

v	Array of vertices.
n	Number of vertices.

Box() [8/12]

Box::Box ( const QVector< Vector > &  v )

explicit

Creates the bounding box of a set of points.

Parameters

v	Array of vertices.

Box() [9/12]

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

explicit

Create a box embedding two boxes.

Parameters

x,y	Argument boxes.

Box() [10/12]

Box::Box ( const Box &  box, const Frame &  frame  )

explicit

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

Parameters

box	The box.
frame	Transformation.

Box() [11/12]

Box::Box ( const Box &  box, const FrameScaled &  frame  )

explicit

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

Parameters

box	The box.
frame	Transformation.

Box() [12/12]

Box::Box ( const Box &  box, const Matrix &  t  )

explicit

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

Parameters

box	The box.
t	Transformation matrix.

Member Function Documentation

Centered()

Box Box::Centered

(

)

const

Compute the box translated to origin.

This is the same as:

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

Cube()

Box Box::Cube

(

)

const

Return the tightest embedding cube from an arbitrarilly shaped box.

See also

SetSubic()

Cut()

Box Box::Cut	(	const Vector &	p,
		const Vector &	n
	)		const

Compute the minimal box embedding the box cut by half space.

The part of the box that will be removed lies in the positive side of the half space.

Parameters

p	Plane point.
n	Plane normal.

Difference()

int Box::Difference	(	const Box &	y,
		Box *	boxes
	)		const

Computes the difference between two boxes.

Parameters

y	Argument box.
boxes	An array of up to 8 boxes.

Edge()

Segment Box::Edge

(

int

k

)

const

Compute the k-th edge segment of the box.

See also

Box::Vertex(int) const

Parameters

k

Integer.

Empty()

bool Box::Empty ( ) const

inline

Check if a box is empty.

The box is empty if one of the coordinates of its lower point is greater than the coordinates of the opposite point.

Extend() [1/2]

void Box::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 Box::Extend

(

const Vector &

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()

Box Box::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.

Face()

Plane Box::Face

(

int

k

)

const

Compute the k-th plane of the box.

Parameters

k

Integer.

Inside() [1/2]

bool Box::Inside ( const Box &  box ) const

inline

Check if an argument box is inside the box.

Parameters

box

The box.

Inside() [2/2]

bool Box::Inside ( const Vector &  p ) const

inline

Check if a point is inside the box.

Parameters

p

Point.

Intersect() [1/7]

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

inline

Check if the box intersects another box.

Parameters

box	Argument box.

Intersect() [2/7]

int Box::Intersect

(

const Ray &

ray

)

const

Check the intersection between a box and a ray.

Although intersection depths are computed internally, none are returned. This function calls the intersection function and hides arguments in local variables.

Parameters

ray

The ray.

Intersect() [3/7]

int Box::Intersect	(	const Ray &	ray,
		double &	t
	)		const

Compute the first positive intersection between the box and a ray.

Parameters

ray	The ray.
t	Intersection depth.

Intersect() [4/7]

int Box::Intersect	(	const Ray &	ray,
		double &	tmin,
		double &	tmax
	)		const

Computes the intersection between a box and a ray.

Sorted intersection depths are returned if intersection occurs.

Parameters

ray	The ray
tmin,tmax	Intersection depths

Intersect() [5/7]

int Box::Intersect	(	const Ray &	ray,
		double &	tmin,
		double &	tmax,
		Vector &	an,
		Vector &	bn
	)		const

Compute the intersection between an axis aligned box and a ray.

Parameters return the sorted intersection depths and the corresponding normal vectors.

Parameters

ray	The ray.
tmin,tmax	Minimum and maximum intersection depths.
an,bn	Normals at intersection points.

Intersect() [6/7]

int Box::Intersect	(	const Ray &	ray,
		double &	t,
		Vector &	n
	)		const

Compute the first positive intersection between the box and a ray.

Parameters

ray	The ray.
t	Intersection depth.
n	Normal at intersection point.

Intersect() [7/7]

int Box::Intersect	(	const Vector &	a,
		const Vector &	b
	)		const

Check if a segment intersects an axis aligned box.

Testing a box and a segment for intersection requires checking only six separating axes: the box's three principal axes, and the vector cross products of these axes with the line direction. Again, the vectors used for these tests do not have to be normalized, and these tests can be simplified by transforming the line segment into the box's coordinate frame.

Parameters

a,b	Line segment.

Intersection()

Box Box::Intersection

(

const Box &

x

)

const

Computes the intersection between two boxes.

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

Parameters

x	Argument box.

Normal()

Vector Box::Normal ( const Vector &  p ) const

inline

Computes the normal vector between a point and a box.

Let q the projection of p onto the box, the normal vector is defined as n=p-q.

Parameters

p

Point.

Octant()

int Box::Octant

(

const Vector &

p

)

const

Compute the octant index of a vertex with respect to the box center.

See also

Vector::Octant()

Parameters

p

Point.

Offsetted()

Box Box::Offsetted

(

const Vector &

v

)

const

Offets a box.

Parameters

v	Offset vector.

See also

Box::Extend

Poisson()

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

Compute a Poisson sphere distribution inside a box.

This function uses a simple O(n³) dart throwing algorithm.

See also

SphereTile

Parameters

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

R() [1/2]

double Box::R

(

const Box &

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 Box::R ( const Vector &  p ) const

inline

Computes the squared Euclidean distance between the box and a point.

Parameters

p

Point.

RandomInside()

Vector Box::RandomInside

(

Random &

random = Random::R239

)

const

Generate a random vector inside the box.

Parameters

random

Random number generator.

RandomSurface()

Vector Box::RandomSurface

(

Random &

random = Random::R239

)

const

Generate a random vector on the surface of the box.

Parameters

random

Random number generator.

RInfinity()

double Box::RInfinity

(

const Box &

y

)

const

Compute the maximum distance between two boxes.

Parameters

y

The box.

Scale() [1/2]

void Box::Scale

(

const double &

s

)

Scales a box.

Note that this function handles negative coefficients in the scaling vector (by swapping coordinates if need be).

Parameters

s

Scaling.

Scale() [2/2]

void Box::Scale

(

const Vector &

s

)

Scales a box.

Note that this function handles negative coefficients in the scaling vector (by swapping coordinates if need be).

Parameters

s	Scaling vector.

Scaled()

Box Box::Scaled

(

const Vector &

s

)

const

Scales a box and return the scaled box.

Parameters

s	Scaling vector.

See also

Box::Scale

SetCubic()

void Box::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.

See also

SetInscribedCubic()

SetInscribedCubic()

void Box::SetInscribedCubic

(

)

Creates the biggest cube iscribed 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 Box::SetParallelepipedic	(	const double &	size,
		int &	x,
		int &	y,
		int &	z
	)

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,z	Three integers.

SetParallelepipedic() [2/2]

void Box::SetParallelepipedic	(	int	n,
		int &	x,
		int &	y,
		int &	z
	)

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

Parameters

n	Fraction.
x,y,z	Three integers.

Signed()

double Box::Signed

(

const Vector &

p

)

const

Computes the signed distance between the box and a point.

Parameters

p

Point.

Size()

Vector Box::Size ( ) const

inline

Compute the size (width, length and height) of a box.

See also

Box::Diagonal()

Sub()

Box Box::Sub

(

int

n

)

const

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

Parameters

n	Octant index.

Translate()

void Box::Translate

(

const Vector &

t

)

Translates a box.

Parameters

t	Translation vector.

Translated()

Box Box::Translated

(

const Vector &

t

)

const

Translated box.

Parameters

t	Translation vector.

Vertex() [1/2]

Vector Box::Vertex ( int  k ) const

inline

Returns the k-th vertex of the box.

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

Vector vertex=Vector((k&1)?b[0]:a[0],(k&2)?b[1]:a[1],(k&4)?b[2]:a[2]);

Vertex() [2/2]

Vector Box::Vertex	(	int	i,
		int	j,
		int	k,
		int	x,
		int	y,
		int	z
	)		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,k	Integer coordinates.
x,y,z	Virtual grid size.

Friends And Related Function Documentation

operator!=

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

friend

Check if two boxes are (strictly) different.

Parameters

a,b

Boxes.

operator+

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

friend

Computes the Minkowski sum of two boxes.

Parameters

a,b	Argument boxes.

operator<<

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

friend

Overloaded.

Parameters

s	Stream.
box	The box.

operator==

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

friend

Check if two boxes are (strictly) equal.

Parameters

a,b

Boxes.

Member Data Documentation

Infinity

const Box Box::Infinity

static

Largest box.

Huge bounding box, which should enclose any other.

Null

const Box Box::Null

static

Null box, equivalent to:

Box(Vector(0.0));