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CGAL 5.5.1 - 2D Convex Hulls and Extreme Points
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Functions

template<class ForwardIterator >
void CGAL::ch_e_point (ForwardIterator first, ForwardIterator beyond, ForwardIterator &e, const Traits &ch_traits=Default_traits)
 The function ch_e_point() finds a point of a given set of input points with maximal x coordinate. More...
 
template<class ForwardIterator >
void CGAL::ch_n_point (ForwardIterator first, ForwardIterator beyond, ForwardIterator &n, const Traits &ch_traits=Default_traits)
 The function ch_n_point() finds a point in a given set of input points with maximal y coordinate. More...
 
template<class ForwardIterator >
void CGAL::ch_ns_point (ForwardIterator first, ForwardIterator beyond, ForwardIterator &n, ForwardIterator &s, const Traits &ch_traits=Default_traits)
 The function ch_ns_point() finds the points of a given set of input points with minimal and maximal x coordinates. More...
 
template<class ForwardIterator >
void CGAL::ch_nswe_point (ForwardIterator first, ForwardIterator beyond, ForwardIterator &n, ForwardIterator &s, ForwardIterator &w, ForwardIterator &e, const Traits &ch_traits=Default_traits)
 The function ch_nswe_point() finds the four extreme points of a given set of input points using a linear scan of the input points. More...
 
template<class ForwardIterator >
void CGAL::ch_s_point (ForwardIterator first, ForwardIterator beyond, ForwardIterator &s, const Traits &ch_traits=Default_traits)
 The function ch_s_point() finds a points in a given set of input points with minimal y coordinates. More...
 
template<class ForwardIterator >
void CGAL::ch_we_point (ForwardIterator first, ForwardIterator beyond, ForwardIterator &w, ForwardIterator &e, const Traits &ch_traits=Default_traits)
 The function ch_we_point() finds two points of a given set of input points with minimal and maximal x coordinates. More...
 
template<class ForwardIterator >
void CGAL::ch_w_point (ForwardIterator first, ForwardIterator beyond, ForwardIterator &w, const Traits &ch_traits=Default_traits)
 The function ch_w_point() finds a point in a given set of input points with minimal x coordinate. More...
 

Function Documentation

◆ ch_e_point()

template<class ForwardIterator >
void CGAL::ch_e_point ( ForwardIterator  first,
ForwardIterator  beyond,
ForwardIterator e,
const Traits &  ch_traits = Default_traits 
)

#include <CGAL/ch_selected_extreme_points_2.h>

The function ch_e_point() finds a point of a given set of input points with maximal x coordinate.

It traverses the range [first,beyond). After execution, the value of e is an iterator in the range such that *e \ge_{xy} *it for all iterators it in the range.

The default traits class Default_traits is the kernel in which the value type of ForwardIterator is defined.

Requirements

Traits defines a type Traits::Less_xy_2 as described in the concept ConvexHullTraits_2 and the corresponding member function that returns an instance of this type.

See also
CGAL::ch_nswe_point()
CGAL::ch_n_point()
CGAL::ch_ns_point()
CGAL::ch_s_point()
CGAL::ch_w_point()
CGAL::ch_we_point()

◆ ch_n_point()

template<class ForwardIterator >
void CGAL::ch_n_point ( ForwardIterator  first,
ForwardIterator  beyond,
ForwardIterator n,
const Traits &  ch_traits = Default_traits 
)

#include <CGAL/ch_selected_extreme_points_2.h>

The function ch_n_point() finds a point in a given set of input points with maximal y coordinate.

It traverses the range [first,beyond). After execution, the value of n is an iterator in the range such that *n \ge_{yx} *it for all iterators it in the range.

The default traits class Default_traits is the kernel in which the type ForwardIterator::value_type is defined.

Requirements

Traits defines the type Traits::Less_yx_2 as specified in the concept ConvexHullTraits_2 and the corresponding member function that returns an instance of this type.

See also
CGAL::ch_e_point()
CGAL::ch_nswe_point()
CGAL::ch_ns_point()
CGAL::ch_s_point()
CGAL::ch_w_point()
CGAL::ch_we_point()

◆ ch_ns_point()

template<class ForwardIterator >
void CGAL::ch_ns_point ( ForwardIterator  first,
ForwardIterator  beyond,
ForwardIterator n,
ForwardIterator s,
const Traits &  ch_traits = Default_traits 
)

#include <CGAL/ch_selected_extreme_points_2.h>

The function ch_ns_point() finds the points of a given set of input points with minimal and maximal x coordinates.

It traverses the range [first,beyond). After execution, the value of n is an iterator in the range such that *n \ge_{yx} *it for all iterators it in the range. Similarly, for s the inequality *s \le_{yx} *it holds for all iterators in the range.

The default traits class Default_traits is the kernel in which the value type of ForwardIterator is defined.

Requirements

Traits defines the type Traits::Less_yx_2 as specified in the concept ConvexHullTraits_2 and the corresponding member function that returns an instance of this type.

See also
CGAL::ch_e_point()
CGAL::ch_nswe_point()
CGAL::ch_n_point()
CGAL::ch_s_point()
CGAL::ch_w_point()
CGAL::ch_we_point()

◆ ch_nswe_point()

template<class ForwardIterator >
void CGAL::ch_nswe_point ( ForwardIterator  first,
ForwardIterator  beyond,
ForwardIterator n,
ForwardIterator s,
ForwardIterator w,
ForwardIterator e,
const Traits &  ch_traits = Default_traits 
)

#include <CGAL/ch_selected_extreme_points_2.h>

The function ch_nswe_point() finds the four extreme points of a given set of input points using a linear scan of the input points.

That is, it determines the points with maximal y, minimal y, minimal x, and maximal x coordinates.

It traverses the range [first,beyond). After execution, the value of n is an iterator in the range such that *n \ge_{yx} *it for all iterators it in the range. Similarly, for s, w, and e the inequalities *s \le_{yx} *it, *w \le_{xy} *it, and *e \ge_{xy} *it hold for all iterators it in the range.

Requirements

Traits contains the following subset of types from the concept ConvexHullTraits_2 and their corresponding member functions that return instances of these types:

  • Traits::Less_xy_2,
  • Traits::Less_yx_2.

The default traits class Default_traits is the kernel in which the type ForwardIterator::value_type is defined.

See also
CGAL::ch_e_point()
CGAL::ch_n_point()
CGAL::ch_ns_point()
CGAL::ch_s_point()
CGAL::ch_w_point()
CGAL::ch_we_point()

◆ ch_s_point()

template<class ForwardIterator >
void CGAL::ch_s_point ( ForwardIterator  first,
ForwardIterator  beyond,
ForwardIterator s,
const Traits &  ch_traits = Default_traits 
)

#include <CGAL/ch_selected_extreme_points_2.h>

The function ch_s_point() finds a points in a given set of input points with minimal y coordinates.

It traverses the range [first,beyond). After execution, the value of s is an iterator in the range such that *s \le_{yx} *it for all iterators it in the range.

The default traits class Default_traits is the kernel in which the type ForwardIterator::value_type is defined.

Requirements

Traits defines the type Traits::Less_yx_2 as specified in the concept ConvexHullTraits_2 and the corresponding member function that returns an instance of this type.

See also
CGAL::ch_e_point()
CGAL::ch_nswe_point()
CGAL::ch_n_point()
CGAL::ch_ns_point()
CGAL::ch_w_point()
CGAL::ch_we_point()

◆ ch_w_point()

template<class ForwardIterator >
void CGAL::ch_w_point ( ForwardIterator  first,
ForwardIterator  beyond,
ForwardIterator w,
const Traits &  ch_traits = Default_traits 
)

#include <CGAL/ch_selected_extreme_points_2.h>

The function ch_w_point() finds a point in a given set of input points with minimal x coordinate.

It traverses the range [first,beyond). After execution, the value of w is an iterator in the range such that *w \le_{xy} *it for all iterators it in the range.

Requirements

Traits defines the type Traits::Less_xy_2 as specified in the concept ConvexHullTraits_2 and the corresponding member function that returns an instance of this type.

The default traits class Default_traits is the kernel in which the type ForwardIterator::value_type is defined.

See also
CGAL::ch_e_point()
CGAL::ch_nswe_point()
CGAL::ch_n_point()
CGAL::ch_ns_point()
CGAL::ch_s_point()
CGAL::ch_we_point()

◆ ch_we_point()

template<class ForwardIterator >
void CGAL::ch_we_point ( ForwardIterator  first,
ForwardIterator  beyond,
ForwardIterator w,
ForwardIterator e,
const Traits &  ch_traits = Default_traits 
)

#include <CGAL/ch_selected_extreme_points_2.h>

The function ch_we_point() finds two points of a given set of input points with minimal and maximal x coordinates.

It traverses the range [first,beyond). After execution, the value of w is an iterator in the range such that *w \le_{xy} *it for all iterators it in the range. Similarly, for e the inequality *e \ge_{xy} *it holds for all iterators in the range.

The default traits class Default_traits is the kernel in which the type ForwardIterator::value_type is defined.

Requirements

Traits defines the type Traits::Less_xy_2 as specified in the concept ConvexHullTraits_2 and the corresponding member function that returns an instance of this type.

See also
CGAL::ch_e_point()
CGAL::ch_nswe_point()
CGAL::ch_n_point()
CGAL::ch_ns_point()
CGAL::ch_s_point()
CGAL::ch_w_point()