CGAL::Segment_2< Kernel > Class Template Reference

#include <CGAL/Segment_2.h>

Definition

template<typename Kernel>
class CGAL::Segment_2< Kernel >

An object s of the data type Segment_2 is a directed straight line segment in the two-dimensional Euclidean plane \( \E^2\), i.e. a straight line segment \( [p,q]\) connecting two points \( p,q \in \mathbb{R}^2\). The segment is topologically closed, i.e. the end points belong to it. Point p is called the source and q is called the target of s. The length of s is the Euclidean distance between p and q. Note that there is only a function to compute the square of the length, because otherwise we had to perform a square root operation which is not defined for all number types, which is expensive, and may not be exact.

Is Model Of:

Kernel::Segment_2

Hashable if Kernel is a cartesian kernel and if Kernel::FT is Hashable

Creation
	Segment_2 (const Point_2< Kernel > &p, const Point_2< Kernel > &q)
	introduces a segment s with source p and target q. More...

Operations
bool	operator== (const Segment_2< Kernel > &q) const
	Test for equality: Two segments are equal, iff their sources and targets are equal. More...
bool	operator!= (const Segment_2< Kernel > &q) const
	Test for inequality. More...
Point_2< Kernel >	source () const
	returns the source of s. More...
Point_2< Kernel >	target () const
	returns the target of s. More...
Point_2< Kernel >	min () const
	returns the point of s with lexicographically smallest coordinate. More...
Point_2< Kernel >	max () const
	returns the point of s with lexicographically largest coordinate. More...
Point_2< Kernel >	vertex (int i) const
	returns source or target of s: vertex(0) returns the source of s, vertex(1) returns the target of s. More...
Point_2< Kernel >	point (int i) const
	returns vertex(i). More...
Point_2< Kernel >	operator[] (int i) const
	returns vertex(i). More...
Kernel::FT	squared_length () const
	returns the squared length of s. More...
Direction_2< Kernel >	direction () const
	returns the direction from source to target of s. More...
Vector_2< Kernel >	to_vector () const
	returns the vector s.target() - s.source(). More...
Segment_2< Kernel >	opposite () const
	returns a segment with source and target point interchanged. More...
Line_2< Kernel >	supporting_line () const
	returns the line l passing through s. More...

Predicates
bool	is_degenerate () const
	segment s is degenerate, if source and target are equal. More...
bool	is_horizontal () const
bool	is_vertical () const
bool	has_on (const Point_2< Kernel > &p) const
	A point is on s, iff it is equal to the source or target of s, or if it is in the interior of s. More...
bool	collinear_has_on (const Point_2< Kernel > &p) const
	checks if point p is on segment s. More...

Miscellaneous
Bbox_2	bbox () const
	returns a bounding box containing s. More...
Segment_2< Kernel >	transform (const Aff_transformation_2< Kernel > &t) const
	returns the segment obtained by applying t on the source and the target of s. More...

Constructor & Destructor Documentation

Segment_2()

template<typename Kernel >

CGAL::Segment_2< Kernel >::Segment_2	(	const Point_2< Kernel > &	p,
		const Point_2< Kernel > &	q
	)

introduces a segment s with source p and target q.

The segment is directed from the source towards the target.

Member Function Documentation

bbox()

template<typename Kernel >

Bbox_2 CGAL::Segment_2< Kernel >::bbox

(

)

const

returns a bounding box containing s.

collinear_has_on()

template<typename Kernel >

bool CGAL::Segment_2< Kernel >::collinear_has_on

(

const Point_2< Kernel > &

p

)

const

checks if point p is on segment s.

This function is faster than function has_on().

Precondition

p is on the supporting line of s.

direction()

template<typename Kernel >

Direction_2<Kernel> CGAL::Segment_2< Kernel >::direction

(

)

const

returns the direction from source to target of s.

has_on()

template<typename Kernel >

bool CGAL::Segment_2< Kernel >::has_on

(

const Point_2< Kernel > &

p

)

const

A point is on s, iff it is equal to the source or target of s, or if it is in the interior of s.

is_degenerate()

template<typename Kernel >

bool CGAL::Segment_2< Kernel >::is_degenerate

(

)

const

segment s is degenerate, if source and target are equal.

is_horizontal()

template<typename Kernel >

bool CGAL::Segment_2< Kernel >::is_horizontal

(

)

const

is_vertical()

template<typename Kernel >

bool CGAL::Segment_2< Kernel >::is_vertical

(

)

const

max()

template<typename Kernel >

Point_2<Kernel> CGAL::Segment_2< Kernel >::max

(

)

const

returns the point of s with lexicographically largest coordinate.

min()

template<typename Kernel >

Point_2<Kernel> CGAL::Segment_2< Kernel >::min

(

)

const

returns the point of s with lexicographically smallest coordinate.

operator!=()

template<typename Kernel >

bool CGAL::Segment_2< Kernel >::operator!=

(

const Segment_2< Kernel > &

q

)

const

Test for inequality.

operator==()

template<typename Kernel >

bool CGAL::Segment_2< Kernel >::operator==

(

const Segment_2< Kernel > &

q

)

const

Test for equality: Two segments are equal, iff their sources and targets are equal.

operator[]()

template<typename Kernel >

Point_2<Kernel> CGAL::Segment_2< Kernel >::operator[]

(

int

i

)

const

returns vertex(i).

opposite()

template<typename Kernel >

Segment_2<Kernel> CGAL::Segment_2< Kernel >::opposite

(

)

const

returns a segment with source and target point interchanged.

point()

template<typename Kernel >

Point_2<Kernel> CGAL::Segment_2< Kernel >::point

(

int

i

)

const

returns vertex(i).

source()

template<typename Kernel >

Point_2<Kernel> CGAL::Segment_2< Kernel >::source

(

)

const

returns the source of s.

squared_length()

template<typename Kernel >

Kernel::FT CGAL::Segment_2< Kernel >::squared_length

(

)

const

returns the squared length of s.

supporting_line()

template<typename Kernel >

Line_2<Kernel> CGAL::Segment_2< Kernel >::supporting_line

(

)

const

returns the line l passing through s.

Line l has the same orientation as segment s.

target()

template<typename Kernel >

Point_2<Kernel> CGAL::Segment_2< Kernel >::target

(

)

const

returns the target of s.

to_vector()

template<typename Kernel >

Vector_2<Kernel> CGAL::Segment_2< Kernel >::to_vector

(

)

const

returns the vector s.target() - s.source().

transform()

template<typename Kernel >

Segment_2<Kernel> CGAL::Segment_2< Kernel >::transform

(

const Aff_transformation_2< Kernel > &

t

)

const

returns the segment obtained by applying t on the source and the target of s.

vertex()

template<typename Kernel >

Point_2<Kernel> CGAL::Segment_2< Kernel >::vertex

(

int

i

)

const

returns source or target of s: vertex(0) returns the source of s, vertex(1) returns the target of s.

The parameter i is taken modulo 2, which gives easy access to the other vertex.