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2D Segment (CGAL_Segment_2)

Definition

An object

s

of the data type CGAL_Segment_2 is a directed straight line segment in the two-dimensional Euclidean plane

E², i.e. a straight line segment

[p,q]

connecting two points

p,q

R². 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, is expensive, and may be inexact.

#include <CGAL/Segment_2.h>

Creation

CGAL_Segment_2<R> s ( CGAL_Point_2<R> p, CGAL_Point_2<R> q);
introduces a segment s with source $p$ and target $q$ . The segment is directed from the source towards the target.

Operations

bool s == q Test for equality: Two segments are equal, iff their sources and targets are equal.

bool s != q Test for inequality.

CGAL_Point_2<R> s.source () returns the source of s.

CGAL_Point_2<R> s.target () returns the target of s.

CGAL_Point_2<R> s.min () returns the point of s with lexicographically smallest coordinate.

CGAL_Point_2<R> s.max () returns the point of s with lexicographically largest coordinate.

CGAL_Point_2<R> s.vertex ( int i) 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.

CGAL_Point_2<R> s.point ( int i) returns vertex(i).

CGAL_Point_2<R> s [ int i] returns vertex(i).

R::FT s.squared_length ()
returns the squared length of s.

CGAL_Direction_2<R>
s.direction () returns the direction from source to target of s.

CGAL_Segment_2<R> s.opposite () returns a segment with source and target point interchanged.

CGAL_Line_2<R> s.supporting_line ()
returns the line $l$ passing through s. Line $l$ has the same orientation as segment s.

Predicates

bool s.is_degenerate () segment s is degenerate, if source and target are equal.

bool s.is_horizontal ()

bool s.is_vertical ()

bool s.has_on ( CGAL_Point_2<R> p)
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.

bool s.collinear_has_on ( CGAL_Point_2<R> p)
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.

Miscellaneous

CGAL_Bbox_2 s.bbox () returns a bounding box containing s.

CGAL_Segment_2<R> s.transform ( CGAL_Aff_transformation_2<R> t)
returns the segment obtained by applying $t$ on the source and the target of s.

Return to chapter: 2D Line, Ray and Segment

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The CGAL Project. Wed, January 20, 1999.

CGAL_Segment_2<R> s ( CGAL_Point_2<R> p, CGAL_Point_2<R> q);
	introduces a segment s with source $p$ and target $q$ . The segment is directed from the source towards the target.

bool	s == q	Test for equality: Two segments are equal, iff their sources and targets are equal.
bool	s != q	Test for inequality.
CGAL_Point_2<R>	s.source ()	returns the source of s.
CGAL_Point_2<R>	s.target ()	returns the target of s.
CGAL_Point_2<R>	s.min ()	returns the point of s with lexicographically smallest coordinate.
CGAL_Point_2<R>	s.max ()	returns the point of s with lexicographically largest coordinate.
CGAL_Point_2<R>	s.vertex ( int i)	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.
CGAL_Point_2<R>	s.point ( int i)	returns vertex(i).
CGAL_Point_2<R>	s [ int i]	returns vertex(i).
R::FT	s.squared_length ()
		returns the squared length of s.
CGAL_Direction_2<R>
	s.direction ()	returns the direction from source to target of s.
CGAL_Segment_2<R>	s.opposite ()	returns a segment with source and target point interchanged.
CGAL_Line_2<R>	s.supporting_line ()
		returns the line $l$ passing through s. Line $l$ has the same orientation as segment s.

bool	s.is_degenerate ()	segment s is degenerate, if source and target are equal.
bool	s.is_horizontal ()
bool	s.is_vertical ()
bool	s.has_on ( CGAL_Point_2<R> p)
		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.
bool	s.collinear_has_on ( CGAL_Point_2<R> p)
		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.

CGAL_Bbox_2	s.bbox ()	returns a bounding box containing s.
CGAL_Segment_2<R>	s.transform ( CGAL_Aff_transformation_2<R> t)
		returns the segment obtained by applying $t$ on the source and the target of s.