Segment2 Class Reference

Segments in the plane. More...

#include <segment.h>

Inheritance diagram for Segment2:

Public Member Functions
	Segment2 ()
	Empty.
	Segment2 (const Vector2 &, const Vector2 &)
	Creates a planar segment given end vertices. More...
	Segment2 (const Segment &)
	Creates a planar segment given a three dimensional segment. More...
	~Segment2 ()
	Empty.
Vector2	Vertex (int) const
	Return one of the end vertex of the axis.
Vector2 &	Vertex (int)
	Return one of the end vertex of the axis.
Vector2	VertexAt (const double &) const
	Compute a point on the segment. More...
Vector2	Center () const
	Compute the center of the segment.
Vector2	GetAxis () const
	Returns the normalized axis vector.
Box2	GetBox () const
	Compute the bounding box of the segment.
Vector2	Orthogonal () const
	Compute an orthogonal vector to the segment. More...
void	Translate (const Vector2 &)
	Translates a segment. More...
void	Rotate (const Matrix2 &)
	Translates a segment. More...
void	Scale (const double &)
	Uniformly scales a segment. More...
double	Length () const
	Return axis length.
void	Draw (QGraphicsScene &, const QPen &=QPen()) const
	Draw a segment. More...
void	DrawArrow (QGraphicsScene &, const double &, const QPen &=QPen(), const QBrush &=QBrush()) const
	Draw a segment as an arrow. More...
double	R (const Vector2 &) const
	Compute the squared distance to the segment. More...
double	R (const Vector2 &, double &) const
	Compute the squared distance to the axis edge characterized by its end points. More...
Vector2	Normal (const Vector2 &) const
	Compute the normal vector between a point and its projection onto the segment. More...
bool	Intersect (const Segment2 &) const
	Test if two segments intersect. More...
bool	IntersectOpen (const Segment2 &) const
	This functions tests if two segments intersect. More...
bool	Intersection (const Segment2 &, Vector2 &) const
	Compute the intersection between two segments. More...

Static Public Member Functions
static Vector2	Intersect (const Vector2 &, const Vector2 &, const double, const double, const double=0.0)
	Compute the intersection between the line f(x)=y and a line such that f(a)=va and f(b)=vb, on the segment ab. More...

Static Public Attributes
static constexpr const double	epsilon = 1e-8
	Epsilon value for intersection test.

Protected Attributes
Vector2	b = Vector2::X
	End vertices of the segment.

Friends
std::ostream &	operator<< (std::ostream &, const Segment2 &)
	Overloaded. More...
bool	operator== (const Segment2 &, const Segment2 &)
	Compare two segments. More...

Detailed Description

Segments in the plane.

A segment stores its end vertices.

Constructor & Destructor Documentation

Segment2() [1/2]

Segment2::Segment2 ( const Vector2 &  a, const Vector2 &  b  )

inlineexplicit

Creates a planar segment given end vertices.

Parameters

a,b	End vertices of the segment.

Segment2() [2/2]

Segment2::Segment2 ( const Segment &  s )

inlineexplicit

Creates a planar segment given a three dimensional segment.

Parameters

s

Segment.

Member Function Documentation

Draw()

void Segment2::Draw	(	QGraphicsScene &	scene,
		const QPen &	pen = QPen()
	)		const

Draw a segment.

Parameters

scene	Graphics scene.
pen	The pen.

DrawArrow()

void Segment2::DrawArrow	(	QGraphicsScene &	scene,
		const double &	s,
		const QPen &	pen = QPen(),
		const QBrush &	brush = QBrush()
	)		const

Draw a segment as an arrow.

Parameters

scene	Graphics scene.
pen	The pen.
brush	The brush.
s	Size of the arrow head.

Intersect() [1/2]

bool Segment2::Intersect

(

const Segment2 &

segment

)

const

Test if two segments intersect.

This function computes the intersection and test the intersection parameters. Two segments that share an end point are detected as intersecting.

Parameters

segment

Other segment.

Intersect() [2/2]

Vector2 Segment2::Intersect ( const Vector2 &  a, const Vector2 &  b, const double  va, const double  vb, const double  y = 0.0  )

static

Compute the intersection between the line f(x)=y and a line such that f(a)=va and f(b)=vb, on the segment ab.

Parameters

a,b	Points.
va,vb	Values.
y	Threshold.

Intersection()

bool Segment2::Intersection	(	const Segment2 &	e,
		Vector2 &	p
	)		const

Compute the intersection between two segments.

Parameters

e	Other segment.
p	Intersection point.

IntersectOpen()

bool Segment2::IntersectOpen

(

const Segment2 &

segment

)

const

This functions tests if two segments intersect.

The algorithm avoids the computation of the intersection. Instead, it checks whether the two points of one segment lie on the same half space defined by the line of the other segment.

Contrary to bool Intersect(const Segment2&), two segments that share one point are not detected as intersecting.

Parameters

segment

Other segment.

Normal()

Vector2 Segment2::Normal

(

const Vector2 &

p

)

const

Compute the normal vector between a point and its projection onto the segment.

Parameters

p

Point.

Orthogonal()

Vector2 Segment2::Orthogonal

(

)

const

Compute an orthogonal vector to the segment.

The returned vector is not normalized.

R() [1/2]

double Segment2::R

(

const Vector2 &

p

)

const

Compute the squared distance to the segment.

Parameters

p

Point.

R() [2/2]

double Segment2::R	(	const Vector2 &	p,
		double &	s
	)		const

Compute the squared distance to the axis edge characterized by its end points.

Parameters

p	Point.
s	Linear coefficient corresponding to the projection of argument point p onto the edge.

Rotate()

void Segment2::Rotate

(

const Matrix2 &

r

)

Translates a segment.

Parameters

r	Rotation matrix.

Scale()

void Segment2::Scale

(

const double &

s

)

Uniformly scales a segment.

Parameters

s	Scaling factor.

Translate()

void Segment2::Translate

(

const Vector2 &

t

)

Translates a segment.

Parameters

t	Translation vector.

VertexAt()

Vector2 Segment2::VertexAt ( const double &  t ) const

inline

Compute a point on the segment.

Parameters

t	Interpolation parameter.

Friends And Related Function Documentation

operator<<

std::ostream & operator<< ( std::ostream &  s, const Segment2 &  segment  )

friend

Overloaded.

Parameters

s	Stream.
segment	The segment.

operator==

bool operator== ( const Segment2 &  a, const Segment2 &  b  )

friend

Compare two segments.

Parameters

a,b

Segments.