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@ -146,7 +146,7 @@ such that the alpha shape satisfies the following two properties
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(i) all data points are either on the boundary or in the interior
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of the regularized version of the alpha shape (no singular faces).
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(ii) The number of components is equal or less than a given number .<BR>
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(ii) The number of components is equal or less than a given number.
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The current implementation is static, that is after its construction
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points cannot be inserted or removed.
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@ -69,7 +69,7 @@ in the chapter on 3D Boolean operations on Nef
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polyhedra \ref chapterNef3.
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Usually, an instance of `Nef_polyhedron_3` does not contain any
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redundant items. However, the function `convex_decomposition_3`
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redundant items. However, the function `::convex_decomposition_3`
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subdivides selected volumes of a given `Nef_polyhedron_3` by
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selected facets. These additional facets are therefore redundant,
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i.e., their insertion alters the representation of the polyhedron, but
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@ -10,7 +10,7 @@ and the plane equations of each face are not computed.
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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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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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@ -44,7 +44,7 @@ and for the second, it is required that
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For both versions, if the kernel `R` of the points determined by `InputIterator::value_type`
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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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\sa `CGAL::convex_hull_incremental_3`
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\sa `CGAL::ch_eddy`
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@ -62,7 +62,7 @@ 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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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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@ -192,7 +192,7 @@ Convex_hull_d<R>(int d, R Kernel = R());
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/// @{
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/*!
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returns the dimension of ambient space
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returns the dimension of ambient space.
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*/
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int dimension() ;
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@ -42,7 +42,7 @@ The convex hull class is parameterized by a traits class that provides
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model <I>e.g.</I>, `Homogeneous<RT>` or `Cartesian<FT>` for use
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with `Convex_hull_d`, where the dimension is fixed to three.
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The validity of the computed convex hull can be checked using the
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member function `is_valid`, which implements the algorithm
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member function `::is_valid`, which implements the algorithm
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of Mehlhorn <I>et al.</I>\cite mnssssu-cgpvg-96 to determine if
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the vertices of a given polytope constitute a strongly convex point
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set or not.
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@ -40,7 +40,7 @@ distributed in a sphere (`Random_points_in_sphere_3`)
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or cube (`Random_points_in_cube_3`) or on the boundary of a sphere
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(`Random_points_on_sphere_3`).
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For generating 3D grid points, we provide the function
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`points_on_cube_grid_3` that writes to
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`::points_on_cube_grid_3` that writes to
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an output iterator.
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For higher dimensions, input iterators are provided for random points uniformly
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@ -316,12 +316,12 @@ parameters::internal::Perturb_options perturb = parameters::perturb(),
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parameters::internal::Exude_options exude = parameters::exude());
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\endcode
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The function `make_mesh_3` generates from scratch a mesh
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The function `::make_mesh_3` generates from scratch a mesh
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of the input domain, while
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the function `refine_mesh_3` refines
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the function `::refine_mesh_3` refines
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an existing mesh of the input domain. Note that as the protection
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of 0- and 1-dimensional features does not rely on Delaunay
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refinement, the function `refine_mesh_3` has no parameter
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refinement, the function `r::efine_mesh_3` has no parameter
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to preserve features.
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## The data structure ##
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@ -499,8 +499,8 @@ appropriate values of these types:
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These parameters are optional and can be passed in any order.
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If one parameter is not passed the default value is used. By default,
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only the perturber and the exuder are activated.
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Note that whatever may be the optimization processes activated by `make_mesh_3`
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or `refine_mesh_3`,
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Note that whatever may be the optimization processes activated by `::make_mesh_3`
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or `::refine_mesh_3`,
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they are always launched in the order that is a suborder
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of the following:
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`odt smoother`, `Lloyd smoother`, `perturber` and
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@ -657,7 +657,7 @@ domain. We add by hand the intersection of the spheres as a sharp feature.
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\anchor Mesh_3_subsection_examples_optimization
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In the previous examples, the mesh generation is launched through a call
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`make_mesh_3(domain,criteria)` with a minimal number of parameters. In such cases,
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`::make_mesh_3(domain,criteria)` with a minimal number of parameters. In such cases,
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the default optimization strategy is applied: after the Delaunay refinement process
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two optimization steps are performed, a perturbation and a sliver exudation.
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The following examples show how to disable default optimization steps
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@ -671,10 +671,10 @@ a perturbation phase which is launched with no time bound
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and an objective of 10 degrees for the minimum dihedral angle
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of the mesh.
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The example shows two ways of achieving the same result. The first way
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issues a single call to `make_mesh_3` with the required optimization
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process activated and tuned. In the second way, `make_mesh_3` is first called
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issues a single call to `::make_mesh_3` with the required optimization
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process activated and tuned. In the second way, `::make_mesh_3` is first called
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without any optimization process and the resulting mesh is next optimized
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through a call to `perturb_mesh_3` with tuned parameters.
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through a call to `::perturb_mesh_3` with tuned parameters.
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\cgalexample{Mesh_3/mesh_optimization_example.cpp}
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@ -398,7 +398,7 @@ Therefore, the `Exact_predicates_inexact_constructions_kernel` should be used.
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\cgalexample{Straight_skeleton_2/Low_level_API.cpp}
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## Exterior Skeletons and Exterior Offset contours ##
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## Exterior Skeletons and Exterior Offset Contours ##
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This \cgal package can only construct the straight skeleton and offset contours in the <I>interior</I> of a polygon with holes. However, constructing exterior skeletons and exterior offsets is possible:
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