A base three-dimensional voxel. More...

#include <array.h>

Inheritance diagram for Voxel:

Public Member Functions
	Voxel (const Array &)
	Create the voxel structure.

	Voxel (const Box &, int)
	Create the voxel structure.

	Voxel (const Box &, int, int, int)
	Create the voxel structure.

	Voxel (const Box &, int, int, int, const QVector< int > &)
	Create and initialize the voxel structure.

int	At (int, int, int) const
	Return the data in the cell of the voxel.

int	At (int) const
	Return the data in the cell of the voxel.

int	AtExtended (int, int, int) const
	Return the data in the cell of the voxel.

int &	operator() (int, int, int)
	Return the data in the cell of the voxel.

int &	operator() (int)
	Return the data in the cell of the voxel.

int &	operator[] (int)
	Return the data in the cell of the voxel.

bool	Inside (const Vector &) const
	Check if a point is inside a non-empty cell.

bool	Inside (int, int, int) const
	Test if a cell is inside or outside of the voxel.

bool	IsVertex (int, int, int) const
	Check if a vertex is a corner of the surface of voxel.

double	Signed (const Vector &) const
	Compute the approximate signed distance to the voxel.

int	OctantCells (const Vector &, int[24], int &, Vector &) const
	Compute the integer coordinates of the (at most) eight octant cells closest to p.

QVector< Vector >	GetCubes (Box &, bool=false) const
	Create a set of cubes representing a voxel.

int	Accessibility (int, int, int) const
	Compute the integer accessibility of a voxel.

unsigned int	Memory () const
	Compute the amount of memory used by the voxel structure.

void	QQCube (int, int, int, int, int)
	Fill the voxel with a cube.

Public Member Functions inherited from Array
	Array ()
	Empty.

	Array (const Box &, int, int, int)
	Create the array structure.

	~Array ()
	Empty.

Array	Extract (int, int, int, int, int, int) const
	Extract an sub-array.

int	VertexSize () const
	Return the size of the array.

int	VertexSize (int) const
	Get the size of the array for every axis.

Box	Cell (int) const
	Return the geometry of the cell.

Box	Cell (int, int, int) const
	Return the geometry of the cell.

Vector	CellCenter (int, int, int) const
	Return the center of the cell.

void	Scale (const Vector &)
	Scales the array structure.

void	Scale (const double &)
	Scales the array structure.

Box	GetBox () const
	Get the box of the array.

Vector	CellDiagonal () const
	Return the cell diagonal.

double	CellVolume () const
	Return the volume of a cell.

Vector	Vertex (int, int, int) const
	Compute the coordinates of a point on the lattice.

int	GetSizeX () const
	Get the size of the array for x axis.

int	GetSizeY () const
	Get the size of the array for y axis.

int	GetSizeZ () const
	Get the size of the array for z axis.

int	CellSize () const
	Return the size of the voxel.

int	CellSizeX () const
	Get the size of the voxel for x axis.

int	CellSizeY () const
	Get the size of the voxel for y axis.

int	CellSizeZ () const
	Get the size of the voxel for z axis.

bool	IsEmpty () const
	Detect if the array is empty.

Box	UnitCell () const
	Return the geometry of a generic cell.

void	Resize (const Box &, int, int, int)
	Resize the voxel with the given parameters.

void	VertexInteger (const Vector &, int &, int &, int &) const
	Compute the coordinates of a vertex inside a cell.

void	VertexIntegerVolume (const Box &, int &, int &, int &, int &, int &, int &) const
	Compute the integer coordinates of the vertices of a box embedding an input box.

void	CellInteger (const Vector &, int &, int &, int &) const
	Compute the coordinates of a vertex inside a cell.

void	CellInteger (const Vector &, int &, int &, int &, double &, double &, double &) const
	Compute the point on the lattice given an input point.

void	CellIntegerVolume (const Box &, int &, int &, int &, int &, int &, int &) const
	Compute the integer coordinates of the cells of the array embedding an input box.

void	OutStream (QDataStream &) const
	Write data to a data stream.

void	InStream (QDataStream &)
	Read data to a data stream.

int	Memory () const
	Compute the size of the array.

constexpr int	VertexIndex (int, int, int) const
	Compute the index of a given vertex.

constexpr bool	InsideVertexIndex (int, int, int) const
	Check if the indexes are within range.

constexpr bool	InsideCellIndex (int, int, int) const
	Check if the indexes are within range.

void	InverseVertexIndex (int, int &, int &, int &) const
	Compute the coordinates of a given vertex.

constexpr int	CellIndex (int, int, int) const
	Compute the index of a given cell.

void	InverseCellIndex (int, int &, int &, int &) const
	Compute the coordinates of a given cell.

Static Public Member Functions
static double	OctantSigned (const Vector &, const Vector &, int)
	Computes the distance between a point a eight octant volumes.

Static Public Member Functions inherited from Array
static Array	CubicCells (Box, int)
	Create an array with enforced cubic cells.

Protected Attributes
QVector< int >	voxel
	Array of integer storing the data.

Protected Attributes inherited from Array
int	nz
	Sizes.

Vector	celldiagonal
	Cell diagonal.

Vector	inversecelldiagonal
	Inverse cell diagonal.

Protected Attributes inherited from Box
Vector	b = Vector(1.0)
	Lower and upper vertexex.

Static Protected Attributes
static const int	octantcellindex [8][24]

Static Protected Attributes inherited from Box
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.

static const Box	Null
	Null box, equivalent to:

static const Box	Unit
	Unit box.

static const int	edge [24]
	Edge vertex indexes.

static const Vector	normal [6]
	Face normals.

Friends
std::ostream &	operator<< (std::ostream &s, const Voxel &voxel)
	Overloaded.

Additional Inherited Members
Protected Member Functions inherited from Box
	Box ()
	Empty.

	Box (const double &)
	Create a cube centered at the origin and of given half side length.

	Box (const Vector &)
	Create an empty box given one vertex.

	Box (const Vector &, const Vector &)
	Create a box given two opposite corners.

	Box (const Vector &, const double &)
	Create a box given a center point and the half side length.

	Box (const Vector &, const double &, const double &, const double &)
	Create a box given a center point and its width, length, and height.

	Box (const double &, const double &, const double &)
	Create a box given its sizes.

	Box (const Vector *, int)
	Creates the bounding box of a set of points.

	Box (const QVector< Vector > &)
	Creates the bounding box of a set of points.

	Box (const Box &, const Box &)
	Create a box embedding two boxes.

	Box (const Box &, const Frame &)
	Creates an axis aligned bounding box from a box and a frame.

	Box (const Box &, const FrameScaled &)
	Creates an axis aligned bounding box from a box and a frame.

	Box (const Box &, const Matrix &)
	Creates an axis aligned bounding box from a box and a transformation matrix.

	~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.

Segment	Edge (int) const
	Compute the k-th edge segment of the box.

Plane	Face (int) const
	Compute the k-th plane of the box.

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

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.

double	Signed (const Vector &) const
	Computes the signed distance between the box and a point.

Vector	Normal (const Vector &) const
	Computes the normal vector between a point and a box.

double	R (const Box &) const
	Compute the squared Euclidean distance between two boxes.

double	RInfinity (const Box &) const
	Compute the maximum distance between two boxes.

int	Intersect (const Ray &) const
	Check the intersection between a box and a ray.

int	Intersect (const Ray &, double &, double &) const
	Computes the intersection between a box and a ray.

int	Intersect (const Ray &, double &) const
	Compute the first positive intersection between the box and a ray.

int	Intersect (const Ray &, double &, double &, Vector &, Vector &) const
	Compute the intersection between an axis aligned box and a ray.

int	Intersect (const Ray &, double &, Vector &) const
	Compute the first positive intersection between the box and a ray.

int	Intersect (const Vector &, const Vector &) const
	Check if a segment intersects an axis aligned box.

bool	Intersect (const Box &) const
	Check if the box intersects another box.

bool	Inside (const Box &) const
	Check if an argument box is inside the box.

bool	Inside (const Vector &) const
	Check if a point is inside the box.

Box	Intersection (const Box &) const
	Computes the intersection between two boxes.

int	Difference (const Box &, Box *) const
	Computes the difference between two boxes.

bool	Empty () const
	Check if a box is empty.

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.

void	SetInscribedCubic ()
	Creates the biggest cube iscribed in the box.

Box	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.

Box	Extended (const double &) const
	Extend the limits of the box by a given distance.

void	Extend (const Vector &)
	Extend the limits of the box given a point.

Box	Extended (const Vector &) const
	Extend the limits of the box by a given vector range.

void	SetParallelepipedic (const double &, int &, int &, int &)
	Creates a parallelepipedic box whose dimensions are integer multiples of a given input reference size.

void	SetParallelepipedic (int, int &, int &, int &)
	Inflates a box so that its dimensions should be a fraction of its maximum side length.

Box	Sub (int) const
	Computes the sub-box in the n-th octant.

int	Octant (const Vector &) const
	Compute the octant index of a vertex with respect to the box center.

void	Translate (const Vector &)
	Translates a box.

Box	Translated (const Vector &) const
	Translated box.

void	Scale (const double &)
	Scales a box.

void	Scale (const Vector &)
	Scales a box.

Box	Scaled (const Vector &) const
	Scales a box and return the scaled box.

Box	Offsetted (const Vector &) const
	Offets a box.

Box	Centered () const
	Compute the box translated to origin.

Box	Cut (const Vector &, const Vector &) const
	Compute the minimal box embedding the box cut by half space.

int	IntegerAxis () const
	Compute the axis which has the greater length.

Vector	RandomInside (Random &=Random::R239) const
	Generate a random vector inside the box.

Vector	RandomSurface (Random &=Random::R239) const
	Generate a random vector on the surface of the box.

QVector< Vector >	Poisson (const double &, int, Random &=Random::R239) const
	Compute a Poisson sphere distribution inside a box.

Detailed Description

A base three-dimensional voxel.

Constructor & Destructor Documentation

◆ Voxel() [1/4]

Voxel::Voxel ( const Array & a )

explicit

Create the voxel structure.

Parameters

a	The array.

◆ Voxel() [2/4]

Voxel::Voxel	(	const Box &	box,
		int	n )

explicit

Create the voxel structure.

Parameters

box	The cubic box.
n	Discretization.

◆ Voxel() [3/4]

Voxel::Voxel	(	const Box &	box,
		int	x,
		int	y,
		int	z )

explicit

Create the voxel structure.

Parameters

box	The box.
x,y,z	Discretization, i.e. number of cells.

◆ Voxel() [4/4]

Voxel::Voxel	(	const Box &	box,
		int	x,
		int	y,
		int	z,
		const QVector< int > &	v )

explicit

Create and initialize the voxel structure.

Parameters

box	The box.
x,y,z	Size of the array, i.e. number of cells.
v	Voxel data.

Member Function Documentation

◆ Accessibility()

int Voxel::Accessibility	(	int	x,
		int	y,
		int	z ) const

Compute the integer accessibility of a voxel.

Uses a 1-neighborhood, thus checking 3³3-1=26 cells.

Parameters

x,y,z Integer coordinates of the cell.

◆ At() [1/2]

int Voxel::At ( int c ) const

inline

Return the data in the cell of the voxel.

Parameters

c	Cell index.

◆ At() [2/2]

int Voxel::At	(	int	i,
		int	j,
		int	k ) const

inline

Return the data in the cell of the voxel.

See also: AtExtended()

Parameters

i,j,k Integer coordinates of the cell.

◆ AtExtended()

int Voxel::AtExtended	(	int	i,
		int	j,
		int	k ) const

inline

Return the data in the cell of the voxel.

This function handles queries outside of the voxel. If the coordinates are outside, function returns 0.

See also: At()

Parameters

i,j,k Integer coordinates of the cell.

◆ GetCubes()

QVector< Vector > Voxel::GetCubes	(	Box &	u,
		bool	surface = false ) const

Create a set of cubes representing a voxel.

Parameters

u	Unit reference box of the voxel.
surface	Only produce cubes that participate to the visible surface.

◆ Inside() [1/2]

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

Check if a point is inside a non-empty cell.

Note that if the point is not inside the box, then it is defined as outside.

Parameters

p Point.

◆ Inside() [2/2]

bool Voxel::Inside	(	int	x,
		int	y,
		int	z ) const

Test if a cell is inside or outside of the voxel.

This function handles queries outside of the voxel. If the coordinates are outside, function returns false.

Parameters

x,y,z Integer coordinates of the cell.

◆ IsVertex()

bool Voxel::IsVertex	(	int	x,
		int	y,
		int	z ) const

Check if a vertex is a corner of the surface of voxel.

This function handles queries outside of the voxel. If the coordinates are outside, function returns false.

Parameters

x,y,z Integer coordinates of the cell.

◆ OctantCells()

int Voxel::OctantCells	(	const Vector &	p,
		int	cells[24],
		int &	configuration,
		Vector &	q ) const

Compute the integer coordinates of the (at most) eight octant cells closest to p.

Parameters

p	Point.
cells	Returned array of integer coordinates.
configuration	Returned configuration.
q	Returned center of the octant that can be used for computing the distance.

Returns: The number of cells in the voxel structure.

◆ OctantSigned()

double Voxel::OctantSigned	(	const Vector &	p,
		const Vector &	q,
		int	c )

static

Computes the distance between a point a eight octant volumes.

The octant configuration is provided as an integer whose bits are set to 0 if octants are empty, 1 otherwise.

See also: Box::Octant(const Vector&)

Parameters

p	Point.
q	Origin of the eight octant volumes.
c	Octant configuration.

◆ operator()() [1/2]

int & Voxel::operator() ( int c )

inline

Return the data in the cell of the voxel.

Parameters

c	Cell index.

◆ operator()() [2/2]

int & Voxel::operator()	(	int	i,
		int	j,
		int	k )

inline

Return the data in the cell of the voxel.

Parameters

i,j,k Integer coordinates of the cell.

◆ operator[]()

int & Voxel::operator[] ( int c )

inline

Return the data in the cell of the voxel.

Parameters

c	Integer cell index.

◆ QQCube()

void Voxel::QQCube	(	int	x,
		int	y,
		int	z,
		int	s,
		int	c )

Fill the voxel with a cube.

Parameters

x,y,z	Lower coordinates.
s	Size.
c	Cell values.

◆ Signed()

double Voxel::Signed ( const Vector & p ) const

Compute the approximate signed distance to the voxel.

Parameters

p Point.

Friends And Related Symbol Documentation

◆ operator<<

std::ostream & operator<<	(	std::ostream &	s,
		const Voxel &	voxel )

friend

Overloaded.

Parameters

s	Stream.
voxel	The voxel.

Member Data Documentation

◆ octantcellindex

const int Voxel::octantcellindex

staticprotected

Initial value:

=
{
  
    {0, 0, 0,-1, 0, 0, 0,-1, 0,-1,-1, 0,
     0, 0,-1,-1, 0,-1, 0,-1,-1,-1,-1,-1},
    {0, 0, 0, 1, 0, 0, 0,-1, 0, 1,-1, 0,
     0, 0,-1, 1, 0,-1, 0,-1,-1, 1,-1,-1},
    {0, 0, 0,-1, 0, 0, 0, 1, 0,-1, 1, 0,
     0, 0,-1,-1, 0,-1, 0, 1,-1,-1, 1,-1},
    {0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0,
     0, 0,-1, 1, 0,-1, 0, 1,-1, 1, 1,-1},
    {0, 0, 0,-1, 0, 0, 0,-1, 0,-1,-1, 0,
     0, 0, 1,-1, 0, 1, 0,-1, 1,-1,-1, 1},
    {0, 0, 0, 1, 0, 0, 0,-1, 0, 1,-1, 0,
     0, 0, 1, 1, 0, 1, 0,-1, 1, 1,-1, 1},
    {0, 0, 0,-1, 0, 0, 0, 1, 0,-1, 1, 0,
     0, 0, 1,-1, 0, 1, 0, 1, 1,-1, 1, 1},
    {0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0,
     0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1}
}

< Set of eight cells, sorted.

Public Member Functions

Static Public Member Functions

Protected Attributes

Static Protected Attributes

Friends

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ Voxel() [1/4]

◆ Voxel() [2/4]

◆ Voxel() [3/4]

◆ Voxel() [4/4]

Member Function Documentation

◆ Accessibility()

◆ At() [1/2]

◆ At() [2/2]

◆ AtExtended()

◆ GetCubes()

◆ Inside() [1/2]

◆ Inside() [2/2]

◆ IsVertex()

◆ OctantCells()

◆ OctantSigned()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator[]()

◆ QQCube()

◆ Signed()

Friends And Related Symbol Documentation

◆ operator<<

Member Data Documentation

◆ octantcellindex