Navigation: Up, Table of Contents, Bibliography, Index, Title Page

3D Segment (CGAL_Segment_3)

Definition

An object

s

of the data type CGAL_Segment_3 is a directed straight line segment in the three-dimensional Euclidean space

E³, i.e. a straight line segment

[p,q]

connecting two points

p,q  is in

R³. 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 not be exact.

#include <CGAL/Segment_3.h>

Creation

CGAL_Segment_3<R> s ( CGAL_Point_3<R> p, CGAL_Point_3<R> q);
introduces a segment s with source $p$ and target $q$ . It 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_3<R> s.source () returns the source of s.

CGAL_Point_3<R> s.target () returns the target of s.

CGAL_Point_3<R> s.min () returns the point of s with smallest coordinate (lexicographically).

CGAL_Point_3<R> s.max () returns the point of s with largest coordinate (lexicographically).

CGAL_Point_3<R> s.vertex ( int i) returns source or target of s: vertex(0) returns the source, vertex(1) returns the target. The parameter i is taken modulo 2, which gives easy access to the other vertex.

CGAL_Point_3<R> s.point ( int i) returns vertex(i).

CGAL_Point_3<R> s [ int i] returns vertex(i).

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

CGAL_Direction_3<R>
s.direction () returns the direction from source to target.

CGAL_Segment_3<R> s.opposite () returns a segment with source and target interchanged.

CGAL_Line_3<R> s.supporting_line ()
returns the line $l$ passing through s. Line $l$ has the same orientation as segment s, that is from the source to the target of s.

bool s.is_degenerate () segment s is degenerate, if source and target fall together.

bool s.has_on ( CGAL_Point_3<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.

CGAL_Bbox_3 s.bbox () returns a bounding box containing s.

CGAL_Segment_3<R> s.transform ( CGAL_Aff_transformation_3<R> t)
returns the segment obtained by applying $t$ on the source and the target of s.

Return to chapter: 3D Line, Ray and Segment

Navigation: Up, Table of Contents, Bibliography, Index, Title Page

The CGAL Project. Wed, January 20, 1999.

CGAL_Segment_3<R> s ( CGAL_Point_3<R> p, CGAL_Point_3<R> q);
	introduces a segment s with source $p$ and target $q$ . It 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_3<R>	s.source ()	returns the source of s.
CGAL_Point_3<R>	s.target ()	returns the target of s.
CGAL_Point_3<R>	s.min ()	returns the point of s with smallest coordinate (lexicographically).
CGAL_Point_3<R>	s.max ()	returns the point of s with largest coordinate (lexicographically).
CGAL_Point_3<R>	s.vertex ( int i)	returns source or target of s: vertex(0) returns the source, vertex(1) returns the target. The parameter i is taken modulo 2, which gives easy access to the other vertex.
CGAL_Point_3<R>	s.point ( int i)	returns vertex(i).
CGAL_Point_3<R>	s [ int i]	returns vertex(i).
R::FT	s.squared_length ()
		returns the squared length of s.
CGAL_Direction_3<R>
	s.direction ()	returns the direction from source to target.
CGAL_Segment_3<R>	s.opposite ()	returns a segment with source and target interchanged.
CGAL_Line_3<R>	s.supporting_line ()
		returns the line $l$ passing through s. Line $l$ has the same orientation as segment s, that is from the source to the target of s.
bool	s.is_degenerate ()	segment s is degenerate, if source and target fall together.
bool	s.has_on ( CGAL_Point_3<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.
CGAL_Bbox_3	s.bbox ()	returns a bounding box containing s.
CGAL_Segment_3<R>	s.transform ( CGAL_Aff_transformation_3<R> t)
		returns the segment obtained by applying $t$ on the source and the target of s.