mirror of https://github.com/CGAL/cgal
Redesigned version of first public release
This commit is contained in:
Sven Schönherr
parent
26d11b7b90
commit
616ea01acb
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@ -0,0 +1,212 @@
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% =============================================================================
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% The CGAL Reference Manual
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% Chapter: Optimisation
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% Section: Traits Class Requirements
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% Subsec.: Requirements of Traits Classes for 2D Smallest Enclosing Circles
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% -----------------------------------------------------------------------------
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% file : spec/Optimisation/requirements_Min_circle_2.tex
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% author: Sven Schönherr (sven@inf.fu-berlin.de)
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% -----------------------------------------------------------------------------
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||||||
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% $Revision$
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||||||
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% $Date$
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% =============================================================================
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\begin{ccHtmlClassFile}{requirements_Min_circle_2.html}{%
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Requirements of Traits Classes for 2D Smallest Enclosing Circles}
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\subsection{Requirements of Traits Classes for 2D Smallest Enclosing Circles}
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\label{sec:min_circle_2_traits_req}
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The class template \ccc{CGAL_Min_circle_2} is parameterized with a
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\ccc{Traits} class which defines the abstract interface between the
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optimisation algorithm and the primitives it uses. The following
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requirements catalog lists the primitives, i.e.\ types, member
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functions etc., that must be defined for a class that can be used to
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parameterize \ccc{CGAL_Min_circle_2}. A traits class implementation
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using the \cgal\ 2D kernel is available and described in
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Section~\ref{sec:opt_traits_impl}. In addition, we provide traits
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class adapters to user supplied point classes, see
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Section~\ref{sec:opt_traits_adapt}. Both, the implementation and the
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adapters, can be used as a starting point for customizing own traits
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classes, e.g.\ through derivation and specialization.
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% =============================================================================
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\ccHtmlNoClassLinks
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\ccHtmlNoClassIndex
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\begin{ccClass}{Traits}
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\subsection*{Traits Class (\ccClassTemplateName)}
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% -----------------------------------------------------------------------------
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\ccDefinition
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A class that satisfies the requirements of a traits class for
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\ccc{CGAL_Min_circle_2} must provide the following primitives.
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% -----------------------------------------------------------------------------
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\ccTypes
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\ccNestedType{Point}{
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The point type must provide default and copy constructor,
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assignment and equality test.}
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\ccNestedType{Circle}{
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The circle type must fulfill the requirements listed below
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in the next section.}
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In addition, if I/O is used, the corresponding I/O operators for
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\ccc{Point} and \ccc{Circle} have to be provided, see topic
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\textbf{I/O} in Section~\ref{sec:min_circle_2_spec}.
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% -----------------------------------------------------------------------------
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\ccHeading{Variables}
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\ccVariable{ Circle circle;}{
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The actual circle. This variable is maintained by the algorithm,
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the user should neither access nor modify it directly.}
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% -----------------------------------------------------------------------------
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\ccCreation
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\ccCreationVariable{traits}
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Only default and copy constructor are required. Note that further
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constructors can be provided.
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\ccConstructor{ Traits( );}{A default constructor.}
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\ccConstructor{ Traits( Traits const&);}{A copy constructor.}
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% -----------------------------------------------------------------------------
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\ccOperations
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The following predicate is only needed, if the member function
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\ccc{is_valid} of \ccc{CGAL_Min_circle_2} is used.
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\ccMemberFunction{ CGAL_Orientation orientation( Point const& p,
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Point const& q,
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Point const& r) const;}{
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returns constants \ccc{CGAL_LEFTTURN}, \ccc{CGAL_COLLINEAR},
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or \ccc{CGAL_RIGHTTURN} iff \ccc{r} lies properly to the left,
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on, or properly to the right of the oriented line through
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\ccc{p} and \ccc{q}, resp.}
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\end{ccClass}
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% =============================================================================
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\ccHtmlNoClassLinks
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\ccHtmlNoClassIndex
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\begin{ccClass}{Circle}
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\subsection*{Circle Type (\ccClassTemplateName)}
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\label{sec:opt_circle_2_req}
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% -----------------------------------------------------------------------------
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\ccDefinition
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An object of the class \ccClassName\ is a circle in two-dimensional
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euclidean plane $\E_2$. Its boundary splits the plane into a bounded
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and an unbounded side. By definition, an empty \ccClassName\ has no
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boundary and no bounded side, i.e.\ its unbounded side equals the
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whole plane $\E_2$. A \ccClassName\ containing exactly one point~$p$
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has no bounded side, its boundary is $\{p\}$, and its unbounded side
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equals $\E_2\mbox{\ccTexHtml{$\setminus$}{-}}\{p\}$.
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% -----------------------------------------------------------------------------
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\ccTypes
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\ccNestedType{Point}{Point type.}
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The following type is only needed, if the member function \ccc{is_valid}
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of \ccc{CGAL_Min_circle_2} is used.
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\ccNestedType{Distance}{Distance type.}
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% -----------------------------------------------------------------------------
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\ccCreation
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\ccCreationVariable{circle}
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\ccMemberFunction{ void set( );}{
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sets \ccVar\ to the empty circle.}
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\ccMemberFunction{ void set( Point const& p);}{
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sets \ccVar\ to the circle containing exactly $\{\mbox{\ccc{p}}\}$.}
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\ccMemberFunction{ void set( Point const& p,
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Point const& q);}{
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sets \ccVar\ to the circle with diameter
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|
$\overline{\mbox{\ccc{p}\ccc{q}}}$. The algorithm
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guarantees that \ccc{set} is never called with two equal points.}
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\ccMemberFunction{ void set( Point const& p,
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Point const& q,
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Point const& r);}{
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sets \ccVar\ to the circle through \ccc{p},\ccc{q},\ccc{r}.
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The algorithm guarantees that \ccc{set} is never called with
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three collinear points.}
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% -----------------------------------------------------------------------------
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\ccPredicates
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\ccMemberFunction{ bool has_on_unbounded_side( Point const& p) const;}{
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returns \ccc{true}, iff \ccc{p} lies properly outside of \ccVar.}
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Each of the following predicates is only needed, if the corresponding
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predicate of \ccc{CGAL_Min_circle_2} is used.
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\ccMemberFunction{ CGAL_Bounded_side
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bounded_side( Point const& p) const;}{
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returns \ccc{CGAL_ON_BOUNDED_SIDE},\ccTexHtml{$\:$}{ }%
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\ccc{CGAL_ON_BOUNDARY}, or \ccc{CGAL_ON_UNBOUNDED_SIDE}
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iff \ccc{p} lies properly inside, on the boundary, or properly
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outside of \ccVar, resp.}
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\ccMemberFunction{ bool has_on_bounded_side( Point const& p) const;}{
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returns \ccc{true}, iff \ccc{p} lies properly inside \ccVar.}
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\ccMemberFunction{ bool has_on_boundary( Point const& p) const;}{
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returns \ccc{true}, iff \ccc{p} lies on the boundary
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of \ccVar.}
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\ccMemberFunction{ bool is_empty( ) const;}{
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returns \ccc{true}, iff \ccVar\ is empty (this implies
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degeneracy).}
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\ccMemberFunction{ bool is_degenerate( ) const;}{
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returns \ccc{true}, iff \ccVar\ is degenerate, i.e.\ if
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\ccVar\ is empty or equal to a single point.}
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% -----------------------------------------------------------------------------
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\ccHeading{Additional Operations for Checking}
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The following operations are only needed, if the member function
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\ccc{is_valid} of \ccc{CGAL_Min_circle_2} is used.
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\ccMemberFunction{ bool operator == ( Circle const& circle2) const;}{
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returns \ccc{true}, iff \ccVar\ and \ccc{circle2} are equal.}
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\ccMemberFunction{ Point center( ) const;}{
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returns the center of \ccVar.}
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\ccMemberFunction{ Distance squared_radius( ) const;}{
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returns the squared radius of \ccVar.}
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% -----------------------------------------------------------------------------
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\ccHeading{I/O}
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The following I/O operators are only needed, if the corresponding I/O
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operators of \ccc{CGAL_Min_circle_2} are used.
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\ccFunction{ ostream& operator << ( ostream& os, Circle const& circle);}{
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writes \ccVar\ to output stream \ccc{os}.}
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\ccFunction{ istream& operator >> ( istream& is, Circle &circle);}{
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reads \ccVar\ from input stream \ccc{is}.}
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% -----------------------------------------------------------------------------
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\end{ccClass}
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% =============================================================================
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||||||
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\end{ccHtmlClassFile}
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||||||
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||||||
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% ===== EOF ===================================================================
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||||||
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|
@ -0,0 +1,212 @@
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% =============================================================================
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|
% The CGAL Reference Manual
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% Chapter: Optimisation
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|
% Section: Traits Class Requirements
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% Subsec.: Requirements of Traits Classes for 2D Smallest Enclosing Circles
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% -----------------------------------------------------------------------------
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|
% file : spec/Optimisation/requirements_Min_circle_2.tex
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% author: Sven Schönherr (sven@inf.fu-berlin.de)
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% -----------------------------------------------------------------------------
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|
% $Revision$
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||||||
|
% $Date$
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||||||
|
% =============================================================================
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||||||
|
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||||||
|
\begin{ccHtmlClassFile}{requirements_Min_circle_2.html}{%
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|
Requirements of Traits Classes for 2D Smallest Enclosing Circles}
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|
\subsection{Requirements of Traits Classes for 2D Smallest Enclosing Circles}
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\label{sec:min_circle_2_traits_req}
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||||||
|
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The class template \ccc{CGAL_Min_circle_2} is parameterized with a
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|
\ccc{Traits} class which defines the abstract interface between the
|
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|
optimisation algorithm and the primitives it uses. The following
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|
requirements catalog lists the primitives, i.e.\ types, member
|
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|
functions etc., that must be defined for a class that can be used to
|
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|
parameterize \ccc{CGAL_Min_circle_2}. A traits class implementation
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|
using the \cgal\ 2D kernel is available and described in
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|
Section~\ref{sec:opt_traits_impl}. In addition, we provide traits
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|
class adapters to user supplied point classes, see
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|
Section~\ref{sec:opt_traits_adapt}. Both, the implementation and the
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|
adapters, can be used as a starting point for customizing own traits
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|
classes, e.g.\ through derivation and specialization.
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|
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% =============================================================================
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|
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|
\ccHtmlNoClassLinks
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||||||
|
\ccHtmlNoClassIndex
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||||||
|
\begin{ccClass}{Traits}
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||||||
|
\subsection*{Traits Class (\ccClassTemplateName)}
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% -----------------------------------------------------------------------------
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||||||
|
\ccDefinition
|
||||||
|
|
||||||
|
A class that satisfies the requirements of a traits class for
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\ccc{CGAL_Min_circle_2} must provide the following primitives.
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% -----------------------------------------------------------------------------
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\ccTypes
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|
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\ccNestedType{Point}{
|
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|
The point type must provide default and copy constructor,
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|
assignment and equality test.}
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|
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\ccNestedType{Circle}{
|
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|
The circle type must fulfill the requirements listed below
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in the next section.}
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In addition, if I/O is used, the corresponding I/O operators for
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\ccc{Point} and \ccc{Circle} have to be provided, see topic
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\textbf{I/O} in Section~\ref{sec:min_circle_2_spec}.
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% -----------------------------------------------------------------------------
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\ccHeading{Variables}
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\ccVariable{ Circle circle;}{
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The actual circle. This variable is maintained by the algorithm,
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the user should neither access nor modify it directly.}
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% -----------------------------------------------------------------------------
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\ccCreation
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|
\ccCreationVariable{traits}
|
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Only default and copy constructor are required. Note that further
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constructors can be provided.
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\ccConstructor{ Traits( );}{A default constructor.}
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\ccConstructor{ Traits( Traits const&);}{A copy constructor.}
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% -----------------------------------------------------------------------------
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\ccOperations
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|
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The following predicate is only needed, if the member function
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\ccc{is_valid} of \ccc{CGAL_Min_circle_2} is used.
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\ccMemberFunction{ CGAL_Orientation orientation( Point const& p,
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Point const& q,
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Point const& r) const;}{
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|
returns constants \ccc{CGAL_LEFTTURN}, \ccc{CGAL_COLLINEAR},
|
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|
or \ccc{CGAL_RIGHTTURN} iff \ccc{r} lies properly to the left,
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on, or properly to the right of the oriented line through
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\ccc{p} and \ccc{q}, resp.}
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\end{ccClass}
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% =============================================================================
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\ccHtmlNoClassLinks
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\ccHtmlNoClassIndex
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\begin{ccClass}{Circle}
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\subsection*{Circle Type (\ccClassTemplateName)}
|
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\label{sec:opt_circle_2_req}
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% -----------------------------------------------------------------------------
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\ccDefinition
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|
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An object of the class \ccClassName\ is a circle in two-dimensional
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|
euclidean plane $\E_2$. Its boundary splits the plane into a bounded
|
||||||
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and an unbounded side. By definition, an empty \ccClassName\ has no
|
||||||
|
boundary and no bounded side, i.e.\ its unbounded side equals the
|
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|
whole plane $\E_2$. A \ccClassName\ containing exactly one point~$p$
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||||||
|
has no bounded side, its boundary is $\{p\}$, and its unbounded side
|
||||||
|
equals $\E_2\mbox{\ccTexHtml{$\setminus$}{-}}\{p\}$.
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% -----------------------------------------------------------------------------
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\ccTypes
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|
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\ccNestedType{Point}{Point type.}
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||||||
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The following type is only needed, if the member function \ccc{is_valid}
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||||||
|
of \ccc{CGAL_Min_circle_2} is used.
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\ccNestedType{Distance}{Distance type.}
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||||||
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% -----------------------------------------------------------------------------
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||||||
|
\ccCreation
|
||||||
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\ccCreationVariable{circle}
|
||||||
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|
||||||
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\ccMemberFunction{ void set( );}{
|
||||||
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sets \ccVar\ to the empty circle.}
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\ccMemberFunction{ void set( Point const& p);}{
|
||||||
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sets \ccVar\ to the circle containing exactly $\{\mbox{\ccc{p}}\}$.}
|
||||||
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||||||
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\ccMemberFunction{ void set( Point const& p,
|
||||||
|
Point const& q);}{
|
||||||
|
sets \ccVar\ to the circle with diameter
|
||||||
|
$\overline{\mbox{\ccc{p}\ccc{q}}}$. The algorithm
|
||||||
|
guarantees that \ccc{set} is never called with two equal points.}
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\ccMemberFunction{ void set( Point const& p,
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||||||
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Point const& q,
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||||||
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Point const& r);}{
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||||||
|
sets \ccVar\ to the circle through \ccc{p},\ccc{q},\ccc{r}.
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||||||
|
The algorithm guarantees that \ccc{set} is never called with
|
||||||
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three collinear points.}
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% -----------------------------------------------------------------------------
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||||||
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\ccPredicates
|
||||||
|
|
||||||
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\ccMemberFunction{ bool has_on_unbounded_side( Point const& p) const;}{
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||||||
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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{CGAL_Min_circle_2} is used.
|
||||||
|
|
||||||
|
\ccMemberFunction{ CGAL_Bounded_side
|
||||||
|
bounded_side( Point const& p) const;}{
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||||||
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returns \ccc{CGAL_ON_BOUNDED_SIDE},\ccTexHtml{$\:$}{ }%
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||||||
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\ccc{CGAL_ON_BOUNDARY}, or \ccc{CGAL_ON_UNBOUNDED_SIDE}
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||||||
|
iff \ccc{p} lies properly inside, on the boundary, or properly
|
||||||
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outside of \ccVar, resp.}
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||||||
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||||||
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\ccMemberFunction{ bool has_on_bounded_side( Point const& p) const;}{
|
||||||
|
returns \ccc{true}, iff \ccc{p} lies properly inside \ccVar.}
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||||||
|
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||||||
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\ccMemberFunction{ bool has_on_boundary( Point const& p) const;}{
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||||||
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returns \ccc{true}, iff \ccc{p} lies on the boundary
|
||||||
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of \ccVar.}
|
||||||
|
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||||||
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\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{Additional Operations for Checking}
|
||||||
|
|
||||||
|
The following operations are only needed, if the member function
|
||||||
|
\ccc{is_valid} of \ccc{CGAL_Min_circle_2} is used.
|
||||||
|
|
||||||
|
\ccMemberFunction{ bool operator == ( Circle const& circle2) const;}{
|
||||||
|
returns \ccc{true}, iff \ccVar\ and \ccc{circle2} are equal.}
|
||||||
|
|
||||||
|
\ccMemberFunction{ Point center( ) const;}{
|
||||||
|
returns the center of \ccVar.}
|
||||||
|
|
||||||
|
\ccMemberFunction{ Distance squared_radius( ) const;}{
|
||||||
|
returns the squared radius of \ccVar.}
|
||||||
|
|
||||||
|
% -----------------------------------------------------------------------------
|
||||||
|
\ccHeading{I/O}
|
||||||
|
|
||||||
|
The following I/O operators are only needed, if the corresponding I/O
|
||||||
|
operators of \ccc{CGAL_Min_circle_2} are used.
|
||||||
|
|
||||||
|
\ccFunction{ ostream& operator << ( ostream& os, Circle const& circle);}{
|
||||||
|
writes \ccVar\ to output stream \ccc{os}.}
|
||||||
|
|
||||||
|
\ccFunction{ istream& operator >> ( istream& is, Circle &circle);}{
|
||||||
|
reads \ccVar\ from input stream \ccc{is}.}
|
||||||
|
|
||||||
|
% -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
\end{ccClass}
|
||||||
|
|
||||||
|
% =============================================================================
|
||||||
|
|
||||||
|
\end{ccHtmlClassFile}
|
||||||
|
|
||||||
|
% ===== EOF ===================================================================
|
||||||
Loading…
Reference in New Issue