Pentagon2 Class Reference

Flat topped pentagon in the plane. More...

#include <pentagon.h>

Public Member Functions
	Pentagon2 ()
	Empty.
	Pentagon2 (const Vector2 &, const double &)
	Create a pentagon.
	Pentagon2 (const double &)
	Create an pentagon.
void	Translate (const Vector2 &)
	Translate a pentagon.
void	Scale (const double &)
	Scale a pentagon.
bool	Inside (const Vector2 &) const
	Test if a point is inside.
double	R (const Vector2 &) const
	Compute the squared Euclidean distance to the pentagon.
double	Signed (const Vector2 &) const
	Compute the signed Euclidean distance to the pentagon.
Vector2	Normal (const Vector2 &) const
	Computes the distance vector between a pentagon and a point.
bool	Intersect (const Ray2 &, double &, double &) const
	Compute the intersection with a ray.
Vector2	Center () const
	Return the center of the pentagon.
double	Radius () const
	Return the radius of the pentagon.
double	InscribedRadius () const
	Inscribed radius.
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
	Computes the bounding box of a pentagon.
double	Area () const
	Area of the pentagon.
double	Perimeter () const
	Perimeter of the pentagon.
double	Edge () const
	Edge length.
Vector2	RandomInside (Random &=Random::R239) const
	Generate a random vector inside the pentagon.
QVector< Vector2 >	Poisson (const double &, int, Random &=Random::R239) const
	Compute a Poisson disc distribution inside the pentagon.
void	Draw (QGraphicsScene &, const QPen &=QPen(), const QBrush &=QBrush()) const
	Draws an pentagon.

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

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

Static Protected Attributes
static const Vector2	vertex [5]
	Array of vertexes.
static const Vector2	normal [5]
	Array of normal vectors to the edges.
static const Vector2	edge [5]
	Unit edge vectors.
static const double	Alpha = 1.0 / (2.0 * sqrt(5.0 - 2.0 * sqrt(5.0)))
	Constant.

Friends
std::ostream &	operator<< (std::ostream &s, const Pentagon2 &pentagon)
	Overloaded.

Detailed Description

Flat topped pentagon in the plane.

Constructor & Destructor Documentation

Pentagon2() [1/2]

Pentagon2::Pentagon2 ( const Vector2 & c, const double & r )

explicit

Create a pentagon.

Parameters

c	Center.
r	Radius.

Pentagon2() [2/2]

Pentagon2::Pentagon2 ( const double & r )

explicit

Create an pentagon.

Parameters

r

Radius.

Member Function Documentation

Draw()

void Pentagon2::Draw	(	QGraphicsScene &	scene,
		const QPen &	pen = QPen(),
		const QBrush &	brush = QBrush() ) const

Draws an pentagon.

Parameters

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

Edge()

Vector2 Pentagon2::Edge ( int k ) const

inline

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

Parameters

k	Index, should be in [0,4].

Inside()

bool Pentagon2::Inside

(

const Vector2 &

p

)

const

Test if a point is inside.

Parameters

p

Point.

Intersect()

bool Pentagon2::Intersect	(	const Ray2 &	ray,
		double &	ta,
		double &	tb ) const

Compute the intersection with a ray.

Parameters

ray	The ray.
ta,tb	Intersection depths

Normal()

Vector2 Pentagon2::Normal

(

const Vector2 &

p

)

const

Computes the distance vector between a pentagon and a point.

Parameters

p

Point.

Poisson()

QVector< Vector2 > Pentagon2::Poisson	(	const double &	r,
		int	n,
		Random &	random = Random::R239 ) const

Compute a Poisson disc distribution inside the pentagon.

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 Pentagon2::R

(

const Vector2 &

p

)

const

Compute the squared Euclidean distance to the pentagon.

Parameters

p

Point.

Radial()

Vector2 Pentagon2::Radial ( int k ) const

inline

Return the radial vector of the k-th vertex.

Parameters

k	Index, should be in [0,4].

RandomInside()

Vector2 Pentagon2::RandomInside

(

Random &

random = Random::R239

)

const

Generate a random vector inside the pentagon.

See also

Triangle::RandomInside

Parameters

random

Random number generator.

Scale()

void Pentagon2::Scale

(

const double &

s

)

Scale a pentagon.

Parameters

s	Scaling factor.

Sector()

int Pentagon2::Sector ( const Vector2 & d )

staticprotected

Compute the sector given an input direction.

Parameters

d	Direction.

Signed()

double Pentagon2::Signed

(

const Vector2 &

p

)

const

Compute the signed Euclidean distance to the pentagon.

Parameters

p

Point.

Translate()

void Pentagon2::Translate

(

const Vector2 &

t

)

Translate a pentagon.

Parameters

t	Translation vector.

Vertex()

Vector2 Pentagon2::Vertex ( int k ) const

inline

Return the coordinates of the k-th vertex.

Parameters

k	Index, should be in [0,4].

Friends And Related Symbol Documentation

operator<<

std::ostream & operator<< ( std::ostream & s, const Pentagon2 & pentagon )

friend

Overloaded.

Parameters

s	Stream.
pentagon	The pentagon.