mirror of https://github.com/CGAL/cgal
cleanup in CH3
This commit is contained in:
Andreas Fabri
parent
625f9f6cd7
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61d0f9b698
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@ -8,8 +8,8 @@ The class `Convex_hull_traits_3` serves as a traits class for the function
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function when `R` is a kernel with exact predicates but inexact constructions
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(note that the type `Plane_3` is a triple of `Point_3` and not `R::Plane_3`).
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\cgalModels ::ConvexHullTraits_3
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\cgalModels ::IsStronglyConvexTraits_3
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\cgalModels `ConvexHullTraits_3`
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\cgalModels `IsStronglyConvexTraits_3`
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*/
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template< typename R >
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@ -12,42 +12,27 @@ the convex hull is stored in `P`.
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\pre There are at least four points in the range
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[`first`, `last`) not all of which are collinear.
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The function `::convex_hull_3()` computes the convex hull of a given set of
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three-dimensional points
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Two versions of this function
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are available. The first can be used when it is known that the result
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will be a polyhedron and the second when a degenerate hull
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may also be possible.
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\cgalRequires `InputIterator::value_type` is equivalent to `Traits::Point_3`.
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\cgalRequires `Traits` is a model of the concept `ConvexHullTraits_3`.
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\tparam InputIterator must be an input iterator with a value type equivalent to `Traits::Point_3`.
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\tparam Polyhedron_3 must be a model of `ConvexHullPolyhedron_3`.
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\tparam Traits must be a model of the concept `ConvexHullTraits_3`.
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For the purposes of checking the postcondition that the convex hull
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is valid, `Traits` should also be a model of the concept
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`IsStronglyConvexTraits_3`.
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\cgalRequires `Polyhedron_3` is a model of `ConvexHullPolyhedron_3`.
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If the kernel `R` of the points determined by `InputIterator::value_type`
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If the kernel `R` of the points determined by the value type of `InputIterator`
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is a kernel with exact predicates but inexact constructions
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(in practice we check `R::Has_filtered_predicates_tag` is `Tag_true` and `R::FT` is a floating point type),
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then the default traits class of `::convex_hull_3()` is `Convex_hull_traits_3<R>`, and `R` otherwise.
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\sa `CGAL::convex_hull_incremental_3()`
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\sa `convex_hull_incremental_3()`
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### Implementation ###
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The algorithm implemented by these functions is the quickhull algorithm of
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Barnard <I>et al.</I> \cite bdh-qach-96.
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### Example ###
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The following program computes the convex hull of a set of 250 random
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points chosen from a sphere of radius 100. It then determines if the resulting
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hull is a segment or a polyhedron. Notice that the traits class is not
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necessary in the call to `::convex_hull_3()` but is used in the definition
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of `Polyhedron_3`.
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\cgalExample{Convex_hull_3/quickhull_3.cpp}
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*/
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@ -64,18 +49,17 @@ a triangle, or a polyhedron, is stored in `ch_object`.
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\attention This function does not compute the plane equations of the faces of `P`
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in case the result is a polyhedron.
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\cgalRequires `InputIterator::value_type` is equivalent to `Traits::Point_3`.
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\cgalRequires `Traits` is a model of the concept `ConvexHullTraits_3`.
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\tparam InputIterator must be an input iterator with a value type equivalent to `Traits::Point_3`.
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\tparam Traits must be model of the concept `ConvexHullTraits_3`.
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For the purposes of checking the postcondition that the convex hull
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is valid, `Traits` should also be a model of the concept
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`IsStronglyConvexTraits_3`.
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\cgalRequires `Traits` defines a type `Polyhedron_3` that is a model of
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`IsStronglyConvexTraits_3`. Furthermore, `Traits` must define a type `Polyhedron_3` that is a model of
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`ConvexHullPolyhedron_3`.
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If the kernel `R` of the points determined by `InputIterator::value_type`
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If the kernel `R` of the points determined by the value type of `InputIterator`
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is a kernel with exact predicates but inexact constructions
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(in practice we check `R::Has_filtered_predicates_tag` is `Tag_true` and `R::FT` is a floating point type),
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then the default traits class of `::convex_hull_3()` is `Convex_hull_traits_3<R>`, and `R` otherwise.
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then the default traits class of `convex_hull_3()` is `Convex_hull_traits_3<R>`, and `R` otherwise.
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*/
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@ -3,8 +3,7 @@ namespace CGAL {
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/*!
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\ingroup PkgConvexHull3Functions
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The function `convex_hull_3_to_polyhedron_3` fills a polyhedron with the convex hull
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of a set of 3D points contained in a 3D triangulation of \cgal.
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fills a polyhedron with the convex hull of a set of 3D points contained in a 3D triangulation of \cgal.
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The polyhedron `P` is cleared and the convex hull of the set of 3D points is stored in `P`.
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@ -12,10 +11,10 @@ The polyhedron `P` is cleared and the convex hull of the set of 3D points is sto
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\pre `T.dimension()`==3.
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\cgalRequires `Triangulation` is a \cgal 3D triangulation.
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\cgalRequires `Polyhedron` is an instantiation of `CGAL::Polyhedron_3<Traits>`.
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\tparam Triangulation is a \cgal 3D triangulation.
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\tparam Polyhedron is an instantiation of `CGAL::Polyhedron_3<Traits>`.
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\sa `CGAL::convex_hull_3`
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\sa `convex_hull_3`
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*/
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template <class Triangulation, class Polyhedron>
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void convex_hull_3_to_polyhedron_3(const Triangulation& T,Polyhedron& P);
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@ -12,20 +12,22 @@ used to determine the correctness of the resulting polyhedron.
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\attention This function is provided for completeness and educational
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purposes. When an efficient incremental implementation is needed,
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using `CGAL::Delaunay_triangulation_3` together with
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`CGAL::convex_hull_3_to_polyhedron_3` is highly recommended.
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using `Delaunay_triangulation_3` together with
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`convex_hull_3_to_polyhedron_3()` is highly recommended.
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\cgalRequires `Polyhedron` must provide a type `Polyhedron::Traits`
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\tparam InputIterator must be an input iterator where the value type must be
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`Polyhedron::Traits::Point`.
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\tparam Polyhedron must provide a type `Polyhedron::Traits`
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that defines the following types
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- `Polyhedron::Traits::R`, which is a model of
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the representation class `R` required by
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`CGAL::Convex_hull_d_traits_3<R>`
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`Convex_hull_d_traits_3<R>`
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- `Polyhedron::Traits::Point`
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\cgalRequires `InputIterator::value_type` must be the same as
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`Polyhedron::Traits::Point`.
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\sa `CGAL::convex_hull_3()`
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\sa `convex_hull_3()`
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\sa `Convex_hull_d`
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### Implementation ###
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@ -34,17 +36,6 @@ algorithm \cite cms-frric-93
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with `d` fixed to 3. The algorithm requires \f$ O(n^2)\f$ time in the
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worst case and \f$ O(n \log n)\f$ expected time.
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\sa `CGAL::Convex_hull_d<R>`
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### Example ###
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The following example computes the convex hull of a set of 250 random
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points chosen uniformly in a sphere of radius 100.
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\cgalExample{Convex_hull_3/incremental_hull_3.cpp}
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*/
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template <class InputIterator, class Polyhedron>
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void
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@ -3,9 +3,9 @@ namespace CGAL {
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/*!
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\ingroup PkgConvexityChecking
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The function `is_strongly_convex_3` determines if the vertices of a given polyhedron
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determines if the vertices of a given polyhedron
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represents a strongly convex set of points or not. A set of points is said
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to be strongly convex if it consists of only extreme points (<I>i.e.</I>,
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to be strongly convex if it consists of only extreme points (i.e.,
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vertices of the convex hull).
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The default traits class is the kernel in which the type
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@ -6,8 +6,15 @@
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/// \defgroup PkgConvexHull3Traits Traits Classes
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/// \ingroup PkgConvexHull3
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/// \defgroup PkgConvexHull3Functions Convex Hull Functions
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/// \ingroup PkgConvexHull3
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/*! \defgroup PkgConvexHull3Functions Convex Hull Functions
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\ingroup PkgConvexHull3
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The function `convex_hull_3()` computes the convex hull of a given set of
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three-dimensional points.
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Two versions of this function are available. The first can be used when it
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is known that the result will be a polyhedron and the second when a
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degenerate hull may also be possible.
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*/
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/// \defgroup PkgConvexityChecking Convexity Checking
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/// \ingroup PkgConvexHull3
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