A base two-dimensional field of Vector2 values. More...

#include <vectorfield.h>

Inheritance diagram for VectorField2:

Public Member Functions
	VectorField2 ()
	Empty.

	VectorField2 (const Box2 &, int, int, const Vector2 &=Vector2::Null)
	Create the field structure. More...

	VectorField2 (const Box2 &, int, int, const AnalyticVectorField2 &)
	Create the field structure from an analytic vector field. More...

	~VectorField2 ()
	Empty.

void	Set (const Vector2 &)
	Set the whole vector field to a constant vector. More...

Vector2	at (int, int) const
	Return the field value at a given array vertex. More...

Vector2	at (const QPoint &) const
	Return the field value at a given array vertex. More...

Vector2 &	operator() (int, int)
	Return the field value at a given array vertex. More...

Vector2 &	operator() (const QPoint &)
	Return the field value at a given array vertex. More...

Vector2	at (int) const
	Return the data in the field. More...

Vector2 &	operator[] (int)
	Return the data in the field. More...

VectorField2 &	operator+= (const VectorField2 &)
	Destructive sum of two vector fields. More...

VectorField2 &	operator-= (const VectorField2 &)
	Destructive difference of two vector fields. More...

ScalarField2	GetNorm () const
	Compute the norm of the vector field.

ScalarField2	GetAngle () const
	Compute the angle of the vector field.

ScalarField2	GetComponent (int) const
	Create and return the scalar field with the x or y components. More...

QImage	CreateAngleImage () const
	Create the angle image.

void	Normalize ()
	Normalize the vector field, i.e. set the range of norm of the vectors [0,1].

void	Unit ()
	Set all vectors to unit, i.e. set the norm of the vectors to 1. More...

VectorField2	Orthogonal () const
	Compute the orthogonal vector field. More...

void	GetRange (Vector2 &, Vector2 &) const
	Compute the range of the vector field. More...

void	GetNormRange (double &, double &) const
	Compute the range of norm the vector field. More...

double	AverageNorm () const
	Compute the average norm.

virtual Vector2	Value (const Vector2 &) const
	Get the field value at a given point. More...

virtual Vector2	Value (int, int) const
	Return the field vector at a given array vertex. More...

virtual ScalarField2	Divergence () const
	Compute the divergence field. More...

virtual double	Divergence (int, int) const
	Compute the divergence at a given sample. More...

void	Add (const VectorField2 &)
	Add two vector fields. More...

void	Sub (const VectorField2 &)
	Subtract two vector fields. More...

void	Mul (const double &)
	Subtract two vector fields. More...

virtual ScalarField2	Curl () const
	Compute the curl of the vector field. More...

virtual double	Curl (int, int) const
	Compute the curl at a given sample. More...

void	Rotate (const Matrix2 &)
	Compute the rotated vector field. More...

void	Lerp (const VectorField2 &, const VectorField2 &, const double &)
	Linear interpolation between two vector fields. More...

void	Multiply (const Vector2 &, const double &, const double &)
	Multiply the vector field by a scaling factor locally. More...

void	Radial (const Vector2 &, const double &, const double &)
	Adds to the vector field a radial component centered at center and goind towards the center (with scaling being positive) and towards the exterior of the center (with scaling being negative) More...

void	Clone (const Vector2 &, const Vector2 &, const Vector2 &, const double &)
	Clone part of the vector field from source to destination positions, with a given radius. The destination is blended with a decreasing weight towards the disk boundary where it is null. More...

void	CloneZone (const Vector2 &, const QPolygon &, int, const VectorField2 *=nullptr)
	Clone part of the vector field from source to destination positions. More...

void	CloneBrokenLine (const QVector< Vector2 > &, const QVector< Vector2 > &, int, const VectorField2 *=nullptr)
	clones the gradient from the sourceLine along the destLine, cloning all points that are less than halfWidth away from the curves

QImage	CreateImage () const
	Create an image from the field.

QImage	CreateBlueRedImage () const
	Create the angle image.

QImage	CreateGradientImage (const double &) const
	Create the gradient image (similar to CreateBlueRedImage() with different color settings and 16 bits depth)

QImage	CreateStreamLines () const
	Create an image from the field.

QImage	CreateImageParticles (const double &) const
	Create an image from the field, showing trajectory with particle and streamlines. More...

void	Draw (QGraphicsScene &, const QPen &=QPen(), const QBrush &=QBrush()) const
	Draw a vector field. More...

Vector2	Euler (const Vector2 &, const double &, bool=false) const
	Compute the new position of a point in the vector field using forward Euler integration. More...

Vector2	RungeKutta (const Vector2 &, const double &) const
	Compute the new position of a point in the vector field using Runge Kutta 4 integration. More...

PointCurve2	EulerSteps (const Vector2 &, const double &, int, bool=false) const
	Compute trajectory of a point using Euler integration. More...

ScalarField2	LineIntegral (int) const
	Compute line integral convolution image. More...

VectorField2	GaussianBlur (const double &) const
	Perform a Gaussian blur. More...

VectorField2	GaussianBlur (int) const
	Perform a Gaussian blur. More...

Public Member Functions inherited from Array2
	Array2 ()
	Empty array, with empty box.

	Array2 (const Box2 &, int, int)
	Create the array structure. More...

	Array2 (const Box2 &, int)
	Create the array structure. More...

Array2	DownSample (int) const
	Downsample the array. More...

Array2	UpSample (int) const
	Upsample the array. More...

	~Array2 ()
	Empty.

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

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

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

int	VertexBorderSize () const
	Return the size of the vertex array.

int	CellSize () const
	Return the size of the cell array.

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

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

QSize	GetQtSize () const
	Return the Qt size of the vertex array.

Box2	Cell (int) const
	Return the geometry of the cell. More...

Box2	Cell (int, int) const
	Return the geometry of the cell. More...

void	HalfCell (int, int, bool, Triangle2 &, Triangle2 &) const
	Return the geometry of the cell. More...

Vector2	CellCenter (int, int) const
	Return the center of the cell. More...

void	Scale (const Vector2 &)
	Scales the array structure. More...

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

Box2	GetBox () const
	Get the box of the array.

Box2	UnitCell () const
	Return the geometry of a generic cell. More...

Vector2	CellDiagonal () const
	Return the cell diagonal vector.

double	CellArea () const
	Return the area of a cell. More...

Vector2	ArrayVertex (int, int) const
	Compute the coordinates of a point on the grid. More...

Vector2	ArrayVertex (const QPoint &) const
	Compute the coordinates of a point on the grid. More...

QVector< Vector2 >	ArrayVertexes (const QVector< QPoint > &) const
	Compute the coordinates of a set of points on the grid. More...

Vector2	Size () const
	Return the size of the array.

QRect	AreaInteger () const
	Return the range of integer values for the domain.

QImage	ImageGrid (const Box2 &, const double &) const
	Create a texture with a regular grid. More...

void	Draw (QGraphicsScene &, const QPen &=QPen(), const QBrush &=QBrush()) const
	Draw the cells of the grid. More...

void	Subdivide ()
	Change the resolution. More...

bool	IsEmpty () const
	Detect if the array is empty, i.e., any dimension equal to zero.

QPoint	VertexBorder (int) const
	Compute the k-th point on the boundary of the domain. More...

int	VertexBorderIndex (int, int) const
	Compute the index of a point on the boundary of the domain. More...

void	VertexInteger (const Vector2 &, int &, int &) const
	Compute the coordinates of a vertex inside a cell. More...

QPoint	VertexInteger (const Vector2 &) const
	Compute the coordinates of a vertex inside a cell. More...

QPoint	VertexInteger (const Vector2 &, double &, double &) const
	Compute the point on the grid given an input point. More...

QRect	VertexIntegerArea (const Box2 &) const
	Compute the integer coordinates of the vertices embedding a box. More...

QRect	VertexIntegerArea (const Circle2 &) const
	Compute the integer coordinates of the vertices embedding a circle. More...

QRect	VertexIntegerArea (const QRect &) const
	Compute the integer coordinates span of the vertices embedding a rectangle. More...

void	CellInteger (const Vector2 &, int &, int &) const
	Compute the coordinates of a vertex inside a cell. More...

void	CellInteger (const Vector2 &, int &, int &, double &, double &) const
	Compute the point on the grid given an input point. More...

QPoint	CellInteger (const Vector2 &) const
	Compute the coordinates of a vertex inside a cell. More...

QPoint	CellInteger (const Vector2 &, double &, double &) const
	Compute the point on the grid given an input point. More...

QRect	CellIntegerArea (const Box2 &) const
	Compute the integer coordinates of the cells of the array embedding an input box. More...

QRect	CellIntegerArea (const Circle2 &) const
	Compute the integer coordinates of the cells of the array embedding an input circle. More...

void	Translate (const Vector2 &)
	Translate the array. More...

Vector2	Center () const
	Return the center of the array.

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

constexpr bool	OutsideVertexIndex (int, int) const
	Check if the indexes are outside or on the border. More...

constexpr bool	InsideVertexIndex (const QPoint &) const
	Check if the indexes are within range. More...

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

bool	Inside (const Vector2 &) const
	Check if a point is in the rectangular domain. More...

constexpr bool	BorderVertexIndex (int, int) const
	Check if the indexes are on the border. More...

constexpr bool	BorderVertexIndex (const QPoint &) const
	Check if the indexes are on the border. More...

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

constexpr int	VertexIndex (const QPoint &) const
	Compute the index of a given cell. More...

QPoint	Next (const QPoint &, int) const
	Compute the point next to another one. More...

QImage	CreateEmptyImage () const
	Create an image with the same size as the array. More...

QString	Statistics () const
	Get statistics.

void	ClampVertexIndex (int &, int &) const
	Clamp vertex indexes to the size of the array. More...

Protected Attributes
QVector< Vector2 >	field
	Field samples.

Protected Attributes inherited from Array2
int	ny = 0
	Sizes.

Vector2	celldiagonal = Vector2::Null
	Cell diagonal.

Vector2	inversecelldiagonal = Vector2::Null
	Inverse cell diagonal.

Protected Attributes inherited from Box2
Vector2	b
	Lower and upper vertices of the box.

Additional Inherited Members
Static Public Member Functions inherited from Array2
static int	NeighborCode (int, int)
	Convert a direction to an 8 bit integer code. More...

static QPoint	codeToDir (int)
	Convert an 8 bit integer code direction into a direction vector. More...

Protected Member Functions inherited from Array2
constexpr void	InverseVertexIndex (int, int &, int &) const
	Compute the coordinates of a given cell. More...

constexpr QPoint	InverseVertexIndex (int) const
	Compute the coordinates of a given cell. More...

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

constexpr int	CellIndex (const QPoint &) const
	Compute the index of a given cell. More...

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

constexpr bool	InsideCellIndex (const QPoint &) const
	Check if the indexes are within range. More...

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

Protected Member Functions inherited from Box2
	Box2 ()
	Empty.

	Box2 (const double &)
	Create a square box centered at the origin and of given half side length. More...

	Box2 (const double &, const double &)
	Create a box centered at the origin and of given dimensions. More...

	Box2 (const Vector2 &)
	Create a box from a single vertex. More...

	Box2 (const Vector2 &, const Vector2 &)
	Create a box. More...

	Box2 (const Vector2 &, const double &)
	Creates a box. More...

	Box2 (const Box &)
	Create a box in the plane given a box. More...

	Box2 (const Box2 &, const Box2 &)
	Create a box embedding two boxes. More...

	Box2 (const Box2 &, const Matrix2 &)
	Creates an axis aligned bounding box from a box and a transformation matrix. More...

	Box2 (const Box2 &, const Frame2 &)
	Creates an axis aligned bounding box from a box and a frame. More...

	Box2 (const QVector< Vector2 > &)
	Compute the bounding box of a set of points. More...

	Box2 (const QSize &)
	Create a box from a Qt size. More...

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. More...

double	Height () const
	Compute the height of a box. More...

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. More...

Vector2	Vertex (int, int, int, int) const
	Compute the coordinates of a grid aligned point. More...

Box2	Sub (int) const
	Computes the sub-box in the n-th quadrant. More...

double	R (const Vector2 &) const
	Compute the squared distance between the box and a point. More...

double	Signed (const Vector2 &) const
	Computes the signed distance between the box and a point. More...

double	R (const Box2 &) const
	Compute the squared Euclidean distance between two boxes. More...

void	Translate (const Vector2 &)
	Translates a box. More...

void	Scale (const Vector2 &)
	Scales a box. More...

void	Scale (const double &)
	Scales a box. More...

Box2	Translated (const Vector2 &) const
	Translated box. More...

Box2	Scaled (const double &) const
	Scales a box and return the scaled box. More...

Box2	Scaled (const Vector2 &) const
	Scales a box and return the scaled box. More...

Box2	Scaled (const QSize &) const
	Scales a box according to a Qt size. More...

Box2	ScaledTo (const double &) const
	Scale the box so that the largest side should equal the argument value. More...

Box2	Rotated (const double &) const
	Compute the box embedding the rotated box. More...

Box2	Rotated (const Matrix2 &) const
	Compute the box embedding the rotated box. More...

Box2	Centered () const
	Compute the box translated to origin. More...

void	SetCubic ()
	Creates the tightest embedding cube from an arbitrarilly shaped box. More...

void	SetInscribedCubic ()
	Creates the biggest cube inscribed in the box. More...

Box2	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...

void	Extend (const Vector2 &)
	Extend the limits of the box given a point. More...

Box2	Extended (const double &) const
	Extend the limits of the box by a given distance. More...

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

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

bool	Inside (const Vector2 &) const
	Test if a point is inside the box. More...

bool	Inside (const Vector2 &, const double &) const
	Test if a point lies withing a given range of the box. More...

bool	Intersect (const Box2 &) const
	Check if the box intersects another box. More...

double	OverlapArea (const Box2 &) const
	Computes the overlapping area of two boxes. More...

Box2	Intersection (const Box2 &) const
	Computes the intersection between two boxes. More...

Box	ToBox (const double &, const double &) const
	Convert a planar Box2 to a Box. More...

int	Quadrant (const Vector2 &) const
	Computes quadrant index of a vertex with respect to the box center. More...

bool	Intersect (const Ray2 &, double &, double &) const
	Computes the intersection between a box and a ray. More...

bool	Intersect (const Ray2 &) const
	Computes the intersection between a box and a ray. More...

bool	Intersect (const Line2 &, double &, double &) const
	Computes the intersection between a box and a line. More...

bool	Intersect (const Segment2 &, double &, double &) const
	Compute the intersection between a box and a segment. More...

bool	Intersect (const Line2 &) const
	Check the intersection between a box and a line. More...

bool	Intersect (const Segment2 &) const
	Check the intersection between a box and a segment. More...

void	Draw (QGraphicsScene &, const QPen &=QPen(), const QBrush &=QBrush()) const
	Draw a rectangle. More...

Vector2	RandomInside (Random &=Random::R239) const
	Generate a random vector inside the box. More...

Vector2	RandomOn (Random &=Random::R239) const
	Generate a random vector on the perimeter of the box. More...

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. More...

Box2	Tile (int, int) const
	Return the tiled the box using integer coordinates. More...

Box2	Tile (const QRect &) const
	Return the tiled the box using integer coordinates. More...

QVector< Vector2 >	Poisson (const double &, int, Random &=Random::R239) const
	Compute a Poisson disc distribution inside a box. More...

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

Static Protected Attributes inherited from Array2
static const QPoint	next [8] = { QPoint(1, 0), QPoint(1, 1), QPoint(0, 1), QPoint(-1, 1), QPoint(-1, 0), QPoint(-1, -1), QPoint(0, -1), QPoint(1, -1) }
	Array of points in the 1-ring neighborhood.

static const double	length [8] = { 1.0, sqrt(2.0), 1.0, sqrt(2.0), 1.0, sqrt(2.0), 1.0, sqrt(2.0) }
	Length to the i-th neighbor.

static const double	inverselength [8] = { 1.0, 1.0 / sqrt(2.0), 1.0, 1.0 / sqrt(2.0), 1.0, 1.0 / sqrt(2.0), 1.0, 1.0 / sqrt(2.0) }
	Inverse length.

Static Protected Attributes inherited from Box2
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. More...

static const Box2	Unit
	Unit box, defined as. More...

Detailed Description

A base two-dimensional field of Vector2 values.

Constructor & Destructor Documentation

◆ VectorField2() [1/2]

VectorField2::VectorField2	(	const Box2 &	box,
		int	x,
		int	y,
		const Vector2 &	v = `Vector2::Null`
	)

explicit

Create the field structure.

Parameters

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

◆ VectorField2() [2/2]

VectorField2::VectorField2	(	const Box2 &	box,
		int	x,
		int	y,
		const AnalyticVectorField2 &	a
	)

explicit

Create the field structure from an analytic vector field.

Parameters

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

Member Function Documentation

◆ Add()

void VectorField2::Add ( const VectorField2 & v )

Add two vector fields.

Parameters

v	Argument vector field. Optimized with AVX

◆ at() [1/3]

Vector2 VectorField2::at ( const QPoint & p ) const

inline

Return the field value at a given array vertex.

Parameters

p	Point with its coordinates.

◆ at() [2/3]

Vector2 VectorField2::at ( int c ) const

inline

Return the data in the field.

Parameters

c Index.

◆ at() [3/3]

Vector2 VectorField2::at	(	int	i,
		int	j
	)		const

inline

Return the field value at a given array vertex.

Parameters

i,j	Integer coordinates of the vertex.

◆ Clone()

void VectorField2::Clone	(	const Vector2 &	center,
		const Vector2 &	source,
		const Vector2 &	strokebegin,
		const double &	radius
	)

Clone part of the vector field from source to destination positions, with a given radius. The destination is blended with a decreasing weight towards the disk boundary where it is null.

Parameters

center	Destination position.
source	Source position.
strokebegin	Stroke starting position.
radius	Scaling of the effect.

◆ CloneZone()

void VectorField2::CloneZone	(	const Vector2 &	center,
		const QPolygon &	lassoedZone,
		int	borderBlendTreshold,
		const VectorField2 *	gradientSource = `nullptr`
	)

Clone part of the vector field from source to destination positions.

The destination is blended with a decreasing weight towards the disk boundary where it is null.

Parameters

center	Target position.
lassoedZone	Selected area.
borderBlendTreshold	Border threshold.
gradientSource	Source.

◆ CreateImageParticles()

QImage VectorField2::CreateImageParticles ( const double & dt ) const

Create an image from the field, showing trajectory with particle and streamlines.

Author: Axel Paris.

Parameters

dt	Time step for tracing particle trajectories.

◆ Curl() [1/2]

ScalarField2 VectorField2::Curl ( ) const

virtual

Compute the curl of the vector field.

See also: Curl(int, int)

◆ Curl() [2/2]

double VectorField2::Curl	(	int	i,
		int	j
	)		const

virtual

Compute the curl at a given sample.

See also: Curl()

Parameters

i,j	Integer coordinates of the sample.

◆ Divergence() [1/2]

ScalarField2 VectorField2::Divergence ( ) const

virtual

Compute the divergence field.

See also: Divergence(int, int)

Author: Mathieu Gaillard

◆ Divergence() [2/2]

double VectorField2::Divergence	(	int	i,
		int	j
	)		const

virtual

Compute the divergence at a given sample.

See also: Divergence()

Author: Mathieu Gaillard

Parameters

i,j	Integer coordinates of the sample.

◆ Draw()

void VectorField2::Draw	(	QGraphicsScene &	scene,
		const QPen &	pen = `QPen()`,
		const QBrush &	brush = `QBrush()`
	)		const

Draw a vector field.

Parameters

scene	Graphics scene.
pen	The pen.
brush	The brush.

◆ Euler()

Vector2 VectorField2::Euler	(	const Vector2 &	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()

PointCurve2 VectorField2::EulerSteps	(	const Vector2 &	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.

◆ GaussianBlur() [1/2]

VectorField2 VectorField2::GaussianBlur ( const double & r ) const

Perform a Gaussian blur.

Parameters

r	Radius of blur.

See also: ScalarField2::GaussianBlur(int)

◆ GaussianBlur() [2/2]

VectorField2 VectorField2::GaussianBlur ( int r ) const

Perform a Gaussian blur.

Parameters

r	Radius (in cells) of blur.

◆ GetComponent()

ScalarField2 VectorField2::GetComponent ( int i ) const

Create and return the scalar field with the x or y components.

Parameters

i Index.

◆ GetNormRange()

void VectorField2::GetNormRange	(	double &	a,
		double &	b
	)		const

Compute the range of norm the vector field.

Parameters

a,b	Returned minimum and maximum norms.

◆ GetRange()

void VectorField2::GetRange	(	Vector2 &	a,
		Vector2 &	b
	)		const

Compute the range of the vector field.

Parameters

a,b	Returned minimum and maximum vector values.

◆ Lerp()

void VectorField2::Lerp	(	const VectorField2 &	a,
		const VectorField2 &	b,
		const double &	t
	)

Linear interpolation between two vector fields.

Parameters

a,b	Scalar fields, should have the same resolution.
t	Interpolant. Optimized with AVX

◆ LineIntegral()

ScalarField2 VectorField2::LineIntegral ( int n ) const

Compute line integral convolution image.

This is the implementation of Cabral, Brian and Leedom, Leith Casey. Imaging Vector Fields Using Line Integral Convolution. Proceedings of SIGGRAPH, 263�270, 1993.

Stalling, Detlev and Hege, Hans-Christian. Fast and resolution independent line integral convolution. Proceedings of SIGGRAPH, 249�256, 1995.

The vector field should be converted to unit direction vector using VectorField2::Unit.

See also: VectorField2::Unit().

Parameters

n	Number of steps.

◆ Mul()

void VectorField2::Mul ( const double & s )

Subtract two vector fields.

Parameters

s	Scalar. Optimized with AVX

◆ Multiply()

void VectorField2::Multiply	(	const Vector2 &	center,
		const double &	radius,
		const double &	scaling
	)

Multiply the vector field by a scaling factor locally.

At the center, the scaling will be applied and at the boundary it will be equal to 1.

Parameters

center	Center.
radius	Radius.
scaling	Scaling of the effect.

◆ operator()() [1/2]

Vector2 & VectorField2::operator() ( const QPoint & p )

inline

Return the field value at a given array vertex.

Parameters

p Point.

◆ operator()() [2/2]

Vector2 & VectorField2::operator()	(	int	i,
		int	j
	)

inline

Return the field value at a given array vertex.

Parameters

i,j	Integer coordinates of the vertex.

◆ operator+=()

VectorField2 & VectorField2::operator+= ( const VectorField2 & f )

Destructive sum of two vector fields.

Parameters

f	Vector field.

◆ operator-=()

VectorField2 & VectorField2::operator-= ( const VectorField2 & f )

Destructive difference of two vector fields.

Parameters

f	Vector field.

◆ operator[]()

Vector2 & VectorField2::operator[] ( int c )

inline

Return the data in the field.

Parameters

c Index.

◆ Orthogonal()

VectorField2 VectorField2::Orthogonal ( ) const

Compute the orthogonal vector field.

Note that this is the same as rotating the field, but more efficient:

VectorField2 v;

v.Rotate(Matrix2(Math::Pi/2)).

Math::Pi

static const double Pi

π.

Definition: mathematics.h:174

Matrix2

This class implements 22 matrix.

Definition: matrix.h:426

VectorField2

A base two-dimensional field of Vector2 values.

Definition: vectorfield.h:26

VectorField2::Rotate

void Rotate(const Matrix2 &)

Compute the rotated vector field.

Definition: vectorfield2.cpp:69

◆ Radial()

void VectorField2::Radial	(	const Vector2 &	center,
		const double &	radius,
		const double &	scaling
	)

Adds to the vector field a radial component centered at center and goind towards the center (with scaling being positive) and towards the exterior of the center (with scaling being negative)

Parameters

center	Center.
radius	Radius.
scaling	Scaling of the effect.

◆ Rotate()

void VectorField2::Rotate ( const Matrix2 & r )

Compute the rotated vector field.

Parameters

r	Rotation matrix.

◆ RungeKutta()

Vector2 VectorField2::RungeKutta	(	const Vector2 &	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 VectorField2::Set ( const Vector2 & v )

Set the whole vector field to a constant vector.

Parameters

v Vector.

◆ Sub()

void VectorField2::Sub ( const VectorField2 & v )

Subtract two vector fields.

Parameters

v	Argument vector field. Optimized with AVX

◆ Unit()

void VectorField2::Unit ( )

Set all vectors to unit, i.e. set the norm of the vectors to 1.

See also: VectorField2::Normalize()

◆ Value() [1/2]

Vector2 VectorField2::Value ( const Vector2 & 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]

Vector2 VectorField2::Value	(	int	i,
		int	j
	)		const

virtual

Return the field vector at a given array vertex.

Parameters

i,j	Integer coordinates of the vertex.

See also: at(int,int)

Public Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ VectorField2() [1/2]

◆ VectorField2() [2/2]

Member Function Documentation

◆ Add()

◆ at() [1/3]

◆ at() [2/3]

◆ at() [3/3]

◆ Clone()

◆ CloneZone()

◆ CreateImageParticles()

◆ Curl() [1/2]

◆ Curl() [2/2]

◆ Divergence() [1/2]

◆ Divergence() [2/2]

◆ Draw()

◆ Euler()

◆ EulerSteps()

◆ GaussianBlur() [1/2]

◆ GaussianBlur() [2/2]

◆ GetComponent()

◆ GetNormRange()

◆ GetRange()

◆ Lerp()

◆ LineIntegral()

◆ Mul()

◆ Multiply()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator+=()

◆ operator-=()

◆ operator[]()

◆ Orthogonal()

◆ Radial()

◆ Rotate()

◆ RungeKutta()

◆ Set()

◆ Sub()

◆ Unit()

◆ Value() [1/2]

◆ Value() [2/2]