mirror of https://github.com/CGAL/cgal
Fix \E_* to \E^* thinko/copy-pasto.
Remove one more \ccTexHtml as well.
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36a53b8873
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@ -14,7 +14,7 @@
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An object of the class \ccRefName\ is the unique annulus (region between
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An object of the class \ccRefName\ is the unique annulus (region between
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two concentric spheres with radii $r$ and $R$, $r \leq R$) enclosing a
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two concentric spheres with radii $r$ and $R$, $r \leq R$) enclosing a
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finite set of points in $d$-dimensional Euclidean space $\E_d$, where the
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finite set of points in $d$-dimensional Euclidean space $\E^d$, where the
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difference $R^2-r^2$ is minimal. For a point set $P$ we denote by $ma(P)$
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difference $R^2-r^2$ is minimal. For a point set $P$ we denote by $ma(P)$
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the smallest annulus that contains all points of $P$. Note that $ma(P)$
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the smallest annulus that contains all points of $P$. Note that $ma(P)$
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can be degenerate\lcTex{\ccIndexSubitem[t]{degeneracies}{\ccFont Min_annulus_d}},
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can be degenerate\lcTex{\ccIndexSubitem[t]{degeneracies}{\ccFont Min_annulus_d}},
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@ -236,7 +236,7 @@ two-, three-, and $d$-dimensional \cgal~kernel, respectively.
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The bounded area of the smallest enclosing annulus lies between the inner
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The bounded area of the smallest enclosing annulus lies between the inner
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and the outer sphere. The boundary is the union of both spheres. By
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and the outer sphere. The boundary is the union of both spheres. By
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definition, an empty annulus has no boundary and no bounded side, i.e.~its
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definition, an empty annulus has no boundary and no bounded side, i.e.~its
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unbounded side equals the whole space $\E_d$.
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unbounded side equals the whole space $\E^d$.
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\ccMemberFunction{ CGAL::Bounded_side
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\ccMemberFunction{ CGAL::Bounded_side
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bounded_side( const Point& p) const;}{
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bounded_side( const Point& p) const;}{
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@ -83,12 +83,12 @@ The following predicate is only needed, if the member function
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\ccDefinition
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\ccDefinition
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An object of the class \ccClassName\ is a circle in two-dimensional
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An object of the class \ccClassName\ is a circle in two-dimensional
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Euclidean plane $\E_2$. Its boundary splits the plane into a bounded
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Euclidean plane $\E^2$. Its boundary splits the plane into a bounded
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and an unbounded side. By definition, an empty \ccClassName\ has no
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and an unbounded side. By definition, an empty \ccClassName\ has no
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boundary and no bounded side, i.e.\ its unbounded side equals the
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boundary and no bounded side, i.e.\ its unbounded side equals the
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whole plane $\E_2$. A \ccClassName\ containing exactly one point~$p$
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whole plane $\E^2$. A \ccClassName\ containing exactly one point~$p$
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has no bounded side, its boundary is $\{p\}$, and its unbounded side
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has no bounded side, its boundary is $\{p\}$, and its unbounded side
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equals $\E_2\mbox{\ccTexHtml{$\setminus$}{-}}\{p\}$.
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equals $\E^2 \setminus \{p\}$.
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% -----------------------------------------------------------------------------
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% -----------------------------------------------------------------------------
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\ccTypes
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\ccTypes
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@ -15,7 +15,7 @@
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An object of the class \ccRefName\ is the unique circle of smallest area
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An object of the class \ccRefName\ is the unique circle of smallest area
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enclosing a finite (multi)set of points in two-dimensional Euclidean
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enclosing a finite (multi)set of points in two-dimensional Euclidean
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space~$\E_2$. For a point set $P$ we denote by $mc(P)$ the smallest circle
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space~$\E^2$. For a point set $P$ we denote by $mc(P)$ the smallest circle
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that contains all points of $P$. Note that $mc(P)$ can be
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that contains all points of $P$. Note that $mc(P)$ can be
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degenerate\lcTex{\ccIndexSubitem[t]{degeneracies}{\ccFont Min_circle_2}},
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degenerate\lcTex{\ccIndexSubitem[t]{degeneracies}{\ccFont Min_circle_2}},
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i.e.~$mc(P)=\emptyset$ if
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i.e.~$mc(P)=\emptyset$ if
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@ -173,7 +173,7 @@ $S$ of $P$.
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\ccIndexMemberFunctionGroup{predicates}
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\ccIndexMemberFunctionGroup{predicates}
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By definition, an empty \ccClassTemplateName\ has no boundary and no
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By definition, an empty \ccClassTemplateName\ has no boundary and no
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bounded side, i.e.\ its unbounded side equals the whole space $\E_2$.
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bounded side, i.e.\ its unbounded side equals the whole space $\E^2$.
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\ccMemberFunction{ CGAL::Bounded_side
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\ccMemberFunction{ CGAL::Bounded_side
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bounded_side( const Point& p) const;}{
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bounded_side( const Point& p) const;}{
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@ -62,10 +62,10 @@ Only default and copy constructor are required.
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\ccDefinition
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\ccDefinition
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An object of the class \ccClassName\ is an ellipse in two-dimensional
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An object of the class \ccClassName\ is an ellipse in two-dimensional
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Euclidean plane $\E_2$. Its boundary splits the plane into a bounded
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Euclidean plane $\E^2$. Its boundary splits the plane into a bounded
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and an unbounded side. By definition, an empty \ccClassName\ has no
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and an unbounded side. By definition, an empty \ccClassName\ has no
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boundary and no bounded side, i.e.\ its unbounded side equals the
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boundary and no bounded side, i.e.\ its unbounded side equals the
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whole plane $\E_2$.
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whole plane $\E^2$.
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% -----------------------------------------------------------------------------
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% -----------------------------------------------------------------------------
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\ccTypes
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\ccTypes
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@ -14,7 +14,7 @@
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An object of the class \ccRefName\ is the unique ellipse of smallest area
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An object of the class \ccRefName\ is the unique ellipse of smallest area
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enclosing a finite (multi)set of points in two-dimensional euclidean
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enclosing a finite (multi)set of points in two-dimensional euclidean
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space~$\E_2$. For a point set $P$ we denote by $me(P)$ the smallest
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space~$\E^2$. For a point set $P$ we denote by $me(P)$ the smallest
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ellipse that contains all points of $P$. Note that $me(P)$ can be
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ellipse that contains all points of $P$. Note that $me(P)$ can be
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degenerate\lcTex{\ccIndexSubitem[t]{degeneracies}{\ccFont Min_ellipse_2}},
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degenerate\lcTex{\ccIndexSubitem[t]{degeneracies}{\ccFont Min_ellipse_2}},
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i.e.~$me(P)=\emptyset$ if
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i.e.~$me(P)=\emptyset$ if
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@ -184,7 +184,7 @@ reconstructing $me(P)$ from a given support set\lcTex{\ccIndexSubitem[t]{support
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\ccIndexMemberFunctionGroup{predicates}
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\ccIndexMemberFunctionGroup{predicates}
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By definition, an empty \ccRefName\ has no boundary and no bounded side,
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By definition, an empty \ccRefName\ has no boundary and no bounded side,
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i.e.\ its unbounded side equals the whole space $\E_2$.
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i.e.\ its unbounded side equals the whole space $\E^2$.
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\ccMemberFunction{ CGAL::Bounded_side
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\ccMemberFunction{ CGAL::Bounded_side
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bounded_side( const Point& p) const;}{
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bounded_side( const Point& p) const;}{
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@ -62,10 +62,10 @@ Only default and copy constructor are required.
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\ccDefinition
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\ccDefinition
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An object of the class \ccClassName\ is an ellipse in two-dimensional
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An object of the class \ccClassName\ is an ellipse in two-dimensional
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Euclidean plane $\E_2$. Its boundary splits the plane into a bounded
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Euclidean plane $\E^2$. Its boundary splits the plane into a bounded
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and an unbounded side. By definition, an empty \ccClassName\ has no
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and an unbounded side. By definition, an empty \ccClassName\ has no
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boundary and no bounded side, i.e.\ its unbounded side equals the
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boundary and no bounded side, i.e.\ its unbounded side equals the
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whole plane $\E_2$.
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whole plane $\E^2$.
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% -----------------------------------------------------------------------------
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% -----------------------------------------------------------------------------
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\ccTypes
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\ccTypes
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@ -12,7 +12,7 @@
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An object of the class \ccRefName\ is the unique sphere of
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An object of the class \ccRefName\ is the unique sphere of
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smallest volume enclosing a finite (multi)set of points in $d$-dimensional
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smallest volume enclosing a finite (multi)set of points in $d$-dimensional
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Euclidean space $\E_d$. For a set $P$ we denote by $ms(P)$ the
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Euclidean space $\E^d$. For a set $P$ we denote by $ms(P)$ the
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smallest sphere that contains all points of $P$. $ms(P)$ can
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smallest sphere that contains all points of $P$. $ms(P)$ can
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be degenerate, i.e.\ $ms(P)=\emptyset$
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be degenerate, i.e.\ $ms(P)=\emptyset$
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if $P=\emptyset$ and $ms(P)=\{p\}$ if
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if $P=\emptyset$ and $ms(P)=\{p\}$ if
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@ -162,7 +162,7 @@ divide.
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\ccIndexMemberFunctionGroup{predicates}
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\ccIndexMemberFunctionGroup{predicates}
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By definition, an empty \ccRefName\ has no boundary and no
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By definition, an empty \ccRefName\ has no boundary and no
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bounded side, i.e.\ its unbounded side equals the whole space $\E_d$.
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bounded side, i.e.\ its unbounded side equals the whole space $\E^d$.
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\ccMemberFunction{ Bounded_side
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\ccMemberFunction{ Bounded_side
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bounded_side( const Point& p) const;}{
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bounded_side( const Point& p) const;}{
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@ -10,7 +10,7 @@
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An object of the class \ccRefName\ is a data structure that represents
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An object of the class \ccRefName\ is a data structure that represents
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the unique sphere of smallest volume enclosing a finite set of spheres
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the unique sphere of smallest volume enclosing a finite set of spheres
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in $d$-dimensional Euclidean space $\E_d$. For a set $S$ of spheres
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in $d$-dimensional Euclidean space $\E^d$. For a set $S$ of spheres
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we denote by $ms(S)$ the smallest sphere that contains all spheres of
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we denote by $ms(S)$ the smallest sphere that contains all spheres of
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$S$; we call $ms(S)$ the \emph{minsphere} of $S$. $ms(S)$ can be
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$S$; we call $ms(S)$ the \emph{minsphere} of $S$. $ms(S)$ can be
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degenerate, i.e., $ms(S)=\emptyset$,
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degenerate, i.e., $ms(S)=\emptyset$,
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@ -16,7 +16,7 @@
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An object of the class \ccRefName\ represents the (squared) distance
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An object of the class \ccRefName\ represents the (squared) distance
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between two convex polytopes, given as the convex hulls of two finite point
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between two convex polytopes, given as the convex hulls of two finite point
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sets in $d$-dimensional Euclidean space $\E_d$. For point sets $P$ and $Q$
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sets in $d$-dimensional Euclidean space $\E^d$. For point sets $P$ and $Q$
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we denote by $pd(P,Q)$ the distance between the convex hulls of $P$ and
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we denote by $pd(P,Q)$ the distance between the convex hulls of $P$ and
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$Q$. Note that $pd(P,Q)$ can be
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$Q$. Note that $pd(P,Q)$ can be
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degenerate\lcTex{\ccIndexSubitem[t]{degeneracies}{\ccFont Polytope_distance_d}},
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degenerate\lcTex{\ccIndexSubitem[t]{degeneracies}{\ccFont Polytope_distance_d}},
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