ScalarHexagonField2 Class Reference

A base two-dimensional field of real values on a hexagonal grid. More...

#include <hexagonscalarfield.h>

Inheritance diagram for ScalarHexagonField2:

Public Member Functions
	ScalarHexagonField2 ()
	Empty.
	ScalarHexagonField2 (const ScalarField2 &)
	Create the hexagonal field.
	ScalarHexagonField2 (const ScalarField2 &, const double &)
	Create the hexagonal field.
	ScalarHexagonField2 (const Vector2 &, const double &, int, int, const double &=0.0)
	Create the field structure.
	ScalarHexagonField2 (const Vector2 &, const double &, int, int, const QVector< double > &)
	Create the field structure.
	~ScalarHexagonField2 ()
	Empty.
void	GetRange (double &, double &) const
	Get the range of the field.
double	Integral () const
	Get the integral of the scalar field.
virtual Vector2	Gradient (int, int) const
	Compute the gradient at a given sample.
virtual double	Value (int, int) const
	Return the field gradient at a given array vertex.
virtual double	K () const
	Compute the Lipschitz constant of the field.
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.
ScalarField2	CreateScalarField () const
	Create a ScalarField2 from the hexagonal field.
ScalarField2	CreateScalarField (const Box2 &, int, int) const
	Create a ScalarField2 from the hexagonal field.
virtual double	Value (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.
void	Fill (const double &)
	Sets the entire field with a constant value.
void	Smooth (const Vector2 &, const double &)
	Smooth the scalar field within a given region.
void	Flatten (const Vector2 &, const double &, const double &=0.25)
	Flatten the scalar field.
void	Gaussian (const Vector2 &, const double &, const double &)
	Add material with gaussian distribution.
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	Translate (const Vector2 &)
	Translate the domain of the scalar field.
void	Scale (const double &)
	Scale the domain of the scalar field.
void	Normalize ()
	Normalize the values of a scalar field to unit interval.
void	Clamp (const double &, const double &)
	Clamp the values of a scalar field.
void	Add (const double &)
	Add a constant to the values the scalar field.
void	Step (const double &, const double &)
	Perform a linear step over the values of a scalar field.
void	SmoothStep (const double &, const double &, bool=false)
	Perform a smooth step over the values of a scalar field.
ScalarHexagonField2	GradientNorm () const
	Compute the gradient norm scalar field.
Public Member Functions inherited from HexagonArray2
	HexagonArray2 (const Vector2 &, const double &, int, int)
	Create and array of hexagons.
	HexagonArray2 (const Box2 &, const double &)
	Create and array of hexagons embedded in a box.
bool	IsEmpty () const
	Detect if the array is empty, i.e., any dimension equal to zero.
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	VertexSize () const
	Return the size of the vertex array.
Box2	GetBox () const
	Compute the bounding box of the centroids of the hexagons.
Box2	GetHexagonBox () const
	Compute the bounding box of all the hexagons.
Vector2	CellCenter (int, int) const
	Compute the center of the hexagonal cell.
void	Translate (const Vector2 &)
	Translate the array.
Vector2	ArrayVertex (int, int) const
	Compute the coordinates of a point on the grid.
constexpr bool	InsideVertexIndex (int, int) const
	Check if the indexes are within range.
bool	Inside (const Vector2 &) const
	Check if a point is in the rectangular domain.
Hexagon2	UnitCell () const
	Return the geometry of a generic cell.
double	CellArea () const
	Return the area of a cell.
QPoint	Next (int, int, int) const
	Compute the index of the neighboring hexagon.
QPoint	Next (const QPoint &, int) const
	Compute the index of the neighboring hexagon.
void	TriangleInteger (const Vector2 &, int &, int &, double &, double &) const
	Compute the coordinates of a vertex inside a triangle of the hexagonal grid.
QPoint	TriangleInteger (const Vector2 &) const
	Compute the coordinates of a vertex inside a triangle of the hexagonal grid.
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.
void	Draw (QGraphicsScene &, const QPen &=QPen(), const QBrush &=QBrush()) const
	Draws the hexagon array.
void	DrawCenters (QGraphicsScene &, const QPen &=QPen(), const QBrush &=QBrush()) const
	Draws the centers of the hexagon grid.

Protected Attributes
QVector< double >	field
	Samples.
Protected Attributes inherited from HexagonArray2
int	ny = 0
	Number of hexagons.
Protected Attributes inherited from Hexagon2
Vector2	c = Vector2::Null
	Center.
double	r = 1.0
	Radius.

Additional Inherited Members
Protected Member Functions inherited from HexagonArray2
constexpr int	VertexIndex (int, int) const
	Compute the index of a given cell.
void	InverseVertexIndex (int, int &, int &) const
	Compute the coordinates of a given cell.
QPoint	InverseVertexIndex (int) const
	Compute the coordinates of a given cell.
bool	InsideCellIndex (int, int) const
	Check if the indexes are within range.
Protected Member Functions inherited from Hexagon2
	Hexagon2 ()
	Empty.
	Hexagon2 (const Vector2 &, const double &)
	Create an hexagon.
	Hexagon2 (const double &)
	Create an hexagon.
void	Translate (const Vector2 &)
	Translate a hexagon.
void	Scale (const double &)
	Scale a hexagon.
double	Width () const
	Width of the hexagon.
double	Height () const
	Height of the hexagon.
bool	Inside (const Vector2 &) const
	Test if a point is inside.
bool	Intersect (const Hexagon2 &) const
	Check if two hexagons intersect.
double	R (const Vector2 &) const
	Compute the squared Euclidean distance to the hexagon.
double	Signed (const Vector2 &) const
	Compute the signed Euclidean distance to the hexagon.
Vector2	Normal (const Vector2 &) const
	Computes the distance vector between a hexagon and a point.
Vector2	Center () const
	Return the center of the hexagonal cell.
double	Radius () const
	Return the radius of the hexagonal cell.
Vector2	Radial (int) const
	Return the radial vector of the k-th vertex.
Vector2	Edge (int) const
	Return the edge vector connecting vertexes k and k+1.
Vector2	Vertex (int) const
	Return the coordinates of the k-th vertex.
Box2	GetBox () const
	Compute the bounding box of a hexagon.
double	Area () const
	Area of the hexagon.
double	Perimeter () const
	Perimeter of the hexagon.
Vector2	RandomInside (Random &=Random::R239) const
	Generate a random vector inside the hexagon.
QVector< Vector2 >	Poisson (const double &, int, Random &=Random::R239) const
	Compute a Poisson disc distribution inside the hexagon.
bool	Intersect (const Circle2 &) const
	Check the intersection with a circle.
void	Draw (QGraphicsScene &, const QPen &=QPen(), const QBrush &=QBrush()) const
	Draws an hexagon.
Static Protected Member Functions inherited from Hexagon2
static int	Sector (const Vector2 &)
	Compute the sector given an input direction.
Static Protected Attributes inherited from HexagonArray2
static int	next [6][2] = { {1,0}, {0,1}, {-1,0 }, {-1,-1}, {0,-1}, {1,-1 } }
	Array of offsets for computing neighbor indexes.
Static Protected Attributes inherited from Hexagon2
static const Vector2	vertex [6]
	Array of vertices.
static const Vector2	normal [6]
	Array of normal vectors to the edges.
static const Vector2	edge [6]
	Unit edge vectors.
static const double	Alpha = sqrt(3.0) / 2.0
	Constant sin(π/6)=√3/2.

Detailed Description

A base two-dimensional field of real values on a hexagonal grid.

Constructor & Destructor Documentation

ScalarHexagonField2() [1/4]

ScalarHexagonField2::ScalarHexagonField2 ( const ScalarField2 & s )

explicit

Create the hexagonal field.

Parameters

s	Scalar field.

ScalarHexagonField2() [2/4]

ScalarHexagonField2::ScalarHexagonField2 ( const ScalarField2 & s, const double & r )

explicit

Create the hexagonal field.

Parameters

s	Scalar field.
r	Sampling distance.

ScalarHexagonField2() [3/4]

ScalarHexagonField2::ScalarHexagonField2 ( const Vector2 & c, const double & r, int x, int y, const double & v = 0.0 )

explicit

Create the field structure.

Parameters

c	Origin.
r	Radius.
x,y	Size of the array.
v	Default value of field.

ScalarHexagonField2() [4/4]

ScalarHexagonField2::ScalarHexagonField2 ( const Vector2 & c, const double & r, int x, int y, const QVector< double > & v )

explicit

Create the field structure.

Parameters

c	Origin.
r	Radius.
x,y	Size of the array.
v	Array of scalar values.

Member Function Documentation

Add()

void ScalarHexagonField2::Add

(

const double &

c

)

Add a constant to the values the scalar field.

Parameters

c

Constant.

at() [1/3]

double ScalarHexagonField2::at ( const QPoint & q ) const

inline

Return the field value at a given array vertex.

Parameters

q

Point.

at() [2/3]

double ScalarHexagonField2::at ( int c ) const

inline

Return the data in the field.

Parameters

c

Index.

at() [3/3]

double ScalarHexagonField2::at ( int i, int j ) const

inline

Return the field value at a given array vertex.

Parameters

i,j	Integer coordinates of the vertex.

BiCubic()

double ScalarHexagonField2::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).

Blur()

void ScalarHexagonField2::Blur

(

)

Blurs the scalar field.

The function uses a 3² blur kernel.

Clamp()

void ScalarHexagonField2::Clamp	(	const double &	a,
		const double &	b )

Clamp the values of a scalar field.

Parameters

a,b

Interval.

CreateScalarField() [1/2]

ScalarField2 ScalarHexagonField2::CreateScalarField

(

)

const

Create a ScalarField2 from the hexagonal field.

This function comptes a rectangular domain inside the hexagonal field, sets grid size equal to the distance between the samples of the hexagonal field, and computes values at the grid points.

CreateScalarField() [2/2]

ScalarField2 ScalarHexagonField2::CreateScalarField	(	const Box2 &	box,
		int	nx,
		int	ny ) const

Create a ScalarField2 from the hexagonal field.

Parameters

box	Box.
nx,ny	Discretization.

CutEpsilon()

void ScalarHexagonField2::CutEpsilon

(

const double &

e = 1e-6

)

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

Parameters

e	Epsilon coefficient.

Fill()

void ScalarHexagonField2::Fill

(

const double &

s

)

Sets the entire field with a constant value.

Parameters

s

Scalar.

Flatten()

void ScalarHexagonField2::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 ScalarHexagonField2::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.

GetRange()

void ScalarHexagonField2::GetRange	(	double &	a,
		double &	b ) const

Get the range of the field.

Parameters

a,b	Returned minimum and maximum.

Gradient()

Vector2 ScalarHexagonField2::Gradient ( int i, int j ) const

virtual

Compute the gradient at a given sample.

Parameters

i,j	Integer coordinates of the sample.

Integral()

double ScalarHexagonField2::Integral

(

)

const

Get the integral of the scalar field.

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

K()

double ScalarHexagonField2::K ( ) const

virtual

Compute the Lipschitz constant of the field.

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.

ScalarHexagonField2 n=f.GradientNorm();
double k=0.0;
for (int i=0;i<f.VertexSize();i++)
{
k=Math::Max(k,f.at(i));
}

Normalize()

void ScalarHexagonField2::Normalize

(

)

Normalize the values of a scalar field to unit interval.

Compute range and apply transformation.

operator()() [1/2]

double & ScalarHexagonField2::operator() ( const QPoint & q )

inline

Return the field value at a given array vertex.

Parameters

q

Point.

operator()() [2/2]

double & ScalarHexagonField2::operator() ( int i, int j )

inline

Return the field value at a given array vertex.

Parameters

i,j	Integer coordinates of the vertex.

operator[]()

double & ScalarHexagonField2::operator[] ( int c )

inline

Return the data in the field.

Parameters

c

Index.

Scale()

void ScalarHexagonField2::Scale

(

const double &

s

)

Scale the domain of the scalar field.

Parameters

s	Scaling factor.

Smooth() [1/3]

void ScalarHexagonField2::Smooth

(

)

Smooth the scalar field using a discrete gaussian kernel.

The function uses a 3² approximation of the Gaussian kernel.

Smooth() [2/3]

void ScalarHexagonField2::Smooth	(	const Vector2 &	center,
		const double &	r )

Smooth the scalar field within a given region.

The smoothing is performed with the cubic falloff function Cubic::Smooth(const double&, const double&)

Parameters

center	Center.
r	Radius.

Smooth() [3/3]

void ScalarHexagonField2::Smooth

(

int

n

)

Applies several smoothing steps to the scalar field.

See also

Smooth()

Parameters

n	Number of smoothing steps.

SmoothStep()

void ScalarHexagonField2::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

Linear::Step(), Quintic::Step()

Parameters

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

Step()

void ScalarHexagonField2::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

Parameters

a,b

Interval.

Translate()

void ScalarHexagonField2::Translate

(

const Vector2 &

t

)

Translate the domain of the scalar field.

Parameters

t	Translation vector.

Value() [1/2]

double ScalarHexagonField2::Value ( const Vector2 & p ) const

virtual

Get the field value with world coordinate system.

This function computes a triangle interpolation of the values.

Parameters

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

Value() [2/2]

double ScalarHexagonField2::Value ( int i, int j ) const

virtual

Return the field gradient at a given array vertex.

Parameters

i,j	Integer coordinates of the vertex.

See also

at(int,int)