CGAL::Polygon_2<PolygonTraits_2, Container>

Definition

The class Polygon_2<PolygonTraits_2, Container> implements polygons. The Polygon_2<PolygonTraits_2, Container> is parameterized by a traits class and a container class. The latter can be any class that fulfills the requirements for an STL container. It defaults to the vector class.

#include <CGAL/Polygon_2.h>

Types

The following types denote iterators that allow to traverse the vertices and edges of a polygon. Since it is questionable whether a polygon should be viewed as a circular or as a linear data structure both circulators and iterators are defined. The circulators and iterators are non-mutable.¹ The iterator category is in all cases bidirectional, except for Vertex_iterator, which has the same iterator category as Container::iterator. N.B. In fact all of them should have the same iterator category as Container::iterator. However, due to compiler problems this is currently not possible.

For vertices we define

Their value type is Point_2.

For edges we define

Their value type is Segment_2.

Creation

Modifiers

Access Functions

Predicates

For convenience we provide the following Boolean functions:

Random access methods

Miscellaneous

Globally defined operators

template <class Traits, class Container1, class Container2>

template <class Traits, class Container1, class Container2>

template <class Transformation, class Traits, class Container>

I/O

The I/O operators are defined for iostream. The format for the iostream is an internal format.

The information output in the iostream is the number of points followed by the output of the coordinates of the vertices.

Implementation

The methods is_simple, is_convex, orientation, oriented_side, bounded_side, bbox, area, left_vertex, right_vertex, top_vertex and bottom_vertex are all implemented using the algorithms on sequences of 2D points. See the corresponding global functions for information about which algorithms were used and what complexity they have.

Example

The following code fragment creates a polygon and checks if it is convex.

File: examples/Polygon/Polygon.cpp

#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/Polygon_2.h>
#include <iostream>

typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
typedef K::Point_2 Point;
typedef CGAL::Polygon_2<K> Polygon_2;
using std::cout; using std::endl;


int main()
{
  Point points[] = { Point(0,0), Point(5.1,0), Point(1,1), Point(0.5,6)};
  Polygon_2 pgn(points, points+4);

  // check if the polygon is simple.
  cout << "The polygon is " <<
    (pgn.is_simple() ? "" : "not ") << "simple." << endl;

  // check if the polygon is convex
  cout << "The polygon is " <<
    (pgn.is_convex() ? "" : "not ") << "convex." << endl;

  return 0;
}

Footnotes