\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.8 - 2D and 3D Linear Geometry Kernel

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CGAL::Segment_2< Kernel > Class Template Reference
2D Kernel Objects

`#include <CGAL/Segment_2.h>`

## Definition

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.

See Also
  `Kernel::Segment_2`

## 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.
bool | operator!= (const Segment_2< Kernel > &q) const
| Test for inequality.
Point_2< Kernel > | source () const
| returns the source of `s`.
Point_2< Kernel > | target () const
| returns the target of `s`.
Point_2< Kernel > | min () const
| returns the point of `s` with lexicographically smallest coordinate.
Point_2< Kernel > | max () const
| returns the point of `s` with lexicographically largest coordinate.
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)`.
Point_2< Kernel > | operator[] (int i) const
| returns `vertex(i)`.
Kernel::FT | squared_length () const
| returns the squared length of `s`.
Direction_2< Kernel > | direction () const
| returns the direction from source to target of `s`.
Vector_2< Kernel > | to_vector () const
| returns the vector `s.target()` - `s.source()`.
Segment_2< Kernel > | opposite () const
| returns a segment with source and target point interchanged.
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.
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`.
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`.
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`.

## Constructor & Destructor Documentation

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

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`.

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`.

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.