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

CGAL 4.8 - Bounding Volumes

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Approximate_min_ellipsoid_d/ellipsoid.cpp
#include <CGAL/Cartesian_d.h>
#include <CGAL/MP_Float.h>
#include <CGAL/point_generators_d.h>
#include <CGAL/Approximate_min_ellipsoid_d.h>
#include <CGAL/Approximate_min_ellipsoid_d_traits_d.h>
#include <vector>
#include <iostream>
typedef CGAL::Cartesian_d<double> Kernel;
typedef CGAL::MP_Float ET;
typedef CGAL::Approximate_min_ellipsoid_d_traits_d<Kernel, ET> Traits;
typedef Traits::Point Point;
typedef std::vector<Point> Point_list;
typedef CGAL::Approximate_min_ellipsoid_d<Traits> AME;
int main()
{
const int n = 1000; // number of points
const int d = 2; // dimension
const double eps = 0.01; // approximation ratio is (1+eps)
// create a set of random points:
Point_list P;
CGAL::Random_points_in_cube_d<Point> rpg(d,100.0);
for (int i = 0; i < n; ++i) {
P.push_back(*rpg);
++rpg;
}
// compute approximation:
Traits traits;
AME ame(eps, P.begin(), P.end(), traits);
// write EPS file:
if (ame.is_full_dimensional() && d == 2)
ame.write_eps("example.eps");
// output center coordinates:
std::cout << "Cartesian center coordinates: ";
for (AME::Center_coordinate_iterator c_it = ame.center_cartesian_begin();
c_it != ame.center_cartesian_end();
++c_it)
std::cout << *c_it << ' ';
std::cout << ".\n";
if (d == 2 || d == 3) {
// output axes:
AME::Axes_lengths_iterator axes = ame.axes_lengths_begin();
for (int i = 0; i < d; ++i) {
std::cout << "Semiaxis " << i << " has length " << *axes++ << "\n"
<< "and Cartesian coordinates ";
for (AME::Axes_direction_coordinate_iterator
d_it = ame.axis_direction_cartesian_begin(i);
d_it != ame.axis_direction_cartesian_end(i); ++d_it)
std::cout << *d_it << ' ';
std::cout << ".\n";
}
}
}