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

CGAL 4.8 - 2D and 3D Linear Geometry Kernel

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Kernel::ConstructBisector_3 Concept Reference
Kernel Function Object Concepts

## Definition

Refines:
  `AdaptableFunctor` (with two arguments)

See Also
  `CGAL::bisector()`

## Operations
A model of this concept must provide:
Kernel::Plane_3 | operator() (const Kernel::Point_3 &p, const Kernel::Point_3 &q)
| constructs the bisector plane of `p` and `q`. More...
Kernel::Plane_3 | operator() (const Kernel::Plane_3 &h1, const Kernel::Plane_3 &h2)
| constructs the bisector of the two planes `h1` and `h2`. More...

## Member Function Documentation

Kernel::Plane_3 Kernel::ConstructBisector_3::operator() | ( | const Kernel::Point_3 & | p,
|  | const Kernel::Point_3 & | q
| ) |  |

constructs the bisector plane of `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.

Kernel::Plane_3 Kernel::ConstructBisector_3::operator() | ( | const Kernel::Plane_3 & | h1,
|  | const Kernel::Plane_3 & | 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.