From 3fab8f07fb76f0beef88af7c89789a8877c876f6 Mon Sep 17 00:00:00 2001 From: Sylvain Pion Date: Sat, 3 Jan 2009 14:29:04 +0000 Subject: [PATCH] Fix \E_* to \E^* thinko/copy-pasto. Remove one more \ccTexHtml as well. --- .../doc_tex/Bounding_volumes_ref/Min_annulus_d.tex | 4 ++-- .../doc_tex/Bounding_volumes_ref/MinCircle2Traits.tex | 6 +++--- Min_circle_2/doc_tex/Bounding_volumes_ref/Min_circle_2.tex | 4 ++-- .../doc_tex/Bounding_volumes_ref/MinEllipse2Traits.tex | 4 ++-- .../doc_tex/Bounding_volumes_ref/Min_ellipse_2.tex | 4 ++-- .../doc_tex/Bounding_volumes_ref/Min_ellipse_2_traits.tex | 4 ++-- Min_sphere_d/doc_tex/Bounding_volumes_ref/Min_sphere_d.tex | 4 ++-- .../Bounding_volumes_ref/Min_sphere_of_spheres_d.tex | 2 +- .../doc_tex/Polytope_distance_d_ref/Polytope_distance_d.tex | 2 +- 9 files changed, 17 insertions(+), 17 deletions(-) diff --git a/Min_annulus_d/doc_tex/Bounding_volumes_ref/Min_annulus_d.tex b/Min_annulus_d/doc_tex/Bounding_volumes_ref/Min_annulus_d.tex index ea2e0fc5981..5868bf1e40f 100644 --- a/Min_annulus_d/doc_tex/Bounding_volumes_ref/Min_annulus_d.tex +++ b/Min_annulus_d/doc_tex/Bounding_volumes_ref/Min_annulus_d.tex @@ -14,7 +14,7 @@ An object of the class \ccRefName\ is the unique annulus (region between 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 +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\lcTex{\ccIndexSubitem[t]{degeneracies}{\ccFont Min_annulus_d}}, @@ -236,7 +236,7 @@ two-, three-, and $d$-dimensional \cgal~kernel, respectively. The bounded area of the smallest enclosing annulus lies between the inner and the outer sphere. The boundary is the union of both spheres. By definition, an empty annulus has no boundary and no bounded side, i.e.~its -unbounded side equals the whole space $\E_d$. +unbounded side equals the whole space $\E^d$. \ccMemberFunction{ CGAL::Bounded_side bounded_side( const Point& p) const;}{ diff --git a/Min_circle_2/doc_tex/Bounding_volumes_ref/MinCircle2Traits.tex b/Min_circle_2/doc_tex/Bounding_volumes_ref/MinCircle2Traits.tex index 1d6fe9b795b..81bf161ea66 100644 --- a/Min_circle_2/doc_tex/Bounding_volumes_ref/MinCircle2Traits.tex +++ b/Min_circle_2/doc_tex/Bounding_volumes_ref/MinCircle2Traits.tex @@ -83,12 +83,12 @@ The following predicate is only needed, if the member function \ccDefinition An object of the class \ccClassName\ is a circle in two-dimensional -Euclidean plane $\E_2$. Its boundary splits the plane into a bounded +Euclidean plane $\E^2$. Its boundary splits the plane into a bounded and an unbounded side. By definition, an empty \ccClassName\ has no boundary and no bounded side, i.e.\ its unbounded side equals the -whole plane $\E_2$. A \ccClassName\ containing exactly one point~$p$ +whole plane $\E^2$. A \ccClassName\ containing exactly one point~$p$ has no bounded side, its boundary is $\{p\}$, and its unbounded side -equals $\E_2\mbox{\ccTexHtml{$\setminus$}{-}}\{p\}$. +equals $\E^2 \setminus \{p\}$. % ----------------------------------------------------------------------------- \ccTypes diff --git a/Min_circle_2/doc_tex/Bounding_volumes_ref/Min_circle_2.tex b/Min_circle_2/doc_tex/Bounding_volumes_ref/Min_circle_2.tex index 9ffc5ab28a5..f96977b0c93 100644 --- a/Min_circle_2/doc_tex/Bounding_volumes_ref/Min_circle_2.tex +++ b/Min_circle_2/doc_tex/Bounding_volumes_ref/Min_circle_2.tex @@ -15,7 +15,7 @@ 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 +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\lcTex{\ccIndexSubitem[t]{degeneracies}{\ccFont Min_circle_2}}, i.e.~$mc(P)=\emptyset$ if @@ -173,7 +173,7 @@ $S$ of $P$. \ccIndexMemberFunctionGroup{predicates} By definition, an empty \ccClassTemplateName\ has no boundary and no -bounded side, i.e.\ its unbounded side equals the whole space $\E_2$. +bounded side, i.e.\ its unbounded side equals the whole space $\E^2$. \ccMemberFunction{ CGAL::Bounded_side bounded_side( const Point& p) const;}{ diff --git a/Min_ellipse_2/doc_tex/Bounding_volumes_ref/MinEllipse2Traits.tex b/Min_ellipse_2/doc_tex/Bounding_volumes_ref/MinEllipse2Traits.tex index 1b41df33bd8..f6cea2f08ea 100644 --- a/Min_ellipse_2/doc_tex/Bounding_volumes_ref/MinEllipse2Traits.tex +++ b/Min_ellipse_2/doc_tex/Bounding_volumes_ref/MinEllipse2Traits.tex @@ -62,10 +62,10 @@ Only default and copy constructor are required. \ccDefinition An object of the class \ccClassName\ is an ellipse in two-dimensional -Euclidean plane $\E_2$. Its boundary splits the plane into a bounded +Euclidean plane $\E^2$. Its boundary splits the plane into a bounded and an unbounded side. By definition, an empty \ccClassName\ has no boundary and no bounded side, i.e.\ its unbounded side equals the -whole plane $\E_2$. +whole plane $\E^2$. % ----------------------------------------------------------------------------- \ccTypes diff --git a/Min_ellipse_2/doc_tex/Bounding_volumes_ref/Min_ellipse_2.tex b/Min_ellipse_2/doc_tex/Bounding_volumes_ref/Min_ellipse_2.tex index 5e3b4f665e0..78b3c4463d0 100644 --- a/Min_ellipse_2/doc_tex/Bounding_volumes_ref/Min_ellipse_2.tex +++ b/Min_ellipse_2/doc_tex/Bounding_volumes_ref/Min_ellipse_2.tex @@ -14,7 +14,7 @@ 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 +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\lcTex{\ccIndexSubitem[t]{degeneracies}{\ccFont Min_ellipse_2}}, i.e.~$me(P)=\emptyset$ if @@ -184,7 +184,7 @@ reconstructing $me(P)$ from a given support set\lcTex{\ccIndexSubitem[t]{support \ccIndexMemberFunctionGroup{predicates} By definition, an empty \ccRefName\ has no boundary and no bounded side, -i.e.\ its unbounded side equals the whole space $\E_2$. +i.e.\ its unbounded side equals the whole space $\E^2$. \ccMemberFunction{ CGAL::Bounded_side bounded_side( const Point& p) const;}{ diff --git a/Min_ellipse_2/doc_tex/Bounding_volumes_ref/Min_ellipse_2_traits.tex b/Min_ellipse_2/doc_tex/Bounding_volumes_ref/Min_ellipse_2_traits.tex index 7b990df427c..a06946191e9 100644 --- a/Min_ellipse_2/doc_tex/Bounding_volumes_ref/Min_ellipse_2_traits.tex +++ b/Min_ellipse_2/doc_tex/Bounding_volumes_ref/Min_ellipse_2_traits.tex @@ -62,10 +62,10 @@ Only default and copy constructor are required. \ccDefinition An object of the class \ccClassName\ is an ellipse in two-dimensional -Euclidean plane $\E_2$. Its boundary splits the plane into a bounded +Euclidean plane $\E^2$. Its boundary splits the plane into a bounded and an unbounded side. By definition, an empty \ccClassName\ has no boundary and no bounded side, i.e.\ its unbounded side equals the -whole plane $\E_2$. +whole plane $\E^2$. % ----------------------------------------------------------------------------- \ccTypes diff --git a/Min_sphere_d/doc_tex/Bounding_volumes_ref/Min_sphere_d.tex b/Min_sphere_d/doc_tex/Bounding_volumes_ref/Min_sphere_d.tex index f5cb9c10347..9fa226e5138 100644 --- a/Min_sphere_d/doc_tex/Bounding_volumes_ref/Min_sphere_d.tex +++ b/Min_sphere_d/doc_tex/Bounding_volumes_ref/Min_sphere_d.tex @@ -12,7 +12,7 @@ An object of the class \ccRefName\ is the unique sphere of smallest volume enclosing a finite (multi)set of points in $d$-dimensional -Euclidean space $\E_d$. For a set $P$ we denote by $ms(P)$ the +Euclidean space $\E^d$. For a set $P$ we denote by $ms(P)$ the smallest sphere that contains all points of $P$. $ms(P)$ can be degenerate, i.e.\ $ms(P)=\emptyset$ if $P=\emptyset$ and $ms(P)=\{p\}$ if @@ -162,7 +162,7 @@ divide. \ccIndexMemberFunctionGroup{predicates} By definition, an empty \ccRefName\ has no boundary and no -bounded side, i.e.\ its unbounded side equals the whole space $\E_d$. +bounded side, i.e.\ its unbounded side equals the whole space $\E^d$. \ccMemberFunction{ Bounded_side bounded_side( const Point& p) const;}{ diff --git a/Min_sphere_of_spheres_d/doc_tex/Bounding_volumes_ref/Min_sphere_of_spheres_d.tex b/Min_sphere_of_spheres_d/doc_tex/Bounding_volumes_ref/Min_sphere_of_spheres_d.tex index 821d54234d7..e3c3be2ee3e 100644 --- a/Min_sphere_of_spheres_d/doc_tex/Bounding_volumes_ref/Min_sphere_of_spheres_d.tex +++ b/Min_sphere_of_spheres_d/doc_tex/Bounding_volumes_ref/Min_sphere_of_spheres_d.tex @@ -10,7 +10,7 @@ An object of the class \ccRefName\ is a data structure that represents the unique sphere of smallest volume enclosing a finite set of spheres -in $d$-dimensional Euclidean space $\E_d$. For a set $S$ of spheres +in $d$-dimensional Euclidean space $\E^d$. For a set $S$ of spheres we denote by $ms(S)$ the smallest sphere that contains all spheres of $S$; we call $ms(S)$ the \emph{minsphere} of $S$. $ms(S)$ can be degenerate, i.e., $ms(S)=\emptyset$, diff --git a/Polytope_distance_d/doc_tex/Polytope_distance_d_ref/Polytope_distance_d.tex b/Polytope_distance_d/doc_tex/Polytope_distance_d_ref/Polytope_distance_d.tex index 77e20a90420..4330e2cc72c 100644 --- a/Polytope_distance_d/doc_tex/Polytope_distance_d_ref/Polytope_distance_d.tex +++ b/Polytope_distance_d/doc_tex/Polytope_distance_d_ref/Polytope_distance_d.tex @@ -16,7 +16,7 @@ An object of the class \ccRefName\ represents the (squared) distance between two convex polytopes, given as the convex hulls of two finite point -sets in $d$-dimensional Euclidean space $\E_d$. For point sets $P$ and $Q$ +sets in $d$-dimensional Euclidean space $\E^d$. For point sets $P$ and $Q$ we denote by $pd(P,Q)$ the distance between the convex hulls of $P$ and $Q$. Note that $pd(P,Q)$ can be degenerate\lcTex{\ccIndexSubitem[t]{degeneracies}{\ccFont Polytope_distance_d}},