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

CGAL 4.8 - Bounding Volumes

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Min_ellipse_2/min_ellipse_2.cpp
#include <CGAL/Cartesian.h>
#include <CGAL/Min_ellipse_2.h>
#include <CGAL/Min_ellipse_2_traits_2.h>
#include <CGAL/Exact_rational.h>
#include <cassert>
typedef CGAL::Exact_rational NT;
typedef CGAL::Cartesian<NT> K;
typedef CGAL::Point_2<K> Point;
typedef CGAL::Min_ellipse_2_traits_2<K> Traits;
typedef CGAL::Min_ellipse_2<Traits> Min_ellipse;
int
main( int, char**)
{
const int n = 200;
Point P[n];
for ( int i = 0; i < n; ++i)
P[ i] = Point( i % 2 ? i : -i , 0);
// (0,0), (-1,0), (2,0), (-3,0)
std::cout << "Computing ellipse (without randomization)...";
std::cout.flush();
Min_ellipse me1( P, P+n, false); // very slow
std::cout << "done." << std::endl;
std::cout << "Computing ellipse (with randomization)...";
std::cout.flush();
Min_ellipse me2( P, P+n, true); // fast
std::cout << "done." << std::endl;
// because all input points are collinear, the ellipse is
// degenerate and equals a line segment; the ellipse has
// two support points
assert(me2.is_degenerate());
assert(me2.number_of_support_points()==2);
// prettyprinting
CGAL::set_pretty_mode( std::cout);
std::cout << me2;
// in general, the ellipse is not explicitly representable
// over the input number type NT; when you use the default
// traits class CGAL::Min_ellipse_2_traits_2<K>, you can
// get double approximations for the coefficients of the
// underlying conic curve. NOTE: this curve only exists
// in the nondegenerate case!
me2.insert(Point(0,1)); // resolves the degeneracy
assert(!me2.is_degenerate());
// get the coefficients
double r,s,t,u,v,w;
me2.ellipse().double_coefficients( r, s, t, u, v, w);
std::cout << "ellipse has the equation " <<
r << " x^2 + " <<
s << " y^2 + " <<
t << " xy + " <<
u << " x + " <<
v << " y + " <<
w << " = 0." << std::endl;
return 0;
}