\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.8 - Inscribed Areas

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Inscribed_areas/extremal_polygon_2_perimeter.cpp
#include <CGAL/Simple_cartesian.h>
#include <CGAL/Polygon_2.h>
#include <CGAL/point_generators_2.h>
#include <CGAL/random_convex_set_2.h>
#include <CGAL/extremal_polygon_2.h>
#include <iostream>
#include <vector>
typedef double FT;
typedef CGAL::Simple_cartesian<FT> Kernel;
typedef Kernel::Point_2 Point;
typedef std::vector<int> Index_cont;
typedef CGAL::Polygon_2<Kernel> Polygon_2;
typedef CGAL::Random_points_in_square_2<Point> Generator;
int main() {
int n = 10;
int k = 5;
// generate random convex polygon:
Polygon_2 p;
CGAL::random_convex_set_2(n, std::back_inserter(p), Generator(1));
std::cout << "Generated Polygon:\n" << p << std::endl;
// compute maximum perimeter incribed k-gon of p:
Polygon_2 k_gon;
CGAL::maximum_perimeter_inscribed_k_gon_2(
p.vertices_begin(), p.vertices_end(), k, std::back_inserter(k_gon));
std::cout << "Maximum perimeter " << k << "-gon:\n"
<< k_gon << std::endl;
return 0;
}