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

CGAL 4.8 - Bounding Volumes

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CGAL::Min_ellipse_2_traits_2< K > Class Template Reference
Bounding Volumes Reference

`#include <CGAL/Min_ellipse_2_traits_2.h>`

## Definition

The class `Min_ellipse_2_traits_2` is a traits class for `CGAL::Min_ellipse_2<Traits>` using the two-di-men-sional CGAL kernel.

The template parameter `K` must be a model for `Kernel`.

Is Model Of:
  `MinEllipse2Traits`

See Also
  `CGAL::Min_ellipse_2<Traits>`
  `MinEllipse2Traits`

Examples:
  Min_ellipse_2/min_ellipse_2.cpp.

## Types
typedef unspecified_type | Point
| typedef to `K::Point_2`.
typedef unspecified_type | Ellipse
| internal type.

## Access Functions
The Ellipse type provides the following access methods not required by the concept `MinEllipse2Traits`.
bool | is_circle ()
| tests whether the ellipse is a circle.
void | double_coefficients (double &r, double &s, double &t, double &u, double &v, double &w)
| gives a double approximation of the ellipse's conic equation. More...

## Creation
| Min_ellipse_2_traits_2 ()
| default constructor.
| Min_ellipse_2_traits_2 (const Min_ellipse_2_traits_2< K > &)
| copy constructor.

## Member Function Documentation

template<typename K>

void CGAL::Min_ellipse_2_traits_2< K >::double_coefficients | ( | double & | r,
|  | double & | s,
|  | double & | t,
|  | double & | u,
|  | double & | v,
|  | double & | w
| ) |  |

gives a double approximation of the ellipse's conic equation.

If `K` is a Cartesian kernel, the ellipse is the set of all points \( (x,y)\) satisfying \( rx^2+sy^2+txy+ux+vy+w=0\). In the Homogeneous case, the ellipse is the set of points \( (hx,hy,hw)\) satisfying \( r(hx)^2+s(hy)^2+t(hx)(hy)+u(hx)(hw)+v(hy)(hw)+w(hw)^2=0\).