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fixed bugs from HTML conversion

This commit is contained in:
Sven Schönherr 1997-12-17 16:36:21 +00:00
parent c0eba4ddc5
commit ef47ecf1ba
10 changed files with 94 additions and 90 deletions
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16
Packages/Min_circle_2/doc_tex/Optimisation/Optimisation_ref/Min_circle_2.tex
View File

@ -98,7 +98,7 @@ reconstructing $mc(P)$ from a given support set $S$ of $P$.
CGAL_Random& random = CGAL_random, CGAL_Random& random = CGAL_random,
Traits const& traits = Traits() );}{ Traits const& traits = Traits() );}{
creates a variable \ccVar\ of type \ccClassTemplateName% creates a variable \ccVar\ of type \ccClassTemplateName%
\SaveSpaceByHand{$\!$}{}. \SaveSpaceByHand\ccTexHtml{$\!$}{}.
It is initialized to $mc(P)$ with $P$ being the set of points It is initialized to $mc(P)$ with $P$ being the set of points
in the range [\ccc{first},\ccc{last}). If \ccc{randomize} is in the range [\ccc{first},\ccc{last}). If \ccc{randomize} is
\ccc{true}, a random permutation of $P$ is computed in \ccc{true}, a random permutation of $P$ is computed in
@ -144,7 +144,7 @@ the \stl\ input stream iterator \ccc{istream_iterator<Point>}.
\ccConstructor{ CGAL_Min_circle_2( Traits const& traits = Traits());}{ \ccConstructor{ CGAL_Min_circle_2( Traits const& traits = Traits());}{
creates a variable \ccVar\ of type \ccClassTemplateName% creates a variable \ccVar\ of type \ccClassTemplateName%
\SaveSpaceByHand{$\!$}{}. \SaveSpaceByHand\ccTexHtml{$\!$}{}.
It is initialized to It is initialized to
$mc(\mbox{\ccTexHtml{$\emptyset$}{&Oslash;}})$, the empty set. $mc(\mbox{\ccTexHtml{$\emptyset$}{&Oslash;}})$, the empty set.
\ccPostcond \ccVar\ccc{.is_empty()} = \ccc{true}.} \ccPostcond \ccVar\ccc{.is_empty()} = \ccc{true}.}
@ -152,7 +152,7 @@ the \stl\ input stream iterator \ccc{istream_iterator<Point>}.
\ccConstructor{ CGAL_Min_circle_2( Point const& p, \ccConstructor{ CGAL_Min_circle_2( Point const& p,
Traits const& traits = Traits());}{ Traits const& traits = Traits());}{
creates a variable \ccVar\ of type \ccClassTemplateName% creates a variable \ccVar\ of type \ccClassTemplateName%
\SaveSpaceByHand{$\!$}{}. \SaveSpaceByHand\ccTexHtml{$\!$}{}.
It is initialized to $mc(\{p\})$, the set $\{p\}$. It is initialized to $mc(\{p\})$, the set $\{p\}$.
\ccPostcond \ccVar\ccc{.is_degenerate()} = \ccc{true}.} \ccPostcond \ccVar\ccc{.is_degenerate()} = \ccc{true}.}
@ -160,7 +160,7 @@ the \stl\ input stream iterator \ccc{istream_iterator<Point>}.
Point const& p2, Point const& p2,
Traits const& traits = Traits());}{ Traits const& traits = Traits());}{
creates a variable \ccVar\ of type \ccClassTemplateName% creates a variable \ccVar\ of type \ccClassTemplateName%
\SaveSpaceByHand{$\!$}{}. \SaveSpaceByHand\ccTexHtml{$\!$}{}.
It is initialized to $mc(\{p1,p2\})$, the circle with diameter It is initialized to $mc(\{p1,p2\})$, the circle with diameter
equal to the segment connecting $p1$ and $p2$.} equal to the segment connecting $p1$ and $p2$.}
@ -169,7 +169,7 @@ the \stl\ input stream iterator \ccc{istream_iterator<Point>}.
Point const& p3, Point const& p3,
Traits const& traits = Traits());}{ Traits const& traits = Traits());}{
creates a variable \ccVar\ of type \ccClassTemplateName% creates a variable \ccVar\ of type \ccClassTemplateName%
\SaveSpaceByHand{$\!$}{}. \SaveSpaceByHand\ccTexHtml{$\!$}{}.
It is initialized to $mc(\{p1,p2,p3\})$.} It is initialized to $mc(\{p1,p2,p3\})$.}
\ccUnchecked \ccUnchecked
@ -233,9 +233,9 @@ bounded side, i.e.\ its unbounded side equals the whole plane $\E_2$.
\ccMemberFunction{ CGAL_Bounded_side \ccMemberFunction{ CGAL_Bounded_side
bounded_side( Point const& p) const;}{ bounded_side( Point const& p) const;}{
returns \ccc{CGAL_ON_BOUNDED_SIDE},% returns \ccc{CGAL_ON_BOUNDED_SIDE},%
\SaveSpaceByHand{}{ }% \SaveSpaceByHand\ccTexHtml{}{ }%
\ccc{CGAL_ON_BOUNDARY}% \ccc{CGAL_ON_BOUNDARY}%
\SaveSpaceByHand{$\!$}{}, \SaveSpaceByHand\ccTexHtml{$\!$}{},
or or
\ccc{CGAL_ON_UNBOUNDED_SIDE} iff \ccc{p} lies properly inside, \ccc{CGAL_ON_UNBOUNDED_SIDE} iff \ccc{p} lies properly inside,
on the boundary, or properly outside of \ccVar, resp.} on the boundary, or properly outside of \ccVar, resp.}
@ -366,7 +366,7 @@ correct.
\ccc{Point} and \ccc{Circle}.} \ccc{Point} and \ccc{Circle}.}
% ----------------------------------------------------------------------------- % -----------------------------------------------------------------------------
\ccSeeAlso \ccHeading{See Also}
\ccc{CGAL_Min_ellipse_2} \ccc{CGAL_Min_ellipse_2}
(Section~\ref{sec:min_ellipse_2_spec}), (Section~\ref{sec:min_ellipse_2_spec}),

11
Packages/Min_circle_2/doc_tex/Optimisation/Optimisation_ref/Min_circle_2_traits.tex
View File

@ -133,8 +133,9 @@ of \ccc{CGAL_Min_circle_2} is used.
\ccMemberFunction{ void set( Point const& p, \ccMemberFunction{ void set( Point const& p,
Point const& q);}{ Point const& q);}{
sets \ccVar\ to the circle with diameter sets \ccVar\ to the circle with diameter
$\overline{\mbox{\ccc{p}\ccc{q}}}$. The algorithm \ccTexHtml{$\overline{\mbox{\ccc{p}\ccc{q}}}$}{<i>pq</i>}.
guarantees that \ccc{set} is never called with two equal points.} The algorithm guarantees that \ccc{set} is never called
with two equal points.}
\ccMemberFunction{ void set( Point const& p, \ccMemberFunction{ void set( Point const& p,
Point const& q, Point const& q,
@ -155,9 +156,9 @@ predicate of \ccc{CGAL_Min_circle_2} is used.
\ccMemberFunction{ CGAL_Bounded_side \ccMemberFunction{ CGAL_Bounded_side
bounded_side( Point const& p) const;}{ bounded_side( Point const& p) const;}{
returns \ccc{CGAL_ON_BOUNDED_SIDE},% returns \ccc{CGAL_ON_BOUNDED_SIDE},%
\SaveSpaceByHand{}{ }% \SaveSpaceByHand\ccTexHtml{}{ }%
\ccc{CGAL_ON_BOUNDARY}% \ccc{CGAL_ON_BOUNDARY}%
\SaveSpaceByHand{$\!$}{}, \SaveSpaceByHand\ccTexHtml{$\!$}{},
or or
\ccc{CGAL_ON_UNBOUNDED_SIDE} iff \ccc{p} lies properly inside, \ccc{CGAL_ON_UNBOUNDED_SIDE} iff \ccc{p} lies properly inside,
on the boundary, or properly outside of \ccVar, resp.} on the boundary, or properly outside of \ccVar, resp.}
@ -198,9 +199,11 @@ The following operations are only needed, if the member function
The following I/O operators are only needed, if the corresponding I/O The following I/O operators are only needed, if the corresponding I/O
operators of \ccc{CGAL_Min_circle_2} are used. operators of \ccc{CGAL_Min_circle_2} are used.
\ccHtmlNoIndex
\ccFunction{ ostream& operator << ( ostream& os, Circle const& circle);}{ \ccFunction{ ostream& operator << ( ostream& os, Circle const& circle);}{
writes \ccVar\ to output stream \ccc{os}.} writes \ccVar\ to output stream \ccc{os}.}
\ccHtmlNoIndex
\ccFunction{ istream& operator >> ( istream& is, Circle &circle);}{ \ccFunction{ istream& operator >> ( istream& is, Circle &circle);}{
reads \ccVar\ from input stream \ccc{is}.} reads \ccVar\ from input stream \ccc{is}.}

16
Packages/Min_circle_2/doc_tex/basic/Optimisation/Optimisation_ref/Min_circle_2.tex
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@ -98,7 +98,7 @@ reconstructing $mc(P)$ from a given support set $S$ of $P$.
CGAL_Random& random = CGAL_random, CGAL_Random& random = CGAL_random,
Traits const& traits = Traits() );}{ Traits const& traits = Traits() );}{
creates a variable \ccVar\ of type \ccClassTemplateName% creates a variable \ccVar\ of type \ccClassTemplateName%
\SaveSpaceByHand{$\!$}{}. \SaveSpaceByHand\ccTexHtml{$\!$}{}.
It is initialized to $mc(P)$ with $P$ being the set of points It is initialized to $mc(P)$ with $P$ being the set of points
in the range [\ccc{first},\ccc{last}). If \ccc{randomize} is in the range [\ccc{first},\ccc{last}). If \ccc{randomize} is
\ccc{true}, a random permutation of $P$ is computed in \ccc{true}, a random permutation of $P$ is computed in
@ -144,7 +144,7 @@ the \stl\ input stream iterator \ccc{istream_iterator<Point>}.
\ccConstructor{ CGAL_Min_circle_2( Traits const& traits = Traits());}{ \ccConstructor{ CGAL_Min_circle_2( Traits const& traits = Traits());}{
creates a variable \ccVar\ of type \ccClassTemplateName% creates a variable \ccVar\ of type \ccClassTemplateName%
\SaveSpaceByHand{$\!$}{}. \SaveSpaceByHand\ccTexHtml{$\!$}{}.
It is initialized to It is initialized to
$mc(\mbox{\ccTexHtml{$\emptyset$}{&Oslash;}})$, the empty set. $mc(\mbox{\ccTexHtml{$\emptyset$}{&Oslash;}})$, the empty set.
\ccPostcond \ccVar\ccc{.is_empty()} = \ccc{true}.} \ccPostcond \ccVar\ccc{.is_empty()} = \ccc{true}.}
@ -152,7 +152,7 @@ the \stl\ input stream iterator \ccc{istream_iterator<Point>}.
\ccConstructor{ CGAL_Min_circle_2( Point const& p, \ccConstructor{ CGAL_Min_circle_2( Point const& p,
Traits const& traits = Traits());}{ Traits const& traits = Traits());}{
creates a variable \ccVar\ of type \ccClassTemplateName% creates a variable \ccVar\ of type \ccClassTemplateName%
\SaveSpaceByHand{$\!$}{}. \SaveSpaceByHand\ccTexHtml{$\!$}{}.
It is initialized to $mc(\{p\})$, the set $\{p\}$. It is initialized to $mc(\{p\})$, the set $\{p\}$.
\ccPostcond \ccVar\ccc{.is_degenerate()} = \ccc{true}.} \ccPostcond \ccVar\ccc{.is_degenerate()} = \ccc{true}.}
@ -160,7 +160,7 @@ the \stl\ input stream iterator \ccc{istream_iterator<Point>}.
Point const& p2, Point const& p2,
Traits const& traits = Traits());}{ Traits const& traits = Traits());}{
creates a variable \ccVar\ of type \ccClassTemplateName% creates a variable \ccVar\ of type \ccClassTemplateName%
\SaveSpaceByHand{$\!$}{}. \SaveSpaceByHand\ccTexHtml{$\!$}{}.
It is initialized to $mc(\{p1,p2\})$, the circle with diameter It is initialized to $mc(\{p1,p2\})$, the circle with diameter
equal to the segment connecting $p1$ and $p2$.} equal to the segment connecting $p1$ and $p2$.}
@ -169,7 +169,7 @@ the \stl\ input stream iterator \ccc{istream_iterator<Point>}.
Point const& p3, Point const& p3,
Traits const& traits = Traits());}{ Traits const& traits = Traits());}{
creates a variable \ccVar\ of type \ccClassTemplateName% creates a variable \ccVar\ of type \ccClassTemplateName%
\SaveSpaceByHand{$\!$}{}. \SaveSpaceByHand\ccTexHtml{$\!$}{}.
It is initialized to $mc(\{p1,p2,p3\})$.} It is initialized to $mc(\{p1,p2,p3\})$.}
\ccUnchecked \ccUnchecked
@ -233,9 +233,9 @@ bounded side, i.e.\ its unbounded side equals the whole plane $\E_2$.
\ccMemberFunction{ CGAL_Bounded_side \ccMemberFunction{ CGAL_Bounded_side
bounded_side( Point const& p) const;}{ bounded_side( Point const& p) const;}{
returns \ccc{CGAL_ON_BOUNDED_SIDE},% returns \ccc{CGAL_ON_BOUNDED_SIDE},%
\SaveSpaceByHand{}{ }% \SaveSpaceByHand\ccTexHtml{}{ }%
\ccc{CGAL_ON_BOUNDARY}% \ccc{CGAL_ON_BOUNDARY}%
\SaveSpaceByHand{$\!$}{}, \SaveSpaceByHand\ccTexHtml{$\!$}{},
or or
\ccc{CGAL_ON_UNBOUNDED_SIDE} iff \ccc{p} lies properly inside, \ccc{CGAL_ON_UNBOUNDED_SIDE} iff \ccc{p} lies properly inside,
on the boundary, or properly outside of \ccVar, resp.} on the boundary, or properly outside of \ccVar, resp.}
@ -366,7 +366,7 @@ correct.
\ccc{Point} and \ccc{Circle}.} \ccc{Point} and \ccc{Circle}.}
% ----------------------------------------------------------------------------- % -----------------------------------------------------------------------------
\ccSeeAlso \ccHeading{See Also}
\ccc{CGAL_Min_ellipse_2} \ccc{CGAL_Min_ellipse_2}
(Section~\ref{sec:min_ellipse_2_spec}), (Section~\ref{sec:min_ellipse_2_spec}),

11
Packages/Min_circle_2/doc_tex/basic/Optimisation/Optimisation_ref/Min_circle_2_traits.tex
View File

@ -133,8 +133,9 @@ of \ccc{CGAL_Min_circle_2} is used.
\ccMemberFunction{ void set( Point const& p, \ccMemberFunction{ void set( Point const& p,
Point const& q);}{ Point const& q);}{
sets \ccVar\ to the circle with diameter sets \ccVar\ to the circle with diameter
$\overline{\mbox{\ccc{p}\ccc{q}}}$. The algorithm \ccTexHtml{$\overline{\mbox{\ccc{p}\ccc{q}}}$}{<i>pq</i>}.
guarantees that \ccc{set} is never called with two equal points.} The algorithm guarantees that \ccc{set} is never called
with two equal points.}
\ccMemberFunction{ void set( Point const& p, \ccMemberFunction{ void set( Point const& p,
Point const& q, Point const& q,
@ -155,9 +156,9 @@ predicate of \ccc{CGAL_Min_circle_2} is used.
\ccMemberFunction{ CGAL_Bounded_side \ccMemberFunction{ CGAL_Bounded_side
bounded_side( Point const& p) const;}{ bounded_side( Point const& p) const;}{
returns \ccc{CGAL_ON_BOUNDED_SIDE},% returns \ccc{CGAL_ON_BOUNDED_SIDE},%
\SaveSpaceByHand{}{ }% \SaveSpaceByHand\ccTexHtml{}{ }%
\ccc{CGAL_ON_BOUNDARY}% \ccc{CGAL_ON_BOUNDARY}%
\SaveSpaceByHand{$\!$}{}, \SaveSpaceByHand\ccTexHtml{$\!$}{},
or or
\ccc{CGAL_ON_UNBOUNDED_SIDE} iff \ccc{p} lies properly inside, \ccc{CGAL_ON_UNBOUNDED_SIDE} iff \ccc{p} lies properly inside,
on the boundary, or properly outside of \ccVar, resp.} on the boundary, or properly outside of \ccVar, resp.}
@ -198,9 +199,11 @@ The following operations are only needed, if the member function
The following I/O operators are only needed, if the corresponding I/O The following I/O operators are only needed, if the corresponding I/O
operators of \ccc{CGAL_Min_circle_2} are used. operators of \ccc{CGAL_Min_circle_2} are used.
\ccHtmlNoIndex
\ccFunction{ ostream& operator << ( ostream& os, Circle const& circle);}{ \ccFunction{ ostream& operator << ( ostream& os, Circle const& circle);}{
writes \ccVar\ to output stream \ccc{os}.} writes \ccVar\ to output stream \ccc{os}.}
\ccHtmlNoIndex
\ccFunction{ istream& operator >> ( istream& is, Circle &circle);}{ \ccFunction{ istream& operator >> ( istream& is, Circle &circle);}{
reads \ccVar\ from input stream \ccc{is}.} reads \ccVar\ from input stream \ccc{is}.}

44
Packages/Min_ellipse_2/doc_tex/Optimisation/Optimisation_ref/Min_ellipse_2.tex
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@ -23,8 +23,8 @@ euclidean space $\E_2$. For a point set $P$ we denote by $me(P)$ the
smallest ellipse that contains all points of $P$. Note that $me(P)$ can be smallest ellipse that contains all points of $P$. Note that $me(P)$ can be
degenerate, i.e.\ $me(P)=\mbox{\ccTexHtml{$\;\emptyset$}{&Oslash;}}$ if degenerate, i.e.\ $me(P)=\mbox{\ccTexHtml{$\;\emptyset$}{&Oslash;}}$ if
$P=\mbox{\ccTexHtml{$\;\emptyset$}{&Oslash;}}$, $me(P)=\{p\}$ if $P=\{p\}$, $P=\mbox{\ccTexHtml{$\;\emptyset$}{&Oslash;}}$, $me(P)=\{p\}$ if $P=\{p\}$,
and $me(P) = \{ (1-\lambda)p + \lambda q \mid 0 \leq \lambda \leq 1 \}$ if and $me(P) = \{ \mbox{\ccTexHtml{$(1-\lambda)p + \lambda q \mid
$P=\{p,q\}$. 0 \leq \lambda \leq 1$}{(1-l)p + l q | 0 <= l <= 1}} \}$ if $P=\{p,q\}$.
An inclusion-minimal subset $S$ of $P$ with $me(S)=me(P)$ is called a An inclusion-minimal subset $S$ of $P$ with $me(S)=me(P)$ is called a
\emph{support set}, the points in $S$ are the \emph{support points}. \emph{support set}, the points in $S$ are the \emph{support points}.
@ -99,9 +99,9 @@ useful for reconstructing $me(P)$ from a given support set $S$ of $P$.
CGAL_Random& random = CGAL_random, CGAL_Random& random = CGAL_random,
Traits const& traits = Traits() );}{ Traits const& traits = Traits() );}{
creates creates
\SaveSpaceByHand{}{a} \SaveSpaceByHand\ccTexHtml{}{a}
variable \ccVar\ of type \ccClassTemplateName% variable \ccVar\ of type \ccClassTemplateName%
\SaveSpaceByHand{$\!$}{}. \SaveSpaceByHand\ccTexHtml{$\!$}{}.
It is initialized to $mc(P)$ with $P$ being the set of points It is initialized to $mc(P)$ with $P$ being the set of points
in the range [\ccc{first},\ccc{last}). If \ccc{randomize} is in the range [\ccc{first},\ccc{last}). If \ccc{randomize} is
\ccc{true}, a random permutation of $P$ is computed in \ccc{true}, a random permutation of $P$ is computed in
@ -147,9 +147,9 @@ the \stl\ input stream iterator \ccc{istream_iterator<Point>}.
\ccConstructor{ CGAL_Min_ellipse_2( Traits const& traits = Traits());}{ \ccConstructor{ CGAL_Min_ellipse_2( Traits const& traits = Traits());}{
creates creates
\SaveSpaceByHand{}{a} \SaveSpaceByHand\ccTexHtml{}{a}
variable \ccVar\ of type \ccClassTemplateName% variable \ccVar\ of type \ccClassTemplateName%
\SaveSpaceByHand{$\!$}{}. \SaveSpaceByHand\ccTexHtml{$\!$}{}.
It is initialized to It is initialized to
$me(\mbox{\ccTexHtml{$\emptyset$}{&Oslash;}})$, the empty set. $me(\mbox{\ccTexHtml{$\emptyset$}{&Oslash;}})$, the empty set.
\ccPostcond \ccVar\ccc{.is_empty()} = \ccc{true}.} \ccPostcond \ccVar\ccc{.is_empty()} = \ccc{true}.}
@ -157,11 +157,9 @@ the \stl\ input stream iterator \ccc{istream_iterator<Point>}.
\ccConstructor{ CGAL_Min_ellipse_2( Point const& p, \ccConstructor{ CGAL_Min_ellipse_2( Point const& p,
Traits const& traits = Traits());}{ Traits const& traits = Traits());}{
creates creates
\SaveSpaceByHand{}{a} \SaveSpaceByHand\ccTexHtml{}{a}
variable \ccVar\ of type \ccClassTemplateName% variable \ccVar\ of type \ccClassTemplateName%
\SaveSpaceByHand{$\!$}{}. \SaveSpaceByHand\ccTexHtml{$\!$}{}.
\SaveSpaceByHand{a}
variable \ccVar\ of type \ccClassTemplateName.
It is initialized to $me(\{p\})$, the set $\{p\}$. It is initialized to $me(\{p\})$, the set $\{p\}$.
\ccPostcond \ccVar\ccc{.is_degenerate()} = \ccc{true}.} \ccPostcond \ccVar\ccc{.is_degenerate()} = \ccc{true}.}
@ -169,9 +167,9 @@ the \stl\ input stream iterator \ccc{istream_iterator<Point>}.
Point const& q, Point const& q,
Traits const& traits = Traits());}{ Traits const& traits = Traits());}{
creates creates
\SaveSpaceByHand{}{a} \SaveSpaceByHand\ccTexHtml{}{a}
variable \ccVar\ of type \ccClassTemplateName% variable \ccVar\ of type \ccClassTemplateName%
\SaveSpaceByHand{$\!$}{}. \SaveSpaceByHand\ccTexHtml{$\!$}{}.
It is initialized to $me(\{p,q\})$, the set It is initialized to $me(\{p,q\})$, the set
$\{ (1-\lambda)p + \lambda q \mid 0 \leq \lambda \leq 1 \}$. $\{ (1-\lambda)p + \lambda q \mid 0 \leq \lambda \leq 1 \}$.
\ccPostcond \ccVar\ccc{.is_degenerate()} = \ccc{true}.} \ccPostcond \ccVar\ccc{.is_degenerate()} = \ccc{true}.}
@ -181,9 +179,9 @@ the \stl\ input stream iterator \ccc{istream_iterator<Point>}.
Point const& p3, Point const& p3,
Traits const& traits = Traits());}{ Traits const& traits = Traits());}{
creates creates
\SaveSpaceByHand{}{a} \SaveSpaceByHand\ccTexHtml{}{a}
variable \ccVar\ of type \ccClassTemplateName% variable \ccVar\ of type \ccClassTemplateName%
\SaveSpaceByHand{$\!$}{}. \SaveSpaceByHand\ccTexHtml{$\!$}{}.
It is initialized to $me(\{p1,p2,p3\})$.} It is initialized to $me(\{p1,p2,p3\})$.}
\ccConstructor{ CGAL_Min_ellipse_2( Point const& p1, \ccConstructor{ CGAL_Min_ellipse_2( Point const& p1,
@ -192,9 +190,9 @@ the \stl\ input stream iterator \ccc{istream_iterator<Point>}.
Point const& p4, Point const& p4,
Traits const& traits = Traits());}{ Traits const& traits = Traits());}{
creates creates
\SaveSpaceByHand{}{a} \SaveSpaceByHand\ccTexHtml{}{a}
variable \ccVar\ of type \ccClassTemplateName% variable \ccVar\ of type \ccClassTemplateName%
\SaveSpaceByHand{$\!$}{}. \SaveSpaceByHand\ccTexHtml{$\!$}{}.
It is initialized to $me(\{p1,p2,p3,p4\})$.} It is initialized to $me(\{p1,p2,p3,p4\})$.}
\ccConstructor{ CGAL_Min_ellipse_2( Point const& p1, \ccConstructor{ CGAL_Min_ellipse_2( Point const& p1,
@ -204,9 +202,9 @@ the \stl\ input stream iterator \ccc{istream_iterator<Point>}.
Point const& p5, Point const& p5,
Traits const& traits = Traits());}{ Traits const& traits = Traits());}{
creates creates
\SaveSpaceByHand{}{a} \SaveSpaceByHand\ccTexHtml{}{a}
variable \ccVar\ of type \ccClassTemplateName% variable \ccVar\ of type \ccClassTemplateName%
\SaveSpaceByHand{$\!$}{}. \SaveSpaceByHand\ccTexHtml{$\!$}{}.
It is initialized to $me(\{p1,p2,p3,p4,p5\})$.} It is initialized to $me(\{p1,p2,p3,p4,p5\})$.}
\ccUnchecked \ccUnchecked
@ -252,10 +250,10 @@ the \stl\ input stream iterator \ccc{istream_iterator<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% returns the \ccc{i}-th support point of \ccVar%
\SaveSpaceByHand{$\!$}{}. \SaveSpaceByHand\ccTexHtml{$\!$}{}.
Between two Between two
modifying operations (see modifying operations (see
\SaveSpaceByHand{$\!$}{} \SaveSpaceByHand\ccTexHtml{$\!$}{}
below) any call to below) any call to
\ccVar\ccc{.support_point(i)} with the same \ccc{i} returns \ccVar\ccc{.support_point(i)} with the same \ccc{i} returns
the same point. the same point.
@ -273,9 +271,9 @@ bounded side, i.e.\ its unbounded side equals the whole plane $\E_2$.
\ccMemberFunction{ CGAL_Bounded_side \ccMemberFunction{ CGAL_Bounded_side
bounded_side( Point const& p) const;}{ bounded_side( Point const& p) const;}{
returns \ccc{CGAL_ON_BOUNDED_SIDE},% returns \ccc{CGAL_ON_BOUNDED_SIDE},%
\SaveSpaceByHand{}{ }% \SaveSpaceByHand\ccTexHtml{}{ }%
\ccc{CGAL_ON_BOUNDARY}% \ccc{CGAL_ON_BOUNDARY}%
\SaveSpaceByHand{$\!$}{}, \SaveSpaceByHand\ccTexHtml{$\!$}{},
or or
\ccc{CGAL_ON_UNBOUNDED_SIDE} iff \ccc{p} lies properly inside, \ccc{CGAL_ON_UNBOUNDED_SIDE} iff \ccc{p} lies properly inside,
on the boundary, or properly outside of \ccVar, resp.} on the boundary, or properly outside of \ccVar, resp.}
@ -410,7 +408,7 @@ correct.
\ccc{Point} and \ccc{Ellipse}.} \ccc{Point} and \ccc{Ellipse}.}
% ----------------------------------------------------------------------------- % -----------------------------------------------------------------------------
\ccSeeAlso \ccHeading{See Also}
\ccc{CGAL_Min_circle_2} \ccc{CGAL_Min_circle_2}
(Section~\ref{sec:min_circle_2_spec}), (Section~\ref{sec:min_circle_2_spec}),

11
Packages/Min_ellipse_2/doc_tex/Optimisation/Optimisation_ref/Min_ellipse_2_traits.tex
View File

@ -112,8 +112,9 @@ whole plane $\E_2$.
\ccMemberFunction{ void set( Point const& p, \ccMemberFunction{ void set( Point const& p,
Point const& q);}{ Point const& q);}{
sets \ccVar\ to the ellipse containing exactly the segment sets \ccVar\ to the ellipse containing exactly the segment
$\overline{\mbox{\ccc{p}\ccc{q}}}$. The algorithm \ccTexHtml{$\overline{\mbox{\ccc{p}\ccc{q}}}$}{<i>pq</i>}.
guarantees that \ccc{set} is never called with two equal points.} The algorithm guarantees that \ccc{set} is never called
with two equal points.}
\ccMemberFunction{ void set( Point const& p, \ccMemberFunction{ void set( Point const& p,
Point const& q, Point const& q,
@ -151,9 +152,9 @@ predicate of \ccc{CGAL_Min_ellipse_2} is used.
\ccMemberFunction{ CGAL_Bounded_side \ccMemberFunction{ CGAL_Bounded_side
bounded_side( Point const& p) const;}{ bounded_side( Point const& p) const;}{
returns \ccc{CGAL_ON_BOUNDED_SIDE},% returns \ccc{CGAL_ON_BOUNDED_SIDE},%
\SaveSpaceByHand{}{ }% \SaveSpaceByHand\ccTexHtml{}{ }%
\ccc{CGAL_ON_BOUNDARY}% \ccc{CGAL_ON_BOUNDARY}%
\SaveSpaceByHand{$\!$}{}, \SaveSpaceByHand\ccTexHtml{$\!$}{},
or or
\ccc{CGAL_ON_UNBOUNDED_SIDE} iff \ccc{p} lies properly inside, \ccc{CGAL_ON_UNBOUNDED_SIDE} iff \ccc{p} lies properly inside,
on the boundary, or properly outside of \ccVar, resp.} on the boundary, or properly outside of \ccVar, resp.}
@ -179,9 +180,11 @@ predicate of \ccc{CGAL_Min_ellipse_2} is used.
The following I/O operators are only needed, if the corresponding I/O The following I/O operators are only needed, if the corresponding I/O
operators of \ccc{CGAL_Min_ellipse_2} are used. operators of \ccc{CGAL_Min_ellipse_2} are used.
\ccHtmlNoIndex
\ccFunction{ ostream& operator << ( ostream& os, Ellipse const& ellipse);}{ \ccFunction{ ostream& operator << ( ostream& os, Ellipse const& ellipse);}{
writes \ccVar\ to output stream \ccc{os}.} writes \ccVar\ to output stream \ccc{os}.}
\ccHtmlNoIndex
\ccFunction{ istream& operator >> ( istream& is, Ellipse &ellipse);}{ \ccFunction{ istream& operator >> ( istream& is, Ellipse &ellipse);}{
reads \ccVar\ from input stream \ccc{is}.} reads \ccVar\ from input stream \ccc{is}.}

44
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@ -23,8 +23,8 @@ euclidean space $\E_2$. For a point set $P$ we denote by $me(P)$ the
smallest ellipse that contains all points of $P$. Note that $me(P)$ can be smallest ellipse that contains all points of $P$. Note that $me(P)$ can be
degenerate, i.e.\ $me(P)=\mbox{\ccTexHtml{$\;\emptyset$}{&Oslash;}}$ if degenerate, i.e.\ $me(P)=\mbox{\ccTexHtml{$\;\emptyset$}{&Oslash;}}$ if
$P=\mbox{\ccTexHtml{$\;\emptyset$}{&Oslash;}}$, $me(P)=\{p\}$ if $P=\{p\}$, $P=\mbox{\ccTexHtml{$\;\emptyset$}{&Oslash;}}$, $me(P)=\{p\}$ if $P=\{p\}$,
and $me(P) = \{ (1-\lambda)p + \lambda q \mid 0 \leq \lambda \leq 1 \}$ if and $me(P) = \{ \mbox{\ccTexHtml{$(1-\lambda)p + \lambda q \mid
$P=\{p,q\}$. 0 \leq \lambda \leq 1$}{(1-l)p + l q | 0 <= l <= 1}} \}$ if $P=\{p,q\}$.
An inclusion-minimal subset $S$ of $P$ with $me(S)=me(P)$ is called a An inclusion-minimal subset $S$ of $P$ with $me(S)=me(P)$ is called a
\emph{support set}, the points in $S$ are the \emph{support points}. \emph{support set}, the points in $S$ are the \emph{support points}.
@ -99,9 +99,9 @@ useful for reconstructing $me(P)$ from a given support set $S$ of $P$.
CGAL_Random& random = CGAL_random, CGAL_Random& random = CGAL_random,
Traits const& traits = Traits() );}{ Traits const& traits = Traits() );}{
creates creates
\SaveSpaceByHand{}{a} \SaveSpaceByHand\ccTexHtml{}{a}
variable \ccVar\ of type \ccClassTemplateName% variable \ccVar\ of type \ccClassTemplateName%
\SaveSpaceByHand{$\!$}{}. \SaveSpaceByHand\ccTexHtml{$\!$}{}.
It is initialized to $mc(P)$ with $P$ being the set of points It is initialized to $mc(P)$ with $P$ being the set of points
in the range [\ccc{first},\ccc{last}). If \ccc{randomize} is in the range [\ccc{first},\ccc{last}). If \ccc{randomize} is
\ccc{true}, a random permutation of $P$ is computed in \ccc{true}, a random permutation of $P$ is computed in
@ -147,9 +147,9 @@ the \stl\ input stream iterator \ccc{istream_iterator<Point>}.
\ccConstructor{ CGAL_Min_ellipse_2( Traits const& traits = Traits());}{ \ccConstructor{ CGAL_Min_ellipse_2( Traits const& traits = Traits());}{
creates creates
\SaveSpaceByHand{}{a} \SaveSpaceByHand\ccTexHtml{}{a}
variable \ccVar\ of type \ccClassTemplateName% variable \ccVar\ of type \ccClassTemplateName%
\SaveSpaceByHand{$\!$}{}. \SaveSpaceByHand\ccTexHtml{$\!$}{}.
It is initialized to It is initialized to
$me(\mbox{\ccTexHtml{$\emptyset$}{&Oslash;}})$, the empty set. $me(\mbox{\ccTexHtml{$\emptyset$}{&Oslash;}})$, the empty set.
\ccPostcond \ccVar\ccc{.is_empty()} = \ccc{true}.} \ccPostcond \ccVar\ccc{.is_empty()} = \ccc{true}.}
@ -157,11 +157,9 @@ the \stl\ input stream iterator \ccc{istream_iterator<Point>}.
\ccConstructor{ CGAL_Min_ellipse_2( Point const& p, \ccConstructor{ CGAL_Min_ellipse_2( Point const& p,
Traits const& traits = Traits());}{ Traits const& traits = Traits());}{
creates creates
\SaveSpaceByHand{}{a} \SaveSpaceByHand\ccTexHtml{}{a}
variable \ccVar\ of type \ccClassTemplateName% variable \ccVar\ of type \ccClassTemplateName%
\SaveSpaceByHand{$\!$}{}. \SaveSpaceByHand\ccTexHtml{$\!$}{}.
\SaveSpaceByHand{a}
variable \ccVar\ of type \ccClassTemplateName.
It is initialized to $me(\{p\})$, the set $\{p\}$. It is initialized to $me(\{p\})$, the set $\{p\}$.
\ccPostcond \ccVar\ccc{.is_degenerate()} = \ccc{true}.} \ccPostcond \ccVar\ccc{.is_degenerate()} = \ccc{true}.}
@ -169,9 +167,9 @@ the \stl\ input stream iterator \ccc{istream_iterator<Point>}.
Point const& q, Point const& q,
Traits const& traits = Traits());}{ Traits const& traits = Traits());}{
creates creates
\SaveSpaceByHand{}{a} \SaveSpaceByHand\ccTexHtml{}{a}
variable \ccVar\ of type \ccClassTemplateName% variable \ccVar\ of type \ccClassTemplateName%
\SaveSpaceByHand{$\!$}{}. \SaveSpaceByHand\ccTexHtml{$\!$}{}.
It is initialized to $me(\{p,q\})$, the set It is initialized to $me(\{p,q\})$, the set
$\{ (1-\lambda)p + \lambda q \mid 0 \leq \lambda \leq 1 \}$. $\{ (1-\lambda)p + \lambda q \mid 0 \leq \lambda \leq 1 \}$.
\ccPostcond \ccVar\ccc{.is_degenerate()} = \ccc{true}.} \ccPostcond \ccVar\ccc{.is_degenerate()} = \ccc{true}.}
@ -181,9 +179,9 @@ the \stl\ input stream iterator \ccc{istream_iterator<Point>}.
Point const& p3, Point const& p3,
Traits const& traits = Traits());}{ Traits const& traits = Traits());}{
creates creates
\SaveSpaceByHand{}{a} \SaveSpaceByHand\ccTexHtml{}{a}
variable \ccVar\ of type \ccClassTemplateName% variable \ccVar\ of type \ccClassTemplateName%
\SaveSpaceByHand{$\!$}{}. \SaveSpaceByHand\ccTexHtml{$\!$}{}.
It is initialized to $me(\{p1,p2,p3\})$.} It is initialized to $me(\{p1,p2,p3\})$.}
\ccConstructor{ CGAL_Min_ellipse_2( Point const& p1, \ccConstructor{ CGAL_Min_ellipse_2( Point const& p1,
@ -192,9 +190,9 @@ the \stl\ input stream iterator \ccc{istream_iterator<Point>}.
Point const& p4, Point const& p4,
Traits const& traits = Traits());}{ Traits const& traits = Traits());}{
creates creates
\SaveSpaceByHand{}{a} \SaveSpaceByHand\ccTexHtml{}{a}
variable \ccVar\ of type \ccClassTemplateName% variable \ccVar\ of type \ccClassTemplateName%
\SaveSpaceByHand{$\!$}{}. \SaveSpaceByHand\ccTexHtml{$\!$}{}.
It is initialized to $me(\{p1,p2,p3,p4\})$.} It is initialized to $me(\{p1,p2,p3,p4\})$.}
\ccConstructor{ CGAL_Min_ellipse_2( Point const& p1, \ccConstructor{ CGAL_Min_ellipse_2( Point const& p1,
@ -204,9 +202,9 @@ the \stl\ input stream iterator \ccc{istream_iterator<Point>}.
Point const& p5, Point const& p5,
Traits const& traits = Traits());}{ Traits const& traits = Traits());}{
creates creates
\SaveSpaceByHand{}{a} \SaveSpaceByHand\ccTexHtml{}{a}
variable \ccVar\ of type \ccClassTemplateName% variable \ccVar\ of type \ccClassTemplateName%
\SaveSpaceByHand{$\!$}{}. \SaveSpaceByHand\ccTexHtml{$\!$}{}.
It is initialized to $me(\{p1,p2,p3,p4,p5\})$.} It is initialized to $me(\{p1,p2,p3,p4,p5\})$.}
\ccUnchecked \ccUnchecked
@ -252,10 +250,10 @@ the \stl\ input stream iterator \ccc{istream_iterator<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% returns the \ccc{i}-th support point of \ccVar%
\SaveSpaceByHand{$\!$}{}. \SaveSpaceByHand\ccTexHtml{$\!$}{}.
Between two Between two
modifying operations (see modifying operations (see
\SaveSpaceByHand{$\!$}{} \SaveSpaceByHand\ccTexHtml{$\!$}{}
below) any call to below) any call to
\ccVar\ccc{.support_point(i)} with the same \ccc{i} returns \ccVar\ccc{.support_point(i)} with the same \ccc{i} returns
the same point. the same point.
@ -273,9 +271,9 @@ bounded side, i.e.\ its unbounded side equals the whole plane $\E_2$.
\ccMemberFunction{ CGAL_Bounded_side \ccMemberFunction{ CGAL_Bounded_side
bounded_side( Point const& p) const;}{ bounded_side( Point const& p) const;}{
returns \ccc{CGAL_ON_BOUNDED_SIDE},% returns \ccc{CGAL_ON_BOUNDED_SIDE},%
\SaveSpaceByHand{}{ }% \SaveSpaceByHand\ccTexHtml{}{ }%
\ccc{CGAL_ON_BOUNDARY}% \ccc{CGAL_ON_BOUNDARY}%
\SaveSpaceByHand{$\!$}{}, \SaveSpaceByHand\ccTexHtml{$\!$}{},
or or
\ccc{CGAL_ON_UNBOUNDED_SIDE} iff \ccc{p} lies properly inside, \ccc{CGAL_ON_UNBOUNDED_SIDE} iff \ccc{p} lies properly inside,
on the boundary, or properly outside of \ccVar, resp.} on the boundary, or properly outside of \ccVar, resp.}
@ -410,7 +408,7 @@ correct.
\ccc{Point} and \ccc{Ellipse}.} \ccc{Point} and \ccc{Ellipse}.}
% ----------------------------------------------------------------------------- % -----------------------------------------------------------------------------
\ccSeeAlso \ccHeading{See Also}
\ccc{CGAL_Min_circle_2} \ccc{CGAL_Min_circle_2}
(Section~\ref{sec:min_circle_2_spec}), (Section~\ref{sec:min_circle_2_spec}),

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@ -112,8 +112,9 @@ whole plane $\E_2$.
\ccMemberFunction{ void set( Point const& p, \ccMemberFunction{ void set( Point const& p,
Point const& q);}{ Point const& q);}{
sets \ccVar\ to the ellipse containing exactly the segment sets \ccVar\ to the ellipse containing exactly the segment
$\overline{\mbox{\ccc{p}\ccc{q}}}$. The algorithm \ccTexHtml{$\overline{\mbox{\ccc{p}\ccc{q}}}$}{<i>pq</i>}.
guarantees that \ccc{set} is never called with two equal points.} The algorithm guarantees that \ccc{set} is never called
with two equal points.}
\ccMemberFunction{ void set( Point const& p, \ccMemberFunction{ void set( Point const& p,
Point const& q, Point const& q,
@ -151,9 +152,9 @@ predicate of \ccc{CGAL_Min_ellipse_2} is used.
\ccMemberFunction{ CGAL_Bounded_side \ccMemberFunction{ CGAL_Bounded_side
bounded_side( Point const& p) const;}{ bounded_side( Point const& p) const;}{
returns \ccc{CGAL_ON_BOUNDED_SIDE},% returns \ccc{CGAL_ON_BOUNDED_SIDE},%
\SaveSpaceByHand{}{ }% \SaveSpaceByHand\ccTexHtml{}{ }%
\ccc{CGAL_ON_BOUNDARY}% \ccc{CGAL_ON_BOUNDARY}%
\SaveSpaceByHand{$\!$}{}, \SaveSpaceByHand\ccTexHtml{$\!$}{},
or or
\ccc{CGAL_ON_UNBOUNDED_SIDE} iff \ccc{p} lies properly inside, \ccc{CGAL_ON_UNBOUNDED_SIDE} iff \ccc{p} lies properly inside,
on the boundary, or properly outside of \ccVar, resp.} on the boundary, or properly outside of \ccVar, resp.}
@ -179,9 +180,11 @@ predicate of \ccc{CGAL_Min_ellipse_2} is used.
The following I/O operators are only needed, if the corresponding I/O The following I/O operators are only needed, if the corresponding I/O
operators of \ccc{CGAL_Min_ellipse_2} are used. operators of \ccc{CGAL_Min_ellipse_2} are used.
\ccHtmlNoIndex
\ccFunction{ ostream& operator << ( ostream& os, Ellipse const& ellipse);}{ \ccFunction{ ostream& operator << ( ostream& os, Ellipse const& ellipse);}{
writes \ccVar\ to output stream \ccc{os}.} writes \ccVar\ to output stream \ccc{os}.}
\ccHtmlNoIndex
\ccFunction{ istream& operator >> ( istream& is, Ellipse &ellipse);}{ \ccFunction{ istream& operator >> ( istream& is, Ellipse &ellipse);}{
reads \ccVar\ from input stream \ccc{is}.} reads \ccVar\ from input stream \ccc{is}.}

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@ -9,18 +9,16 @@
% $Date$ % $Date$
% ============================================================================= % =============================================================================
\newcommand{\ccSeeAlso}{\ccHeading{See Also}} \newcommand{\ccSetThreeColumnsByHand}{\ccTexHtml{\ccSetThreeColumns}{}}
\newcommand{\ccSetThreeColumnsByHand}{\ccSetThreeColumns}
\newcommand{\linebreakByHand}{\ccTexHtml{\\}{}} \newcommand{\linebreakByHand}{\ccTexHtml{\\}{}}
\newcommand{\SaveSpaceByHand}[2]{\ccTexHtml{#1}{#2}} \newcommand{\SaveSpaceByHand}{} %%%% [2]{\ccTexHtml{#1}{#2}}
\chapter{Optimisation} \label{Optimisation} \chapter{Optimisation} \label{Optimisation}
\RCSdefDate{\OptRCSDate}{$Date$} \RCSdefDate{\OptRCSDate}{$Date$}
\ccChapterRelease{Release: 1.2 \quad \OptRCSDate} \ccChapterRelease{Release: 1.2 \ccTexHtml{\quad}{ , } \OptRCSDate}
\ccChapterAuthor{Bernd Gärtner} \par \ccChapterAuthor{Bernd Gärtner}\ccTexHtml{\par}{<br>}
\ccChapterAuthor{Sven Schönherr} \ccChapterAuthor{Sven Schönherr}
\ccTexHtml{\thispagestyle{empty}}{} \ccTexHtml{\thispagestyle{empty}}{}

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@ -9,18 +9,16 @@
% $Date$ % $Date$
% ============================================================================= % =============================================================================
\newcommand{\ccSeeAlso}{\ccHeading{See Also}} \newcommand{\ccSetThreeColumnsByHand}{\ccTexHtml{\ccSetThreeColumns}{}}
\newcommand{\ccSetThreeColumnsByHand}{\ccSetThreeColumns}
\newcommand{\linebreakByHand}{\ccTexHtml{\\}{}} \newcommand{\linebreakByHand}{\ccTexHtml{\\}{}}
\newcommand{\SaveSpaceByHand}[2]{\ccTexHtml{#1}{#2}} \newcommand{\SaveSpaceByHand}{} %%%% [2]{\ccTexHtml{#1}{#2}}
\chapter{Optimisation} \label{Optimisation} \chapter{Optimisation} \label{Optimisation}
\RCSdefDate{\OptRCSDate}{$Date$} \RCSdefDate{\OptRCSDate}{$Date$}
\ccChapterRelease{Release: 1.2 \quad \OptRCSDate} \ccChapterRelease{Release: 1.2 \ccTexHtml{\quad}{ , } \OptRCSDate}
\ccChapterAuthor{Bernd Gärtner} \par \ccChapterAuthor{Bernd Gärtner}\ccTexHtml{\par}{<br>}
\ccChapterAuthor{Sven Schönherr} \ccChapterAuthor{Sven Schönherr}
\ccTexHtml{\thispagestyle{empty}}{} \ccTexHtml{\thispagestyle{empty}}{}