Hexagon2 Class Reference

Flat topped hexagon in the plane. More...

#include <hexagon.h>

Inheritance diagram for Hexagon2:

Public Member Functions
	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
static int	Sector (const Vector2 &)
	Compute the sector given an input direction.

Protected Attributes
Vector2	c = Vector2::Null
	Center.
double	r = 1.0
	Radius.

Static Protected Attributes
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.

Friends
std::ostream &	operator<< (std::ostream &s, const Hexagon2 &hex)
	Overloaded.

Detailed Description

Flat topped hexagon in the plane.

Constructor & Destructor Documentation

Hexagon2() [1/2]

Hexagon2::Hexagon2 ( const Vector2 & c, const double & r )

explicit

Create an hexagon.

Parameters

c	Center.
r	Radius.

Hexagon2() [2/2]

Hexagon2::Hexagon2 ( const double & r )

explicit

Create an hexagon.

Parameters

r

Radius.

Member Function Documentation

Draw()

void Hexagon2::Draw	(	QGraphicsScene &	scene,
		const QPen &	pen = QPen(),
		const QBrush &	brush = QBrush() ) const

Draws an hexagon.

Parameters

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

Edge()

Vector2 Hexagon2::Edge ( int k ) const

inline

Return the edge vector connecting vertexes k and k+1.

Parameters

k	Index, should be in [0,5].

Inside()

bool Hexagon2::Inside

(

const Vector2 &

p

)

const

Test if a point is inside.

Parameters

p

Point.

Intersect() [1/2]

bool Hexagon2::Intersect

(

const Circle2 &

circle

)

const

Check the intersection with a circle.

Accurate intersection test using the distance from the center of the circle to the hexagon.

Parameters

circle

The circle.

Intersect() [2/2]

bool Hexagon2::Intersect

(

const Hexagon2 &

hexagon

)

const

Check if two hexagons intersect.

Parameters

hexagon

Hexagon.

Normal()

Vector2 Hexagon2::Normal

(

const Vector2 &

p

)

const

Computes the distance vector between a hexagon and a point.

Parameters

p

Point.

Poisson()

QVector< Vector2 > Hexagon2::Poisson	(	const double &	r,
		int	n,
		Random &	random = Random::R239 ) const

Compute a Poisson disc distribution inside the hexagon.

This function uses a simple dart throwing algorithm.

Parameters

r	Radius of the discs.
n	Number of candidate points.
random	Random number generator.

R()

double Hexagon2::R

(

const Vector2 &

p

)

const

Compute the squared Euclidean distance to the hexagon.

Parameters

p

Point.

Radial()

Vector2 Hexagon2::Radial ( int k ) const

inline

Return the radial vector of the k-th vertex.

Parameters

k	Index, should be in [0,5].

RandomInside()

Vector2 Hexagon2::RandomInside

(

Random &

random = Random::R239

)

const

Generate a random vector inside the hexagon.

See also

Triangle::RandomInside

Parameters

random

Random number generator.

Scale()

void Hexagon2::Scale

(

const double &

s

)

Scale a hexagon.

Parameters

s	Scaling factor.

Sector()

int Hexagon2::Sector ( const Vector2 & d )

staticprotected

Compute the sector given an input direction.

Parameters

d	Direction.

Signed()

double Hexagon2::Signed

(

const Vector2 &

p

)

const

Compute the signed Euclidean distance to the hexagon.

Parameters

p

Point.

Translate()

void Hexagon2::Translate

(

const Vector2 &

t

)

Translate a hexagon.

Parameters

t	Translation vector.

Vertex()

Vector2 Hexagon2::Vertex ( int k ) const

inline

Return the coordinates of the k-th vertex.

Parameters

k	Index, should be in [0,5].

Friends And Related Symbol Documentation

operator<<

std::ostream & operator<< ( std::ostream & s, const Hexagon2 & hex )

friend

Overloaded.

Parameters

s	Stream.
hex	The hexagon.