CGAL 5.1.2 - Optimal Distances
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The optimization code uses infix OPTIMISATION
in the assertions, e.g. defining the compiler flag CGAL_OPTIMISATION_NO_PRECONDITIONS
switches precondition checking off, cf. Section Checks.
CGAL::Polytope_distance_d<Traits>
CGAL::Polytope_distance_d_traits_2<K,ET,NT>
CGAL::Polytope_distance_d_traits_3<K,ET,NT>
CGAL::Polytope_distance_d_traits_d<K,ET,NT>
PolytopeDistanceDTraits
Modules | |
Concepts | |
Classes | |
class | CGAL::Polytope_distance_d< Traits > |
An object of the class Polytope_distance_d represents the (squared) distance between two convex polytopes, given as the convex hulls of two finite point sets in \( d\)-dimensional Euclidean space \( \E^d\). More... | |
class | CGAL::Polytope_distance_d_traits_2< K, ET, NT > |
The class Polytope_distance_d_traits_2 is a traits class for the \( d\)-dimensional optimisation algorithms using the two-dimensional CGAL kernel. More... | |
class | CGAL::Polytope_distance_d_traits_3< K, ET, NT > |
The class Polytope_distance_d_traits_3 is a traits class for the \( d\)-dimensional optimisation algorithms using the three-dimensional CGAL kernel. More... | |
class | CGAL::Polytope_distance_d_traits_d< K, ET, NT > |
The class Polytope_distance_d_traits_d is a traits class for the \( d\)-dimensional optimisation algorithms using the \( d\)-dimensional CGAL kernel. More... | |
class | CGAL::Width_3< Traits > |
Given a set of points \( \mathcal{S}=\left\{p_1,\ldots , p_n\right\}\) in \( \mathbb{R}^3\). More... | |
class | CGAL::Width_default_traits_3< K > |
The class Width_default_traits_3 is a traits class for Width_3<Traits> using the three-dimensional CGAL kernel. More... | |
Functions | |
template<class RandomAccessIterator , class OutputIterator , class Traits > | |
OutputIterator | CGAL::all_furthest_neighbors_2 (RandomAccessIterator points_begin, RandomAccessIterator points_end, OutputIterator o, Traits t=Default_traits) |
computes all furthest neighbors for the vertices of the convex polygon described by the range [points_begin , points_end ), writes their indices (relative to points_begin ) to o the furthest neighbor of points_begin[i] is points_begin[i-th number written to o] and returns the past-the-end iterator of this sequence. More... | |
OutputIterator CGAL::all_furthest_neighbors_2 | ( | RandomAccessIterator | points_begin, |
RandomAccessIterator | points_end, | ||
OutputIterator | o, | ||
Traits | t = Default_traits |
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#include <CGAL/all_furthest_neighbors_2.h>
computes all furthest neighbors for the vertices of the convex polygon described by the range [points_begin
, points_end
), writes their indices (relative to points_begin
) to o
the furthest neighbor of points_begin[i]
is points_begin[i-th number written to o]
and returns the past-the-end iterator of this sequence.
The function all_furthest_neighbors_2()
computes all furthest neighbors for the vertices of a convex polygon \( P\), i.e. for each vertex \( v\) of \( P\) a vertex \( f_v\) of \( P\) such that the distance between \( v\) and \( f_v\) is maximized.
points_begin
, points_end
) form the boundary of a convex polygon \( P\) (oriented clock- or counterclockwise).The geometric types and operations to be used for the computation are specified by the traits class parameter t
. This parameter can be omitted if RandomAccessIterator
refers to a point type from a Kernel
. In this case, the kernel is used as default traits class.
Requires
t
is specified explicitly, Traits
is a model for AllFurthestNeighborsTraits_2
. RandomAccessIterator
is Traits::Point_2
or, if t
is not specified explicitly, K::Point_2
where K
is a model for Kernel
. OutputIterator
accepts int
as value type. AllFurthestNeighborsTraits_2
CGAL::monotone_matrix_search()
Implementation
The implementation uses monotone matrix search [1]. Its runtime complexity is linear in the number of vertices of \( P\).
Example
The following code generates a random convex polygon p
with ten vertices, computes all furthest neighbors and writes the sequence of their indices (relative to points_begin
) to cout
(e.g. a sequence of 4788911224
means the furthest neighbor of points_begin[0]
is points_begin[4]
, the furthest neighbor of points_begin[1]
is points_begin[7]
etc.).
File Polytope_distance_d/all_furthest_neighbors_2.cpp