 CGAL 5.0 - 2D and 3D Linear Geometry Kernel
CGAL::Segment_3< Kernel > Class Template Reference

#include <CGAL/Segment_3.h>

## Definition

An object s of the data type Segment_3 is a directed straight line segment in the three-dimensional Euclidean space $$\E^3$$, that is a straight line segment $$[p,q]$$ connecting two points $$p,q \in \R^3$$.

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_3

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

## Creation

Segment_3 (const Point_3< Kernel > &p, const Point_3< Kernel > &q)
introduces a segment s with source p and target q. More...

## Operations

bool operator== (const Segment_3< Kernel > &q) const
Test for equality: Two segments are equal, iff their sources and targets are equal.

bool operator!= (const Segment_3< Kernel > &q) const
Test for inequality.

Point_3< Kernelsource () const
returns the source of s.

Point_3< Kerneltarget () const
returns the target of s.

Point_3< Kernelmin () const
returns the point of s with smallest coordinate (lexicographically).

Point_3< Kernelmax () const
returns the point of s with largest coordinate (lexicographically).

Point_3< Kernelvertex (int i) const
returns source or target of s: vertex(0) returns the source, vertex(1) returns the target. More...

Point_3< Kernelpoint (int i) const
returns vertex(i).

Point_3< Kerneloperator[] (int i) const
returns vertex(i).

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

Vector_3< Kernelto_vector () const
returns the vector s.target() - s. More...

Direction_3< Kerneldirection () const
returns the direction from source to target.

Segment_3< Kernelopposite () const
returns a segment with source and target interchanged.

Line_3< Kernelsupporting_line () const
returns the line l passing through s. More...

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

bool has_on (const Point_3< 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.

Bbox_3 bbox () const
returns a bounding box containing s.

Segment_3< Kerneltransform (const Aff_transformation_3< Kernel > &t) const
returns the segment obtained by applying t on the source and the target of s.

## ◆ Segment_3()

template<typename Kernel >
 CGAL::Segment_3< Kernel >::Segment_3 ( const Point_3< Kernel > & p, const Point_3< Kernel > & q )

introduces a segment s with source p and target q.

It is directed from the source towards the target.

## ◆ supporting_line()

template<typename Kernel >
 Line_3 CGAL::Segment_3< Kernel >::supporting_line ( ) const

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.

## ◆ to_vector()

template<typename Kernel >
 Vector_3 CGAL::Segment_3< Kernel >::to_vector ( ) const

returns the vector s.target() - s.

source().

## ◆ vertex()

template<typename Kernel >
 Point_3 CGAL::Segment_3< Kernel >::vertex ( int i ) const

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.