Polygons in the plane. More...

#include <polygon.h>

Inheritance diagram for Polygon2:

Public Member Functions
	Polygon2 ()
	Create an empty polygon.

	Polygon2 (Vector2 *, int)
	Create a polygon given an array of points. More...

	Polygon2 (const Vector2 &, const Vector2 &, const Vector2 &)
	Create a triangle. More...

	Polygon2 (const Vector2 &, const Vector2 &, const Vector2 &, const Vector2 &)
	Create a quadrangle. More...

	Polygon2 (const QVector< Vector > &)
	Create a polygon. More...

	Polygon2 (const QVector< Vector2 > &)
	Create a polygon. More...

	Polygon2 (const Triangle2 &)
	Create a triangle. More...

	Polygon2 (const Box2 &)
	Create a polygon from a box. More...

	Polygon2 (const Hexagon2 &)
	Create a hexagon. More...

	Polygon2 (const Pentagon2 &)
	Create a pentagon. More...

	Polygon2 (const Quadrangle2 &)
	Create a quadrangle. More...

	Polygon2 (const Polygonal &)
	Create a planar polygon for a polygon. More...

Box2	GetBox () const
	Compute the bounding box of the polygon. More...

void	Translate (const Vector2 &)
	Translate the polygon by a given vector. More...

void	Scale (const double &)
	Scale the polygon by a given factor. More...

void	Rotate (const Matrix2 &)
	Rotate the polygon. More...

void	Append (const Vector2 &)
	Add a vertex to the polygon. More...

Vector2 &	Vertex (int)
	Read write access to the i-th point. More...

Vector2	Vertex (int) const
	Read only access to the i-th point. More...

QVector< Vector2 >	Vertices ()
	Get the array of vertices.

const QVector< Vector2 > &	Vertices () const
	Get the array of vertices.

Vector2	Edge (int) const
	Return the i-th edge, starting from the i-th vertex. More...

int	Size () const
	Return the number of vertices of the polygon.

double	Length () const
	Compute the perimeter of the polygon.

bool	IsConvex () const
	Check whether the polygon is convex.

Vector2	PointAtLength (const double &) const
	Return the position of the point on the polygon at a given length from the starting point. More...

Vector2	NormalAtLength (const double &) const
	Return the normal at the position of the point on the polygon. More...

bool	Inside (const Vector2 &) const
	Check if a point is inside or outside of the polygon. More...

double	R (const Vector2 &) const
	Compute the squared distance between a point and a polygon. More...

double	RC (const Vector2 &) const
	Compute the squared distance between a point and the contour of the polygon. More...

double	R (const Line2 &) const
	Compute the distance from a polygon to a line. More...

double	Signed (const Vector2 &) const
	Compute the signed distance between a point and a polygon. More...

bool	IntersectSegment (const Segment2 &) const
	Test if a segment intersects the polygon. More...

double	Area () const
	Compute the area of the polygon.

Vector2	Centroid () const
	Compute the centroid of the polygon. More...

Vector2	Center () const
	Compute the barycenter of the polygon. More...

void	Subdivide (int, QVector< Vector2 > &, QVector< int > &) const
	Create an n-adic subdivision of a polygon. More...

void	Expand (const double &)
	Expand the polygon by a given distance. More...

void	Draw (QGraphicsScene &, const QPen &=QPen(), const QBrush &=QBrush()) const
	Draw a polygon. More...

Polygon2	Resampled (const double &) const
	Resample the edges of the polygon. More...

QVector< int >	EarClip () const
	Compute a simple polygon triangulation using a ear clipping method. More...

Static Public Member Functions
static bool	Inside (const QVector< Polygon2 > &, const Vector2 &)
	Test if a point is inside the union of a set of polygons. More...

static double	R (const QVector< Polygon2 > &, const Vector2 &)
	Compute the squared distance between a point and a set of polygons. More...

Protected Attributes
QVector< Vector2 >	q
	Array of vertices.

Friends
std::ostream &	operator<< (std::ostream &, const Polygon2 &)
	Overloaded stream operator. More...

Detailed Description

Polygons in the plane.

Note that polygons can be non-convex or even self intersecting.

Constructor & Destructor Documentation

◆ Polygon2() [1/11]

Polygon2::Polygon2	(	Vector2 *	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.

◆ Polygon2() [2/11]

Polygon2::Polygon2	(	const Vector2 &	a,
		const Vector2 &	b,
		const Vector2 &	c
	)

explicit

Create a triangle.

Parameters

a,b,c Points.

◆ Polygon2() [3/11]

Polygon2::Polygon2	(	const Vector2 &	a,
		const Vector2 &	b,
		const Vector2 &	c,
		const Vector2 &	d
	)

explicit

Create a quadrangle.

Parameters

a,b,c,d Points.

◆ Polygon2() [4/11]

Polygon2::Polygon2 ( const QVector< Vector > & p )

explicit

Create a polygon.

Parameters

p	Array of points.

◆ Polygon2() [5/11]

Polygon2::Polygon2 ( const QVector< Vector2 > & p )

explicit

Create a polygon.

Parameters

p	Array of points.

◆ Polygon2() [6/11]

Polygon2::Polygon2 ( const Triangle2 & t )

explicit

Create a triangle.

Parameters

t Triangle.

◆ Polygon2() [7/11]

Polygon2::Polygon2 ( const Box2 & box )

explicit

Create a polygon from a box.

See also: Polygon2(const Hexagon2&)

Parameters

box The box.

◆ Polygon2() [8/11]

Polygon2::Polygon2 ( const Hexagon2 & hexagon )

explicit

Create a hexagon.

See also: Polygon2(const Box2&)

Parameters

hexagon Hexagon.

◆ Polygon2() [9/11]

Polygon2::Polygon2 ( const Pentagon2 & pentagon )

explicit

Create a pentagon.

See also: Polygon2(const Box2&)

Parameters

pentagon Pentagon.

◆ Polygon2() [10/11]

Polygon2::Polygon2 ( const Quadrangle2 & quadrangle )

explicit

Create a quadrangle.

See also: Polygon2(const Box2&)

Parameters

quadrangle Quadrangle.

◆ Polygon2() [11/11]

Polygon2::Polygon2 ( const Polygonal & p )

explicit

Create a planar polygon for a polygon.

Parameters

p	Array of points.

Member Function Documentation

◆ Append()

void Polygon2::Append ( const Vector2 & p )

inline

Add a vertex to the polygon.

Parameters

p Point.

◆ Center()

Vector2 Polygon2::Center ( ) const

Compute the barycenter of the polygon.

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

See also: Centroid

◆ Centroid()

Vector2 Polygon2::Centroid ( ) const

Compute the centroid of the polygon.

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

See also: Barycenter

◆ Draw()

void Polygon2::Draw	(	QGraphicsScene &	scene,
		const QPen &	pen = `QPen()`,
		const QBrush &	brush = `QBrush()`
	)		const

Draw a polygon.

Parameters

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

◆ EarClip()

QVector< int > Polygon2::EarClip ( ) const

Compute a simple polygon triangulation using a ear clipping method.

Returns: Indices triplet which define triangles.

◆ Edge()

Vector2 Polygon2::Edge ( int i ) const

inline

Return the i-th edge, starting from the i-th vertex.

Parameters

i Index.

◆ Expand()

void Polygon2::Expand ( const double & e )

Expand the polygon by a given distance.

Parameters

e	Expansion factor.

◆ GetBox()

Box2 Polygon2::GetBox ( ) const

Compute the bounding box of the polygon.

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

◆ Inside() [1/2]

bool Polygon2::Inside	(	const QVector< Polygon2 > &	s,
		const Vector2 &	p
	)

static

Test if a point is inside the union of a set of polygons.

Polygons should be non-intersecting. Polygons inside others will be considered as holes.

Parameters

s	Set of polygons.
p	Point.

◆ Inside() [2/2]

bool Polygon2::Inside ( const Vector2 & p ) const

Check if a point is inside or outside of the polygon.

Parameters

p Point.

◆ IntersectSegment()

bool Polygon2::IntersectSegment ( const Segment2 & s ) const

Test if a segment intersects the polygon.

Parameters

s Segment.

◆ NormalAtLength()

Vector2 Polygon2::NormalAtLength ( const double & length ) const

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

Parameters

length Perimeter length from the starting point.

◆ PointAtLength()

Vector2 Polygon2::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. It should be less than the perimeter of the polygon, still a modulo operation is performed inside.

◆ R() [1/3]

double Polygon2::R ( const Line2 & line ) const

Compute the distance from a polygon to a line.

Parameters

line Line.

◆ R() [2/3]

double Polygon2::R	(	const QVector< Polygon2 > &	s,
		const Vector2 &	p
	)

static

Compute the squared distance between a point and a set of polygons.

Parameters

p	Point.
s	Set of polygons.

◆ R() [3/3]

double Polygon2::R ( const Vector2 & p ) const

Compute the squared distance between a point and a polygon.

Parameters

p Point.

◆ RC()

double Polygon2::RC ( const Vector2 & p ) const

Compute the squared distance between a point and the contour of the polygon.

Parameters

p Point.

◆ Resampled()

Polygon2 Polygon2::Resampled ( const double & x ) const

Resample the edges of the polygon.

Generate points separated by a given input distance on the edges.

Parameters

x Distance

◆ Rotate()

void Polygon2::Rotate ( const Matrix2 & r )

Rotate the polygon.

Parameters

r	Rotation matrix.

◆ Scale()

void Polygon2::Scale ( const double & s )

Scale the polygon by a given factor.

Parameters

s	Scaling factor.

◆ Signed()

double Polygon2::Signed ( const Vector2 & p ) const

Compute the signed distance between a point and a polygon.

Parameters

p Point.

◆ Subdivide()

void Polygon2::Subdivide	(	int	n,
		QVector< Vector2 > &	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 Polygon2::Translate ( const Vector2 & t )

Translate the polygon by a given vector.

Parameters

t Vector.

◆ Vertex() [1/2]

Vector2 & Polygon2::Vertex ( int i )

inline

Read write access to the i-th point.

Parameters

i Index.

◆ Vertex() [2/2]

Vector2 Polygon2::Vertex ( int i ) const

inline

Read only access to the i-th point.

Parameters

i Index.

Friends And Related Function Documentation

◆ operator<<

std::ostream & operator<<	(	std::ostream &	s,
		const Polygon2 &	p
	)

friend

Overloaded stream operator.

Parameters

s	Stream.
p	Polygon.

Public Member Functions

Static Public Member Functions

Protected Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ Polygon2() [1/11]

◆ Polygon2() [2/11]

◆ Polygon2() [3/11]

◆ Polygon2() [4/11]

◆ Polygon2() [5/11]

◆ Polygon2() [6/11]

◆ Polygon2() [7/11]

◆ Polygon2() [8/11]

◆ Polygon2() [9/11]

◆ Polygon2() [10/11]

◆ Polygon2() [11/11]

Member Function Documentation

◆ Append()

◆ Center()

◆ Centroid()

◆ Draw()

◆ EarClip()

◆ Edge()

◆ Expand()

◆ GetBox()

◆ Inside() [1/2]

◆ Inside() [2/2]

◆ IntersectSegment()

◆ NormalAtLength()

◆ PointAtLength()

◆ R() [1/3]

◆ R() [2/3]

◆ R() [3/3]

◆ RC()

◆ Resampled()

◆ Rotate()

◆ Scale()

◆ Signed()

◆ Subdivide()

◆ Translate()

◆ Vertex() [1/2]

◆ Vertex() [2/2]

Friends And Related Function Documentation

◆ operator<<