songsenand
/
cgal
mirror of https://github.com/CGAL/cgal
1
0
Fork 0
Code Issues Packages Projects Releases Wiki Activity

changed: structure of Optimisation chapter, one section per algorithm

This commit is contained in:
Sven Schönherr 1998-03-25 14:33:43 +00:00
parent c2dde9d49d
commit 709a6adcc1
4 changed files with 128 additions and 72 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

46
Packages/Min_circle_2/doc_tex/Optimisation/Optimisation_ref/Min_circle_2.tex
View File

@ -38,8 +38,8 @@ $P$ may be empty or points may occur more than once. The algorithm
computes a support set $S$ which remains fixed until the next insert
or clear operation.
\emph{Note:} In this release correct results are only guaranteed if
exact arithmetic is used, see Section~\ref{sec:opt_traits_impl}.
\emph{Note:} In this release correct results are only guaranteed if exact
arithmetic is used, see Section~\ref{sec:min_circle_2_traits_impl_2D_kernel}.
\ccInclude{CGAL/Min_circle_2.h}
@ -52,11 +52,13 @@ primitives it uses. For example \ccc{Traits::Point} is a mapping on a
point class. Think of it as 2D points in the Euclidean plane.
We provide a traits class implementation using the \cgal\ 2D kernel as
described in Section~\ref{sec:opt_traits_impl}. Traits class adapters
to user supplied point classes are available, see
Section~\ref{sec:opt_traits_adapt}. Customizing own traits classes for
optimisation algorithms can be done according to the requirements for
traits classes listed in Section~\ref{sec:opt_traits_req}.
described in Section~\ref{sec:min_circle_2_traits_impl_2D_kernel}.
Traits class adapters to user supplied point classes are available,
see Sections~\ref{sec:min_circle_2_traits_adapterC2}
and~\ref{sec:min_circle_2_traits_adapterH2}. Customizing own traits
classes for optimisation algorithms can be done according to the
requirements for traits classes listed in
Section~\ref{sec:min_circle_2_traits_req}.
% -----------------------------------------------------------------------------
\ccTypes
@ -312,11 +314,11 @@ An object \ccVar\ is valid, iff
\item $S$ is minimal, i.e.\ no support point is redundant.
\end{itemize}
Using the traits class implementation for the \cgal\ kernel with exact
arithmetic as described in Section~\ref{sec:opt_traits_impl}
guarantees validity of \ccVar. The following function is mainly
intended for debugging user supplied traits classes but also for
convincing the anxious user that the traits class implementation is
correct.
arithmetic as described in
Section~\ref{sec:min_circle_2_traits_impl_2D_kernel} guarantees
validity of \ccVar. The following function is mainly intended for
debugging user supplied traits classes but also for convincing the
anxious user that the traits class implementation is correct.
\begin{ccAdvanced}
\ccMemberFunction{ bool is_valid( bool verbose = false,
int level = 0 ) const;}{
@ -363,8 +365,8 @@ correct.
\ccc{CGAL_Min_ellipse_2}
\ccTexHtml{(Section~\ref{sec:min_ellipse_2_spec})}{},
\ccc{CGAL_Optimisation_traits_2}
\ccTexHtml{(Section~\ref{sec:opt_traits_impl_2D_kernel})}{},
\ccc{CGAL_Min_circle_2_traits_2}
\ccTexHtml{(Section~\ref{sec:min_circle_2_traits_impl_2D_kernel})}{},
\linebreakByHand
\ccc{CGAL_Min_circle_2_adapterC2}
\ccTexHtml{(Section~\ref{sec:min_circle_2_traits_adapterC2})}{},
@ -393,13 +395,13 @@ randomization can be useful in certain cases, we give an example.
#include <CGAL/Gmpz.h>
#include <CGAL/Homogeneous.h>
#include <CGAL/Point_2.h>
#include <CGAL/Optimisation_traits_2.h>
#include <CGAL/Min_circle_2_traits_2.h>
#include <CGAL/Min_circle_2.h>
typedef CGAL_Gmpz NT;
typedef CGAL_Homogeneous<NT> R;
typedef CGAL_Point_2<R> Point;
typedef CGAL_Optimisation_traits_2<R> Traits;
typedef CGAL_Min_circle_2_traits_2<R> Traits;
typedef CGAL_Min_circle_2<Traits> Min_circle;
int main()
@ -424,4 +426,16 @@ int main()
\end{ccClassTemplate}
% =============================================================================
\input{Min_circle_2_traits_2}
\input{Min_circle_2_adapterC2}
\input{Min_circle_2_adapterH2}
\input{requirements_adapterC2}
\input{requirements_adapterH2}
\input{requirements_Min_circle_2}
% ===== EOF ===================================================================

46
Packages/Min_circle_2/doc_tex/basic/Optimisation/Optimisation_ref/Min_circle_2.tex
View File

@ -38,8 +38,8 @@ $P$ may be empty or points may occur more than once. The algorithm
computes a support set $S$ which remains fixed until the next insert
or clear operation.
\emph{Note:} In this release correct results are only guaranteed if
exact arithmetic is used, see Section~\ref{sec:opt_traits_impl}.
\emph{Note:} In this release correct results are only guaranteed if exact
arithmetic is used, see Section~\ref{sec:min_circle_2_traits_impl_2D_kernel}.
\ccInclude{CGAL/Min_circle_2.h}
@ -52,11 +52,13 @@ primitives it uses. For example \ccc{Traits::Point} is a mapping on a
point class. Think of it as 2D points in the Euclidean plane.
We provide a traits class implementation using the \cgal\ 2D kernel as
described in Section~\ref{sec:opt_traits_impl}. Traits class adapters
to user supplied point classes are available, see
Section~\ref{sec:opt_traits_adapt}. Customizing own traits classes for
optimisation algorithms can be done according to the requirements for
traits classes listed in Section~\ref{sec:opt_traits_req}.
described in Section~\ref{sec:min_circle_2_traits_impl_2D_kernel}.
Traits class adapters to user supplied point classes are available,
see Sections~\ref{sec:min_circle_2_traits_adapterC2}
and~\ref{sec:min_circle_2_traits_adapterH2}. Customizing own traits
classes for optimisation algorithms can be done according to the
requirements for traits classes listed in
Section~\ref{sec:min_circle_2_traits_req}.
% -----------------------------------------------------------------------------
\ccTypes
@ -312,11 +314,11 @@ An object \ccVar\ is valid, iff
\item $S$ is minimal, i.e.\ no support point is redundant.
\end{itemize}
Using the traits class implementation for the \cgal\ kernel with exact
arithmetic as described in Section~\ref{sec:opt_traits_impl}
guarantees validity of \ccVar. The following function is mainly
intended for debugging user supplied traits classes but also for
convincing the anxious user that the traits class implementation is
correct.
arithmetic as described in
Section~\ref{sec:min_circle_2_traits_impl_2D_kernel} guarantees
validity of \ccVar. The following function is mainly intended for
debugging user supplied traits classes but also for convincing the
anxious user that the traits class implementation is correct.
\begin{ccAdvanced}
\ccMemberFunction{ bool is_valid( bool verbose = false,
int level = 0 ) const;}{
@ -363,8 +365,8 @@ correct.
\ccc{CGAL_Min_ellipse_2}
\ccTexHtml{(Section~\ref{sec:min_ellipse_2_spec})}{},
\ccc{CGAL_Optimisation_traits_2}
\ccTexHtml{(Section~\ref{sec:opt_traits_impl_2D_kernel})}{},
\ccc{CGAL_Min_circle_2_traits_2}
\ccTexHtml{(Section~\ref{sec:min_circle_2_traits_impl_2D_kernel})}{},
\linebreakByHand
\ccc{CGAL_Min_circle_2_adapterC2}
\ccTexHtml{(Section~\ref{sec:min_circle_2_traits_adapterC2})}{},
@ -393,13 +395,13 @@ randomization can be useful in certain cases, we give an example.
#include <CGAL/Gmpz.h>
#include <CGAL/Homogeneous.h>
#include <CGAL/Point_2.h>
#include <CGAL/Optimisation_traits_2.h>
#include <CGAL/Min_circle_2_traits_2.h>
#include <CGAL/Min_circle_2.h>
typedef CGAL_Gmpz NT;
typedef CGAL_Homogeneous<NT> R;
typedef CGAL_Point_2<R> Point;
typedef CGAL_Optimisation_traits_2<R> Traits;
typedef CGAL_Min_circle_2_traits_2<R> Traits;
typedef CGAL_Min_circle_2<Traits> Min_circle;
int main()
@ -424,4 +426,16 @@ int main()
\end{ccClassTemplate}
% =============================================================================
\input{Min_circle_2_traits_2}
\input{Min_circle_2_adapterC2}
\input{Min_circle_2_adapterH2}
\input{requirements_adapterC2}
\input{requirements_adapterH2}
\input{requirements_Min_circle_2}
% ===== EOF ===================================================================

54
Packages/Min_ellipse_2/doc_tex/Optimisation/Optimisation_ref/Min_ellipse_2.tex
View File

@ -39,8 +39,8 @@ $P$ may be empty or points may occur more than once. The algorithm
computes a support set $S$ which remains fixed until the next insert
or clear operation.
\emph{Note:} In this release correct results are only guaranteed if
exact arithmetic is used, see Section~\ref{sec:opt_traits_impl}.
\emph{Note:} In this release correct results are only guaranteed if exact
arithmetic is used, see Section~\ref{sec:min_ellipse_2_traits_impl_2D_kernel}.
\ccInclude{CGAL/Min_ellipse_2.h}
@ -53,11 +53,13 @@ primitives it uses. For example \ccc{Traits::Point} is a mapping on a
point class. Think of it as 2D points in the Euclidean plane.
We provide a traits class implementation using the \cgal\ 2D kernel as
described in Section~\ref{sec:opt_traits_impl}. Traits class adapters
to user supplied point classes are available, see
Section~\ref{sec:opt_traits_adapt}. Customizing own traits classes for
optimisation algorithms can be done according to the requirements for
traits classes listed in Section~\ref{sec:opt_traits_req}.
described in Section~\ref{sec:min_ellipse_2_traits_impl_2D_kernel}.
Traits class adapters to user supplied point classes are available,
see Sections~\ref{sec:min_ellipse_2_traits_adapterC2}
and~\ref{sec:min_ellipse_2_traits_adapterH2}. Customizing own traits
classes for optimisation algorithms can be done according to the
requirements for traits classes listed in
Section~\ref{sec:min_ellipse_2_traits_req}.
% -----------------------------------------------------------------------------
\ccTypes
@ -334,11 +336,11 @@ An object \ccVar\ is valid, iff
validity check.
Using the traits class implementation for the \cgal\ kernel with exact
arithmetic as described in Section~\ref{sec:opt_traits_impl}
guarantees validity of \ccVar. The following function is mainly
intended for debugging user supplied traits classes but also for
convincing the anxious user that the traits class implementation is
correct.
arithmetic as described in
Section~\ref{sec:min_ellipse_2_traits_impl_2D_kernel} guarantees
validity of \ccVar. The following function is mainly intended for
debugging user supplied traits classes but also for convincing the
anxious user that the traits class implementation is correct.
\begin{ccAdvanced}
\ccMemberFunction{ bool is_valid( bool verbose = false,
int level = 0 ) const;}{
@ -386,8 +388,8 @@ correct.
\ccc{CGAL_Min_circle_2}
\ccTexHtml{(Section~\ref{sec:min_circle_2_spec})}{},
\ccc{CGAL_Optimisation_traits_2}
\ccTexHtml{(Section~\ref{sec:opt_traits_impl_2D_kernel})}{},
\ccc{CGAL_Min_ellipse_2_traits_2}
\ccTexHtml{(Section~\ref{sec:min_ellipse_2_traits_impl_2D_kernel})}{},
\linebreakByHand
\ccc{CGAL_Min_ellipse_2_adapterC2}
\ccTexHtml{(Section~\ref{sec:min_ellipse_2_traits_adapterC2})}{},
@ -417,14 +419,14 @@ randomization can be useful in certain cases, we give an example.
#include <CGAL/Gmpz.h>
#include <CGAL/Homogeneous.h>
#include <CGAL/Point_2.h>
#include <CGAL/Optimisation_traits_2.h>
#include <CGAL/Min_ellipse_2_traits_2.h>
#include <CGAL/Min_ellipse_2.h>
typedef CGAL_Gmpz NT;
typedef CGAL_Homogeneous<NT> R;
typedef CGAL_Point_2<R> Point;
typedef CGAL_Optimisation_traits_2<R> Traits;
typedef CGAL_Min_ellipse_2<Traits> Min_ellipse;
typedef CGAL_Gmpz NT;
typedef CGAL_Homogeneous<NT> R;
typedef CGAL_Point_2<R> Point;
typedef CGAL_Min_ellipse_2_traits_2<R> Traits;
typedef CGAL_Min_ellipse_2<Traits> Min_ellipse;
int main()
{
@ -448,4 +450,16 @@ int main()
\end{ccClassTemplate}
% =============================================================================
\input{Min_ellipse_2_traits_2}
\input{Min_ellipse_2_adapterC2}
\input{Min_ellipse_2_adapterH2}
\input{requirements_adapterC2}
\input{requirements_adapterH2}
\input{requirements_Min_ellipse_2}
% ===== EOF ===================================================================

54
Packages/Min_ellipse_2/doc_tex/basic/Optimisation/Optimisation_ref/Min_ellipse_2.tex
View File

@ -39,8 +39,8 @@ $P$ may be empty or points may occur more than once. The algorithm
computes a support set $S$ which remains fixed until the next insert
or clear operation.
\emph{Note:} In this release correct results are only guaranteed if
exact arithmetic is used, see Section~\ref{sec:opt_traits_impl}.
\emph{Note:} In this release correct results are only guaranteed if exact
arithmetic is used, see Section~\ref{sec:min_ellipse_2_traits_impl_2D_kernel}.
\ccInclude{CGAL/Min_ellipse_2.h}
@ -53,11 +53,13 @@ primitives it uses. For example \ccc{Traits::Point} is a mapping on a
point class. Think of it as 2D points in the Euclidean plane.
We provide a traits class implementation using the \cgal\ 2D kernel as
described in Section~\ref{sec:opt_traits_impl}. Traits class adapters
to user supplied point classes are available, see
Section~\ref{sec:opt_traits_adapt}. Customizing own traits classes for
optimisation algorithms can be done according to the requirements for
traits classes listed in Section~\ref{sec:opt_traits_req}.
described in Section~\ref{sec:min_ellipse_2_traits_impl_2D_kernel}.
Traits class adapters to user supplied point classes are available,
see Sections~\ref{sec:min_ellipse_2_traits_adapterC2}
and~\ref{sec:min_ellipse_2_traits_adapterH2}. Customizing own traits
classes for optimisation algorithms can be done according to the
requirements for traits classes listed in
Section~\ref{sec:min_ellipse_2_traits_req}.
% -----------------------------------------------------------------------------
\ccTypes
@ -334,11 +336,11 @@ An object \ccVar\ is valid, iff
validity check.
Using the traits class implementation for the \cgal\ kernel with exact
arithmetic as described in Section~\ref{sec:opt_traits_impl}
guarantees validity of \ccVar. The following function is mainly
intended for debugging user supplied traits classes but also for
convincing the anxious user that the traits class implementation is
correct.
arithmetic as described in
Section~\ref{sec:min_ellipse_2_traits_impl_2D_kernel} guarantees
validity of \ccVar. The following function is mainly intended for
debugging user supplied traits classes but also for convincing the
anxious user that the traits class implementation is correct.
\begin{ccAdvanced}
\ccMemberFunction{ bool is_valid( bool verbose = false,
int level = 0 ) const;}{
@ -386,8 +388,8 @@ correct.
\ccc{CGAL_Min_circle_2}
\ccTexHtml{(Section~\ref{sec:min_circle_2_spec})}{},
\ccc{CGAL_Optimisation_traits_2}
\ccTexHtml{(Section~\ref{sec:opt_traits_impl_2D_kernel})}{},
\ccc{CGAL_Min_ellipse_2_traits_2}
\ccTexHtml{(Section~\ref{sec:min_ellipse_2_traits_impl_2D_kernel})}{},
\linebreakByHand
\ccc{CGAL_Min_ellipse_2_adapterC2}
\ccTexHtml{(Section~\ref{sec:min_ellipse_2_traits_adapterC2})}{},
@ -417,14 +419,14 @@ randomization can be useful in certain cases, we give an example.
#include <CGAL/Gmpz.h>
#include <CGAL/Homogeneous.h>
#include <CGAL/Point_2.h>
#include <CGAL/Optimisation_traits_2.h>
#include <CGAL/Min_ellipse_2_traits_2.h>
#include <CGAL/Min_ellipse_2.h>
typedef CGAL_Gmpz NT;
typedef CGAL_Homogeneous<NT> R;
typedef CGAL_Point_2<R> Point;
typedef CGAL_Optimisation_traits_2<R> Traits;
typedef CGAL_Min_ellipse_2<Traits> Min_ellipse;
typedef CGAL_Gmpz NT;
typedef CGAL_Homogeneous<NT> R;
typedef CGAL_Point_2<R> Point;
typedef CGAL_Min_ellipse_2_traits_2<R> Traits;
typedef CGAL_Min_ellipse_2<Traits> Min_ellipse;
int main()
{
@ -448,4 +450,16 @@ int main()
\end{ccClassTemplate}
% =============================================================================
\input{Min_ellipse_2_traits_2}
\input{Min_ellipse_2_adapterC2}
\input{Min_ellipse_2_adapterH2}
\input{requirements_adapterC2}
\input{requirements_adapterH2}
\input{requirements_Min_ellipse_2}
% ===== EOF ===================================================================