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

#include <vectorfield.h>

Inheritance diagram for VectorField:

Public Member Functions
	VectorField ()
	Empty.

	VectorField (const Box &, int, int, int, const Vector &=Vector::Null)
	Create the field structure.

	VectorField (const Box &, int, int, int, const AnalyticVectorField &)
	Create the field structure from an analytic vector field.

	~VectorField ()
	Empty.

void	Set (const Vector &)
	Set the whole vector field to a constant vector.

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

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

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

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

virtual Vector	Value (const Vector &) const
	Get the field value at a given point.

virtual Vector	Value (int, int, int) const
	Return the field vector at a given array vertex.

Vector	Euler (const Vector &, const double &, bool=false) const
	Compute the new position of a point in the vector field using forward Euler integration.

Vector	RungeKutta (const Vector &, const double &) const
	Compute the new position of a point in the vector field using Runge Kutta 4 integration.

PointCurve	EulerSteps (const Vector &, const double &, int, bool=false) const
	Compute trajectory of a point using Euler integration.

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.

Protected Attributes
QVector< Vector >	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.

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

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.

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.

Detailed Description

A base three-dimensional field of Vector values.

Constructor & Destructor Documentation

◆ VectorField() [1/2]

VectorField::VectorField	(	const Box &	box,
		int	x,
		int	y,
		int	z,
		const Vector &	v = Vector::Null )

explicit

Create the field structure.

Parameters

box	The box.
x,y,z	Size of the array.
v	Default value of field.

◆ VectorField() [2/2]

VectorField::VectorField	(	const Box &	box,
		int	x,
		int	y,
		int	z,
		const AnalyticVectorField &	a )

explicit

Create the field structure from an analytic vector field.

Parameters

box	The box.
x,y,z	Size of the array.
a	The analytic vector field.

Member Function Documentation

◆ at() [1/2]

Vector VectorField::at ( int c ) const

inline

Return the data in the field.

Parameters

c Index.

◆ at() [2/2]

Vector VectorField::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.

◆ Euler()

Vector VectorField::Euler	(	const Vector &	p,
		const double &	t,
		bool	s = false ) const

Compute the new position of a point in the vector field using forward Euler integration.

Direct forward Euler integration simply returns p + t v(p), error is bounded by O(t²).

Improved Euler�s method use a prediction-correction scheme, error is bounded by O(t³).

Parameters

p	Point.
t	Time step.
s	Scheme: false is simple Euler method, true for prediction-correction.

◆ EulerSteps()

PointCurve VectorField::EulerSteps	(	const Vector &	p,
		const double &	t,
		int	n,
		bool	s = false ) const

Compute trajectory of a point using Euler integration.

Parameters

p	Point.
t	Time step.
n	Number of steps.
s	Scheme: false is simple Euler method, true for prediction-correction.

◆ operator()()

Vector & VectorField::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[]()

Vector & VectorField::operator[] ( int c )

inline

Return the data in the field.

Parameters

c Index.

◆ RungeKutta()

Vector VectorField::RungeKutta	(	const Vector &	p,
		const double &	t ) const

Compute the new position of a point in the vector field using Runge Kutta 4 integration.

Error is bounded by O(t⁴).

Parameters

p	Point.
t	Time step.

◆ Set()

void VectorField::Set ( const Vector & v )

Set the whole vector field to a constant vector.

Parameters

v Vector.

◆ Value() [1/2]

Vector VectorField::Value ( const Vector & p ) const

virtual

Get the field value at a given point.

This function relies on a bi-linear interpolation of the vectors.

See also: Math::Bilinear

Parameters

p Point.

◆ Value() [2/2]

Vector VectorField::Value	(	int	i,
		int	j,
		int	k ) const

virtual

Return the field vector at a given array vertex.

Parameters

i,j,k Integer coordinates of the vertex.

See also: at(int,int,int)

Public Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ VectorField() [1/2]

◆ VectorField() [2/2]

Member Function Documentation

◆ at() [1/2]

◆ at() [2/2]

◆ Euler()

◆ EulerSteps()

◆ operator()()

◆ operator[]()

◆ RungeKutta()

◆ Set()

◆ Value() [1/2]

◆ Value() [2/2]