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

CGAL 4.8 - 2D and 3D Linear Geometry Kernel

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Functions
CGAL::orientation()
Global Kernel Functions

##

See Also
  `CGAL::collinear()`
  `CGAL::left_turn()`
  `CGAL::right_turn()`

## Functions
template<typename Kernel >
Orientation | CGAL::orientation (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r)
| returns `CGAL::LEFT_TURN`, if `r` lies to the left of the oriented line `l` defined by `p` and `q`, returns `CGAL::RIGHT_TURN` if `r` lies to the right of `l`, and returns `CGAL::COLLINEAR` if `r` lies on `l`.
template<typename Kernel >
Orientation | CGAL::orientation (const CGAL::Vector_2< Kernel > &u, const CGAL::Vector_2< Kernel > &v)
| returns `CGAL::LEFT_TURN` if `u` and `v` form a left turn, returns `CGAL::RIGHT_TURN` if `u` and `v` form a right turn, and returns `CGAL::COLLINEAR` if `u` and `v` are collinear.
template<typename Kernel >
Orientation | CGAL::orientation (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &s)
| returns `CGAL::POSITIVE`, if `s` lies on the positive side of the oriented plane `h` defined by `p`, `q`, and `r`, returns `CGAL::NEGATIVE` if `s` lies on the negative side of `h`, and returns `CGAL::COPLANAR` if `s` lies on `h`.
template<typename Kernel >
Orientation | CGAL::orientation (const CGAL::Vector_3< Kernel > &u, const CGAL::Vector_3< Kernel > &v, const CGAL::Vector_3< Kernel > &w)
| returns `CGAL::NEGATIVE` if `u`, `v` and `w` are negatively oriented, `CGAL::POSITIVE` if `u`, `v` and `w` are positively oriented, and `CGAL::COPLANAR` if `u`, `v` and `w` are coplanar.