Loading [MathJax]/extensions/TeX/newcommand.js
\newcommand{\E}{\mathrm{E}} \newcommand{\A}{\mathrm{A}} \newcommand{\R}{\mathrm{R}} \newcommand{\N}{\mathrm{N}} \newcommand{\Q}{\mathrm{Q}} \newcommand{\Z}{\mathrm{Z}} \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }
CGAL 4.14.3 - 2D Convex Hulls and Extreme Points
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template<class ForwardIterator , class Traits >
bool CGAL::is_ccw_strongly_convex_2 (ForwardIterator first, ForwardIterator beyond, const Traits &ch_traits=Default_traits)
 The function is_ccw_strongly_convex_2() determines if a given sequence of points defines a counterclockwise-oriented, strongly convex polygon. More...
 
template<class ForwardIterator , class Traits >
bool CGAL::is_cw_strongly_convex_2 (ForwardIterator first, ForwardIterator beyond, const Traits &ch_traits=Default_traits)
 The function is_cw_strongly_convex_2() determines if a given sequence of points defines a clockwise-oriented, strongly convex polygon. More...
 

Function Documentation

◆ is_ccw_strongly_convex_2()

template<class ForwardIterator , class Traits >
bool CGAL::is_ccw_strongly_convex_2 ( ForwardIterator  first,
ForwardIterator  beyond,
const Traits &  ch_traits = Default_traits 
)

#include <CGAL/convexity_check_2.h>

The function is_ccw_strongly_convex_2() determines if a given sequence of points defines a counterclockwise-oriented, strongly convex polygon.

It returns true, iff the point elements in [first,beyond) form a counterclockwise-oriented strongly convex polygon.

A set of points is said to be strongly convex if it consists of only extreme points (i.e., vertices of the convex hull).

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

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::Equal_2,
  • Traits::Left_turn_2.
See also
CGAL::is_cw_strongly_convex_2()
CGAL::is_strongly_convex_3()

Implementation

The algorithm requires O(n) time for a set of n input points.

◆ is_cw_strongly_convex_2()

template<class ForwardIterator , class Traits >
bool CGAL::is_cw_strongly_convex_2 ( ForwardIterator  first,
ForwardIterator  beyond,
const Traits &  ch_traits = Default_traits 
)

#include <CGAL/convexity_check_2.h>

The function is_cw_strongly_convex_2() determines if a given sequence of points defines a clockwise-oriented, strongly convex polygon.

It returns true, iff the point elements in [first,beyond) form a clockwise-oriented strongly convex polygon.

A set of points is said to be strongly convex if it consists of only extreme points (i.e., vertices of the convex hull).

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

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::Equal_2,
  • Traits::Less_xy_2,
  • Traits::Left_turn_2.
See also
CGAL::is_ccw_strongly_convex_2()
CGAL::is_strongly_convex_3()

Implementation

The algorithm requires O(n) time for a set of n input points.