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

CGAL 4.3 - 2D Minkowski Sums

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Minkowski_sum_2/exact_inset.cpp
// Computing the exact inner offset of a polygon.
#include <CGAL/basic.h>
#ifndef CGAL_USE_CORE
#include <iostream>
int main ()
{
std::cout << "Sorry, this example needs CORE ..." << std::endl;
return (0);
}
#else
#include <CGAL/Cartesian.h>
#include <CGAL/CORE_algebraic_number_traits.h>
#include <CGAL/Arr_conic_traits_2.h>
#include <CGAL/offset_polygon_2.h>
#include <CGAL/Timer.h>
#include <iostream>
typedef CGAL::CORE_algebraic_number_traits Nt_traits;
typedef Nt_traits::Rational Rational;
typedef Nt_traits::Algebraic Algebraic;
struct Rat_kernel : public CGAL::Cartesian<Rational> {};
struct Alg_kernel : public CGAL::Cartesian<Algebraic> {};
struct Conic_traits_2 : public CGAL::Arr_conic_traits_2<Rat_kernel,
Alg_kernel,
Nt_traits> {};
typedef CGAL::Polygon_2<Rat_kernel> Polygon_2;
typedef CGAL::Gps_traits_2<Conic_traits_2> Gps_traits_2;
typedef Gps_traits_2::Polygon_2 Offset_polygon_2;
int main ()
{
// Open the input file.
std::ifstream in_file ("tight.dat");
if (! in_file.is_open())
{
std::cerr << "Failed to open the input file." << std::endl;
return (1);
}
// Read the input polygon.
Polygon_2 P;
in_file >> P;
in_file.close();
std::cout << "Read an input polygon with "
<< P.size() << " vertices." << std::endl;
// Compute the inner offset of the polygon.
Conic_traits_2 traits;
const Rational radius = 1;
std::list<Offset_polygon_2> inset_polygons;
std::list<Offset_polygon_2>::iterator iit;
CGAL::Timer timer;
timer.start();
inset_polygon_2 (P, radius, traits,
std::back_inserter (inset_polygons));
timer.stop();
std::cout << "The inset comprises "
<< inset_polygons.size() << " polygon(s)." << std::endl;
for (iit = inset_polygons.begin(); iit != inset_polygons.end(); ++iit)
{
std::cout << " Polygon with "
<< iit->size() << " vertices." << std::endl;
}
std::cout << "Inset computation took "
<< timer.time() << " seconds." << std::endl;
return (0);
}
#endif