CGAL 6.2 - 2D and 3D Linear Geometry Kernel: CGAL::bisector()

CGAL 6.2 - 2D and 3D Linear Geometry Kernel

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Functions
CGAL::bisector()
Reference Manual » Global Kernel Functions

##

## Functions
template<typename Kernel >
CGAL::Line_2< Kernel > | CGAL::bisector (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q)
| constructs the bisector line of the two points `p` and `q`.
template<typename Kernel >
CGAL::Line_2< Kernel > | CGAL::bisector (const CGAL::Line_2< Kernel > &l1, const CGAL::Line_2< Kernel > &l2)
| constructs the bisector of the two lines `l1` and `l2`.
template<typename Kernel >
CGAL::Plane_3< Kernel > | CGAL::bisector (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q)
| constructs the bisector plane of the two points `p` and `q`.
template<typename Kernel >
CGAL::Plane_3< Kernel > | CGAL::bisector (const CGAL::Plane_3< Kernel > &h1, const CGAL::Plane_3< Kernel > &h2)
| constructs the bisector of the two planes `h1` and `h2`.

## Function Documentation

## ◆ bisector() [1/4]

template<typename Kernel >

CGAL::Line_2< Kernel > CGAL::bisector | ( | const CGAL::Line_2< Kernel > & | l1,
|  | const CGAL::Line_2< Kernel > & | l2
| ) |  |

`#include <CGAL/Kernel/global_functions.h>`

constructs the bisector of the two lines `l1` and `l2`.

In the general case, the bisector has the direction of the vector which is the sum of the normalized directions of the two lines, and which passes through the intersection of `l1` and `l2`. If `l1` and `l2` are parallel, then the bisector is defined as the line which has the same direction as `l1`, and which is at the same distance from `l1` and `l2`. If `Kernel::FT` is not a model of `FieldWithSqrt` an approximation of the square root will be used in this function, impacting the exactness of the result even with an (exact) multiprecision number type.

## ◆ bisector() [2/4]

template<typename Kernel >

CGAL::Plane_3< Kernel > CGAL::bisector | ( | const CGAL::Plane_3< Kernel > & | h1,
|  | const CGAL::Plane_3< Kernel > & | h2
| ) |  |

`#include <CGAL/Kernel/global_functions.h>`

constructs the bisector of the two planes `h1` and `h2`.

In the general case, the bisector has a normal vector which has the same direction as the sum of the normalized normal vectors of the two planes, and passes through the intersection of `h1` and `h2`. If `h1` and `h2` are parallel, then the bisector is defined as the plane which has the same oriented normal vector as `l1`, and which is at the same distance from `h1` and `h2`. If `Kernel::FT` is not a model of `FieldWithSqrt` an approximation of the square root will be used in this function, impacting the exactness of the result even with an (exact) multiprecision number type.

## ◆ bisector() [3/4]

template<typename Kernel >

CGAL::Line_2< Kernel > CGAL::bisector | ( | const CGAL::Point_2< Kernel > & | p,
|  | const CGAL::Point_2< Kernel > & | q
| ) |  |

`#include <CGAL/Kernel/global_functions.h>`

constructs the bisector line of the two points `p` and `q`.

The bisector is oriented in such a way that `p` lies on its positive side.

Precondition
  `p != q`.

## ◆ bisector() [4/4]

template<typename Kernel >

CGAL::Plane_3< Kernel > CGAL::bisector | ( | const CGAL::Point_3< Kernel > & | p,
|  | const CGAL::Point_3< Kernel > & | q
| ) |  |

`#include <CGAL/Kernel/global_functions.h>`

constructs the bisector plane of the two points `p` and `q`.

The bisector is oriented in such a way that `p` lies on its positive side.

Precondition
  `p != q`.