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Interface Re-Design, Min_ellipse_2 removed, HTML compliant

This commit is contained in:
Sven Schönherr 1997-05-26 14:54:43 +00:00
parent 04826fdf5d
commit e6ed712c2a
2 changed files with 60 additions and 60 deletions
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56
Packages/Min_circle_2/doc_tex/Optimisation/Optimisation_ref/Min_circle_2.tex
View File

@ -19,8 +19,9 @@ An object of the class \ccClassTemplateName\ is the unique circle of
smallest area enclosing a finite set of points in two-dimensional smallest area enclosing a finite set of points in two-dimensional
euclidean space $\E_2$. For a point set $P$ we denote by $mc(P)$ the euclidean space $\E_2$. For a point set $P$ we denote by $mc(P)$ the
smallest circle that contains all points of $P$. Note that $mc(P)$ can smallest circle that contains all points of $P$. Note that $mc(P)$ can
be degenerate, i.e.\ $mc(P)=$\ccTexHtml{$\;\emptyset$}{Ø} if be degenerate, i.e.\ $mc(P)=\mbox{\ccTexHtml{$\;\emptyset$}{Ø}}$
$P=$\ccTexHtml{$\;\emptyset$}{Ø} and $mc(P)=\{p\}$ if $P=\{p\}$. if $P=\mbox{\ccTexHtml{$\;\emptyset$}{Ø}}$ and $mc(P)=\{p\}$ if
$P=\{p\}$.
An inclusion-minimal subset $S$ of $P$ with $mc(S)=mc(P)$ is called a An inclusion-minimal subset $S$ of $P$ with $mc(S)=mc(P)$ is called a
{\em support set}, the points in $S$ are the {\em support points}. A {\em support set}, the points in $S$ are the {\em support points}. A
@ -58,10 +59,15 @@ requirements for interface classes listed in Section~\ref{sec:opt_I_Req}.
\ccNestedType{I}{Interface type.} \ccNestedType{I}{Interface type.}
\ccGlueBegin \ccGlueBegin
\ccUnchecked
\ccTypedef{typedef I::Point Point; }{Point type.} \ccTypedef{typedef I::Point Point; }{Point type.}
\ccTypedef{typedef I::Circle Circle;}{Circle type.} \ccUnchecked
\ccTypedef{typedef I::Distance Distance;}{Distance type.}
\ccGlueEnd \ccGlueEnd
\ccUnchecked
\ccTypedef{typedef I::Circle Circle; }{Circle type.}
The following types denote iterators that allow to traverse all points The following types denote iterators that allow to traverse all points
and support points of the smallest enclosing circle, resp. The and support points of the smallest enclosing circle, resp. The
iterators are non-mutable and their value type is \ccc{Point}. The iterators are non-mutable and their value type is \ccc{Point}. The
@ -87,9 +93,10 @@ reconstructing $mc(P)$ from a given support set $S$ of $P$.
\ccConstructor{ CGAL_Min_circle_2( I const& i = I());}{ \ccConstructor{ CGAL_Min_circle_2( I const& i = I());}{
introduces a variable \ccVar\ of type \ccClassTemplateName. introduces a variable \ccVar\ of type \ccClassTemplateName.
It is initialized to It is initialized to
$mc($\ccTexHtml{$\emptyset$}{Ø}$)$, the empty set. $mc(\mbox{\ccTexHtml{$\emptyset$}{Ø}})$, the empty set.
\ccPostcond \ccc{\ccVar.is_empty()} = \ccc{true}.} \ccPostcond \ccVar\ccc{.is_empty()} = \ccc{true}.}
\ccUnchecked
\ccHidden \ccHidden
\ccConstructor{ CGAL_Min_circle_2( CGAL_Min_circle_2<I> const&);}{ \ccConstructor{ CGAL_Min_circle_2( CGAL_Min_circle_2<I> const&);}{
copy constructor.} copy constructor.}
@ -97,7 +104,7 @@ reconstructing $mc(P)$ from a given support set $S$ of $P$.
\ccConstructor{ CGAL_Min_circle_2( Point const& p, I const& i = I());}{ \ccConstructor{ CGAL_Min_circle_2( Point const& p, I const& i = I());}{
introduces a variable \ccVar\ of type \ccClassTemplateName. introduces a variable \ccVar\ of type \ccClassTemplateName.
It is initialized to $mc(\{p\})$, the set $\{p\}$. It is initialized to $mc(\{p\})$, the set $\{p\}$.
\ccPostcond \ccc{\ccVar.is_degenerate()} = \ccc{true}.} \ccPostcond \ccVar\ccc{.is_degenerate()} = \ccc{true}.}
\ccConstructor{ CGAL_Min_circle_2( Point const& p1, \ccConstructor{ CGAL_Min_circle_2( Point const& p1,
Point const& p2, Point const& p2,
@ -157,6 +164,7 @@ for the STL sequence containers \ccc{vector<Point>} and \ccc{list<Point>}.
\ccConstructor{ ~CGAL_Min_circle_2( );}{ \ccConstructor{ ~CGAL_Min_circle_2( );}{
destructor.} destructor.}
\ccUnchecked
\ccHidden \ccHidden
\ccMemberFunction{ CGAL_Min_circle_2<I>& \ccMemberFunction{ CGAL_Min_circle_2<I>&
operator = ( CGAL_Min_circle_2<I> const&);}{ operator = ( CGAL_Min_circle_2<I> const&);}{
@ -185,14 +193,15 @@ for the STL sequence containers \ccc{vector<Point>} and \ccc{list<Point>}.
\ccMemberFunction{ Point const& support_point( int i) const;}{ \ccMemberFunction{ Point const& support_point( int i) const;}{
returns the \ccc{i}-th support point of \ccVar. Between two returns the \ccc{i}-th support point of \ccVar. Between two
insert operations any call to \ccc{\ccVar.support_point(i)} insert operations any call to \ccVar\ccc{.support_point(i)}
with the same \ccc{i} returns the same point. with the same \ccc{i} returns the same point.
\ccPrecond $0 \leq i <$ \ccc{\ccVar.number_of_support_points()}.} \ccPrecond $0 \leq i <$ \ccVar\ccc{.number_of_support_points()}.}
\ccMemberFunction{ Circle circle( ) const;}{
returns a circle with same center and same squared radius
as \ccVar, if \ccVar is not empty. Otherwise the default
circle, i.e.\ \ccc{Circle()}, is returned.}
\ccMemberFunction{ Circle const& circle( ) const;}{
returns an oriented circle with same center $c$ and same
squared radius $r$ as \ccVar\ and positive orientation.
\ccPrecond \ccc{\ccVar.is_empty()} = \ccc{false}.}
% ----------------------------------------------------------------------------- % -----------------------------------------------------------------------------
\ccPredicates \ccPredicates
@ -227,7 +236,7 @@ bounded side, i.e.\ its unbounded side equals the whole plane $\E_2$.
the number of support points is less than 2.} the number of support points is less than 2.}
% ----------------------------------------------------------------------------- % -----------------------------------------------------------------------------
\ccModifiers \ccHeading{Modifiers}
New points can be added to an existing $\ccVar$, allowing to build New points can be added to an existing $\ccVar$, allowing to build
$mc(P)$ incrementally, e.g.\ if $P$ is not known in advance. Compared $mc(P)$ incrementally, e.g.\ if $P$ is not known in advance. Compared
@ -243,9 +252,9 @@ the construction method is incremental itself.
An object \ccVar\ is valid, iff An object \ccVar\ is valid, iff
\begin{itemize} \begin{itemize}
\item[a)] \ccVar\ contains all points of its defining set $P$, \item \ccVar\ contains all points of its defining set $P$,
\item[b)] \ccVar\ is the smallest circle spanned by its support set $S$, and \item \ccVar\ is the smallest circle spanned by its support set $S$, and
\item[c)] $S$ is minimal, i.e.\ no support point is redundant. \item $S$ is minimal, i.e.\ no support point is redundant.
\end{itemize} \end{itemize}
Using the ready-made implementation for the interface class with exact Using the ready-made implementation for the interface class with exact
arithmetic as described in Section~\ref{sec:opt_I_Impl} guarantees arithmetic as described in Section~\ref{sec:opt_I_Impl} guarantees
@ -268,7 +277,8 @@ debugging user supplied interface classes.
\ccFunction{ ostream& operator << ( ostream& os, \ccFunction{ ostream& operator << ( ostream& os,
CGAL_Min_circle_2<I> const& min_circle);}{ CGAL_Min_circle_2<I> const& min_circle);}{
writes \ccVar\ to output stream \ccc{os}. writes \ccVar\ to output stream \ccc{os}.
\ccPrecond The output operator is defined for \ccc{I::Point}.} \ccPrecond The output operator is defined for \ccc{I::Point}
(and for \ccc{I::Circle}, if pretty printing is used).}
\ccFunction{ istream& operator >> ( istream& is, \ccFunction{ istream& operator >> ( istream& is,
CGAL_Min_circle_2<I> &min_circle);}{ CGAL_Min_circle_2<I> &min_circle);}{
@ -277,6 +287,7 @@ debugging user supplied interface classes.
\ccInclude{CGAL/IO/Window_stream.h} \ccInclude{CGAL/IO/Window_stream.h}
\ccUnchecked
\ccFunction{ CGAL_Window_stream& \ccFunction{ CGAL_Window_stream&
operator << ( CGAL_Window_stream& ws, operator << ( CGAL_Window_stream& ws,
CGAL_Min_circle_2<I> const& min_circle);}{ CGAL_Min_circle_2<I> const& min_circle);}{
@ -295,17 +306,6 @@ linear time, but substantially less than computing the new smallest
enclosing circle from scratch. The check for validity takes linear enclosing circle from scratch. The check for validity takes linear
time. time.
%We provide a specialization with homogeneous representation and
%numbertype \ccc{integer} that uses floating-point filter for the sign
%calculations in the predicates (see~\cite{MehlhornNaeher94}). This
%decreaes computation time by a factor of four compared to the generic
%implementation. If both \ccc{<CGAL/Integer.h>} and
%\ccc{<CGAL/Homogeneous.h>} are included before
%\ccc{<CGAL/Min_circle_2.h>} then the specialization for
%\ccc{CGAL_Min_circle_2< CGAL_Optimisation_default_interface<
% CGAL_Homogeneous<integer> > >} is used instead of the generic
%implementation.
% ----------------------------------------------------------------------------- % -----------------------------------------------------------------------------
\ccExample \ccExample

56
Packages/Min_circle_2/doc_tex/basic/Optimisation/Optimisation_ref/Min_circle_2.tex
View File

@ -19,8 +19,9 @@ An object of the class \ccClassTemplateName\ is the unique circle of
smallest area enclosing a finite set of points in two-dimensional smallest area enclosing a finite set of points in two-dimensional
euclidean space $\E_2$. For a point set $P$ we denote by $mc(P)$ the euclidean space $\E_2$. For a point set $P$ we denote by $mc(P)$ the
smallest circle that contains all points of $P$. Note that $mc(P)$ can smallest circle that contains all points of $P$. Note that $mc(P)$ can
be degenerate, i.e.\ $mc(P)=$\ccTexHtml{$\;\emptyset$}{&Oslash;} if be degenerate, i.e.\ $mc(P)=\mbox{\ccTexHtml{$\;\emptyset$}{&Oslash;}}$
$P=$\ccTexHtml{$\;\emptyset$}{&Oslash;} and $mc(P)=\{p\}$ if $P=\{p\}$. if $P=\mbox{\ccTexHtml{$\;\emptyset$}{&Oslash;}}$ and $mc(P)=\{p\}$ if
$P=\{p\}$.
An inclusion-minimal subset $S$ of $P$ with $mc(S)=mc(P)$ is called a An inclusion-minimal subset $S$ of $P$ with $mc(S)=mc(P)$ is called a
{\em support set}, the points in $S$ are the {\em support points}. A {\em support set}, the points in $S$ are the {\em support points}. A
@ -58,10 +59,15 @@ requirements for interface classes listed in Section~\ref{sec:opt_I_Req}.
\ccNestedType{I}{Interface type.} \ccNestedType{I}{Interface type.}
\ccGlueBegin \ccGlueBegin
\ccUnchecked
\ccTypedef{typedef I::Point Point; }{Point type.} \ccTypedef{typedef I::Point Point; }{Point type.}
\ccTypedef{typedef I::Circle Circle;}{Circle type.} \ccUnchecked
\ccTypedef{typedef I::Distance Distance;}{Distance type.}
\ccGlueEnd \ccGlueEnd
\ccUnchecked
\ccTypedef{typedef I::Circle Circle; }{Circle type.}
The following types denote iterators that allow to traverse all points The following types denote iterators that allow to traverse all points
and support points of the smallest enclosing circle, resp. The and support points of the smallest enclosing circle, resp. The
iterators are non-mutable and their value type is \ccc{Point}. The iterators are non-mutable and their value type is \ccc{Point}. The
@ -87,9 +93,10 @@ reconstructing $mc(P)$ from a given support set $S$ of $P$.
\ccConstructor{ CGAL_Min_circle_2( I const& i = I());}{ \ccConstructor{ CGAL_Min_circle_2( I const& i = I());}{
introduces a variable \ccVar\ of type \ccClassTemplateName. introduces a variable \ccVar\ of type \ccClassTemplateName.
It is initialized to It is initialized to
$mc($\ccTexHtml{$\emptyset$}{&Oslash;}$)$, the empty set. $mc(\mbox{\ccTexHtml{$\emptyset$}{&Oslash;}})$, the empty set.
\ccPostcond \ccc{\ccVar.is_empty()} = \ccc{true}.} \ccPostcond \ccVar\ccc{.is_empty()} = \ccc{true}.}
\ccUnchecked
\ccHidden \ccHidden
\ccConstructor{ CGAL_Min_circle_2( CGAL_Min_circle_2<I> const&);}{ \ccConstructor{ CGAL_Min_circle_2( CGAL_Min_circle_2<I> const&);}{
copy constructor.} copy constructor.}
@ -97,7 +104,7 @@ reconstructing $mc(P)$ from a given support set $S$ of $P$.
\ccConstructor{ CGAL_Min_circle_2( Point const& p, I const& i = I());}{ \ccConstructor{ CGAL_Min_circle_2( Point const& p, I const& i = I());}{
introduces a variable \ccVar\ of type \ccClassTemplateName. introduces a variable \ccVar\ of type \ccClassTemplateName.
It is initialized to $mc(\{p\})$, the set $\{p\}$. It is initialized to $mc(\{p\})$, the set $\{p\}$.
\ccPostcond \ccc{\ccVar.is_degenerate()} = \ccc{true}.} \ccPostcond \ccVar\ccc{.is_degenerate()} = \ccc{true}.}
\ccConstructor{ CGAL_Min_circle_2( Point const& p1, \ccConstructor{ CGAL_Min_circle_2( Point const& p1,
Point const& p2, Point const& p2,
@ -157,6 +164,7 @@ for the STL sequence containers \ccc{vector<Point>} and \ccc{list<Point>}.
\ccConstructor{ ~CGAL_Min_circle_2( );}{ \ccConstructor{ ~CGAL_Min_circle_2( );}{
destructor.} destructor.}
\ccUnchecked
\ccHidden \ccHidden
\ccMemberFunction{ CGAL_Min_circle_2<I>& \ccMemberFunction{ CGAL_Min_circle_2<I>&
operator = ( CGAL_Min_circle_2<I> const&);}{ operator = ( CGAL_Min_circle_2<I> const&);}{
@ -185,14 +193,15 @@ for the STL sequence containers \ccc{vector<Point>} and \ccc{list<Point>}.
\ccMemberFunction{ Point const& support_point( int i) const;}{ \ccMemberFunction{ Point const& support_point( int i) const;}{
returns the \ccc{i}-th support point of \ccVar. Between two returns the \ccc{i}-th support point of \ccVar. Between two
insert operations any call to \ccc{\ccVar.support_point(i)} insert operations any call to \ccVar\ccc{.support_point(i)}
with the same \ccc{i} returns the same point. with the same \ccc{i} returns the same point.
\ccPrecond $0 \leq i <$ \ccc{\ccVar.number_of_support_points()}.} \ccPrecond $0 \leq i <$ \ccVar\ccc{.number_of_support_points()}.}
\ccMemberFunction{ Circle circle( ) const;}{
returns a circle with same center and same squared radius
as \ccVar, if \ccVar is not empty. Otherwise the default
circle, i.e.\ \ccc{Circle()}, is returned.}
\ccMemberFunction{ Circle const& circle( ) const;}{
returns an oriented circle with same center $c$ and same
squared radius $r$ as \ccVar\ and positive orientation.
\ccPrecond \ccc{\ccVar.is_empty()} = \ccc{false}.}
% ----------------------------------------------------------------------------- % -----------------------------------------------------------------------------
\ccPredicates \ccPredicates
@ -227,7 +236,7 @@ bounded side, i.e.\ its unbounded side equals the whole plane $\E_2$.
the number of support points is less than 2.} the number of support points is less than 2.}
% ----------------------------------------------------------------------------- % -----------------------------------------------------------------------------
\ccModifiers \ccHeading{Modifiers}
New points can be added to an existing $\ccVar$, allowing to build New points can be added to an existing $\ccVar$, allowing to build
$mc(P)$ incrementally, e.g.\ if $P$ is not known in advance. Compared $mc(P)$ incrementally, e.g.\ if $P$ is not known in advance. Compared
@ -243,9 +252,9 @@ the construction method is incremental itself.
An object \ccVar\ is valid, iff An object \ccVar\ is valid, iff
\begin{itemize} \begin{itemize}
\item[a)] \ccVar\ contains all points of its defining set $P$, \item \ccVar\ contains all points of its defining set $P$,
\item[b)] \ccVar\ is the smallest circle spanned by its support set $S$, and \item \ccVar\ is the smallest circle spanned by its support set $S$, and
\item[c)] $S$ is minimal, i.e.\ no support point is redundant. \item $S$ is minimal, i.e.\ no support point is redundant.
\end{itemize} \end{itemize}
Using the ready-made implementation for the interface class with exact Using the ready-made implementation for the interface class with exact
arithmetic as described in Section~\ref{sec:opt_I_Impl} guarantees arithmetic as described in Section~\ref{sec:opt_I_Impl} guarantees
@ -268,7 +277,8 @@ debugging user supplied interface classes.
\ccFunction{ ostream& operator << ( ostream& os, \ccFunction{ ostream& operator << ( ostream& os,
CGAL_Min_circle_2<I> const& min_circle);}{ CGAL_Min_circle_2<I> const& min_circle);}{
writes \ccVar\ to output stream \ccc{os}. writes \ccVar\ to output stream \ccc{os}.
\ccPrecond The output operator is defined for \ccc{I::Point}.} \ccPrecond The output operator is defined for \ccc{I::Point}
(and for \ccc{I::Circle}, if pretty printing is used).}
\ccFunction{ istream& operator >> ( istream& is, \ccFunction{ istream& operator >> ( istream& is,
CGAL_Min_circle_2<I> &min_circle);}{ CGAL_Min_circle_2<I> &min_circle);}{
@ -277,6 +287,7 @@ debugging user supplied interface classes.
\ccInclude{CGAL/IO/Window_stream.h} \ccInclude{CGAL/IO/Window_stream.h}
\ccUnchecked
\ccFunction{ CGAL_Window_stream& \ccFunction{ CGAL_Window_stream&
operator << ( CGAL_Window_stream& ws, operator << ( CGAL_Window_stream& ws,
CGAL_Min_circle_2<I> const& min_circle);}{ CGAL_Min_circle_2<I> const& min_circle);}{
@ -295,17 +306,6 @@ linear time, but substantially less than computing the new smallest
enclosing circle from scratch. The check for validity takes linear enclosing circle from scratch. The check for validity takes linear
time. time.
%We provide a specialization with homogeneous representation and
%numbertype \ccc{integer} that uses floating-point filter for the sign
%calculations in the predicates (see~\cite{MehlhornNaeher94}). This
%decreaes computation time by a factor of four compared to the generic
%implementation. If both \ccc{<CGAL/Integer.h>} and
%\ccc{<CGAL/Homogeneous.h>} are included before
%\ccc{<CGAL/Min_circle_2.h>} then the specialization for
%\ccc{CGAL_Min_circle_2< CGAL_Optimisation_default_interface<
% CGAL_Homogeneous<integer> > >} is used instead of the generic
%implementation.
% ----------------------------------------------------------------------------- % -----------------------------------------------------------------------------
\ccExample \ccExample