CGAL 4.7 - 2D and 3D Linear Geometry Kernel: CGAL::bisector()

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

CGAL 4.7 - 2D and 3D Linear Geometry Kernel

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Functions
CGAL::bisector()
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`. More...
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`. More...
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`. More...
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`. More...

## Function Documentation

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`.

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

Precondition
  `p` and `q` are not equal.

`#include <CGAL/global_functions.h>`

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`.

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`. This function requires that `Kernel::RT` supports the `sqrt()` operation.

`#include <CGAL/global_functions.h>`

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`.

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

Precondition
  `p` and `q` are not equal.

`#include <CGAL/global_functions.h>`

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`.

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`. This function requires that `Kernel::RT` supports the `sqrt()` operation.

`#include <CGAL/global_functions.h>`