diff --git a/Packages/Min_annulus_d/changes.txt b/Packages/Min_annulus_d/changes.txt index 9c3ee287e6f..283004365be 100644 --- a/Packages/Min_annulus_d/changes.txt +++ b/Packages/Min_annulus_d/changes.txt @@ -1,5 +1,8 @@ Changes done to the `Min_annulus_d' package +Version 1.1.8 on 16-Sep-2003 +- Undo 17-Jun change, but protect the indexing commands by \lcTex. + Version 1.1.7 on 2-Sep-2003 [mh] - Fix CGAL_NTS. diff --git a/Packages/Min_annulus_d/doc_tex/Optimisation_ref/Min_annulus_d.tex b/Packages/Min_annulus_d/doc_tex/Optimisation_ref/Min_annulus_d.tex index 5b198f5d791..f9da77bd6a4 100644 --- a/Packages/Min_annulus_d/doc_tex/Optimisation_ref/Min_annulus_d.tex +++ b/Packages/Min_annulus_d/doc_tex/Optimisation_ref/Min_annulus_d.tex @@ -30,13 +30,13 @@ two concentric spheres with radii $r$ and $R$, $r \leq R$) enclosing a finite set of points in $d$-dimensional Euclidean space $\E_d$, where the difference $R^2-r^2$ is minimal. For a point set $P$ we denote by $ma(P)$ the smallest annulus that contains all points of $P$. Note that $ma(P)$ -can be degenerate\ccIndexSubitem[t]{degeneracies}{\ccc{Min_annulus_d}}, +can be degenerate\lcTex{\ccIndexSubitem[t]{degeneracies}{\ccFont Min_annulus_d}}, i.e.~$ma(P)=\mbox{\ccTexHtml{$\;\emptyset$}{Ø}}$ if $P=\mbox{\ccTexHtml{$\;\emptyset$}{Ø}}$ and $ma(P)=\{p\}$ if $P=\{p\}$. An inclusion-minimal subset $S$ of $P$ with $ma(S)=ma(P)$ is called a -\emph{support set}\ccIndexSubitem[t]{support set}{\ccc{Min_annulus_d}}, +\emph{support set}\lcTex{\ccIndexSubitem[t]{support set}{\ccFont Min_annulus_d}}, the points in $S$ are the \emph{support points}. A support set has size at most $d+2$, and all its points lie on the boundary of $ma(P)$. In general, the support set is not necessarily unique. @@ -142,7 +142,7 @@ two-, three-, and $d$-dimensional \cgal~kernel, respectively. \ccMemberFunction{ int number_of_support_points( ) const;}{ returns the number of support points of \ccVar, i.e.~$|S|$.} -\ccIndexSubitem[t]{support set}{\ccc{Min_annulus_d}} +\lcTex{\ccIndexSubitem[t]{support set}{\ccFont Min_annulus_d}} \ccMemberFunction{ int number_of_inner_support_points( ) const;}{ returns the number of support points of \ccVar{} @@ -277,7 +277,7 @@ unbounded side equals the whole space $\E_d$. \ccMemberFunction{ bool is_degenerate( ) const;}{ returns \ccc{true}, iff \ccVar\ is degenerate, i.e.~if \ccVar\ is empty or equal to a single point.} -\ccIndexSubitem[t]{degeneracies}{\ccc{Min_annulus_d}} +\lcTex{\ccIndexSubitem[t]{degeneracies}{\ccFont Min_annulus_d}} % ----------------------------------------------------------------------------- \ccModifiers @@ -312,7 +312,7 @@ unbounded side equals the whole space $\E_d$. % ----------------------------------------------------------------------------- \ccHeading{Validity Check} \ccIndexMemberFunctionGroup{validity check} -\ccIndexSubitem[t]{validity check}{\ccc{Min_annulus_d}} +\lcTex{\ccIndexSubitem[t]{validity check}{\ccFont Min_annulus_d}} An object \ccVar\ is valid, iff \begin{itemize} @@ -380,7 +380,7 @@ validity check. The problem of finding the smallest enclosing annulus of a finite point set can be formulated as an optimization problem with linear constraints and a linear objective -function\ccIndexSubitem[t]{linear program}{\ccc{Min_annulus_d}}. +function\lcTex{\ccIndexSubitem[t]{linear program}{\ccFont Min_annulus_d}}. The solution is obtained using our exact solver for linear and quadratic programs~\cite{gs-eegqp-00}. diff --git a/Packages/Min_annulus_d/doc_tex/basic/Optimisation_ref/Min_annulus_d.tex b/Packages/Min_annulus_d/doc_tex/basic/Optimisation_ref/Min_annulus_d.tex index 5b198f5d791..f9da77bd6a4 100644 --- a/Packages/Min_annulus_d/doc_tex/basic/Optimisation_ref/Min_annulus_d.tex +++ b/Packages/Min_annulus_d/doc_tex/basic/Optimisation_ref/Min_annulus_d.tex @@ -30,13 +30,13 @@ two concentric spheres with radii $r$ and $R$, $r \leq R$) enclosing a finite set of points in $d$-dimensional Euclidean space $\E_d$, where the difference $R^2-r^2$ is minimal. For a point set $P$ we denote by $ma(P)$ the smallest annulus that contains all points of $P$. Note that $ma(P)$ -can be degenerate\ccIndexSubitem[t]{degeneracies}{\ccc{Min_annulus_d}}, +can be degenerate\lcTex{\ccIndexSubitem[t]{degeneracies}{\ccFont Min_annulus_d}}, i.e.~$ma(P)=\mbox{\ccTexHtml{$\;\emptyset$}{Ø}}$ if $P=\mbox{\ccTexHtml{$\;\emptyset$}{Ø}}$ and $ma(P)=\{p\}$ if $P=\{p\}$. An inclusion-minimal subset $S$ of $P$ with $ma(S)=ma(P)$ is called a -\emph{support set}\ccIndexSubitem[t]{support set}{\ccc{Min_annulus_d}}, +\emph{support set}\lcTex{\ccIndexSubitem[t]{support set}{\ccFont Min_annulus_d}}, the points in $S$ are the \emph{support points}. A support set has size at most $d+2$, and all its points lie on the boundary of $ma(P)$. In general, the support set is not necessarily unique. @@ -142,7 +142,7 @@ two-, three-, and $d$-dimensional \cgal~kernel, respectively. \ccMemberFunction{ int number_of_support_points( ) const;}{ returns the number of support points of \ccVar, i.e.~$|S|$.} -\ccIndexSubitem[t]{support set}{\ccc{Min_annulus_d}} +\lcTex{\ccIndexSubitem[t]{support set}{\ccFont Min_annulus_d}} \ccMemberFunction{ int number_of_inner_support_points( ) const;}{ returns the number of support points of \ccVar{} @@ -277,7 +277,7 @@ unbounded side equals the whole space $\E_d$. \ccMemberFunction{ bool is_degenerate( ) const;}{ returns \ccc{true}, iff \ccVar\ is degenerate, i.e.~if \ccVar\ is empty or equal to a single point.} -\ccIndexSubitem[t]{degeneracies}{\ccc{Min_annulus_d}} +\lcTex{\ccIndexSubitem[t]{degeneracies}{\ccFont Min_annulus_d}} % ----------------------------------------------------------------------------- \ccModifiers @@ -312,7 +312,7 @@ unbounded side equals the whole space $\E_d$. % ----------------------------------------------------------------------------- \ccHeading{Validity Check} \ccIndexMemberFunctionGroup{validity check} -\ccIndexSubitem[t]{validity check}{\ccc{Min_annulus_d}} +\lcTex{\ccIndexSubitem[t]{validity check}{\ccFont Min_annulus_d}} An object \ccVar\ is valid, iff \begin{itemize} @@ -380,7 +380,7 @@ validity check. The problem of finding the smallest enclosing annulus of a finite point set can be formulated as an optimization problem with linear constraints and a linear objective -function\ccIndexSubitem[t]{linear program}{\ccc{Min_annulus_d}}. +function\lcTex{\ccIndexSubitem[t]{linear program}{\ccFont Min_annulus_d}}. The solution is obtained using our exact solver for linear and quadratic programs~\cite{gs-eegqp-00}. diff --git a/Packages/Min_circle_2/changes.txt b/Packages/Min_circle_2/changes.txt index 1e15047128d..dc220046bd1 100644 --- a/Packages/Min_circle_2/changes.txt +++ b/Packages/Min_circle_2/changes.txt @@ -1,4 +1,8 @@ Changes done to the `Min_circle_2' package + +Version 3.23 on 16-Sep-2003 +- Undo 17-Jun change, but protect the indexing commands by \lcTex. + Version 3.22 on 10-Sep-2003 - Qt_help_window class is in the CGAL namespace [rursu] diff --git a/Packages/Min_circle_2/doc_tex/Optimisation_ref/Min_circle_2.tex b/Packages/Min_circle_2/doc_tex/Optimisation_ref/Min_circle_2.tex index 4fab1759ca3..a996362c3f1 100644 --- a/Packages/Min_circle_2/doc_tex/Optimisation_ref/Min_circle_2.tex +++ b/Packages/Min_circle_2/doc_tex/Optimisation_ref/Min_circle_2.tex @@ -30,13 +30,13 @@ An object of the class \ccRefName\ is the unique circle of smallest area enclosing a finite (multi)set of points in two-dimensional 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 be -degenerate\ccIndexSubitem[t]{degeneracies}{\ccc{Min_circle_2}}, +degenerate\lcTex{\ccIndexSubitem[t]{degeneracies}{\ccFont Min_circle_2}}, i.e.~$mc(P)=\mbox{\ccTexHtml{$\;\emptyset$}{Ø}}$ 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 -\emph{support set}\ccIndexSubitem[t]{support set}{\ccc{Min_circle_2}}, +\emph{support set}\lcTex{\ccIndexSubitem[t]{support set}{\ccFont Min_circle_2}}, the points in $S$ are the \emph{support points}. A support set has size at most three, and all its points lie on the boundary of $mc(P)$. In general, neither the support set nor its size are necessarily unique. @@ -86,7 +86,7 @@ We provide the model \ccc{Min_circle_2_traits_2} using the two-dimensional A \ccRefName\ object can be created from an arbitrary point set $P$ and by specialized construction methods expecting no, one, two or three points as arguments. The latter methods can be useful for reconstructing $mc(P)$ from -a given support~set\ccIndexSubitem[t]{support set}{\ccc{Min_circle_2}} +a given support~set\lcTex{\ccIndexSubitem[t]{support set}{\ccFont Min_circle_2}} $S$ of $P$. \ccConstructor{ template < class InputIterator > @@ -138,7 +138,7 @@ $S$ of $P$. \ccMemberFunction{ int number_of_support_points( ) const;}{ returns the number of support points of \ccVar, i.e.\ $|S|$.} -\ccIndexSubitem[t]{support set}{\ccc{Min_circle_2}} +\lcTex{\ccIndexSubitem[t]{support set}{\ccFont Min_circle_2}} \ccGlueBegin \ccMemberFunction{ Point_iterator points_begin() const;}{ @@ -198,7 +198,7 @@ bounded side, i.e.\ its unbounded side equals the whole space $\E_2$. returns \ccc{true}, iff \ccVar\ is degenerate, i.e.~if \ccVar\ is empty or equal to a single point, equivalently if the number of support points is less than 2.} -\ccIndexSubitem[t]{degeneracies}{\ccc{Min_circle_2}} +\lcTex{\ccIndexSubitem[t]{degeneracies}{\ccFont Min_circle_2}} % ----------------------------------------------------------------------------- \ccModifiers @@ -230,7 +230,7 @@ method is incremental itself. % ----------------------------------------------------------------------------- \ccHeading{Validity Check} \ccIndexMemberFunctionGroup{validity check} -\ccIndexSubitem[t]{validity check}{\ccc{Min_circle_2}} +\lcTex{\ccIndexSubitem[t]{validity check}{\ccFont Min_circle_2}} An object \ccVar\ is valid, iff \begin{itemize} @@ -303,13 +303,13 @@ An object \ccVar\ is valid, iff \ccImplementation \ccIndexImplementation -We implement the incremental algorithm\ccIndexSubitem[t]{incremental - algorithm}{\ccc{Min_circle_2}} of Welzl, with move-to-front -heuristic~\cite{w-sedbe-91a}\ccIndexSubitem[t]{move-to-front - heuristic}{\ccc{Min_circle_2}}. The whole implementation is described +We implement the incremental algorithm\lcTex{\ccIndexSubitem[t]{incremental + algorithm}{\ccFont Min_circle_2}} of Welzl, with move-to-front +heuristic~\cite{w-sedbe-91a}\lcTex{\ccIndexSubitem[t]{move-to-front + heuristic}{\ccFont Min_circle_2}}. The whole implementation is described in~\cite{gs-seceg-98}. -If randomization\ccIndexSubitem[t]{randomization}{\ccc{Min_circle_2}} is +If randomization\lcTex{\ccIndexSubitem[t]{randomization}{\ccFont Min_circle_2}} is chosen, the creation time is almost always linear in the number of points. Access functions and predicates take constant time, inserting a point might take up to linear time, but substantially less than computing the new diff --git a/Packages/Min_circle_2/doc_tex/basic/Optimisation_ref/Min_circle_2.tex b/Packages/Min_circle_2/doc_tex/basic/Optimisation_ref/Min_circle_2.tex index 4fab1759ca3..a996362c3f1 100644 --- a/Packages/Min_circle_2/doc_tex/basic/Optimisation_ref/Min_circle_2.tex +++ b/Packages/Min_circle_2/doc_tex/basic/Optimisation_ref/Min_circle_2.tex @@ -30,13 +30,13 @@ An object of the class \ccRefName\ is the unique circle of smallest area enclosing a finite (multi)set of points in two-dimensional 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 be -degenerate\ccIndexSubitem[t]{degeneracies}{\ccc{Min_circle_2}}, +degenerate\lcTex{\ccIndexSubitem[t]{degeneracies}{\ccFont Min_circle_2}}, i.e.~$mc(P)=\mbox{\ccTexHtml{$\;\emptyset$}{Ø}}$ 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 -\emph{support set}\ccIndexSubitem[t]{support set}{\ccc{Min_circle_2}}, +\emph{support set}\lcTex{\ccIndexSubitem[t]{support set}{\ccFont Min_circle_2}}, the points in $S$ are the \emph{support points}. A support set has size at most three, and all its points lie on the boundary of $mc(P)$. In general, neither the support set nor its size are necessarily unique. @@ -86,7 +86,7 @@ We provide the model \ccc{Min_circle_2_traits_2} using the two-dimensional A \ccRefName\ object can be created from an arbitrary point set $P$ and by specialized construction methods expecting no, one, two or three points as arguments. The latter methods can be useful for reconstructing $mc(P)$ from -a given support~set\ccIndexSubitem[t]{support set}{\ccc{Min_circle_2}} +a given support~set\lcTex{\ccIndexSubitem[t]{support set}{\ccFont Min_circle_2}} $S$ of $P$. \ccConstructor{ template < class InputIterator > @@ -138,7 +138,7 @@ $S$ of $P$. \ccMemberFunction{ int number_of_support_points( ) const;}{ returns the number of support points of \ccVar, i.e.\ $|S|$.} -\ccIndexSubitem[t]{support set}{\ccc{Min_circle_2}} +\lcTex{\ccIndexSubitem[t]{support set}{\ccFont Min_circle_2}} \ccGlueBegin \ccMemberFunction{ Point_iterator points_begin() const;}{ @@ -198,7 +198,7 @@ bounded side, i.e.\ its unbounded side equals the whole space $\E_2$. returns \ccc{true}, iff \ccVar\ is degenerate, i.e.~if \ccVar\ is empty or equal to a single point, equivalently if the number of support points is less than 2.} -\ccIndexSubitem[t]{degeneracies}{\ccc{Min_circle_2}} +\lcTex{\ccIndexSubitem[t]{degeneracies}{\ccFont Min_circle_2}} % ----------------------------------------------------------------------------- \ccModifiers @@ -230,7 +230,7 @@ method is incremental itself. % ----------------------------------------------------------------------------- \ccHeading{Validity Check} \ccIndexMemberFunctionGroup{validity check} -\ccIndexSubitem[t]{validity check}{\ccc{Min_circle_2}} +\lcTex{\ccIndexSubitem[t]{validity check}{\ccFont Min_circle_2}} An object \ccVar\ is valid, iff \begin{itemize} @@ -303,13 +303,13 @@ An object \ccVar\ is valid, iff \ccImplementation \ccIndexImplementation -We implement the incremental algorithm\ccIndexSubitem[t]{incremental - algorithm}{\ccc{Min_circle_2}} of Welzl, with move-to-front -heuristic~\cite{w-sedbe-91a}\ccIndexSubitem[t]{move-to-front - heuristic}{\ccc{Min_circle_2}}. The whole implementation is described +We implement the incremental algorithm\lcTex{\ccIndexSubitem[t]{incremental + algorithm}{\ccFont Min_circle_2}} of Welzl, with move-to-front +heuristic~\cite{w-sedbe-91a}\lcTex{\ccIndexSubitem[t]{move-to-front + heuristic}{\ccFont Min_circle_2}}. The whole implementation is described in~\cite{gs-seceg-98}. -If randomization\ccIndexSubitem[t]{randomization}{\ccc{Min_circle_2}} is +If randomization\lcTex{\ccIndexSubitem[t]{randomization}{\ccFont Min_circle_2}} is chosen, the creation time is almost always linear in the number of points. Access functions and predicates take constant time, inserting a point might take up to linear time, but substantially less than computing the new diff --git a/Packages/Min_ellipse_2/changes.txt b/Packages/Min_ellipse_2/changes.txt index c03161ec3d0..35bc50f004f 100644 --- a/Packages/Min_ellipse_2/changes.txt +++ b/Packages/Min_ellipse_2/changes.txt @@ -1,5 +1,8 @@ Changes done to the `Min_ellipse_2' package. +Version 3.28 on 16-Sep-2003 +- Undo 17-Jun change, but protect the indexing commands by \lcTex. + Version 3.27 on 10-Sep-2003 [rursu] - Qt_help_window is in the CGAL namespace now. diff --git a/Packages/Min_ellipse_2/doc_tex/Optimisation_ref/Min_ellipse_2.tex b/Packages/Min_ellipse_2/doc_tex/Optimisation_ref/Min_ellipse_2.tex index a19f31cc3a4..448bb3f35b7 100644 --- a/Packages/Min_ellipse_2/doc_tex/Optimisation_ref/Min_ellipse_2.tex +++ b/Packages/Min_ellipse_2/doc_tex/Optimisation_ref/Min_ellipse_2.tex @@ -29,14 +29,14 @@ An object of the class \ccRefName\ is the unique ellipse of smallest area enclosing a finite (multi)set of points in two-dimensional 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 -degenerate\ccIndexSubitem[t]{degeneracies}{\ccc{Min_ellipse_2}}, +degenerate\lcTex{\ccIndexSubitem[t]{degeneracies}{\ccFont Min_ellipse_2}}, i.e.~$me(P)=\mbox{\ccTexHtml{$\;\emptyset$}{Ø}}$ if $P=\mbox{\ccTexHtml{$\;\emptyset$}{Ø}}$, $me(P)=\{p\}$ if $P=\{p\}$, and $me(P) = \{ \mbox{\ccTexHtml{$(1-\lambda)p + \lambda q \mid 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 -\emph{support set}\ccIndexSubitem[t]{support set}{\ccc{Min_ellipse_2}}, +\emph{support set}\lcTex{\ccIndexSubitem[t]{support set}{\ccFont Min_ellipse_2}}, the points in $S$ are the \emph{support points}. A support set has size at most five, and all its points lie on the boundary of $me(P)$. In general, neither the support set nor its size are necessarily unique. @@ -86,8 +86,8 @@ We provide the model \ccc{Min_ellipse_2_traits_2} using the two-dimensional A \ccRefName\ object can be created from an arbitrary point set $P$ and by specialized construction methods expecting no, one, two, three, four or five points as arguments. The latter methods can be useful for -reconstructing $me(P)$ from a given support set\ccIndexSubitem[t]{support - set}{\ccc{Min_ellipse_2}} $S$ of $P$. +reconstructing $me(P)$ from a given support set\lcTex{\ccIndexSubitem[t]{support + set}{\ccFont Min_ellipse_2}} $S$ of $P$. \ccConstructor{ template < class InputIterator > Min_Ellipse_2( InputIterator first, @@ -158,7 +158,7 @@ reconstructing $me(P)$ from a given support set\ccIndexSubitem[t]{support \ccMemberFunction{ int number_of_support_points( ) const;}{ returns the number of support points of \ccVar, i.e.\ $|S|$.} -\ccIndexSubitem[t]{support set}{\ccc{Min_ellipse_2}} +\lcTex{\ccIndexSubitem[t]{support set}{\ccFont Min_ellipse_2}} \ccGlueBegin \ccMemberFunction{ Point_iterator points_begin() const;}{ @@ -171,11 +171,11 @@ reconstructing $me(P)$ from a given support set\ccIndexSubitem[t]{support \ccGlueBegin \ccMemberFunction{ Support_point_iterator support_points_begin() const;}{ returns an iterator referring to the first support point of \ccVar.} -\ccIndexSubitem[t]{support set}{\ccc{Min_ellipse_2}} +\lcTex{\ccIndexSubitem[t]{support set}{\ccFont Min_ellipse_2}} % \ccMemberFunction{ Support_point_iterator support_points_end() const;}{ returns the corresponding past-the-end iterator.} -\ccIndexSubitem[t]{support set}{\ccc{Min_ellipse_2}} +\lcTex{\ccIndexSubitem[t]{support set}{\ccFont Min_ellipse_2}} \ccGlueEnd \ccMemberFunction{ const Point& support_point( int i) const;}{ @@ -184,7 +184,7 @@ reconstructing $me(P)$ from a given support set\ccIndexSubitem[t]{support \ccVar\ccc{.support_point(i)} with the same \ccc{i} returns the same point. \ccPrecond $0 \leq i< \mbox{\ccVar\ccc{.number_of_support_points()}}$.} -\ccIndexSubitem[t]{support set}{\ccc{Min_ellipse_2}} +\lcTex{\ccIndexSubitem[t]{support set}{\ccFont Min_ellipse_2}} \ccMemberFunction{ const Ellipse& ellipse( ) const;}{ returns the current ellipse of \ccVar.} @@ -222,7 +222,7 @@ i.e.\ its unbounded side equals the whole space $\E_2$. i.e.~if \ccVar\ is empty, equal to a single point or equal to a segment, equivalently if the number of support points is less than~3.} -\ccIndexSubitem[t]{degeneracies}{\ccc{Min_ellipse_2}} +\lcTex{\ccIndexSubitem[t]{degeneracies}{\ccFont Min_ellipse_2}} % ----------------------------------------------------------------------------- \ccModifiers @@ -254,7 +254,7 @@ method is incremental itself. % ----------------------------------------------------------------------------- \ccHeading{Validity Check} \ccIndexMemberFunctionGroup{validity check} -\ccIndexSubitem[t]{validity check}{\ccc{Min_ellipse_2}} +\lcTex{\ccIndexSubitem[t]{validity check}{\ccFont Min_ellipse_2}} An object \ccVar\ is valid, iff \begin{itemize} @@ -329,14 +329,14 @@ validity check. \ccImplementation \ccIndexImplementation -We implement the incremental algorithm\ccIndexSubitem[t]{incremental - algorithm}{\ccc{Min_ellipse_2}} of Welzl, with move-to-front -heuristic~\cite{w-sedbe-91a}\ccIndexSubitem[t]{move-to-front - heuristic}{\ccc{Min_ellipse_2}}, using the primitives as described +We implement the incremental algorithm\lcTex{\ccIndexSubitem[t]{incremental + algorithm}{\ccFont Min_ellipse_2}} of Welzl, with move-to-front +heuristic~\cite{w-sedbe-91a}\lcTex{\ccIndexSubitem[t]{move-to-front + heuristic}{\ccFont Min_ellipse_2}}, using the primitives as described in~\cite{gs-epsee-97,gs-seefe-97a}. The whole implementation is described in~\cite{gs-seeeg-98}. -If randomization\ccIndexSubitem[t]{randomization}{\ccc{Min_ellipse_2}} is +If randomization\lcTex{\ccIndexSubitem[t]{randomization}{\ccFont Min_ellipse_2}} is chosen, the creation time is almost always linear in the number of points. Access functions and predicates take constant time, inserting a point might take up to linear time, but substantially less than computing the new diff --git a/Packages/Min_ellipse_2/doc_tex/basic/Optimisation_ref/Min_ellipse_2.tex b/Packages/Min_ellipse_2/doc_tex/basic/Optimisation_ref/Min_ellipse_2.tex index a19f31cc3a4..448bb3f35b7 100644 --- a/Packages/Min_ellipse_2/doc_tex/basic/Optimisation_ref/Min_ellipse_2.tex +++ b/Packages/Min_ellipse_2/doc_tex/basic/Optimisation_ref/Min_ellipse_2.tex @@ -29,14 +29,14 @@ An object of the class \ccRefName\ is the unique ellipse of smallest area enclosing a finite (multi)set of points in two-dimensional 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 -degenerate\ccIndexSubitem[t]{degeneracies}{\ccc{Min_ellipse_2}}, +degenerate\lcTex{\ccIndexSubitem[t]{degeneracies}{\ccFont Min_ellipse_2}}, i.e.~$me(P)=\mbox{\ccTexHtml{$\;\emptyset$}{Ø}}$ if $P=\mbox{\ccTexHtml{$\;\emptyset$}{Ø}}$, $me(P)=\{p\}$ if $P=\{p\}$, and $me(P) = \{ \mbox{\ccTexHtml{$(1-\lambda)p + \lambda q \mid 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 -\emph{support set}\ccIndexSubitem[t]{support set}{\ccc{Min_ellipse_2}}, +\emph{support set}\lcTex{\ccIndexSubitem[t]{support set}{\ccFont Min_ellipse_2}}, the points in $S$ are the \emph{support points}. A support set has size at most five, and all its points lie on the boundary of $me(P)$. In general, neither the support set nor its size are necessarily unique. @@ -86,8 +86,8 @@ We provide the model \ccc{Min_ellipse_2_traits_2} using the two-dimensional A \ccRefName\ object can be created from an arbitrary point set $P$ and by specialized construction methods expecting no, one, two, three, four or five points as arguments. The latter methods can be useful for -reconstructing $me(P)$ from a given support set\ccIndexSubitem[t]{support - set}{\ccc{Min_ellipse_2}} $S$ of $P$. +reconstructing $me(P)$ from a given support set\lcTex{\ccIndexSubitem[t]{support + set}{\ccFont Min_ellipse_2}} $S$ of $P$. \ccConstructor{ template < class InputIterator > Min_Ellipse_2( InputIterator first, @@ -158,7 +158,7 @@ reconstructing $me(P)$ from a given support set\ccIndexSubitem[t]{support \ccMemberFunction{ int number_of_support_points( ) const;}{ returns the number of support points of \ccVar, i.e.\ $|S|$.} -\ccIndexSubitem[t]{support set}{\ccc{Min_ellipse_2}} +\lcTex{\ccIndexSubitem[t]{support set}{\ccFont Min_ellipse_2}} \ccGlueBegin \ccMemberFunction{ Point_iterator points_begin() const;}{ @@ -171,11 +171,11 @@ reconstructing $me(P)$ from a given support set\ccIndexSubitem[t]{support \ccGlueBegin \ccMemberFunction{ Support_point_iterator support_points_begin() const;}{ returns an iterator referring to the first support point of \ccVar.} -\ccIndexSubitem[t]{support set}{\ccc{Min_ellipse_2}} +\lcTex{\ccIndexSubitem[t]{support set}{\ccFont Min_ellipse_2}} % \ccMemberFunction{ Support_point_iterator support_points_end() const;}{ returns the corresponding past-the-end iterator.} -\ccIndexSubitem[t]{support set}{\ccc{Min_ellipse_2}} +\lcTex{\ccIndexSubitem[t]{support set}{\ccFont Min_ellipse_2}} \ccGlueEnd \ccMemberFunction{ const Point& support_point( int i) const;}{ @@ -184,7 +184,7 @@ reconstructing $me(P)$ from a given support set\ccIndexSubitem[t]{support \ccVar\ccc{.support_point(i)} with the same \ccc{i} returns the same point. \ccPrecond $0 \leq i< \mbox{\ccVar\ccc{.number_of_support_points()}}$.} -\ccIndexSubitem[t]{support set}{\ccc{Min_ellipse_2}} +\lcTex{\ccIndexSubitem[t]{support set}{\ccFont Min_ellipse_2}} \ccMemberFunction{ const Ellipse& ellipse( ) const;}{ returns the current ellipse of \ccVar.} @@ -222,7 +222,7 @@ i.e.\ its unbounded side equals the whole space $\E_2$. i.e.~if \ccVar\ is empty, equal to a single point or equal to a segment, equivalently if the number of support points is less than~3.} -\ccIndexSubitem[t]{degeneracies}{\ccc{Min_ellipse_2}} +\lcTex{\ccIndexSubitem[t]{degeneracies}{\ccFont Min_ellipse_2}} % ----------------------------------------------------------------------------- \ccModifiers @@ -254,7 +254,7 @@ method is incremental itself. % ----------------------------------------------------------------------------- \ccHeading{Validity Check} \ccIndexMemberFunctionGroup{validity check} -\ccIndexSubitem[t]{validity check}{\ccc{Min_ellipse_2}} +\lcTex{\ccIndexSubitem[t]{validity check}{\ccFont Min_ellipse_2}} An object \ccVar\ is valid, iff \begin{itemize} @@ -329,14 +329,14 @@ validity check. \ccImplementation \ccIndexImplementation -We implement the incremental algorithm\ccIndexSubitem[t]{incremental - algorithm}{\ccc{Min_ellipse_2}} of Welzl, with move-to-front -heuristic~\cite{w-sedbe-91a}\ccIndexSubitem[t]{move-to-front - heuristic}{\ccc{Min_ellipse_2}}, using the primitives as described +We implement the incremental algorithm\lcTex{\ccIndexSubitem[t]{incremental + algorithm}{\ccFont Min_ellipse_2}} of Welzl, with move-to-front +heuristic~\cite{w-sedbe-91a}\lcTex{\ccIndexSubitem[t]{move-to-front + heuristic}{\ccFont Min_ellipse_2}}, using the primitives as described in~\cite{gs-epsee-97,gs-seefe-97a}. The whole implementation is described in~\cite{gs-seeeg-98}. -If randomization\ccIndexSubitem[t]{randomization}{\ccc{Min_ellipse_2}} is +If randomization\lcTex{\ccIndexSubitem[t]{randomization}{\ccFont Min_ellipse_2}} is chosen, the creation time is almost always linear in the number of points. Access functions and predicates take constant time, inserting a point might take up to linear time, but substantially less than computing the new diff --git a/Packages/Min_sphere_d/changes.txt b/Packages/Min_sphere_d/changes.txt index 5fe4bc48c2a..3bbaebb218a 100644 --- a/Packages/Min_sphere_d/changes.txt +++ b/Packages/Min_sphere_d/changes.txt @@ -124,3 +124,6 @@ Changes from 2.32 Changes from 2.33 - Replace \ccFont by \ccc for the HTML index. + +Changes from 2.34 + - Undo last change, but protect the indexing commands by \lcTex. diff --git a/Packages/Min_sphere_d/doc_tex/Optimisation_ref/Min_sphere_d.tex b/Packages/Min_sphere_d/doc_tex/Optimisation_ref/Min_sphere_d.tex index 7baf56cda95..6fb55144928 100644 --- a/Packages/Min_sphere_d/doc_tex/Optimisation_ref/Min_sphere_d.tex +++ b/Packages/Min_sphere_d/doc_tex/Optimisation_ref/Min_sphere_d.tex @@ -120,7 +120,7 @@ or clear operation. \begin{ccIndexMemberFunctions} \ccIndexMemberFunctionGroup{access} -\ccIndexSubitem[t]{support set}{\ccc{Min_sphere_d}} +\lcTex{\ccIndexSubitem[t]{support set}{\ccFont Min_sphere_d}} \ccMemberFunction{ int number_of_points( ) const;}{ returns the number of points of \ccVar, i.e.\ $|P|$.} @@ -190,7 +190,7 @@ bounded side, i.e.\ its unbounded side equals the whole space $\E_d$. returns \ccc{true}, iff \ccVar\ is empty (this implies degeneracy).} -\ccIndexSubitem[t]{degeneracies}{\ccc{Min_sphere_d}} +\lcTex{\ccIndexSubitem[t]{degeneracies}{\ccFont Min_sphere_d}} \ccMemberFunction{ bool is_degenerate( ) const;}{ returns \ccc{true}, iff \ccVar\ is degenerate, i.e.\ if \ccVar\ is empty or equal to a single point, equivalently if @@ -237,7 +237,7 @@ bounded side, i.e.\ its unbounded side equals the whole space $\E_d$. % ----------------------------------------------------------------------------- \ccHeading{Validity Check} \ccIndexMemberFunctionGroup{validity check} - \ccIndexSubitem[t]{validity check}{\ccc{Min_sphere_d}} + \lcTex{\ccIndexSubitem[t]{validity check}{\ccFont Min_sphere_d}} An object \ccVar\ is valid, iff \begin{itemize} \item \ccVar\ contains all points of its defining set $P$, @@ -302,8 +302,8 @@ bounded side, i.e.\ its unbounded side equals the whole space $\E_d$. \ccImplementation \ccIndexImplementation - \ccIndexSubitem[t]{incremental algorithm}{\ccc{Min_sphere_d}} - \ccIndexSubitem[t]{move-to-front heuristic}{\ccc{Min_sphere_d}} + \lcTex{\ccIndexSubitem[t]{incremental algorithm}{\ccFont Min_sphere_d}} + \lcTex{\ccIndexSubitem[t]{move-to-front heuristic}{\ccFont Min_sphere_d}} We implement the algorithm of Welzl with move-to-front heuristic~\cite{w-sedbe-91a} for small point sets, combined with a new efficient method for large sets, which is particularly tuned for diff --git a/Packages/Min_sphere_d/doc_tex/basic/Optimisation_ref/Min_sphere_d.tex b/Packages/Min_sphere_d/doc_tex/basic/Optimisation_ref/Min_sphere_d.tex index 7baf56cda95..6fb55144928 100644 --- a/Packages/Min_sphere_d/doc_tex/basic/Optimisation_ref/Min_sphere_d.tex +++ b/Packages/Min_sphere_d/doc_tex/basic/Optimisation_ref/Min_sphere_d.tex @@ -120,7 +120,7 @@ or clear operation. \begin{ccIndexMemberFunctions} \ccIndexMemberFunctionGroup{access} -\ccIndexSubitem[t]{support set}{\ccc{Min_sphere_d}} +\lcTex{\ccIndexSubitem[t]{support set}{\ccFont Min_sphere_d}} \ccMemberFunction{ int number_of_points( ) const;}{ returns the number of points of \ccVar, i.e.\ $|P|$.} @@ -190,7 +190,7 @@ bounded side, i.e.\ its unbounded side equals the whole space $\E_d$. returns \ccc{true}, iff \ccVar\ is empty (this implies degeneracy).} -\ccIndexSubitem[t]{degeneracies}{\ccc{Min_sphere_d}} +\lcTex{\ccIndexSubitem[t]{degeneracies}{\ccFont Min_sphere_d}} \ccMemberFunction{ bool is_degenerate( ) const;}{ returns \ccc{true}, iff \ccVar\ is degenerate, i.e.\ if \ccVar\ is empty or equal to a single point, equivalently if @@ -237,7 +237,7 @@ bounded side, i.e.\ its unbounded side equals the whole space $\E_d$. % ----------------------------------------------------------------------------- \ccHeading{Validity Check} \ccIndexMemberFunctionGroup{validity check} - \ccIndexSubitem[t]{validity check}{\ccc{Min_sphere_d}} + \lcTex{\ccIndexSubitem[t]{validity check}{\ccFont Min_sphere_d}} An object \ccVar\ is valid, iff \begin{itemize} \item \ccVar\ contains all points of its defining set $P$, @@ -302,8 +302,8 @@ bounded side, i.e.\ its unbounded side equals the whole space $\E_d$. \ccImplementation \ccIndexImplementation - \ccIndexSubitem[t]{incremental algorithm}{\ccc{Min_sphere_d}} - \ccIndexSubitem[t]{move-to-front heuristic}{\ccc{Min_sphere_d}} + \lcTex{\ccIndexSubitem[t]{incremental algorithm}{\ccFont Min_sphere_d}} + \lcTex{\ccIndexSubitem[t]{move-to-front heuristic}{\ccFont Min_sphere_d}} We implement the algorithm of Welzl with move-to-front heuristic~\cite{w-sedbe-91a} for small point sets, combined with a new efficient method for large sets, which is particularly tuned for