mirror of https://github.com/CGAL/cgal
tmp version
This commit is contained in:
Sven Schönherr
parent
9818b20822
commit
95b971db9c
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@ -2,12 +2,12 @@
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% The CGAL Reference Manual
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% Section: 2D Smallest Enclosing Circle
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% -----------------------------------------------------------------------------
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% source: Min_circle_2.tex
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% author: Sven Schönherr (sven@inf.fu-berlin.de)
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% file : Min_circle_2.tex
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% author: Bernd Gärtner, Sven Schönherr (sven@inf.fu-berlin.de)
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% $Id$
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% =============================================================================
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\begin{CCclassTemplate}{CGAL_Min_circle_2<R>}
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\begin{ccClassTemplate}{CGAL_Min_circle_2<R>}
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\ccSection{2D Smallest Enclosing Circle}
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\ccDefinition
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@ -24,9 +24,9 @@ is no circle containing $P$ with $B$ on the boundary.
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The smallest enclosing circle of a point set $P$ is determined by at
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most three points on the boundary. A minimal subset $S$ of $P$ with
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$\textit{mc}(S,\emptyset) = \textit{mc}(P,\emptyset)$ is called a {\em
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support set}, the points in $S$ are the {\em support points}. Note
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that in general the set $S$ is not unique.
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$\textit{mc}(S,\emptyset) = \textit{mc}(P,\emptyset)$ is called a
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\emph{support set}, the points in $S$ are the \emph{support points}.
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Note that in general the set $S$ is not unique.
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The underlying algorithm can cope with all kinds of input, e.g.\ one
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or both of the point sets $P$ or $B$ may be empty, $B$ may contain
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@ -38,10 +38,8 @@ fixed until the next update operation.
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\ccCreation
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\ccCreationVariable{min_circle}
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\ccSetThreeColumns
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{CGAL_Bounded_side}
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{}
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{returns \ccStyle{CGAL_ON_BOUNDED_SIDE}, \ccStyle{CGAL_ON_BOUNDARY},}
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\ccSetThreeColumns{CGAL_Bounded_side}{}{
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returns \ccStyle{CGAL_ON_BOUNDED_SIDE}, \ccStyle{CGAL_ON_BOUNDARY},}
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\ccPropagateThreeToTwoColumns
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\ccStyle{#include <CGAL/Min_circle_2.h>}
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@ -56,31 +54,33 @@ fixed until the next update operation.
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\ccConstructor{ CGAL_Min_circle_2( const CGAL_Min_circle_2<R>& min_circle2);}{
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copy constructor.}
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\ccConstructor{ CGAL_Min_circle_2( const Point_2<R>& p);}{
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\ccConstructor{ CGAL_Min_circle_2( const CGAL_Point_2<R>& p);}{
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introduces a variable \ccVar\ of type \ccClassTemplateName.
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It is initialized to $\textit{mc}(\emptyset,\{\ccStyle{p}\})$,
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i.e.\ to the set $\{\ccStyle{p}\}$.
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\ccPostcond \ccVar\ccStyle{.is_degenerate()}.}
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\ccConstructor{ CGAL_Min_circle_2( const Point_2<R>& p1,
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const Point_2<R>& p2);}{
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\ccConstructor{ CGAL_Min_circle_2( const CGAL_Point_2<R>& p1,
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const CGAL_Point_2<R>& p2);}{
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introduces a variable \ccVar\ of type \ccClassTemplateName.
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It is initialized to
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$\textit{mc}(\emptyset,\{\ccStyle{p1},\ccStyle{p2}\})$,
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i.e.\ to the circle with diameter
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$\overline{\ccStyle{p1}\ccStyle{p2}}$.}
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$\textit{mc}(\emptyset,\{\ccStyle{p1},\ccStyle{p2}\})$, i.e.\
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to the circle with diameter
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$\overline{\ccStyle{p1}\ccStyle{p2}}$, if $\ccStyle{p1} \neq
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\ccStyle{p2}$, or to the set $\{\ccStyle{p1}\}$ otherwise.}
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\ccConstructor{ CGAL_Min_circle_2( const Point_2<R>& p1,
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const Point_2<R>& p2,
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const Point_2<R>& p3);}{
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\ccConstructor{ CGAL_Min_circle_2( const CGAL_Point_2<R>& p1,
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const CGAL_Point_2<R>& p2,
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const CGAL_Point_2<R>& p3);}{
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introduces a variable \ccVar\ of type \ccClassTemplateName.
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It is initialized to $\textit{mc}(\emptyset,
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\{\ccStyle{p1},\ccStyle{p2},\ccStyle{p3}\})$,
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i.e.\ to the unique circle with \ccStyle{p1}, \ccStyle{p2} and
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\ccStyle{p3} on the boundary.}
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\{\ccStyle{p1},\ccStyle{p2},\ccStyle{p3}\})$, i.e.\ to the
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unique circle with \ccStyle{p1}, \ccStyle{p2} and \ccStyle{p3}
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on the boundary, if it exists. Otherwise \ccVar\ is
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undefined.}
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\ccConstructor{ CGAL_Min_circle_2( forward_iterator< Point_2<R> > first,
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forward_iterator< Point_2<R> > last,
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\ccConstructor{ CGAL_Min_circle_2( forward_iterator< CGAL_Point_2<R> > first,
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forward_iterator< CGAL_Point_2<R> > last,
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bool randomize = false);}{
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introduces a variable \ccVar\ of type \ccClassTemplateName. It
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is initialized to $\textit{mc}(P,\emptyset)$ with $P$ being
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@ -89,19 +89,25 @@ fixed until the next update operation.
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\ccStyle{true}, a random permutation of $P$ is computed in
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advance.}
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\ccConstructor{ CGAL_Min_circle_2( forward_iterator< Point_2<R> > p_first,
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forward_iterator< Point_2<R> > p_last,
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forward_iterator< Point_2<R> > b_first,
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forward_iterator< Point_2<R> > b_last,
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\ccConstructor{ CGAL_Min_circle_2( forward_iterator< CGAL_Point_2<R> > p_first,
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forward_iterator< CGAL_Point_2<R> > p_last,
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forward_iterator< CGAL_Point_2<R> > b_first,
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forward_iterator< CGAL_Point_2<R> > b_last,
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bool randomize = false);}{
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introduces a variable \ccVar\ of type \ccClassTemplateName. It
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is initialized to $\textit{mc}(P,B)$ with $P$ being the set of
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points in the range $[\ccStyle{p_first},\ccStyle{p_last})$ and
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$B$ being the set of points in the range
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is initialized to $\textit{mc}(P,B)$ (if it exists, to
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undefined otherwise) with $P$ being the set of points in the
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range $[\ccStyle{p_first},\ccStyle{p_last})$ and $B$ being the
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set of points in the range
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$[\ccStyle{b_first},\ccStyle{b_last})$. If \ccStyle{randomize}
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is \ccStyle{true}, a random permutation of $P$ is computed in
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advance.}
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\ccHidden
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\ccMemberFunction{ const Min_circle_2<R>&
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operator = ( const Min_circle_2<R>& min_circle2);}{
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assignment operator.}
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\ccHeading{Access operations}
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returns the number of points of \ccVar, i.e.\ $|P|+|B|$.}
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\ccMemberFunction{ int number_of_support_points( ) const;}{
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returns the number of support points of \ccVar, i.e.\ $|S|$.}
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returns the number of support points of \ccVar, i.e.\ $|S|$,
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if \ccVar\ is defined, $-1$ otherwise.}
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\ccMemberFunction{ const CGAL_Point_2<R>& point( int i) const;}{
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returns the \ccStyle{i}'th point of \ccVar. Between two update
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@ -133,17 +140,33 @@ fixed until the next update operation.
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squared radius $r$ as \ccVar\ and positive orientation. If
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\ccVar\ is the empty set, $c$ is undefined und $r$ is set to
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zero. If \ccVar\ contains exactly one point $p$, $c$ is set to
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$p$ and $r$ is set to zero.}
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$p$ and $r$ is set to zero.
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\ccPrecond $\ccVar\ccStyle{.is_undefined()} = \ccStyle{false}$.}
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\ccMemberFunction{ CGAL_Bbox_2 bbox( ) const;}{
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returns a bounding box containing \ccVar.}
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returns a bounding box containing \ccVar.
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\ccPrecond $\ccVar\ccStyle{.is_undefined()} = \ccStyle{false}$.}
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\ccHeading{Update operations}
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\ccMemberFunction{ void insert( const CGAL_Point_2<R>& p);}{
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inserts \ccStyle{p} in \ccVar\ and recomputes the smallest
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enclosing circle.}
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enclosing circle.
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\ccPrecond $\ccVar\ccStyle{.is_undefined()} = \ccStyle{false}$.}
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\ccMemberFunction{ void reserve( int n);}{
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reserves storage for at least \ccStyle{n} points in \ccVar.
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It can be used, if the number of insert operations is known in
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advance.
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\ccPrecond $\ccVar\ccStyle{.is_undefined()} = \ccStyle{false}$.}
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\ccUnchecked
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\ccHidden
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\ccMemberFunction{ void reset( );}{
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resets \ccVar\ to $\textit{mc}(\emptyset,\emptyset)$,
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i.e.\ to the empty set.
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\ccPostcond \ccVar\ccStyle{.is_empty()}.}
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\ccHeading{Tests}
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@ -153,18 +176,25 @@ fixed until the next update operation.
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returns \ccStyle{CGAL_ON_BOUNDED_SIDE},
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\ccStyle{CGAL_ON_BOUNDARY}, or
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\ccStyle{CGAL_ON_UNBOUNDED_SIDE} iff \ccStyle{p} lies inside,
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on the boundary, or outside of \ccVar, respectively.}
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on the boundary, or outside of \ccVar, respectively.
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\ccPrecond $\ccVar\ccStyle{.is_undefined()} = \ccStyle{false}$.}
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\ccMemberFunction{ bool has_on_bounded_side( const CGAL_Point_2<R>& p) const;}{
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returns \ccStyle{true}, iff \ccStyle{p} lies inside \ccVar.}
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returns \ccStyle{true}, iff \ccStyle{p} lies inside \ccVar.
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\ccPrecond $\ccVar\ccStyle{.is_undefined()} = \ccStyle{false}$.}
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\ccMemberFunction{ bool has_on_boundary( const CGAL_Point_2<R>& p) const;}{
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returns \ccStyle{true}, iff \ccStyle{p} lies on the boundary
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of \ccVar.}
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of \ccVar.
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\ccPrecond $\ccVar\ccStyle{.is_undefined()} = \ccStyle{false}$.}
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\ccMemberFunction{ bool
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has_on_unbounded_side( const CGAL_Point_2<R>& p) const;}{
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returns \ccStyle{true}, iff \ccStyle{p} lies outside of \ccVar.}
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returns \ccStyle{true}, iff \ccStyle{p} lies outside of \ccVar.
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\ccPrecond $\ccVar\ccStyle{.is_undefined()} = \ccStyle{false}$.}
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\ccMemberFunction{ bool is_empty( ) const;}{
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returns \ccStyle{true}, iff \ccVar\ is empty.}
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\ccMemberFunction{ bool is_degenerate( ) const;}{
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returns \ccStyle{true}, iff \ccVar\ is degenerate.}
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@ -172,6 +202,6 @@ fixed until the next update operation.
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\ccMemberFunction{ bool is_undefined( ) const;}{
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returns \ccStyle{true}, iff \ccVar\ is undefined.}
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\end{CCclassTemplate}
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\end{ccClassTemplate}
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% ===== EOF ===================================================================
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@ -2,12 +2,12 @@
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% The CGAL Reference Manual
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% Section: 2D Smallest Enclosing Circle
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% -----------------------------------------------------------------------------
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% source: Min_circle_2.tex
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% author: Sven Schönherr (sven@inf.fu-berlin.de)
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% file : Min_circle_2.tex
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% author: Bernd Gärtner, Sven Schönherr (sven@inf.fu-berlin.de)
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% $Id$
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% =============================================================================
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\begin{CCclassTemplate}{CGAL_Min_circle_2<R>}
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\begin{ccClassTemplate}{CGAL_Min_circle_2<R>}
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\ccSection{2D Smallest Enclosing Circle}
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\ccDefinition
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@ -24,9 +24,9 @@ is no circle containing $P$ with $B$ on the boundary.
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The smallest enclosing circle of a point set $P$ is determined by at
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most three points on the boundary. A minimal subset $S$ of $P$ with
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$\textit{mc}(S,\emptyset) = \textit{mc}(P,\emptyset)$ is called a {\em
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support set}, the points in $S$ are the {\em support points}. Note
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that in general the set $S$ is not unique.
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$\textit{mc}(S,\emptyset) = \textit{mc}(P,\emptyset)$ is called a
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\emph{support set}, the points in $S$ are the \emph{support points}.
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Note that in general the set $S$ is not unique.
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The underlying algorithm can cope with all kinds of input, e.g.\ one
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or both of the point sets $P$ or $B$ may be empty, $B$ may contain
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@ -38,10 +38,8 @@ fixed until the next update operation.
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\ccCreation
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\ccCreationVariable{min_circle}
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\ccSetThreeColumns
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{CGAL_Bounded_side}
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{}
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{returns \ccStyle{CGAL_ON_BOUNDED_SIDE}, \ccStyle{CGAL_ON_BOUNDARY},}
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\ccSetThreeColumns{CGAL_Bounded_side}{}{
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returns \ccStyle{CGAL_ON_BOUNDED_SIDE}, \ccStyle{CGAL_ON_BOUNDARY},}
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\ccPropagateThreeToTwoColumns
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\ccStyle{#include <CGAL/Min_circle_2.h>}
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@ -56,31 +54,33 @@ fixed until the next update operation.
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\ccConstructor{ CGAL_Min_circle_2( const CGAL_Min_circle_2<R>& min_circle2);}{
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copy constructor.}
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\ccConstructor{ CGAL_Min_circle_2( const Point_2<R>& p);}{
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\ccConstructor{ CGAL_Min_circle_2( const CGAL_Point_2<R>& p);}{
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introduces a variable \ccVar\ of type \ccClassTemplateName.
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It is initialized to $\textit{mc}(\emptyset,\{\ccStyle{p}\})$,
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i.e.\ to the set $\{\ccStyle{p}\}$.
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\ccPostcond \ccVar\ccStyle{.is_degenerate()}.}
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\ccConstructor{ CGAL_Min_circle_2( const Point_2<R>& p1,
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const Point_2<R>& p2);}{
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\ccConstructor{ CGAL_Min_circle_2( const CGAL_Point_2<R>& p1,
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const CGAL_Point_2<R>& p2);}{
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introduces a variable \ccVar\ of type \ccClassTemplateName.
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It is initialized to
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$\textit{mc}(\emptyset,\{\ccStyle{p1},\ccStyle{p2}\})$,
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i.e.\ to the circle with diameter
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$\overline{\ccStyle{p1}\ccStyle{p2}}$.}
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$\textit{mc}(\emptyset,\{\ccStyle{p1},\ccStyle{p2}\})$, i.e.\
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to the circle with diameter
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$\overline{\ccStyle{p1}\ccStyle{p2}}$, if $\ccStyle{p1} \neq
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\ccStyle{p2}$, or to the set $\{\ccStyle{p1}\}$ otherwise.}
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\ccConstructor{ CGAL_Min_circle_2( const Point_2<R>& p1,
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const Point_2<R>& p2,
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const Point_2<R>& p3);}{
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\ccConstructor{ CGAL_Min_circle_2( const CGAL_Point_2<R>& p1,
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const CGAL_Point_2<R>& p2,
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const CGAL_Point_2<R>& p3);}{
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introduces a variable \ccVar\ of type \ccClassTemplateName.
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It is initialized to $\textit{mc}(\emptyset,
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\{\ccStyle{p1},\ccStyle{p2},\ccStyle{p3}\})$,
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i.e.\ to the unique circle with \ccStyle{p1}, \ccStyle{p2} and
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\ccStyle{p3} on the boundary.}
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\{\ccStyle{p1},\ccStyle{p2},\ccStyle{p3}\})$, i.e.\ to the
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unique circle with \ccStyle{p1}, \ccStyle{p2} and \ccStyle{p3}
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on the boundary, if it exists. Otherwise \ccVar\ is
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undefined.}
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\ccConstructor{ CGAL_Min_circle_2( forward_iterator< Point_2<R> > first,
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forward_iterator< Point_2<R> > last,
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\ccConstructor{ CGAL_Min_circle_2( forward_iterator< CGAL_Point_2<R> > first,
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forward_iterator< CGAL_Point_2<R> > last,
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bool randomize = false);}{
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introduces a variable \ccVar\ of type \ccClassTemplateName. It
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is initialized to $\textit{mc}(P,\emptyset)$ with $P$ being
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@ -89,19 +89,25 @@ fixed until the next update operation.
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\ccStyle{true}, a random permutation of $P$ is computed in
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advance.}
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\ccConstructor{ CGAL_Min_circle_2( forward_iterator< Point_2<R> > p_first,
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forward_iterator< Point_2<R> > p_last,
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forward_iterator< Point_2<R> > b_first,
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forward_iterator< Point_2<R> > b_last,
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\ccConstructor{ CGAL_Min_circle_2( forward_iterator< CGAL_Point_2<R> > p_first,
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forward_iterator< CGAL_Point_2<R> > p_last,
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forward_iterator< CGAL_Point_2<R> > b_first,
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forward_iterator< CGAL_Point_2<R> > b_last,
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bool randomize = false);}{
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introduces a variable \ccVar\ of type \ccClassTemplateName. It
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is initialized to $\textit{mc}(P,B)$ with $P$ being the set of
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points in the range $[\ccStyle{p_first},\ccStyle{p_last})$ and
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$B$ being the set of points in the range
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is initialized to $\textit{mc}(P,B)$ (if it exists, to
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undefined otherwise) with $P$ being the set of points in the
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range $[\ccStyle{p_first},\ccStyle{p_last})$ and $B$ being the
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set of points in the range
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$[\ccStyle{b_first},\ccStyle{b_last})$. If \ccStyle{randomize}
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is \ccStyle{true}, a random permutation of $P$ is computed in
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advance.}
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\ccHidden
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\ccMemberFunction{ const Min_circle_2<R>&
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operator = ( const Min_circle_2<R>& min_circle2);}{
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assignment operator.}
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\ccHeading{Access operations}
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@ -109,7 +115,8 @@ fixed until the next update operation.
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returns the number of points of \ccVar, i.e.\ $|P|+|B|$.}
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\ccMemberFunction{ int number_of_support_points( ) const;}{
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returns the number of support points of \ccVar, i.e.\ $|S|$.}
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returns the number of support points of \ccVar, i.e.\ $|S|$,
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if \ccVar\ is defined, $-1$ otherwise.}
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\ccMemberFunction{ const CGAL_Point_2<R>& point( int i) const;}{
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returns the \ccStyle{i}'th point of \ccVar. Between two update
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@ -133,17 +140,33 @@ fixed until the next update operation.
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squared radius $r$ as \ccVar\ and positive orientation. If
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\ccVar\ is the empty set, $c$ is undefined und $r$ is set to
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zero. If \ccVar\ contains exactly one point $p$, $c$ is set to
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$p$ and $r$ is set to zero.}
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$p$ and $r$ is set to zero.
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\ccPrecond $\ccVar\ccStyle{.is_undefined()} = \ccStyle{false}$.}
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\ccMemberFunction{ CGAL_Bbox_2 bbox( ) const;}{
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returns a bounding box containing \ccVar.}
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returns a bounding box containing \ccVar.
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\ccPrecond $\ccVar\ccStyle{.is_undefined()} = \ccStyle{false}$.}
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\ccHeading{Update operations}
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\ccMemberFunction{ void insert( const CGAL_Point_2<R>& p);}{
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inserts \ccStyle{p} in \ccVar\ and recomputes the smallest
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enclosing circle.}
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enclosing circle.
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\ccPrecond $\ccVar\ccStyle{.is_undefined()} = \ccStyle{false}$.}
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\ccMemberFunction{ void reserve( int n);}{
|
||||
reserves storage for at least \ccStyle{n} points in \ccVar.
|
||||
It can be used, if the number of insert operations is known in
|
||||
advance.
|
||||
\ccPrecond $\ccVar\ccStyle{.is_undefined()} = \ccStyle{false}$.}
|
||||
|
||||
\ccUnchecked
|
||||
\ccHidden
|
||||
\ccMemberFunction{ void reset( );}{
|
||||
resets \ccVar\ to $\textit{mc}(\emptyset,\emptyset)$,
|
||||
i.e.\ to the empty set.
|
||||
\ccPostcond \ccVar\ccStyle{.is_empty()}.}
|
||||
|
||||
|
||||
\ccHeading{Tests}
|
||||
|
|
@ -153,18 +176,25 @@ fixed until the next update operation.
|
|||
returns \ccStyle{CGAL_ON_BOUNDED_SIDE},
|
||||
\ccStyle{CGAL_ON_BOUNDARY}, or
|
||||
\ccStyle{CGAL_ON_UNBOUNDED_SIDE} iff \ccStyle{p} lies inside,
|
||||
on the boundary, or outside of \ccVar, respectively.}
|
||||
on the boundary, or outside of \ccVar, respectively.
|
||||
\ccPrecond $\ccVar\ccStyle{.is_undefined()} = \ccStyle{false}$.}
|
||||
|
||||
\ccMemberFunction{ bool has_on_bounded_side( const CGAL_Point_2<R>& p) const;}{
|
||||
returns \ccStyle{true}, iff \ccStyle{p} lies inside \ccVar.}
|
||||
returns \ccStyle{true}, iff \ccStyle{p} lies inside \ccVar.
|
||||
\ccPrecond $\ccVar\ccStyle{.is_undefined()} = \ccStyle{false}$.}
|
||||
|
||||
\ccMemberFunction{ bool has_on_boundary( const CGAL_Point_2<R>& p) const;}{
|
||||
returns \ccStyle{true}, iff \ccStyle{p} lies on the boundary
|
||||
of \ccVar.}
|
||||
of \ccVar.
|
||||
\ccPrecond $\ccVar\ccStyle{.is_undefined()} = \ccStyle{false}$.}
|
||||
|
||||
\ccMemberFunction{ bool
|
||||
has_on_unbounded_side( const CGAL_Point_2<R>& p) const;}{
|
||||
returns \ccStyle{true}, iff \ccStyle{p} lies outside of \ccVar.}
|
||||
returns \ccStyle{true}, iff \ccStyle{p} lies outside of \ccVar.
|
||||
\ccPrecond $\ccVar\ccStyle{.is_undefined()} = \ccStyle{false}$.}
|
||||
|
||||
\ccMemberFunction{ bool is_empty( ) const;}{
|
||||
returns \ccStyle{true}, iff \ccVar\ is empty.}
|
||||
|
||||
\ccMemberFunction{ bool is_degenerate( ) const;}{
|
||||
returns \ccStyle{true}, iff \ccVar\ is degenerate.}
|
||||
|
|
@ -172,6 +202,6 @@ fixed until the next update operation.
|
|||
\ccMemberFunction{ bool is_undefined( ) const;}{
|
||||
returns \ccStyle{true}, iff \ccVar\ is undefined.}
|
||||
|
||||
\end{CCclassTemplate}
|
||||
\end{ccClassTemplate}
|
||||
|
||||
% ===== EOF ===================================================================
|
||||
|
|
|
|||
Loading…
Reference in New Issue