HexagonArray2 Class Reference

A core hexagonal grid. More...

#include <hexagonarray.h>

Inheritance diagram for HexagonArray2:

Public Member Functions
	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 Member Functions
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.

Protected Attributes
int	ny = 0
	Number of hexagons.
Protected Attributes inherited from Hexagon2
Vector2	c = Vector2::Null
	Center.
double	r = 1.0
	Radius.

Static Protected Attributes
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.

Additional Inherited Members
Static Protected Member Functions inherited from Hexagon2
static int	Sector (const Vector2 &)
	Compute the sector given an input direction.

Detailed Description

A core hexagonal grid.

Constructor & Destructor Documentation

HexagonArray2() [1/2]

HexagonArray2::HexagonArray2 ( const Vector2 & c, const double & r, int x, int y )

explicit

Create and array of hexagons.

Parameters

c	Origin.
r	Side length of equilateral triangles.
x,y	Size of the array.

HexagonArray2() [2/2]

HexagonArray2::HexagonArray2 ( const Box2 & box, const double & r )

explicit

Create and array of hexagons embedded in a box.

Compute the largest array of hexagons centered and embedded in the argument box.

Parameters

box	The box.
r	Side length of equilateral triangles.

Member Function Documentation

ArrayVertex()

Vector2 HexagonArray2::ArrayVertex	(	int	i,
		int	j ) const

Compute the coordinates of a point on the grid.

Parameters

i,j	Point coordinates.

CellArea()

double HexagonArray2::CellArea

(

)

const

Return the area of a cell.

This is convenience function, which is the same as the following code, but more efficient:

HexagonArray2 array;
double a=array.UnitCell().Area();

CellCenter()

Vector2 HexagonArray2::CellCenter	(	int	i,
		int	j ) const

Compute the center of the hexagonal cell.

Parameters

i,j	Cell coordinates.

Draw()

void HexagonArray2::Draw	(	QGraphicsScene &	scene,
		const QPen &	pen = QPen(),
		const QBrush &	brush = QBrush() ) const

Draws the hexagon array.

Parameters

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

DrawCenters()

void HexagonArray2::DrawCenters	(	QGraphicsScene &	scene,
		const QPen &	pen = QPen(),
		const QBrush &	brush = QBrush() ) const

Draws the centers of the hexagon grid.

Parameters

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

GetBox()

Box2 HexagonArray2::GetBox

(

)

const

Compute the bounding box of the centroids of the hexagons.

Note that is is smaller than the bounding box of the hexagons.

GetHexagonBox()

Box2 HexagonArray2::GetHexagonBox

(

)

const

Compute the bounding box of all the hexagons.

Note that is is smaller than the bounding box of the hexagons.

Inside()

bool HexagonArray2::Inside

(

const Vector2 &

p

)

const

Check if a point is in the rectangular domain.

Parameters

p

Point.

InsideCellIndex()

bool HexagonArray2::InsideCellIndex ( int i, int j ) const

protected

Check if the indexes are within range.

Parameters

i,j	Integer coordinates of the vertex.

InsideVertexIndex()

bool HexagonArray2::InsideVertexIndex ( int i, int j ) const

inlineconstexpr

Check if the indexes are within range.

Parameters

i,j	Integer coordinates of the vertex.

InverseVertexIndex() [1/2]

QPoint HexagonArray2::InverseVertexIndex ( int c ) const

inlineprotected

Compute the coordinates of a given cell.

Parameters

c	Index of the cell.

InverseVertexIndex() [2/2]

void HexagonArray2::InverseVertexIndex ( int c, int & i, int & j ) const

inlineprotected

Compute the coordinates of a given cell.

Parameters

c	Index of the cell.
i,j	Integer coordinates of the cell.

Next() [1/2]

QPoint HexagonArray2::Next ( const QPoint & p, int k ) const

inline

Compute the index of the neighboring hexagon.

Parameters

p	Center. point
k	Neighbor, should be in [0,5].

Next() [2/2]

QPoint HexagonArray2::Next ( int i, int j, int k ) const

inline

Compute the index of the neighboring hexagon.

Parameters

i,j	Center.
k	Neighbor, should be in [0,5].

Translate()

void HexagonArray2::Translate

(

const Vector2 &

t

)

Translate the array.

Parameters

t	Translation vector.

TriangleInteger() [1/2]

QPoint HexagonArray2::TriangleInteger

(

const Vector2 &

p

)

const

Compute the coordinates of a vertex inside a triangle of the hexagonal grid.

Parameters

p

Point.

TriangleInteger() [2/2]

void HexagonArray2::TriangleInteger	(	const Vector2 &	p,
		int &	i,
		int &	j,
		double &	u,
		double &	v ) const

Compute the coordinates of a vertex inside a triangle of the hexagonal grid.

Parameters

p	Point.
i,j	Integer coordinates of the lower vertex.
u,v	Coordinates of the point in the corresponding triangle.

UnitCell()

Hexagon2 HexagonArray2::UnitCell

(

)

const

Return the geometry of a generic cell.

This is a hexagon, centered at origin, with the right size.

VertexIndex()

int HexagonArray2::VertexIndex ( int i, int j ) const

inlineconstexprprotected

Compute the index of a given cell.

Parameters

i,j	Integer coordinates of the cell.

VertexIntegerArea() [1/2]

QRect HexagonArray2::VertexIntegerArea

(

const Box2 &

box

)

const

Compute the integer coordinates of the vertices embedding a box.

The coordinates are clamped to the size of the array.

Parameters

box

Box.

VertexIntegerArea() [2/2]

QRect HexagonArray2::VertexIntegerArea

(

const Circle2 &

circle

)

const

Compute the integer coordinates of the vertices embedding a circle.

The coordinates are clamped to the size of the array.

Parameters

circle

Circle.