Polygonal Class Reference

Polygons. More...

#include <polygon.h>

Public Member Functions
	Polygonal ()
	Create an empty polygon.
	Polygonal (Vector *, int)
	Create a polygon given an array of points. More...
	Polygonal (const QVector< Vector > &)
	Create a polygon. More...
	Polygonal (const QVector< Vector2 > &)
	Create a planar polygon. More...
	Polygonal (const QVector< Segment > &)
	Create a polygon from a set of segments. More...
	Polygonal (const Box2 &)
	Create a polygon from a box. More...
Box	GetBox () const
	Compute the bounding box. More...
void	Translate (const Vector &)
	Translate the polygon by a given vector. More...
void	Scale (const double &)
	Scale the polygon by a given factor. More...
void	Rotate (const Matrix &)
	Rotate the polygon. More...
void	Append (const Vector &)
	Add a vertex to the polygon. More...
Vector &	Vertex (int)
	Read write access to the i-th point.
Vector	Vertex (int) const
	Read only access to the i-th point.
int	Size () const
	Return the number of vertices of the polygon.
double	Length () const
	Compute the perimeter of the polygon.
double	PlanarLength () const
	Compute the perimeter of the projection of the polygon on the horizontal plane. More...
Vector	PointAtLength (const double &) const
	Return the position of the point on the polygon at a given length from the starting point. More...
Vector	NormalAtLength (const double &) const
	Return the normal at the position of the point on the polygon. More...
double	Area () const
	Compute the area of the polygon.
Vector	Centroid () const
	Compute the centroid of the polygon. More...
Vector	Center () const
	Compute the barycenter of the polygon. More...
void	Subdivide (int, QVector< Vector > &, QVector< int > &) const
	Create an n-adic subdivision of a polygon. More...

Protected Attributes
QVector< Vector >	q
	Array of vertices.

Friends
std::ostream &	operator<< (std::ostream &, const Polygonal &)
	Overloaded stream operator. More...

Detailed Description

Polygons.

The name of this class was chosen to avoid conflicts with a pre-defined windows open-GL class.

Note that polygons can be non-convex.

Constructor & Destructor Documentation

Polygonal() [1/5]

Polygonal::Polygonal ( Vector *  a, int  n  )

explicit

Create a polygon given an array of points.

Note that the points should be provided in trigonometric order.

Parameters

a	Array of vertices.
n	Size.

Polygonal() [2/5]

Polygonal::Polygonal ( const QVector< Vector > &  p )

explicit

Create a polygon.

Parameters

p	Array of points.

Polygonal() [3/5]

Polygonal::Polygonal ( const QVector< Vector2 > &  p )

explicit

Create a planar polygon.

Parameters

p	Array of points.

Polygonal() [4/5]

Polygonal::Polygonal ( const QVector< Segment > &  e )

explicit

Create a polygon from a set of segments.

The polygon is created from the first vertices of all segments.

Parameters

e	Array of segments.

Polygonal() [5/5]

Polygonal::Polygonal ( const Box2 &  box )

explicit

Create a polygon from a box.

Parameters

box

The box.

Member Function Documentation

Append()

void Polygonal::Append ( const Vector &  p )

inline

Add a vertex to the polygon.

Parameters

p

Point.

Center()

Vector Polygonal::Center

(

)

const

Compute the barycenter of the polygon.

Note that the barycenter is not the same as the centroid.

See also

Centroid

Centroid()

Vector Polygonal::Centroid

(

)

const

Compute the centroid of the polygon.

Note that the centroid is not the same as the barycenter.

See also

Barycenter

GetBox()

Box Polygonal::GetBox

(

)

const

Compute the bounding box.

The polygon should have some vertices, otherwise the result is undefined.

NormalAtLength()

Vector Polygonal::NormalAtLength

(

const double &

length

)

const

Return the normal at the position of the point on the polygon.

Parameters

length

Given length from the starting point.

PlanarLength()

double Polygonal::PlanarLength

(

)

const

Compute the perimeter of the projection of the polygon on the horizontal plane.

This is equivalent to projecting the polygon on the plane and computing its perimeter:

Polygonal p;
double length = Polygon2(p).Length();

PointAtLength()

Vector Polygonal::PointAtLength

(

const double &

length

)

const

Return the position of the point on the polygon at a given length from the starting point.

Parameters

length

Distance on the perimeter of the polygon. Note that it should be less than the perimeter of the polygon, still a modulo operation is performed inside.

Rotate()

void Polygonal::Rotate

(

const Matrix &

r

)

Rotate the polygon.

Parameters

r	Rotation matrix.

Scale()

void Polygonal::Scale

(

const double &

s

)

Scale the polygon by a given factor.

Parameters

s	Scaling factor.

Subdivide()

void Polygonal::Subdivide	(	int	n,
		QVector< Vector > &	vertex,
		QVector< int > &	index
	)		const

Create an n-adic subdivision of a polygon.

Note that the polygon should be star-shaped.

This function first computes the barycenter of the polygon and uses it to create triangles which are subdivided.

Parameters

n	Subdivision level.
vertex	Array of points.
index	Array of indexes defining the triangles.

Translate()

void Polygonal::Translate

(

const Vector &

t

)

Translate the polygon by a given vector.

Parameters

t

Vector.

Friends And Related Function Documentation

operator<<

std::ostream & operator<< ( std::ostream &  s, const Polygonal &  p  )

friend

Overloaded stream operator.

Parameters

s	Stream.
p	Polygon.