mirror of https://github.com/CGAL/cgal
109 lines
3.6 KiB
Plaintext
109 lines
3.6 KiB
Plaintext
/// \defgroup PkgConvexHull2Ref 2D Convex Hulls and Extreme Points Reference
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/// \defgroup PkgConvexHull2Concepts Concepts
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/// \ingroup PkgConvexHull2Ref
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/// \defgroup PkgConvexHull2Traits Traits Classes
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/// \ingroup PkgConvexHull2Ref
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/// \defgroup PkgConvexHull2Functions Convex Hull Functions
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/// \ingroup PkgConvexHull2Ref
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/// \defgroup PkgConvexHull2Convexity Convexity Checking
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/// \ingroup PkgConvexHull2Ref
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/// \defgroup PkgConvexHull2Subsequence Hull Subsequence Functions
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/// \ingroup PkgConvexHull2Ref
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/// \defgroup PkgConvexHull2Extreme Extreme Point Functions
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/// \ingroup PkgConvexHull2Ref
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/*!
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\addtogroup PkgConvexHull2Ref
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\cgalPkgDescriptionBegin{2D Convex Hulls and Extreme Points,PkgConvexHull2}
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\cgalPkgPicture{Convex_hull_2/fig/convex_hull.png}
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\cgalPkgSummaryBegin
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\cgalPkgAuthors{Susan Hert and Stefan Schirra}
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\cgalPkgDesc{This package provides functions for computing convex hulls in two dimensions as well as functions for checking if sets of points are strongly convex are not. There are also a number of functions described for computing particular extreme points and subsequences of hull points, such as the lower and upper hull of a set of points.}
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\cgalPkgManuals{Chapter_2D_Convex_Hulls_and_Extreme_Points,PkgConvexHull2Ref}
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\cgalPkgSummaryEnd
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\cgalPkgShortInfoBegin
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\cgalPkgSince{1.0}
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\cgalPkgBib{cgal:hs-chep2}
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\cgalPkgLicense{\ref licensesGPL "GPL"}
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\cgalPkgDemo{See Bounding Volumes,bounding_volumes_2.zip}
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\cgalPkgShortInfoEnd
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\cgalPkgDescriptionEnd
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A subset \f$S \subseteq \mathbb{R}^2 \f$ is convex if for any two points `p` and `q`
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in the set the line segment with endpoints `p` and `q` is contained in \f$ S \f$.
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The convex hull of a set \f$ S \f$ is the smallest convex set containing \f$ S \f$.
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The convex hull of a set of points `P` is a convex polygon with vertices in `P`.
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A point in `P` is an extreme point (with respect to `P`) if it is a vertex
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of the convex hull of `P`.
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\cgal provides functions for computing convex hulls in two dimensions as well
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as functions for testing if a given set of points is strongly convex or not.
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There are also a number of functions available for computing particular extreme
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points in 2D and subsequences of the hull points, such as the lower hull or
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upper hull of a set of points.
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\cgalClassifedRefPages
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\cgalCRPSection{Assertions}
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The assertion flags for the convex hull and extreme point algorithms
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use `CH` in their names (<I>e.g.</I>, `CGAL_CH_NO_POSTCONDITIONS`).
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For the convex hull algorithms, the postcondition
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check tests only convexity (if not disabled), but not containment of the
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input points in the polygon or polyhedron defined by the output points.
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The latter is considered an expensive checking and can be enabled by
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defining `CGAL_CH_CHECK_EXPENSIVE`.
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\cgalCRPSection{Concepts}
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- `ConvexHullTraits_2`
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\cgalCRPSection{Traits Classes}
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- `CGAL::Convex_hull_constructive_traits_2<R>`
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- `CGAL::Convex_hull_traits_2<R>`
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- `CGAL::Convex_hull_traits_adapter_2<R,P>`
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\cgalCRPSection{Convex Hull Functions}
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- `CGAL::ch_akl_toussaint()`
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- `CGAL::ch_bykat()`
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- `CGAL::ch_eddy()`
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- `CGAL::ch_graham_andrew()`
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- `CGAL::ch_jarvis()`
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- `CGAL::ch_melkman()`
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- `CGAL::convex_hull_2()`
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\cgalCRPSection{Convexity Checking Functions}
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- `CGAL::is_ccw_strongly_convex_2()`
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- `CGAL::is_cw_strongly_convex_2()`
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\cgalCRPSection{Hull Subsequence Functions}
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- `CGAL::ch_graham_andrew_scan()`
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- `CGAL::ch_jarvis_march()`
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- `CGAL::lower_hull_points_2()`
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- `CGAL::upper_hull_points_2()`
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\cgalCRPSection{Extreme Point Functions}
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- `CGAL::ch_e_point()`
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- `CGAL::ch_nswe_point()`
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- `CGAL::ch_n_point()`
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- `CGAL::ch_ns_point()`
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- `CGAL::ch_s_point()`
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- `CGAL::ch_w_point()`
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- `CGAL::ch_we_point()`
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*/
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