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

CGAL 4.3 - 2D Minkowski Sums

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Minkowski_sum_2/approx_offset.cpp
// Computing the approximated offset of a polygon.
#include "ms_rational_nt.h"
#include <CGAL/Lazy_exact_nt.h>
#include <CGAL/Cartesian.h>
#include <CGAL/approximated_offset_2.h>
#include <CGAL/offset_polygon_2.h>
#include <CGAL/Timer.h>
#include <iostream>
typedef CGAL::Lazy_exact_nt<Number_type> Lazy_exact_nt;
struct Kernel : public CGAL::Cartesian<Lazy_exact_nt> {};
typedef CGAL::Polygon_2<Kernel> Polygon_2;
typedef CGAL::Gps_circle_segment_traits_2<Kernel> Gps_traits_2;
typedef Gps_traits_2::Polygon_2 Offset_polygon_2;
typedef Gps_traits_2::Polygon_with_holes_2 Offset_polygon_with_holes_2;
int main ()
{
// Open the input file.
std::ifstream in_file ("spiked.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;
// Approximate the offset polygon.
const Number_type radius = 5;
const double err_bound = 0.00001;
Offset_polygon_with_holes_2 offset;
CGAL::Timer timer;
timer.start();
offset = approximated_offset_2 (P, radius, err_bound);
timer.stop();
std::cout << "The offset polygon has "
<< offset.outer_boundary().size() << " vertices, "
<< offset.number_of_holes() << " holes." << std::endl;
std::cout << "Offset computation took "
<< timer.time() << " seconds." << std::endl;
return (0);
}