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

#include <scalarfield.h>

Inheritance diagram for ScalarField2:

Public Member Functions
	ScalarField2 ()
	Empty.

	ScalarField2 (const Array2 &, const double &=0.0)
	Create the field structure.

	ScalarField2 (const Box2 &, int, int, const double &=0.0)
	Create the field structure.

	ScalarField2 (const Box2 &, int, int, const QVector< double > &)
	Create the field structure.

	ScalarField2 (const Box2 &, const QImage &, const double &=0.0, const double &=256.0 *256.0 - 1.0, bool=true)
	Create a field structure from an image.

	ScalarField2 (const QImage &, const double &=1.0, const double &=1.0, bool=true)
	Create a field structure from an image.

	ScalarField2 (const QString &, double=0.0, double=1.0)
	Create a field structure from an image.

virtual	~ScalarField2 ()
	Empty.

Array2	GetArray () const
	Return the array representing the grid domain.

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.

double	Average () const
	Compute the average value of the elements in the scalar field.

double	ScaledNorm () const
	Compute the norm of the scalar field.

void	Symmetry (bool=true, bool=false)
	Perform a symmetry.

void	Rotate ()
	Counter-clockwise rotation, keep the center of the domain unchanged.

Histogram	GetHistogram (int) const
	Compute the histogram of the scalar field.

Histogram	GetHistogram (int, double, double) const
	Compute the histogram of the scalar field.

QVector< std::pair< double, int > >	OldHistogram (int) const
	Compute a histogram.

QVector< std::pair< double, int > >	CumulativeHistogram (int) const
	Compute a cumulative histogram.

QVector< std::pair< double, double > >	CumulativeNormedHistogram (int) const
	Compute a normalized cumulative histogram.

virtual Vector2	Gradient (int, int) const
	Compute the gradient at a given array vertex.

virtual Vector2	GradientSmooth (int, int) const
	Compute the smooth gradient at a given array vertex using a second order approximation.

virtual Matrix2	Hessian (int, int) const
	Compute the hessian at a given array vertex.

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

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

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

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

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

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

double &	operator() (const QPoint &)
	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.

double	StandardDeviation () const
	Compute the standard deviation.

double	StandardDeviation (const double &) const
	Compute the standard deviation.

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

QImage	CreateImage (const AnalyticPalette &, bool=false, bool=false) const
	Create an image from the field using a palette.

QImage	CreateImage (const double &, const double &, const AnalyticPalette &, bool=false) const
	Create an image from the field using a palette.

QImage	CreateImage (const Palette &) const
	Create an image from the field using a palette.

QImage	CreateImage (const double &, const double &, const GenericPalette &, bool=false) const
	Create an image from the field using a palette.

QImage	CreateImage (const GenericPalette &) const
	Create an image from the field using a palette.

QImage	CreateImage (const double &, const double &, bool=true) const
	Create an image from the field.

bool	ExportPGM (const QString &) const
	Export the scalarfield as a PGM file in 16 bits.

bool	ExportPGM (const QString &, const double &, const double &) const
	Export the scalarfield as a PGM file in 16 bits.

ScalarField2	SetResolution (int, int, bool=false) const
	Change the resolution of the scalar field.

ScalarField2	Sample (const Box2 &, int, int, bool=false) const
	Resample a rectangular region in the scalar field.

ScalarField2	Sample (const Segment2 &, const double &, int, int) const
	Sample along a thick segment.

ScalarField2	Sample (const Segment2 &, const double &) const
	Sample along a thick segment.

ScalarField2	Crop (const QPoint &, const QPoint &) const
	Crops a rectangular region in the scalar field.

ScalarField2	DownSample (int) const
	Lower the resolution of the scalarfield.

ScalarField2	UpSample (int, bool=false) const
	Upsampling of the scalarfield.

virtual double	Value (const Vector2 &) const
	Get the field value with world coordinate system.

virtual double	Triangular (const Vector2 &) const
	Get the field value with world coordinate system.

virtual double	BiCubic (const Vector2 &) const
	Get the field value with world coordinate system.

virtual double	BiCubicValue (const Vector2 &) const
	Compute the bicubic interpolation.

ScalarField2	SummedAreaTable () const
	Compute the summed area table of a scalar field.

void	Fill (const double &)
	Sets the entire field with a constant value.

void	Subdivide ()
	Subdivide the scalar field.

void	Smooth (const Vector2 &, double)
	Smooth the scalar field within a given region.

void	Flatten (const Vector2 &, const double &, const double &=0.25)
	Flatten the scalar field.

void	Multiply (const Vector2 &, const double &, const double &=1.0)
	Multiply the scalar field by a scaling factor locally (not equivalent to Flatten())

void	Level (const Vector2 &, const double &, const double &)
	Level the scalar field.

void	Gaussian (const Vector2 &, const double &, const double &)
	Add material with gaussian distribution.

void	Add (const Vector2 &, const double &)
	Add a value to the scalar field with diffusion.

ScalarField2	MedianFilter () const
	Compute the median filtered scalar field.

void	Smooth ()
	Smooth the scalar field using a discrete gaussian kernel.

void	Smooth (int)
	Applies several smoothing steps to the scalar field.

void	Blur ()
	Blurs the scalar field.

void	Blur (int)
	Applies several blurring steps to the scalar field.

void	SmoothSmall ()
	Small smoothing of the scalar field using a discrete gaussian kernel.

void	MedianFilter ()
	Filter with median filter.

ScalarField2	GaussianBlur (int) const
	Perform a Gaussian blur.

ScalarField2	GaussianBlur (const double &) const
	Perform a Gaussian blur.

void	Translate (const Vector2 &)
	Translate the domain of the scalar field.

void	Scale (const Vector2 &)
	Scale the domain of the scalar field.

void	Scale (const double &)
	Scale the scalar field.

void	Normalize ()
	Normalize the values of a scalar field to unit interval.

void	Unitize ()
	Linearly scale the values of a scalar field to unit interval.

void	Clamp (const double &, const double &)
	Clamp the values of a scalar field.

ScalarField2 &	operator*= (const ScalarField2 &)
	Multiplication.

ScalarField2 &	operator*= (const double &)
	Scale the values of a scalar field.

ScalarField2 &	operator/= (const double &)
	Scale the values of a scalar field.

ScalarField2 &	operator-= (const ScalarField2 &)
	Subtraction.

ScalarField2 &	operator-= (const double &)
	Subtract a constant to the values the scalar field.

ScalarField2 &	operator+= (const ScalarField2 &)
	Addition.

ScalarField2 &	operator+= (const double &)
	Add a constant to the values the scalar field.

ScalarField2	operator- () const
	Negates the values of the scalar field.

void	Pow (const double &)
	Power.

void	Atan ()
	Compute the arctangent of the values of a scalar field, may be usefull for converting slope to angles.

void	Step (const double &, const double &)
	Perform a linear step over the values of a scalar field.

void	SetRange (const double &, const double &)
	Scales the scalar field to a given range interval.

void	Binarize (const double &)
	Transform the field into a binary (0, 1 values) field using a threshold.

void	Invert ()
	Inversion (take the opposite of each field value)

void	Negate ()
	Negate (invert 0 and 1 values of a binary field)

void	SmoothStep (const double &, const double &, bool=false)
	Perform a smooth step over the values of a scalar field.

void	Abs ()
	Compute the absolute value of a scalar field.

void	Lerp (const ScalarField2 &, const ScalarField2 &, const double &)
	Linear interpolation between two scalar fields.

void	Lerp (const ScalarField2 &, const ScalarField2 &, const ScalarField2 &)
	Interpolation between two scalar fields with an alpha scalar field.

void	AdaptiveBilateralFiltering (double, double)
	Adaptive bilateral filtering.

void	AdaptiveBilateralFiltering (int, double)
	Adaptive bilateral filtering.

ScalarField2	Convolution (double[], int)
	Convolution of the field using a kernel.

void	MorphDilate ()
	Dilate the binary field using a D4 structuring element.

void	MorphErode ()
	Erode the binary field using a D4 structuring element.

void	MorphRemoveEnds ()
	Remove the ends of lines by authorizing at least 3 pixels.

void	MorphHitAndMiss (double[], int)
	Perform a hit and miss operation on the field.

void	MorphThin (double[], int)
	Thinning by using a kernel.

ScalarField2	MorphSkeleton (int)
	Compute the skeleton using successive erosion/dilatations.

ScalarField2	MorphSkeletonConnected (int)
	Compute the skeleton using thinning.

VectorField2	Gradient () const
	Compute the gradient field.

VectorField2	GradientSmooth () const
	Compute the smooth gradient field.

ScalarField2	GradientNorm () const
	Compute the gradient norm scalar field.

ScalarField2	GradientSmoothNorm () const
	Compute the gradient norm scalar field.

ScalarField2	Ln () const
	Compute the logarithm of the scalar field.

ScalarField2	Sqrt () const
	Compute the square root of the scalar field.

ScalarField2	Cbrt () const
	Compute the quartic root of the scalar field.

ScalarField2	Qurt () const
	Compute the quartic root of the scalar field.

void	Sqrted ()
	Compute the square root of the scalar field.

void	SelfOp (const std::function< double(double)> &)
	Applies a function to the scalar field.

ScalarField2	Op (const std::function< double(double)> &) const
	Applies a function to the scalar field.

ScalarField2	Op (const std::function< double(const ScalarField2 &, int, int)> &) const
	Applies a function to the scalar field.

virtual ScalarField2	Laplacian () const
	Compute the Laplacian field.

virtual double	Laplacian (int, int) const
	Compute the Laplacian at a given sample.

QVector< ScalarPoint2 >	GetScalarPoints () const
	Create the set of scalar points.

FloatArray	GetAsFloats () const
	Compute and return an array of 4 byte floats.

Vector2	Dichotomy (Vector2, Vector2, double, double, double, const double &, const double &) const
	Compute the intersection between a segment and the scalar field.

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

void	SignalError (const ScalarField2 &, double &, double &) const
	Compute PSNR and RMSE between two fields.

void	SignalError (const ScalarField2 &, double &, double &, double &) const
	Compute PSNR, MSE and RMSE between two fields.

ScalarField2	MaxFilter (int) const
	Compute the max filtered scalar field.

ScalarField2	MinFilter (int) const
	Compute the min filtered scalar field.

Mesh2	Polygonize (const double &=0.0) const
	Polygonize the scalar field into a surface mesh using the marching square algorithm.

SegmentSet2	LineSegments (const double &, bool=false) const
	Compute the iso-contour of the scalar field.

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

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

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

	Array2 (const Array &)
	Create the lattice structure.

Array2	DownSample (int) const
	Downsample the array.

Array2	UpSample (int) const
	Upsample the array.

	~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 number of vertices on the boundary of the rectangle.

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.

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

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

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

void	Scale (const Vector2 &)
	Scales the lattice structure.

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

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

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

Vector2	CellDiagonal () const
	Return the cell diagonal vector.

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

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

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

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

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.

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

void	Subdivide ()
	Change the resolution.

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.

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

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

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

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

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

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

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

QRect	VertexIntegerArea (int, int, int) const
	Compute the integer coordinates of the vertices embedding a cell with prescribed integer radius.

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

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

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

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

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

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

void	Translate (const Vector2 &)
	Translate the array.

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

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

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

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

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

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

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

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

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

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

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

QString	Statistics () const
	Get statistics.

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

Vector2	VertexUV (const Vector2 &) const
	Compute the coordinates of a point inside the box given uv coordinates.

Static Public Member Functions
static ScalarField2	LoadFromR32 (const Box2 &, const QString &)
	Import FAW Float 32 bits format that comes from World Machine.

static ScalarField2	Load (Box2, const QString &, double=0.0, double=1.0)
	Loads a scalar field from an image.

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

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

Protected Member Functions
void	SetBorder (const double &=0.0)
	Set the border of the scalar field to a constant value.

Matrix	Local (int, int) const
	Compute the local neighborhood in the one-ring aroung a point.

void	CopyEdges (ScalarField2 &) const
	Copy the values of the edges to a new field.

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

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

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

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

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

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

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

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.

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

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

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

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

	Box2 (const Vector2 &, const double &, const double &)
	Create a box given a center point and its width, length, and height.

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

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

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

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

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

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

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.

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

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.

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

Vector2	VertexUV (const Vector2 &) const
	Compute the coordinates of a point inside the box given uv coordinates.

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

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

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

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

void	Translate (const Vector2 &)
	Translates a box.

void	Scale (const Vector2 &)
	Scales a box.

void	Scale (const double &)
	Scales a box.

Box2	Translated (const Vector2 &) const
	Translated box.

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

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

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

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

Box2	ScaledCentered (const double &) const
	Scales a box while preserving its center.

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

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

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

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

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

Box2	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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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.

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

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

Segment2	GetSegment (const double &, bool=true) const
	Compute the horizontal or vertical segment dividing the box into u and 1-u parts.

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

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

Protected Attributes
QVector< double >	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 = Vector2(1.0)
	Lower and upper vertexes of the box.

Friends
ScalarField2	operator- (const double &x, const ScalarField2 &a)
	Subtraction.

ScalarField2	operator- (const ScalarField2 &a, const double &x)
	Subtraction.

ScalarField2	operator- (const ScalarField2 &a, const ScalarField2 &b)
	Subtraction.

ScalarField2	operator+ (const ScalarField2 &a, const ScalarField2 &b)
	Addition.

ScalarField2	operator+ (const ScalarField2 &a, const double &x)
	Addition.

ScalarField2	operator* (const ScalarField2 &a, const double &x)
	Multiplication.

ScalarField2	operator* (const double &x, const ScalarField2 &a)
	Multiplication.

ScalarField2	operator* (const ScalarField2 &a, const ScalarField2 &b)
	Multiplication.

ScalarField2	operator/ (const ScalarField2 &a, const double &x)
	Division.

ScalarField2	operator/ (const double &x, const ScalarField2 &a)
	Inverse.

std::ostream &	operator<< (std::ostream &s, const ScalarField2 &scalar)
	Overloaded.

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

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.

static const Box2	Unit
	Unit box, defined as.

Detailed Description

A base two-dimensional field of real values.

Constructor & Destructor Documentation

◆ ScalarField2() [1/6]

ScalarField2::ScalarField2	(	const Array2 &	a,
		const double &	v = 0.0 )

Create the field structure.

Parameters

a	Array representing the grid domain.
v	Constant value of field.

◆ ScalarField2() [2/6]

ScalarField2::ScalarField2	(	const Box2 &	box,
		int	x,
		int	y,
		const double &	v = 0.0 )

explicit

Create the field structure.

Parameters

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

◆ ScalarField2() [3/6]

ScalarField2::ScalarField2	(	const Box2 &	box,
		int	x,
		int	y,
		const QVector< double > &	v )

explicit

Create the field structure.

Parameters

box	The box.
x,y	Size of the array.
v	Array of scalar values.

◆ ScalarField2() [4/6]

ScalarField2::ScalarField2	(	const Box2 &	box,
		const QImage &	image,
		const double &	a = 0.0,
		const double &	b = 256.0 * 256.0 - 1.0,
		bool	grayscale = true )

explicit

Create a field structure from an image.

Parameters

box	The box.
image	The image.
a,b	Range of values to scale the image.
grayscale	Read image as grayscale if set to true, otherwize use color for a better accuracy.

◆ ScalarField2() [5/6]

ScalarField2::ScalarField2	(	const QImage &	image,
		const double &	v = 1.0,
		const double &	d = 1.0,
		bool	grayscale = true )

explicit

Create a field structure from an image.

Parameters

image	The image.
v	Range of values to scale the image, values will vary between 0.0 and v.
d	Distance between samples.
grayscale	Read image as grayscale if set to true, otherwize use color for a better accuracy.

◆ ScalarField2() [6/6]

ScalarField2::ScalarField2	(	const QString &	name,
		double	a = 0.0,
		double	b = 1.0 )

explicit

Create a field structure from an image.

This is a convenience constructor which is the same as:

ScalarField2 s(Box2(0.5), QImage(name),0.0,1.0,true);

Box2::Box2

Box2()

Empty.

Definition box.h:322

ScalarField2::ScalarField2

ScalarField2()

Empty.

Definition scalarfield.h:329

Parameters

name	Name of the image.
a,b	Range of values to scale the image.

Member Function Documentation

◆ AdaptiveBilateralFiltering() [1/2]

void ScalarField2::AdaptiveBilateralFiltering	(	double	w,
		double	s )

Adaptive bilateral filtering.

Parameters

w	Width of spatial gaussian kernel.
s	Intensity gaussian kernel.

Author: Hugo Schott

◆ AdaptiveBilateralFiltering() [2/2]

void ScalarField2::AdaptiveBilateralFiltering	(	int	spatial_sigma,
		double	range_sigma )

Adaptive bilateral filtering.

Parameters

spatial_sigma	Width (in number of cells) of spatial gaussian kernel.
range_sigma	Intensity gaussian kernel.

Author: Hugo Schott

◆ Add()

void ScalarField2::Add	(	const Vector2 &	p,
		const double &	x )

Add a value to the scalar field with diffusion.

The value is distributed among the neighboring vertices.

Parameters

p	Point.
x	Value.

◆ at() [1/3]

double ScalarField2::at ( const QPoint & q ) const

inline

Return the field value at a given array vertex.

Parameters

q Point.

◆ at() [2/3]

double ScalarField2::at ( int c ) const

inline

Return the data in the field.

Parameters

c Index.

◆ at() [3/3]

double ScalarField2::at	(	int	i,
		int	j ) const

inline

Return the field value at a given array vertex.

Parameters

i,j	Integer coordinates of the vertex.

◆ Atan()

void ScalarField2::Atan ( )

Compute the arctangent of the values of a scalar field, may be usefull for converting slope to angles.

Optimized with AVX

◆ Average()

double ScalarField2::Average ( ) const

Compute the average value of the elements in the scalar field.

Optimized with AVX

See also: Sum()

◆ BiCubic()

double ScalarField2::BiCubic ( const Vector2 & p ) const

virtual

Get the field value with world coordinate system.

This function computes a bicubic interpolation of the values, with null derivatives.

See also: Math::BiCubic

Parameters

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

◆ BiCubicValue()

double ScalarField2::BiCubicValue ( const Vector2 & p ) const

virtual

Compute the bicubic interpolation.

Author: Lois Paulin.

Parameters

p Point.

◆ Binarize()

void ScalarField2::Binarize ( const double & t )

Transform the field into a binary (0, 1 values) field using a threshold.

Parameters

t	Threshold.

◆ Blur() [1/2]

void ScalarField2::Blur ( )

Blurs the scalar field.

The function uses a 3² blur kernel.

◆ Blur() [2/2]

void ScalarField2::Blur ( int n )

Applies several blurring steps to the scalar field.

See also: Blur()

Parameters

n	Number of blurring steps.

◆ Cbrt()

ScalarField2 ScalarField2::Cbrt ( ) const

Compute the quartic root of the scalar field.

Direct quartic root computation is more efficicent that calling ScalarField2::Sqrt() twice.

Optimized with AVX

◆ Clamp()

void ScalarField2::Clamp	(	const double &	a,
		const double &	b )

Clamp the values of a scalar field.

Parameters

a,b Interval.

◆ Convolution()

ScalarField2 ScalarField2::Convolution	(	double	t[],
		int	s )

Convolution of the field using a kernel.

Parameters

t	Array of scalar values.
s	Size (odd number) of the square kernel.

◆ CopyEdges()

void ScalarField2::CopyEdges ( ScalarField2 & s ) const

protected

Copy the values of the edges to a new field.

Parameters

s	New scalar field.

◆ CreateImage() [1/7]

QImage ScalarField2::CreateImage ( bool grayscale = true ) const

Create an image from the field.

Parameters

grayscale Export as grayscale if set to true, and to color otherwise (provides a better precision).

◆ CreateImage() [2/7]

QImage ScalarField2::CreateImage	(	const AnalyticPalette &	palette,
		bool	symmetric = false,
		bool	transparent = false ) const

Create an image from the field using a palette.

Parameters

palette	The palette.
symmetric	If set to true, adapt the range interval so that shading should be performed with median alignment.
transparent	If set to true, the lowest values of the scalar field will be transparent.

◆ CreateImage() [3/7]

QImage ScalarField2::CreateImage	(	const double &	a,
		const double &	b,
		bool	grayscale = true ) const

Create an image from the field.

Parameters

a,b	Range of elevation that will be mapped to image scale.
grayscale	Export as grayscale if set to true, color otherwise.

◆ CreateImage() [4/7]

QImage ScalarField2::CreateImage	(	const double &	a,
		const double &	b,
		const AnalyticPalette &	palette,
		bool	transparent = false ) const

Create an image from the field using a palette.

Parameters

a,b	Range of elevation that will be mapped to image scale.
palette	The palette.
transparent	If set to true, the lowest values of the scalar field will be transparent.

◆ CreateImage() [5/7]

QImage ScalarField2::CreateImage	(	const double &	a,
		const double &	b,
		const GenericPalette &	palette,
		bool	transparent = false ) const

Create an image from the field using a palette.

Parameters

a,b	Range of elevation that will be mapped to image scale.
palette	The palette.
transparent	If set to true, the lowest values of the scalar field will be transparent.

◆ CreateImage() [6/7]

QImage ScalarField2::CreateImage ( const GenericPalette & palette ) const

Create an image from the field using a palette.

Parameters

palette The palette.

◆ CreateImage() [7/7]

QImage ScalarField2::CreateImage ( const Palette & palette ) const

Create an image from the field using a palette.

Parameters

palette The palette.

◆ Crop()

ScalarField2 ScalarField2::Crop	(	const QPoint &	a,
		const QPoint &	b ) const

Crops a rectangular region in the scalar field.

Note that the corners of the region of the scalar field are (0,0) and (nx-1,ny-1).

Parameters

a,b	Rectangular region.

◆ CumulativeHistogram()

QVector< std::pair< double, int > > ScalarField2::CumulativeHistogram ( int n ) const

Compute a cumulative histogram.

See also: Histogram

Parameters

n	Discretization.

◆ CumulativeNormedHistogram()

QVector< std::pair< double, double > > ScalarField2::CumulativeNormedHistogram ( int n ) const

Compute a normalized cumulative histogram.

See also: Histogram

Parameters

n	Discretization.

◆ CutEpsilon()

void ScalarField2::CutEpsilon ( const double & e = 1e-6 )

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

Parameters

e	Epsilon coefficient.

◆ Dichotomy()

Vector2 ScalarField2::Dichotomy	(	Vector2	a,
		Vector2	b,
		double	va,
		double	vb,
		double	length,
		const double &	T,
		const double &	epsilon ) const

Compute the intersection between a segment and the scalar field.

Parameters

a,b	End vertices of the segment straddling the surface.
va,vb	Field function value at those end vertices.
length	Distance between vertices.
epsilon	Precision.
T	Threshold value.

Returns: Point.

◆ DownSample()

ScalarField2 ScalarField2::DownSample ( int f ) const

Lower the resolution of the scalarfield.

Parameters

f	Lowering factor.

◆ ExportPGM() [1/2]

bool ScalarField2::ExportPGM ( const QString & url ) const

Export the scalarfield as a PGM file in 16 bits.

Parameters

url	File name.

◆ ExportPGM() [2/2]

bool ScalarField2::ExportPGM	(	const QString &	url,
		const double &	a,
		const double &	b ) const

Export the scalarfield as a PGM file in 16 bits.

Parameters

url	File name.
a,b	Interval range, values in the field will be clamped to [a,b] and rescaled 16 bits range.

◆ Fill()

void ScalarField2::Fill ( const double & s )

Sets the entire field with a constant value.

Parameters

s Scalar.

◆ Flatten()

void ScalarField2::Flatten	(	const Vector2 &	center,
		const double &	radius,
		const double &	scaling = 0.25 )

Flatten the scalar field.

Parameters

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

◆ Gaussian()

void ScalarField2::Gaussian	(	const Vector2 &	center,
		const double &	radius,
		const double &	height )

Add material with gaussian distribution.

Parameters

center	Center of the distribution.
radius	Radius
height	Maximum height of the distribution.

◆ GaussianBlur() [1/2]

ScalarField2 ScalarField2::GaussianBlur ( const double & r ) const

Perform a Gaussian blur.

Parameters

r	Radius of blur.

See also: ScalarField2::GaussianBlur(int)

◆ GaussianBlur() [2/2]

ScalarField2 ScalarField2::GaussianBlur ( int r ) const

Perform a Gaussian blur.

Parameters

r	Radius (in cells) of blur.

◆ GetHistogram() [1/2]

Histogram ScalarField2::GetHistogram ( int n ) const

Compute the histogram of the scalar field.

Parameters

n	Discretization.

◆ GetHistogram() [2/2]

Histogram ScalarField2::GetHistogram	(	int	n,
		double	a,
		double	b ) const

Compute the histogram of the scalar field.

Parameters

a,b	Interval.
n	Discretization.

◆ GetRange()

void ScalarField2::GetRange	(	double &	a,
		double &	b ) const

Get the range of the field.

Optimized with AVX

Parameters

a,b	Returned minimum and maximum.

◆ Gradient()

Vector2 ScalarField2::Gradient	(	int	i,
		int	j ) const

virtual

Compute the gradient at a given array vertex.

Parameters

i,j	Integer coordinates of the array vertex.

◆ GradientSmooth()

Vector2 ScalarField2::GradientSmooth	(	int	i,
		int	j ) const

virtual

Compute the smooth gradient at a given array vertex using a second order approximation.

Parameters

i,j	Integer coordinates of the array vertex.

◆ Hessian()

Matrix2 ScalarField2::Hessian	(	int	i,
		int	j ) const

virtual

Compute the hessian at a given array vertex.

Parameters

i,j	Integer coordinates of the array vertex.

◆ Integral()

double ScalarField2::Integral ( ) const

Get the integral of the scalar field.

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

See also: Sum()

◆ K()

double ScalarField2::K ( ) const

virtual

Compute the Lipschitz constant of the elevation function.

Note that this is equivalent to the following code, with the difference that this function does not store the norm of the gradient in memory.

ScalarField2 n=f.GradientNorm();
double k=0.0;
for (int i=0;i<f.VertexSize();i++)
{
k=Math::Max(k,f.at(i));
}

◆ Laplacian() [1/2]

ScalarField2 ScalarField2::Laplacian ( ) const

virtual

Compute the Laplacian field.

Returns a discrete approximation of Laplace�s differential operator applied to the field. The implementation is equivalent to the 4*del2(U) Matlab function, except on the edges of the field.

See also: Laplacian(int, int)

Author: Mathieu Gaillard

◆ Laplacian() [2/2]

double ScalarField2::Laplacian	(	int	i,
		int	j ) const

virtual

Compute the Laplacian at a given sample.

Returns a discrete approximation of Laplace�s differential operator applied to the field. The implementation is equivalent to the 4*del2(U) Matlab function, except on the edges of the field.

See also: Laplacian()

Author: Mathieu Gaillard

Parameters

i,j	Integer coordinates of the sample.

◆ Lerp() [1/2]

void ScalarField2::Lerp	(	const ScalarField2 &	a,
		const ScalarField2 &	b,
		const double &	t )

Linear interpolation between two scalar fields.

Parameters

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

◆ Lerp() [2/2]

void ScalarField2::Lerp	(	const ScalarField2 &	a,
		const ScalarField2 &	b,
		const ScalarField2 &	t )

Interpolation between two scalar fields with an alpha scalar field.

Compute (1-t) a + t b.

Parameters

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

◆ Level()

void ScalarField2::Level	(	const Vector2 &	center,
		const double &	radius,
		const double &	z )

Level the scalar field.

Parameters

center	Center.
radius	Radius.
z	Elevation.

◆ LineSegments()

SegmentSet2 ScalarField2::LineSegments	(	const double &	T,
		bool	closed = false ) const

Compute the iso-contour of the scalar field.

Parameters

T	Threshold.
closed	Set to true if polylines should be closed at the border of the domain.

◆ Load()

ScalarField2 ScalarField2::Load	(	Box2	box,
		const QString &	path,
		double	a = 0.0,
		double	b = 1.0 )

static

Loads a scalar field from an image.

The function uses a specific image reader with unlimited allocation limit.

Parameters

box	The box.
path	Name of the image.
a,b	Range of values to scale the image.

◆ LoadFromR32()

ScalarField2 ScalarField2::LoadFromR32	(	const Box2 &	box,
		const QString &	filename )

static

Import FAW Float 32 bits format that comes from World Machine.

Suppose that the domain is a square.

◆ Local()

Matrix ScalarField2::Local	(	int	i,
		int	j ) const

protected

Compute the local neighborhood in the one-ring aroung a point.

Parameters

i,j Point.

◆ MaxFilter()

ScalarField2 ScalarField2::MaxFilter ( int w ) const

Compute the max filtered scalar field.

Parameters

w	Window size.

◆ MedianFilter()

ScalarField2 ScalarField2::MedianFilter ( ) const

Compute the median filtered scalar field.

Edges are not processed.

◆ MinFilter()

ScalarField2 ScalarField2::MinFilter ( int w ) const

Compute the min filtered scalar field.

Parameters

w	Window size.

◆ MorphHitAndMiss()

void ScalarField2::MorphHitAndMiss	(	double	k[],
		int	s )

Perform a hit and miss operation on the field.

Parameters

k	is the kernel, containing 1 and -1 for hit and miss resp. and 0 for "don't care"
s	Size of the kernel (should be odd)

◆ MorphSkeleton()

ScalarField2 ScalarField2::MorphSkeleton ( int n )

Compute the skeleton using successive erosion/dilatations.

Parameters

n	Maximum number of iterations, which is related to the maximum thickness of the shape.

◆ MorphSkeletonConnected()

ScalarField2 ScalarField2::MorphSkeletonConnected ( int n )

Compute the skeleton using thinning.

Parameters

n	Maximum number of iterations, which is related to the maximum thickness of the shape.

◆ MorphThin()

void ScalarField2::MorphThin	(	double	k[],
		int	s )

Thinning by using a kernel.

Parameters

k	Kernel, containing 1 and -1 for hit and miss respectively, and 0 for don't care.
s	Size of the kernel (should be odd).

◆ Multiply()

void ScalarField2::Multiply	(	const Vector2 &	center,
		const double &	radius,
		const double &	scaling = 1.0 )

Multiply the scalar field by a scaling factor locally (not equivalent to Flatten())

Parameters

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

◆ Normalize()

void ScalarField2::Normalize ( )

Normalize the values of a scalar field to unit interval.

Compute range and apply the affine transformation to map values to [0,1].

See also: Unitize() Optimized with AVX

◆ OldHistogram()

QVector< std::pair< double, int > > ScalarField2::OldHistogram ( int n ) const

Compute a histogram.

Compute the range of values taken by the scalar field, and compute the histogram.

Parameters

n	Discretization.

◆ Op() [1/2]

ScalarField2 ScalarField2::Op ( const std::function< double(const ScalarField2 &, int, int)> & function ) const

Applies a function to the scalar field.

Parameters

function The function.

Returns: A scalarfield with computed values.

◆ Op() [2/2]

ScalarField2 ScalarField2::Op ( const std::function< double(double)> & function ) const

Applies a function to the scalar field.

Parameters

function The function.

Returns: A scalarfield with computed values.

See also: ScalarField2::SelfOp(const std::function<double(double)>&)

◆ operator()() [1/2]

double & ScalarField2::operator() ( const QPoint & q )

inline

Return the field value at a given array vertex.

Parameters

q Point.

◆ operator()() [2/2]

double & ScalarField2::operator()	(	int	i,
		int	j )

inline

Return the field value at a given array vertex.

Parameters

i,j	Integer coordinates of the vertex.

◆ operator*=() [1/2]

ScalarField2 & ScalarField2::operator*= ( const double & s )

Scale the values of a scalar field.

Parameters

s	Scaling factor.

◆ operator*=() [2/2]

ScalarField2 & ScalarField2::operator*= ( const ScalarField2 & s )

Multiplication.

Parameters

s	Scalar field.

◆ operator+=() [1/2]

ScalarField2 & ScalarField2::operator+= ( const double & c )

Add a constant to the values the scalar field.

Parameters

c Constant.

◆ operator+=() [2/2]

ScalarField2 & ScalarField2::operator+= ( const ScalarField2 & s )

Addition.

Parameters

s	Scalar field. Optimized with AVX

◆ operator-=() [1/2]

ScalarField2 & ScalarField2::operator-= ( const double & c )

inline

Subtract a constant to the values the scalar field.

Provided out of consistency, simply calls ScalarField2::operator+=(const double&) with the negated constant.

Parameters

c Constant.

◆ operator-=() [2/2]

ScalarField2 & ScalarField2::operator-= ( const ScalarField2 & s )

Subtraction.

Parameters

s	Scalar field.

Optimized with AVX

◆ operator/=()

ScalarField2 & ScalarField2::operator/= ( const double & s )

inline

Scale the values of a scalar field.

Parameters

s	Scaling factor.

◆ operator[]()

double & ScalarField2::operator[] ( int c )

inline

Return the data in the field.

Parameters

c Index.

◆ Polygonize()

Mesh2 ScalarField2::Polygonize ( const double & T = 0.0 ) const

Polygonize the scalar field into a surface mesh using the marching square algorithm.

Parameters

T	Threshold.

Returns: The mesh.

◆ Pow()

void ScalarField2::Pow ( const double & s )

Power.

Parameters

s Real.

◆ Qurt()

ScalarField2 ScalarField2::Qurt ( ) const

Compute the quartic root of the scalar field.

Direct quartic root computation is more efficicent that calling ScalarField2::Sqrt() twice.

Optimized with AVX

◆ Sample() [1/3]

ScalarField2 ScalarField2::Sample	(	const Box2 &	box,
		int	x,
		int	y,
		bool	bicubic = false ) const

Resample a rectangular region in the scalar field.

Parameters

box	Rectangular region, should be strictly inside the domain.
x,y	Sampling size.
bicubic	Bicubic flag, set to true to use bicubic interpolation.

◆ Sample() [2/3]

ScalarField2 ScalarField2::Sample	(	const Segment2 &	segment,
		const double &	radius ) const

Sample along a thick segment.

Parameters

segment	The segment.
radius	Distance in the orthogonal direction to the segment.

Discretization is adapted from the resolution of the scalar field.

◆ Sample() [3/3]

ScalarField2 ScalarField2::Sample	(	const Segment2 &	segment,
		const double &	radius,
		int	nx,
		int	ny ) const

Sample along a thick segment.

Parameters

segment	The segment.
radius	Distance in the orthogonal direction to the segment.
nx,ny	Discretization.

◆ Scale() [1/2]

void ScalarField2::Scale ( const double & s )

Scale the scalar field.

This function also scales the values, it is different from ScalarField2::Scale(const Vector2&);

Parameters

s	Scaling factor.

◆ Scale() [2/2]

void ScalarField2::Scale ( const Vector2 & s )

Scale the domain of the scalar field.

Parameters

s	Scaling factor.

◆ ScaledNorm()

double ScalarField2::ScaledNorm ( ) const

Compute the norm of the scalar field.

Optimized with AVX

See also: Average()

◆ SelfOp()

void ScalarField2::SelfOp ( const std::function< double(double)> & function )

Applies a function to the scalar field.

Parameters

function The function.

ScalarField2 s;

s.SelfOp([&](double x) { return x-pow(x, 0.7); });

ScalarField2::SelfOp

void SelfOp(const std::function< double(double)> &)

Applies a function to the scalar field.

Definition scalarfield2.cpp:2988

◆ SetBorder()

void ScalarField2::SetBorder ( const double & c = 0.0 )

protected

Set the border of the scalar field to a constant value.

Parameters

c Constant.

◆ SetRange()

void ScalarField2::SetRange	(	const double &	a,
		const double &	b )

Scales the scalar field to a given range interval.

Parameters

a,b Interval.

◆ SetResolution()

ScalarField2 ScalarField2::SetResolution	(	int	x,
		int	y,
		bool	bicubic = false ) const

Change the resolution of the scalar field.

Note that because the box should be strictly inside the original domain, this function is not the same as:

ScalarField field(Box2(Vector2(-2.0),Vector(3.0),5,5); // Original field

ScalarField s=Sample(field.GetBox(),12,12);

ScalarField2::Sample

ScalarField2 Sample(const Box2 &, int, int, bool=false) const

Resample a rectangular region in the scalar field.

Definition scalarfield2.cpp:1155

ScalarField2::field

QVector< double > field

Field samples.

Definition scalarfield.h:326

ScalarField

A base three-dimensional field of real values.

Definition scalarfield.h:623

Vector2

Vectors in two dimensions.

Definition evector.h:628

Vector

Vectors in three dimensions.

Definition evector.h:20

Parameters

x,y	Sampling size.
bicubic	Bicubic flag, set to true to use bicubic interpolation.

◆ SignalError() [1/2]

void ScalarField2::SignalError	(	const ScalarField2 &	s,
		double &	psnr,
		double &	rmse ) const

Compute PSNR and RMSE between two fields.

PSNR is computed assuming the data has a normalized [0,1] range.

Parameters

s	Second scalar field.
psnr	Returned PSNR.
rmse	Returned RMSE.

◆ SignalError() [2/2]

void ScalarField2::SignalError	(	const ScalarField2 &	s,
		double &	psnr,
		double &	mse,
		double &	rmse ) const

Compute PSNR, MSE and RMSE between two fields.

Parameters

s	Second scalar field.
psnr	Returned PSNR.
mse	Returned MSE.
rmse	Returned RMSE.

◆ Smooth() [1/3]

void ScalarField2::Smooth ( )

Smooth the scalar field using a discrete gaussian kernel.

The function uses a 3² approximation of the Gaussian kernel.

◆ Smooth() [2/3]

void ScalarField2::Smooth	(	const Vector2 &	center,
		double	r )

Smooth the scalar field within a given region.

The smoothing will be applied using the cubic falloff function Cubic::Smooth(const double&, const double&)

Parameters

center	Center.
r	Radius.

◆ Smooth() [3/3]

void ScalarField2::Smooth ( int n )

Applies several smoothing steps to the scalar field.

See also: Smooth()

Parameters

n	Number of smoothing steps.

◆ SmoothSmall()

void ScalarField2::SmoothSmall ( )

Small smoothing of the scalar field using a discrete gaussian kernel.

The function uses a 3² approximation of the Gaussian kernel.

◆ SmoothStep()

void ScalarField2::SmoothStep	(	const double &	a,
		const double &	b,
		bool	s = false )

Perform a smooth step over the values of a scalar field.

Either the function Cubic::Step() or Quintic::Step() is applied to all the values of the field.

See also: Cubic::Step(), Quintic::Step()

Parameters

a,b	Interval.
s	Smoothing Boolean value, apply a quintic smoothing kernel if set to true.

◆ Sqrt()

ScalarField2 ScalarField2::Sqrt ( ) const

Compute the square root of the scalar field.

Optimized with AVX

◆ Sqrted()

void ScalarField2::Sqrted ( )

Compute the square root of the scalar field.

This function changes the values of the field.

See also: ScalarField2::Sqrt() const Optimized with AVX

◆ StandardDeviation() [1/2]

double ScalarField2::StandardDeviation ( ) const

Compute the standard deviation.

Optimized with AVX

◆ StandardDeviation() [2/2]

double ScalarField2::StandardDeviation ( const double & m ) const

Compute the standard deviation.

Parameters

m Mean.

◆ Step()

void ScalarField2::Step	(	const double &	a,
		const double &	b )

Perform a linear step over the values of a scalar field.

The function Linear::Step() is applied to all the values of the field.

See also: Linear::Step(); ScalarField2::Normalize()

Parameters

a,b Interval.

◆ Subdivide()

void ScalarField2::Subdivide ( )

Subdivide the scalar field.

Simply doubles the resolution and interpolate the values from the existing ones.

◆ Sum()

double ScalarField2::Sum ( ) const

Compute the sum of the elements in the scalar field.

Optimized with AVX

See also: Integral(), Average()

◆ Symmetry()

void ScalarField2::Symmetry	(	bool	x = true,
		bool	y = false )

Perform a symmetry.

Parameters

x,y	Axes of symmetry.

◆ Translate()

void ScalarField2::Translate ( const Vector2 & t )

Translate the domain of the scalar field.

Parameters

t	Translation vector.

◆ Triangular()

double ScalarField2::Triangular ( const Vector2 & p ) const

virtual

Get the field value with world coordinate system.

This function computes a triangular interpolation of the values.

Parameters

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

◆ Unitize()

void ScalarField2::Unitize ( )

Linearly scale the values of a scalar field to unit interval.

This function differs from ScalarField2::Normalize() which maps values to [0,1]. Instead, we divide scalard field values by the maximum of the absolute value of the scalar field, which maps values to [-1,1] and preserves 0.

See also: Normalize()

Optimized with AVX

◆ UpSample()

ScalarField2 ScalarField2::UpSample	(	int	f,
		bool	bicubic = false ) const

Upsampling of the scalarfield.

Parameters

f	Upsampling factor.
bicubic	Bicubic flag, set to true to use bicubic interpolation.

See also: ScalarField2::SetResolution

◆ Value() [1/2]

double ScalarField2::Value ( const Vector2 & p ) const

virtual

Get the field value with world coordinate system.

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

See also: Math::Bilinear

Parameters

p	Point position (should be strictly inside the box domain).

◆ Value() [2/2]

double ScalarField2::Value	(	int	i,
		int	j ) const

virtual

Return the field value at a given array vertex.

Parameters

i,j	Integer coordinates of the array vertex.

See also: at(int,int)

Friends And Related Symbol Documentation

◆ operator* [1/3]

ScalarField2 operator*	(	const double &	x,
		const ScalarField2 &	a )

friend

Multiplication.

Parameters

a	Scalar field.
x	Real.

◆ operator* [2/3]

ScalarField2 operator*	(	const ScalarField2 &	a,
		const double &	x )

friend

Multiplication.

Parameters

a	Scalar field.
x	Real.

◆ operator* [3/3]

ScalarField2 operator*	(	const ScalarField2 &	a,
		const ScalarField2 &	b )

friend

Multiplication.

Parameters

a	Scalar field.
b	Scalar field.

◆ operator+ [1/2]

ScalarField2 operator+	(	const ScalarField2 &	a,
		const double &	x )

friend

Addition.

Parameters

a	Scalar field.
x	Real.

◆ operator+ [2/2]

ScalarField2 operator+	(	const ScalarField2 &	a,
		const ScalarField2 &	b )

friend

Addition.

Parameters

a,b	Scalar fields.

◆ operator- [1/3]

ScalarField2 operator-	(	const double &	x,
		const ScalarField2 &	a )

friend

Subtraction.

Parameters

x	Real.
a	Scalar field.

◆ operator- [2/3]

ScalarField2 operator-	(	const ScalarField2 &	a,
		const double &	x )

friend

Subtraction.

Parameters

a	Scalar field.
x	Real.

◆ operator- [3/3]

ScalarField2 operator-	(	const ScalarField2 &	a,
		const ScalarField2 &	b )

friend

Subtraction.

Parameters

a,b	Scalar fields.

◆ operator/ [1/2]

ScalarField2 operator/	(	const double &	x,
		const ScalarField2 &	a )

friend

Inverse.

Parameters

a	Scalar field.
x	Real.

◆ operator/ [2/2]

ScalarField2 operator/	(	const ScalarField2 &	a,
		const double &	x )

friend

Division.

Rely on multiplication by inverse.

Parameters

a	Scalar field.
x	Real.

◆ operator<<

std::ostream & operator<<	(	std::ostream &	s,
		const ScalarField2 &	scalar )

friend

Overloaded.

Parameters

s	Stream.
scalar	The scalar field.

Public Member Functions

Static Public Member Functions

Protected Member Functions

Protected Attributes

Friends

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ ScalarField2() [1/6]

◆ ScalarField2() [2/6]

◆ ScalarField2() [3/6]

◆ ScalarField2() [4/6]

◆ ScalarField2() [5/6]

◆ ScalarField2() [6/6]

Member Function Documentation

◆ AdaptiveBilateralFiltering() [1/2]

◆ AdaptiveBilateralFiltering() [2/2]

◆ Add()

◆ at() [1/3]

◆ at() [2/3]

◆ at() [3/3]

◆ Atan()

◆ Average()

◆ BiCubic()

◆ BiCubicValue()

◆ Binarize()

◆ Blur() [1/2]

◆ Blur() [2/2]

◆ Cbrt()

◆ Clamp()

◆ Convolution()

◆ CopyEdges()

◆ CreateImage() [1/7]

◆ CreateImage() [2/7]

◆ CreateImage() [3/7]

◆ CreateImage() [4/7]

◆ CreateImage() [5/7]

◆ CreateImage() [6/7]

◆ CreateImage() [7/7]

◆ Crop()

◆ CumulativeHistogram()

◆ CumulativeNormedHistogram()

◆ CutEpsilon()

◆ Dichotomy()

◆ DownSample()

◆ ExportPGM() [1/2]

◆ ExportPGM() [2/2]

◆ Fill()

◆ Flatten()

◆ Gaussian()

◆ GaussianBlur() [1/2]

◆ GaussianBlur() [2/2]

◆ GetHistogram() [1/2]

◆ GetHistogram() [2/2]

◆ GetRange()

◆ Gradient()

◆ GradientSmooth()

◆ Hessian()

◆ Integral()

◆ K()

◆ Laplacian() [1/2]

◆ Laplacian() [2/2]

◆ Lerp() [1/2]

◆ Lerp() [2/2]

◆ Level()

◆ LineSegments()

◆ Load()

◆ LoadFromR32()

◆ Local()

◆ MaxFilter()

◆ MedianFilter()

◆ MinFilter()

◆ MorphHitAndMiss()

◆ MorphSkeleton()

◆ MorphSkeletonConnected()

◆ MorphThin()

◆ Multiply()

◆ Normalize()

◆ OldHistogram()

◆ Op() [1/2]