A base three-dimensional field of real values. More...

#include <scalarfield.h>

Inheritance diagram for ScalarField:

Public Member Functions
	ScalarField (bool=true)
	Empty.

	ScalarField (const Array &, const double &=0.0, bool=true)
	Create the field structure.

	ScalarField (const Box &, int, int, int, const double &=0.0, bool=true)
	Create the field structure.

	ScalarField (const Box &, int, int, int, const QVector< double > &, bool=true)
	Create the field structure.

	~ScalarField ()
	Empty.

void	GetRange (double &, double &) const
	Get the range of the field.

double	Integral () const
	Get the integral of the scalar field.

double	Sum () const
	Compute the sum of the elements in the scalar field.

virtual Vector	Gradient (int, int, int) const
	Compute the gradient at a given sample.

virtual Matrix	Hessian (int, int, int) const
	Compute the Hessian symmetric matrix of the field.

virtual double	Value (int, int, int) const
	Access to array of data.

virtual double	K () const
	Compute the Lipschitz constant of the field.

Vector	Normal (const Vector &) const
	Compute the normal.

void	CutEpsilon (const double &=1e-6)
	Set all values in the field that are lower than epsilon to true zero.

double	at (int, int, int) const
	Return the field value at a given array vertex.

double &	operator() (int, int, int)
	Return the field value at a given array vertex.

double	at (int) const
	Return the data in the field.

double &	operator[] (int)
	Return the data in the field.

ScalarField &	operator+= (const ScalarField &)
	Sum two scalar fields.

ScalarField &	operator*= (const double &)
	Scale the values of a scalar field.

virtual double	Value (const Vector &) const
	Get the field value with world coordinate system.

virtual double	BicubicValue (const Vector &) const
	Return the intensity at a point.

Vector	Gradient (const Vector &) const
	Compute the gradient.

virtual Matrix	Hessian (const Vector &) const
	Compute the Hessian symmetric matrix of the field function.

void	Translate (const Vector &)
	Translate the domain of the scalar field.

void	Scale (const Vector &)
	Scale the domain of the scalar field.

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

Mesh	Polygonize () const
	Polygonization.

void	Dual (Mesh &) const
	Polygonization using Dual Marching Cubes.

int	DualCellCode (int, int, int) const
	Compute the configuration for the voxel corners of the cell.

void	Save (const QString &) const
	Save as data file.

void	Read (const QString &)
	Read data file.

void	DualVertex (int, int, int, int, Vector &) const
	Compute the dual point.

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 Attributes
static int	TriangleTable [256][16]
	Two dimensionnal array storing the straddling edges for every marching cubes configuration.

static int	edgeTable [256]
	Array storing straddling edges for every marching cubes configuration.

Protected Member Functions
void	Blend (const double &, double[4]) const
	Compute the blending coefficients using cubic polynomials.

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.

Protected Attributes
bool	sign
	Sign convention, used for normal computation.

QVector< double >	field
	Field samples.

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 constexpr double	Epsilon = 1.0e-6
	Epsilon value for partial derivatives.

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.

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

Detailed Description

A base three-dimensional field of real values.

Constructor & Destructor Documentation

◆ ScalarField() [1/4]

ScalarField::ScalarField ( bool s = true )

inline

Empty.

Constructor.

Parameters

s	Sign, by default, set sign convention to true, i.e., negative values inside and positive outside.

◆ ScalarField() [2/4]

ScalarField::ScalarField	(	const Array &	a,
		const double &	v = 0.0,
		bool	s = true )

Create the field structure.

Parameters

a	The array.
v	Default value of field.
s	Sign, by default, set sign convention to true, i.e., negative values inside and positive outside.

◆ ScalarField() [3/4]

ScalarField::ScalarField	(	const Box &	box,
		int	x,
		int	y,
		int	z,
		const double &	v = 0.0,
		bool	s = true )

Create the field structure.

Parameters

box	The box.
x,y,z	Size of the array.
v	Default value of field.
s	Sign, by default, set sign convention to true, i.e., negative values inside and positive outside.

◆ ScalarField() [4/4]

ScalarField::ScalarField	(	const Box &	box,
		int	x,
		int	y,
		int	z,
		const QVector< double > &	v,
		bool	s = true )

Create the field structure.

Parameters

box	The box.
x,y,z	Size of the array.
v	Array of scalar values.
s	Sign, by default, set sign convention to true, i.e., negative values inside and positive outside.

Member Function Documentation

◆ at() [1/2]

double ScalarField::at ( int c ) const

inline

Return the data in the field.

Parameters

c Index.

◆ at() [2/2]

double ScalarField::at	(	int	i,
		int	j,
		int	k ) const

inline

Return the field value at a given array vertex.

Parameters

i,j,k Integer coordinates of the vertex.

◆ BicubicValue()

double ScalarField::BicubicValue ( const Vector & p ) const

virtual

Return the intensity at a point.

The function returns -1.0 if point sample is outside the bounding box. Otherwise, the intensity is computed by blending the intensity at the vertices of the voxel grid with cubic polynomials.

Parameters

p Point.

◆ Blend()

void ScalarField::Blend	(	const double &	u,
		double	b[4] ) const

protected

Compute the blending coefficients using cubic polynomials.

After Allen Van Gelder and Jane Wilhels, Topological considerations in iso-surface generation, ACM Transactions on Graphics, 13(4):21-28, 1994.

◆ CutEpsilon()

void ScalarField::CutEpsilon ( const double & e = 1e-6 )

Set all values in the field that are lower than epsilon to true zero.

Parameters

e	Epsilon coefficient.

◆ Dual()

void ScalarField::Dual ( Mesh & g ) const

Polygonization using Dual Marching Cubes.

This function implements a modified version of the dual marching cubes presented in: G. Nielson. Dual Marching Cubes. Proceedings of the Conference on Visualization, 489-496, 2004.

A vertex in standard marching cubes is shared by 4 faces (as it lies on an edge, thus shared by four cubes), thus the dual mesh is made from quadrangles. Manifold mesh is produced by using the modifications described in R. Wenger. Isosurfaces: Geometry, Topology, and Algorithms.

Parameters

g	Returned mesh.

◆ DualCellCode()

int ScalarField::DualCellCode	(	int	cx,
		int	cy,
		int	cz ) const

Compute the configuration for the voxel corners of the cell.

Parameters

cx,cy,cz Cell coordinates.

◆ DualVertex()

void ScalarField::DualVertex	(	int	cx,
		int	cy,
		int	cz,
		int	c,
		Vector &	v ) const

Compute the dual point.

The dual point is defined as the mean of the face vertices belonging to the marching cubes face.

Parameters

c	Configuration.
cx,cy,cz	Coordinates.
v	Returned vertex.

◆ GetRange()

void ScalarField::GetRange	(	double &	a,
		double &	b ) const

Get the range of the field.

Parameters

a,b	Returned minimum and maximum.

◆ Gradient() [1/2]

Vector ScalarField::Gradient ( const Vector & p ) const

Compute the gradient.

Parameters

p Point.

◆ Gradient() [2/2]

Vector ScalarField::Gradient	(	int	i,
		int	j,
		int	k ) const

virtual

Compute the gradient at a given sample.

Parameters

i,j,k Integer coordinates of the sample.

◆ Hessian() [1/2]

Matrix ScalarField::Hessian ( const Vector & p ) const

virtual

Compute the Hessian symmetric matrix of the field function.

Parameters

p Point.

Returns: Hessian matrix.

◆ Hessian() [2/2]

Matrix ScalarField::Hessian	(	int	i,
		int	j,
		int	k ) const

virtual

Compute the Hessian symmetric matrix of the field.

Parameters

i,j,k Integer coordinates of the point.

Returns: Hessian matrix.

◆ Integral()

double ScalarField::Integral ( ) const

Get the integral of the scalar field.

Simply compute the sum of all the elements and make the product by the area of small cell element.

See also: Sum()

◆ Normal()

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

Compute the normal.

Parameters

p	Point (should be on the surface).

◆ operator()()

double & ScalarField::operator()	(	int	i,
		int	j,
		int	k )

inline

Return the field value at a given array vertex.

Parameters

i,j,k Integer coordinates of the vertex.

◆ operator*=()

ScalarField & ScalarField::operator*= ( const double & s )

Scale the values of a scalar field.

Parameters

s	Scaling factor.

◆ operator+=()

ScalarField & ScalarField::operator+= ( const ScalarField & s )

Sum two scalar fields.

Scalar fields should have the same size.

Parameters

s	Argument scalar field.

◆ operator[]()

double & ScalarField::operator[] ( int c )

inline

Return the data in the field.

Parameters

c Index.

◆ Polygonize()

Mesh ScalarField::Polygonize ( ) const

Polygonization.

Returns: The mesh.

◆ Read()

void ScalarField::Read ( const QString & name )

Read data file.

Parameters

name Filename.

◆ Save()

void ScalarField::Save ( const QString & name ) const

Save as data file.

Parameters

name Filename.

◆ Scale()

void ScalarField::Scale ( const Vector & s )

Scale the domain of the scalar field.

Parameters

s	Scaling factor.

◆ Sum()

double ScalarField::Sum ( ) const

Compute the sum of the elements in the scalar field.

Optimized with AVX

See also: Integral(), Average()

◆ Translate()

void ScalarField::Translate ( const Vector & t )

Translate the domain of the scalar field.

Parameters

t	Translation vector.

◆ Value() [1/2]

double ScalarField::Value ( const Vector & p ) const

virtual

Get the field value with world coordinate system.

This function computes a tri-linear interpolation of the values.

See also: Math::Trilinear

Parameters

p	Point position (should be strictly within bounding box of the domain).

◆ Value() [2/2]

double ScalarField::Value	(	int	i,
		int	j,
		int	k ) const

virtual

Access to array of data.

Parameters

i,j,k Integer coordinates.

Public Member Functions

Static Public Attributes

Protected Member Functions

Protected Attributes

Static Protected Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ ScalarField() [1/4]

◆ ScalarField() [2/4]

◆ ScalarField() [3/4]

◆ ScalarField() [4/4]

Member Function Documentation

◆ at() [1/2]

◆ at() [2/2]

◆ BicubicValue()

◆ Blend()

◆ CutEpsilon()

◆ Dual()

◆ DualCellCode()

◆ DualVertex()

◆ GetRange()

◆ Gradient() [1/2]

◆ Gradient() [2/2]

◆ Hessian() [1/2]

◆ Hessian() [2/2]

◆ Integral()

◆ Normal()

◆ operator()()

◆ operator*=()

◆ operator+=()

◆ operator[]()

◆ Polygonize()

◆ Read()

◆ Save()

◆ Scale()

◆ Sum()

◆ Translate()

◆ Value() [1/2]

◆ Value() [2/2]