% -*- latex -*-
% =============================================================================
% The CGAL Reference Manual
% Chapter: Geometric Optimisation
% Concept: MinEllipse2Traits
% -----------------------------------------------------------------------------
% file   : doc_tex/basic/Optimisation/Optimisation_ref/MinEllipse2Traits.tex
% package: Min_ellipse_2
% author : Sven Schönherr <sven@inf.ethz.ch>
% -----------------------------------------------------------------------------
% $Id$
% $Date$
% =============================================================================

\begin{ccRefConcept}{MinEllipse2Traits}

% -----------------------------------------------------------------------------
\ccDefinition

This concept defines the requirements for traits classes of
\ccGlobalScope\ccc{Min_ellipse_2<Traits>}.

% -----------------------------------------------------------------------------
\ccTypes

\ccNestedType{Point}{
        The point type must provide default and copy constructor,
        assignment and equality test.}

\ccNestedType{Ellipse}{
        The ellipse type must fulfill the requirements listed below
        in the next section.}

% -----------------------------------------------------------------------------
\ccHeading{Variables}

\ccVariable{ Ellipse  ellipse;}{
        The current ellipse. This variable is maintained by the algorithm,
        the user should neither access nor modify it directly.}

% -----------------------------------------------------------------------------
\ccCreation
\ccCreationVariable{traits}

Only default and copy constructor are required.

\ccConstructor{ Traits( );}{}
\ccConstructor{ Traits( const Traits&);}{}

% -----------------------------------------------------------------------------
\ccHasModels

\ccRefIdfierPage{CGAL::Min_ellipse_2_traits_2<K>}

% -----------------------------------------------------------------------------
\ccSeeAlso

\ccIndexTraitsClassRequirements[C]{Min_ellipse_2}
\ccRefIdfierPage{CGAL::Min_ellipse_2<Traits>}

% -----------------------------------------------------------------------------

\end{ccRefConcept}

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\ccAutoIndexingOff
\ccHtmlNoClassToc
\ccHtmlNoClassLinks
\ccHtmlNoClassIndex
\begin{ccClass}{Ellipse}
\subsection*{Ellipse Type (\ccClassTemplateName)}

% -----------------------------------------------------------------------------
\ccDefinition
 
An object of the class \ccClassName\ is an ellipse in two-dimensional
Euclidean plane $\E_2$. Its boundary splits the plane into a bounded
and an unbounded side. By definition, an empty \ccClassName\ has no
boundary and no bounded side, i.e.\ its unbounded side equals the
whole plane $\E_2$.

% -----------------------------------------------------------------------------
\ccTypes
 
\ccNestedType{Point}{Point type.}

% -----------------------------------------------------------------------------
\ccCreation
\ccCreationVariable{ellipse}
 
\ccMemberFunction{ void  set( );}{
        sets \ccVar\ to the empty ellipse.}

\ccMemberFunction{ void  set( const Point& p);}{
        sets \ccVar\ to the ellipse containing exactly $\{\mbox{\ccc{p}}\}$.}

\ccMemberFunction{ void  set( const Point& p,
                              const Point& q);}{
        sets \ccVar\ to the ellipse containing exactly the segment
        connecting \ccc{p} and \ccc{q}. The algorithm guarantees
        that \ccc{set} is never called with two equal points.}

\ccMemberFunction{ void  set( const Point& p,
                              const Point& q,
                              const Point& r);}{
        sets \ccVar\ to the smallest ellipse through \ccc{p},\ccc{q},\ccc{r}.
        The algorithm guarantees that \ccc{set} is never called with
        three collinear points.}

\ccMemberFunction{ void  set( const Point& p,
                              const Point& q,
                              const Point& r,
                              const Point& s);}{
        sets \ccVar\ to the smallest ellipse through
        \ccc{p},\ccc{q},\ccc{r},\ccc{s}. The algorithm guarantees that
        this ellipse exists.}

\ccMemberFunction{ void  set( const Point& p,
                              const Point& q,
                              const Point& r,
                              const Point& s,
                              const Point& t);}{
        sets \ccVar\ to the unique conic through
        \ccc{p},\ccc{q},\ccc{r},\ccc{s},\ccc{t}. The algorithm
        guarantees that this conic is an ellipse.}

% -----------------------------------------------------------------------------
\ccPredicates

\ccMemberFunction{ bool  has_on_unbounded_side( const Point& p) const;}{
        returns \ccc{true}, iff \ccc{p} lies properly outside of \ccVar.}

Each of the following predicates is only needed, if the corresponding
predicate of \ccc{Min_ellipse_2} is used.

\ccMemberFunction{ CGAL::Bounded_side
                   bounded_side( const Point& p) const;}{
        returns \ccGlobalScope\ccc{ON_BOUNDED_SIDE},
        \ccGlobalScope\ccc{ON_BOUNDARY}, or
        \ccGlobalScope\ccc{ON_UNBOUNDED_SIDE} iff \ccc{p} lies properly
        inside, on the boundary, or properly outside of \ccVar, resp.}

\ccMemberFunction{ bool  has_on_bounded_side( const Point& p) const;}{
        returns \ccc{true}, iff \ccc{p} lies properly inside \ccVar.}

\ccMemberFunction{ bool  has_on_boundary( const Point& p) const;}{
        returns \ccc{true}, iff \ccc{p} lies on the boundary
        of \ccVar.}

\ccMemberFunction{ bool  is_empty( ) const;}{
        returns \ccc{true}, iff \ccVar\ is empty (this implies
        degeneracy).}

\ccMemberFunction{ bool  is_degenerate( ) const;}{
        returns \ccc{true}, iff \ccVar\ is degenerate, i.e.\ if
        \ccVar\ is empty or equal to a single point.}

% -----------------------------------------------------------------------------
\ccHeading{I/O}

The following I/O operators are only needed, if the corresponding I/O
operators of \ccc{Min_ellipse_2} are used.

\ccHtmlNoIndex
\ccFunction{ ostream& operator << ( ostream& os, const Ellipse& ellipse);}{
        writes \ccVar\ to output stream \ccc{os}.}

\ccHtmlNoIndex
\ccFunction{ Window_stream&
             operator << ( Window_stream& ws, const Ellipse& ellipse);}{
        writes \ccVar\ to window stream \ccc{ws}.}

% -----------------------------------------------------------------------------

\end{ccClass}
\ccAutoIndexingOn

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