Quadrangle2 Class Reference

Convex quadrangles in the plane. More...

#include <quadrangle.h>

Public Member Functions
	Quadrangle2 ()
	Empty.
	Quadrangle2 (const Vector2 &, const Vector2 &, const Vector2 &, const Vector2 &)
	Create a quadrangle. More...
	Quadrangle2 (const Quadrangle &)
	Create a planr quadrangle from a quadrangle. More...
	~Quadrangle2 ()
	Empty.
Vector2	Vertex (const double &, const double &) const
	Compute the position of a vertex inside the quadrangle. More...
bool	InverseBilinear (const Vector2 &, double &, double &) const
	Compute the inverse bi-linear coordinates of a point in the quadrangle. More...
Box2	GetBox () const
	Compute the box embedding the shape.
bool	Inside (const Vector2 &) const
	Check if a point is inside the quadrangle. More...
double	R (const Vector2 &) const
	Compute the squared distance between a point and the quadrangle. More...
Vector2	Normal (const Vector2 &) const
	Computes the normal vector between a point and a quadrangle. More...
void	Translate (const Vector2 &)
	Translate the quadrangle. More...
void	Scale (const double &)
	Scale the quadrangle. More...
void	Rotate (const Matrix2 &)
	Rotate the quadrangle. More...
void	Transform (const Frame2 &)
	Transform a quadrangle. More...
double	Perimeter () const
	Compute the perimeter of the quadrangle.
double	Area () const
	Compute the area of the quadrangle. More...
void	Draw (QGraphicsScene &, const QPen &=QPen(), const QBrush &=QBrush()) const
	Draw the quadrangle. More...

Static Public Member Functions
static bool	InverseBilinear (const Vector2 &, const Vector2 &, const Vector2 &, const Vector2 &, const Vector2 &, double &, double &)
	Inverse bilinear coordinates of a point in a quadrangle. More...

Protected Attributes
Vector2	p [4] = { Vector2::Null,Vector2::X,Vector2::X + Vector2::Y,Vector2::Y }
	Vertices, stored in counter-clockwize order.

Static Protected Attributes
static double	epsilon = 1.0e-10
	Internal \epsilon; constant.

Friends
std::ostream &	operator<< (std::ostream &, const Quadrangle2 &)
	Overloaded. More...

Detailed Description

Convex quadrangles in the plane.

Note that the quadrangle should be convex, otherwise some functions will not work properly.

Some functions such as the squared distance R() and normal Normal() are computationally intensive.

Constructor & Destructor Documentation

Quadrangle2() [1/2]

Quadrangle2::Quadrangle2 ( const Vector2 &  a, const Vector2 &  b, const Vector2 &  c, const Vector2 &  d  )

explicit

Create a quadrangle.

Parameters

a,b,c,d

Vertices (given in trigonometric order).

Quadrangle2() [2/2]

Quadrangle2::Quadrangle2 ( const Quadrangle &  q )

explicit

Create a planr quadrangle from a quadrangle.

Parameters

q	Quadrangle.

Member Function Documentation

Area()

double Quadrangle2::Area

(

)

const

Compute the area of the quadrangle.

The area is defined by Bretschneider's formula. The trigonometric adjustment in Bretschneider's formula for non-cyclicality of the quadrilateral can be rewritten non-trigonometrically in terms of the sides and the diagonals:

A²=(s-a)(s-b)(s-c)(s-d)-1/4(ac+bd+pq)(ac+bd-pq).

Draw()

void Quadrangle2::Draw	(	QGraphicsScene &	scene,
		const QPen &	pen = QPen(),
		const QBrush &	brush = QBrush()
	)		const

Draw the quadrangle.

Parameters

scene	Graphics scene.
pen	The pen.
brush	The brush, should the triangle be filled.

Inside()

bool Quadrangle2::Inside

(

const Vector2 &

q

)

const

Check if a point is inside the quadrangle.

Parameters

q

Point.

InverseBilinear() [1/2]

bool Quadrangle2::InverseBilinear ( const Vector2 &  a, const Vector2 &  b, const Vector2 &  c, const Vector2 &  d, const Vector2 &  p, double &  u, double &  v  )

static

Inverse bilinear coordinates of a point in a quadrangle.

Parameters

a,b,c,d	Vertices of the quadrangle.
p	Point.
u,v	Bi-linear coordinates.

InverseBilinear() [2/2]

bool Quadrangle2::InverseBilinear	(	const Vector2 &	q,
		double &	u,
		double &	v
	)		const

Compute the inverse bi-linear coordinates of a point in the quadrangle.

Parameters

q	Point.
u,v	Bi-linear coordinates.

Returns

Boolean that checks whether a solution has been found.

Normal()

Vector2 Quadrangle2::Normal

(

const Vector2 &

q

)

const

Computes the normal vector between a point and a quadrangle.

Let q the projection of p onto the box, the normal vector is defined as n=p-q. The returned vector is null if the point is inside the quadrangle.

Parameters

q

Point.

R()

double Quadrangle2::R

(

const Vector2 &

q

)

const

Compute the squared distance between a point and the quadrangle.

Parameters

q

Point.

See also

Normal()

Rotate()

void Quadrangle2::Rotate

(

const Matrix2 &

r

)

Rotate the quadrangle.

Parameters

r	Rotation matrix.

Scale()

void Quadrangle2::Scale

(

const double &

s

)

Scale the quadrangle.

Parameters

s	Scaling factor.

Transform()

void Quadrangle2::Transform

(

const Frame2 &

f

)

Transform a quadrangle.

Parameters

f	Transform.

Translate()

void Quadrangle2::Translate

(

const Vector2 &

t

)

Translate the quadrangle.

Parameters

t	Translation vector.

Vertex()

Vector2 Quadrangle2::Vertex	(	const double &	u,
		const double &	v
	)		const

Compute the position of a vertex inside the quadrangle.

Parameters

u,v	Parametric coordinates of the vertex.

Friends And Related Function Documentation

operator<<

std::ostream & operator<< ( std::ostream &  s, const Quadrangle2 &  q  )

friend

Overloaded.

Parameters

s	Stream.
q	The Quadrangle.