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

CGAL 4.8 - 2D and 3D Linear Geometry Kernel

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Kernel::ConstructBisector_2 Concept Reference
Kernel Function Object Concepts

## Definition

Refines:
  AdaptableFunctor

See Also
  `CGAL::bisector()`

## Operations
A model of this concept must provide:
Kernel::Line_2 | operator() (const Kernel::Point_2 &p, const Kernel::Point_2 &q)
| constructs the bisector of `p` and `q`. More...
Kernel::Line_2 | operator() (const Kernel::Line_2 &l1, const Kernel::Line_2 &l2)
| constructs the bisector of the two lines `l1` and `l2`. More...

## Member Function Documentation

Kernel::Line_2 Kernel::ConstructBisector_2::operator() | ( | const Kernel::Point_2 & | p,
|  | const Kernel::Point_2 & | q
| ) |  |

constructs the bisector 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::Line_2 Kernel::ConstructBisector_2::operator() | ( | const Kernel::Line_2 & | l1,
|  | const Kernel::Line_2 & | 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.