/// \defgroup PkgConvexHull3Ref Reference Manual

/// \defgroup PkgConvexHull3Concepts Concepts
/// \ingroup PkgConvexHull3Ref

/// \defgroup PkgConvexHull3Traits Traits Classes
/// \ingroup PkgConvexHull3Ref

/*! \defgroup PkgConvexHull3Functions Convex Hull Functions
   \ingroup PkgConvexHull3Ref
The function `convex_hull_3()` computes the convex hull of a given set of
three-dimensional points.

Two versions of this function are available. The first can be used when it
is known that the result will be a polyhedron and the second when a
degenerate hull may also be possible.
*/

/// \defgroup PkgConvexityChecking Convexity Checking
/// \ingroup PkgConvexHull3Ref

/*!
\addtogroup PkgConvexHull3Ref
\todo fix or keep the `Default_traits`

\cgalPkgDescriptionBegin{3D Convex Hulls,PkgConvexHull3}
\cgalPkgPicture{Convex_hull_3/fig/bunny.png}
\cgalPkgSummaryBegin
\cgalPkgAuthors{Susan Hert and Stefan Schirra}
\cgalPkgDesc{This package provides functions  for computing convex hulls in three dimensions as well as functions for checking if sets of points are strongly convex or not. One can compute the convex hull of a set of points in three dimensions in two ways: using a static algorithm or using a triangulation to get a fully dynamic computation.}
\cgalPkgManuals{Chapter_3D_Convex_Hulls,PkgConvexHull3Ref}
\cgalPkgSummaryEnd
\cgalPkgShortInfoBegin
\cgalPkgSince{1.1}
\cgalPkgDependsOn{The dynamic algorithms depend on \ref PkgTriangulation3 "3D Triangulations".}
\cgalPkgBib{cgal:hs-ch3}
\cgalPkgLicense{\ref licensesGPL  "GPL"}
\cgalPkgDemo{CGAL Lab,CGALlab.zip}
\cgalPkgShortInfoEnd
\cgalPkgDescriptionEnd

A subset \f$S \subseteq \mathbb{R}^3 \f$ is convex if for any two points `p` and `q`
in the set the line segment with endpoints `p` and `q` is contained
in \f$S\f$. The convex hull of a set \f$ S \f$ is the smallest convex set containing
\f$ S \f$. The convex hull of a set of points `P` is a convex
polytope with vertices in `P`.  A point in `P` is an extreme point
(with respect to `P`) if it is a vertex of the convex hull of `P`.

\cgal provides functions for computing convex hulls in two, three
and arbitrary dimensions as well as functions for testing if a given set of
points in is strongly convex or not.  This chapter describes the functions
available for three dimensions.

\cgalCRPSection{Assertions}
For the convex hull algorithms, the postcondition
check tests only convexity (if not disabled), but not containment of the
input points in the polygon or polyhedron defined by the output points.
The latter is considered an expensive checking and can be enabled by
defining `CGAL_CHECK_EXPENSIVE`.

\cgalClassifedRefPages

\cgalCRPSection{Concepts}

- `ConvexHullTraits_3`
- `IsStronglyConvexTraits_3`

\cgalCRPSection{Traits Classes}

- `CGAL::Convex_hull_traits_3<R>`
- `CGAL::Extreme_points_traits_adapter_3`

\cgalCRPSection{Convex Hull Functions}

- `CGAL::convex_hull_3`
- `CGAL::extreme_points_3`
- `CGAL::make_extreme_points_traits_adapter`

\cgalCRPSection{Convexity Checking Function}

- `CGAL::is_strongly_convex_3`

\cgalCRPSection{Halfspace Intersection Functions}

- `CGAL::halfspace_intersection_3()`
- `CGAL::halfspace_intersection_with_constructions_3()`
- `CGAL::halfspace_intersection_interior_point_3()`

*/
