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This commit is contained in:
Sylvain Pion 2007-04-17 13:21:11 +00:00
parent ae477f90de
commit 9dee39a730
22 changed files with 28 additions and 28 deletions
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2
Convex_hull_2/doc_tex/Convex_hull_2/convex_hull_2.tex
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@ -60,7 +60,7 @@ simple polygonal chains (or polygons) is available through the function
In the following example a convex hull is constructed from point data read In the following example a convex hull is constructed from point data read
from standard input using \ccc{Graham_Andrew} algorithm. The resulting convex from standard input using \ccc{Graham_Andrew} algorithm. The resulting convex
polygon is shown at the standard ouput console. The same results could be polygon is shown at the standard output console. The same results could be
achieved by substituting the function \ccc{CGAL::ch_graham_andrew} by other achieved by substituting the function \ccc{CGAL::ch_graham_andrew} by other
function like \ccc{CGAL::ch_bykat}. function like \ccc{CGAL::ch_bykat}.

2
Convex_hull_2/doc_tex/Convex_hull_2/traits_classes_2.tex
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@ -1,7 +1,7 @@
\section{Traits Classes} \section{Traits Classes}
Each of the functions used to compute convex hulls or extreme points Each of the functions used to compute convex hulls or extreme points
is paramterized by a traits class, which specifies the types and geometric is parameterized by a traits class, which specifies the types and geometric
primitives to be used in the computation. There are several implementations primitives to be used in the computation. There are several implementations
of 2D traits classes provided in the library. The class of 2D traits classes provided in the library. The class
\ccc{Convex_hull_traits_2<R>}\ccIndexMainItem[C]{Convex_hull_traits_2} \ccc{Convex_hull_traits_2<R>}\ccIndexMainItem[C]{Convex_hull_traits_2}

2
Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_akl_toussaint.tex
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@ -44,7 +44,7 @@ type \ccc{ForwardIterator::value_type} is defined.
\ccc{OutputIterator::value_type} \ccc{OutputIterator::value_type}
are equivalent to \ccc{Traits::Point_2}. are equivalent to \ccc{Traits::Point_2}.
\item \ccc{Traits} defines the following subset of types from \item \ccc{Traits} defines the following subset of types from
the concept ConvexHullTraits\_2 and their corresponding member the concept \ccc{ConvexHullTraits_2} and their corresponding member
%\ccIndexMainItem[c]{ConvexHullTraits_2} %\ccIndexMainItem[c]{ConvexHullTraits_2}
functions that return instances of these types: functions that return instances of these types:
\begin{itemize} \begin{itemize}

4
Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_bykat.tex
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@ -45,7 +45,7 @@ type \ccc{ForwardIterator::value_type} is defined.
\ccc{OutputIterator::value_type} \ccc{OutputIterator::value_type}
are equivalent to \ccc{Traits::Point_2}. are equivalent to \ccc{Traits::Point_2}.
\item \ccc{Traits} defines the following subset of types from \item \ccc{Traits} defines the following subset of types from
the concept ConvexHullTraits\_2 and their corresponding member the concept \ccc{ConvexHullTraits_2} and their corresponding member
%\ccIndexMainItem[c]{ConvexHullTraits_2} %\ccIndexMainItem[c]{ConvexHullTraits_2}
functions that return instances of these types: functions that return instances of these types:
\begin{itemize} \begin{itemize}
@ -67,7 +67,7 @@ type \ccc{ForwardIterator::value_type} is defined.
\ccRefIdfierPage{CGAL::convex_hull_2} \ccRefIdfierPage{CGAL::convex_hull_2}
\ccImplementation \ccImplementation
This function implements the non-recursive varitaion of This function implements the non-recursive variation of
Eddy's algorithm \cite{e-nchap-77} described in \cite{b-chfsp-78}. Eddy's algorithm \cite{e-nchap-77} described in \cite{b-chfsp-78}.
This algorithm requires $O(n h)$ time This algorithm requires $O(n h)$ time
in the worst case for $n$ input points with $h$ extreme points. in the worst case for $n$ input points with $h$ extreme points.

2
Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_e_point.tex
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@ -32,7 +32,7 @@ type \ccc{ForwardIterator::value_type} is defined.
\ccHeading{Requirements} \ccHeading{Requirements}
\ccc{Traits} defines a type \ccc{Traits::Less_xy_2} as described in \ccc{Traits} defines a type \ccc{Traits::Less_xy_2} as described in
the concept ConvexHullTraits\_2 and the corresponding member the concept \ccc{ConvexHullTraits_2} and the corresponding member
%\ccIndexMainItem[c]{ConvexHullTraits_2} %\ccIndexMainItem[c]{ConvexHullTraits_2}
function that returns an instance of this type. function that returns an instance of this type.

2
Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_eddy.tex
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@ -45,7 +45,7 @@ type \ccc{ForwardIterator::value_type} is defined.
\ccc{OutputIterator::value_type} \ccc{OutputIterator::value_type}
are equivalent to \ccc{Traits::Point_2}. are equivalent to \ccc{Traits::Point_2}.
\item \ccc{Traits} defines the following subset of types from \item \ccc{Traits} defines the following subset of types from
the concept ConvexHullTraits\_2 and their corresponding member the concept \ccc{ConvexHullTraits_2} and their corresponding member
%\ccIndexMainItem[c]{ConvexHullTraits_2} %\ccIndexMainItem[c]{ConvexHullTraits_2}
functions that return instances of these types: functions that return instances of these types:
\begin{itemize} \begin{itemize}

4
Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_graham_andrew.tex
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@ -44,7 +44,7 @@ type \ccc{InputIterator::value_type} is defined.
\ccc{OutputIterator::value_type} \ccc{OutputIterator::value_type}
are equivalent to \ccc{Traits::Point_2}. are equivalent to \ccc{Traits::Point_2}.
\item \ccc{Traits} defines the following subset of types from \item \ccc{Traits} defines the following subset of types from
the concept ConvexHullTraits\_2 and their corresponding member the concept \ccc{ConvexHullTraits_2} and their corresponding member
%\ccIndexMainItem[c]{ConvexHullTraits_2} %\ccIndexMainItem[c]{ConvexHullTraits_2}
functions that return instances of these types: functions that return instances of these types:
\begin{itemize} \begin{itemize}
@ -69,7 +69,7 @@ type \ccc{InputIterator::value_type} is defined.
\ccImplementation \ccImplementation
This function implements Andrew's variant of the Graham This function implements Andrew's variant of the Graham
scan algorithm \cite{a-aeach-79} and follows the presenation of Mehlhorn scan algorithm \cite{a-aeach-79} and follows the presentation of Mehlhorn
\cite{m-mdscg-84}. This algorithm requires $O(n \log n)$ time \cite{m-mdscg-84}. This algorithm requires $O(n \log n)$ time
in the worst case for $n$ input points. in the worst case for $n$ input points.

4
Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_graham_andrew_scan.tex
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@ -50,7 +50,7 @@ type \ccc{BidirectionalIterator::value_type} is defined.
\ccc{OutputIterator::value_type} \ccc{OutputIterator::value_type}
are equivalent to \ccc{Traits::Point_2}. are equivalent to \ccc{Traits::Point_2}.
\item \ccc{Traits} defines the following two types from \item \ccc{Traits} defines the following two types from
the concept ConvexHullTraits\_2 and their corresponding member the concept \ccc{ConvexHullTraits_2} and their corresponding member
%\ccIndexMainItem[c]{ConvexHullTraits_2} %\ccIndexMainItem[c]{ConvexHullTraits_2}
functions that return instances of these types: functions that return instances of these types:
\begin{itemize} \begin{itemize}
@ -78,7 +78,7 @@ In the following example \ccc{ch_graham_andrew_scan()} is used to
realize Anderson's variant \cite{a-readc-78} of the Graham Scan realize Anderson's variant \cite{a-readc-78} of the Graham Scan
\cite{g-eadch-72}. The points are sorted counterclockwise around the leftmost \cite{g-eadch-72}. The points are sorted counterclockwise around the leftmost
point using the \ccc{Less_rotate_ccw_2} predicate, as defined in point using the \ccc{Less_rotate_ccw_2} predicate, as defined in
the concept ConvexHullTraits\_2. According to the definition the concept \ccc{ConvexHullTraits_2}. According to the definition
of \ccc{Less_rotate_ccw_2}, the leftmost point is the last point in the sorted of \ccc{Less_rotate_ccw_2}, the leftmost point is the last point in the sorted
sequence and its predecessor on the convex hull is the first point in the sequence and its predecessor on the convex hull is the first point in the
sorted sequence. It is not hard to see that the preconditions of sorted sequence. It is not hard to see that the preconditions of

2
Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_jarvis.tex
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@ -45,7 +45,7 @@ type \ccc{InputIterator::value_type} is defined.
\ccc{OutputIterator::value_type} \ccc{OutputIterator::value_type}
are equivalent to \ccc{Traits::Point_2}. are equivalent to \ccc{Traits::Point_2}.
\item \ccc{Traits} defines the following subset of types from \item \ccc{Traits} defines the following subset of types from
the concept ConvexHullTraits\_2 and their corresponding member the concept \ccc{ConvexHullTraits_2} and their corresponding member
%\ccIndexMainItem[c]{ConvexHullTraits_2} %\ccIndexMainItem[c]{ConvexHullTraits_2}
functions that return instances of these types: functions that return instances of these types:
\begin{itemize} \begin{itemize}

2
Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_jarvis_march.tex
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@ -48,7 +48,7 @@ type \ccc{ForwardIterator::value_type} is defined.
\ccc{OutputIterator::value_type} \ccc{OutputIterator::value_type}
are equivalent to \ccc{Traits::Point_2}. are equivalent to \ccc{Traits::Point_2}.
\item \ccc{Traits} defines the following subset of types from \item \ccc{Traits} defines the following subset of types from
the concept ConvexHullTraits\_2 and their corresponding member the concept \ccc{ConvexHullTraits_2} and their corresponding member
%\ccIndexMainItem[c]{ConvexHullTraits_2} %\ccIndexMainItem[c]{ConvexHullTraits_2}
functions that return instances of these types: functions that return instances of these types:
\begin{itemize} \begin{itemize}

2
Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_melkman.tex
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@ -42,7 +42,7 @@ type \ccc{InputIterator::value_type} is defined.
\item \ccc{InputIterator::value_type} and \ccc{OutputIterator::value_type} \item \ccc{InputIterator::value_type} and \ccc{OutputIterator::value_type}
are equivalent to \ccc{Traits::Point_2}. are equivalent to \ccc{Traits::Point_2}.
\item \ccc{Traits} contains the following subset of types from \item \ccc{Traits} contains the following subset of types from
the concept ConvexHullTraits\_2 and their corresponding member the concept \ccc{ConvexHullTraits_2} and their corresponding member
%\ccIndexMainItem[c]{ConvexHullTraits_2} %\ccIndexMainItem[c]{ConvexHullTraits_2}
functions that return instances of these types: functions that return instances of these types:
\begin{itemize} \begin{itemize}

2
Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_n_point.tex
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@ -33,7 +33,7 @@ The default traits class \ccc{Default_traits} is the kernel in which the type
\ccHeading{Requirements} \ccHeading{Requirements}
\ccc{Traits} defines the type \ccc{Traits::Less_yx_2} as specified in \ccc{Traits} defines the type \ccc{Traits::Less_yx_2} as specified in
the concept ConvexHullTraits\_2 and the corresponding member the concept \ccc{ConvexHullTraits_2} and the corresponding member
function that returns an instance of this type. function that returns an instance of this type.

2
Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_ns_point.tex
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@ -36,7 +36,7 @@ type \ccc{ForwardIterator::value_type} is defined.
\ccHeading{Requirements} \ccHeading{Requirements}
\ccc{Traits} defines the type \ccc{Traits::Less_yx_2} as specified in \ccc{Traits} defines the type \ccc{Traits::Less_yx_2} as specified in
the concept ConvexHullTraits\_2 and the corresponding member the concept \ccc{ConvexHullTraits_2} and the corresponding member
function that returns an instance of this type. function that returns an instance of this type.

2
Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_nswe_point.tex
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@ -39,7 +39,7 @@ minimal $x$, and maximal $x$ coordinates.
\ccHeading{Requirements} \ccHeading{Requirements}
\ccc{Traits} contains the following subset of types from \ccc{Traits} contains the following subset of types from
the concept ConvexHullTraits\_2 and their corresponding member the concept \ccc{ConvexHullTraits_2} and their corresponding member
functions that return instances of these types: functions that return instances of these types:
\begin{itemize} \begin{itemize}
\item \ccc{Traits::Less_xy_2}, \item \ccc{Traits::Less_xy_2},

2
Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_s_point.tex
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@ -33,7 +33,7 @@ type \ccc{ForwardIterator::value_type} is defined.
\ccHeading{Requirements} \ccHeading{Requirements}
\ccc{Traits} defines the type \ccc{Traits::Less_yx_2} as specified in \ccc{Traits} defines the type \ccc{Traits::Less_yx_2} as specified in
the concept ConvexHullTraits\_2 and the corresponding member the concept \ccc{ConvexHullTraits_2} and the corresponding member
function that returns an instance of this type. function that returns an instance of this type.

2
Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_w_point.tex
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@ -30,7 +30,7 @@ of input points with minimal $x$ coordinate.
\ccHeading{Requirements} \ccHeading{Requirements}
\ccc{Traits} defines the type \ccc{Traits::Less_xy_2} as specified in \ccc{Traits} defines the type \ccc{Traits::Less_xy_2} as specified in
the concept ConvexHullTraits\_2 and the corresponding member the concept \ccc{ConvexHullTraits_2} and the corresponding member
function that returns an instance of this type. function that returns an instance of this type.

2
Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_we_point.tex
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@ -36,7 +36,7 @@ type \ccc{ForwardIterator::value_type} is defined.
\ccHeading{Requirements} \ccHeading{Requirements}
\ccc{Traits} defines the type \ccc{Traits::Less_xy_2} as specified in \ccc{Traits} defines the type \ccc{Traits::Less_xy_2} as specified in
the concept ConvexHullTraits\_2 and the corresponding member the concept \ccc{ConvexHullTraits_2} and the corresponding member
function that returns an instance of this type. function that returns an instance of this type.

2
Convex_hull_2/doc_tex/Convex_hull_2_ref/convex_hull_2.tex
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@ -40,7 +40,7 @@ the type \ccc{InputIterator::value_type} is defined.
\item \ccc{InputIterator::value_type} and \ccc{OutputIterator::value_type} \item \ccc{InputIterator::value_type} and \ccc{OutputIterator::value_type}
are equivalent to \ccc{Traits::Point_2}. are equivalent to \ccc{Traits::Point_2}.
\item \ccc{Traits} contains the following subset of types from \item \ccc{Traits} contains the following subset of types from
the concept ConvexHullTraits\_2 and their corresponding member the concept \ccc{ConvexHullTraits_2} and their corresponding member
%\ccIndexMainItem[c]{ConvexHullTraits_2} %\ccIndexMainItem[c]{ConvexHullTraits_2}
functions that return instances of these types: functions that return instances of these types:
\begin{itemize} \begin{itemize}

4
Convex_hull_2/doc_tex/Convex_hull_2_ref/is_ccw_strongly_convex_2.tex
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@ -15,7 +15,7 @@
\ccDefinition \ccDefinition
The function \ccRefName\ determines if a given sequence of points defines The function \ccRefName\ determines if a given sequence of points defines
a counterclockwise-oriented, stongly convex polygon. a counterclockwise-oriented, strongly convex polygon.
A set of points is said to be strongly convex A set of points is said to be strongly convex
if it consists of only extreme points if it consists of only extreme points
(\textit{i.e.}, vertices of the convex hull). (\textit{i.e.}, vertices of the convex hull).
@ -39,7 +39,7 @@ type \ccc{ForwardIterator::value_type} is defined.
\ccHeading{Requirements} \ccHeading{Requirements}
\ccc{Traits} contains the following subset of types from \ccc{Traits} contains the following subset of types from
the concept ConvexHullTraits\_2 and their corresponding member the concept \ccc{ConvexHullTraits_2} and their corresponding member
%\ccIndexMainItem[c]{ConvexHullTraits_2} %\ccIndexMainItem[c]{ConvexHullTraits_2}
functions that return instances of these types: functions that return instances of these types:
\begin{itemize} \begin{itemize}

4
Convex_hull_2/doc_tex/Convex_hull_2_ref/is_cw_strongly_convex_2.tex
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@ -15,7 +15,7 @@
\ccDefinition \ccDefinition
The function \ccRefName\ determines if a given sequence of points defines The function \ccRefName\ determines if a given sequence of points defines
a clockwise-oriented, stongly convex polygon. a clockwise-oriented, strongly convex polygon.
A set of points is said to be strongly convex % A set of points is said to be strongly convex %
\ccIndexMainItemDef{strongly convex} if it consists of only extreme points \ccIndexMainItemDef{strongly convex} if it consists of only extreme points
(\textit{i.e.}, vertices of the convex hull). (\textit{i.e.}, vertices of the convex hull).
@ -40,7 +40,7 @@ type \ccc{ForwardIterator::value_type} is defined.
\ccHeading{Requirements} \ccHeading{Requirements}
\ccc{Traits} contains the following subset of types from \ccc{Traits} contains the following subset of types from
the concept ConvexHullTraits\_2 and their corresponding member the concept \ccc{ConvexHullTraits_2} and their corresponding member
%\ccIndexMainItem[c]{ConvexHullTraits_2} %\ccIndexMainItem[c]{ConvexHullTraits_2}
functions that return instances of these types: functions that return instances of these types:
\begin{itemize} \begin{itemize}

2
Convex_hull_2/doc_tex/Convex_hull_2_ref/lower_hull_points_2.tex
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@ -48,7 +48,7 @@ points gives the sequence of extreme points.
\item \ccc{InputIterator::value_type} and \ccc{OutputIterator::value_type} \item \ccc{InputIterator::value_type} and \ccc{OutputIterator::value_type}
are equivalent to \ccc{Traits::Point_2}. are equivalent to \ccc{Traits::Point_2}.
\item \ccc{Traits} contains the following subset of types from \item \ccc{Traits} contains the following subset of types from
the concept ConvexHullTraits\_2 and their corresponding member the concept \ccc{ConvexHullTraits_2} and their corresponding member
functions that return instances of these types: functions that return instances of these types:
\begin{itemize} \begin{itemize}
\item \ccc{Traits::Point_2}, \item \ccc{Traits::Point_2},

4
Convex_hull_2/doc_tex/Convex_hull_2_ref/upper_hull_points_2.tex
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@ -46,9 +46,9 @@ points gives the sequence of extreme points.
\ccHeading{Requirements} \ccHeading{Requirements}
\begin{enumerate} \begin{enumerate}
\item \ccc{InputIterator::value_type} and \ccc{OutputIterator::value_type} \item \ccc{InputIterator::value_type} and \ccc{OutputIterator::value_type}
are equilvalent to \ccc{Traits::Point_2}. are equivalent to \ccc{Traits::Point_2}.
\item \ccc{Traits} contains the following subset of types from \item \ccc{Traits} contains the following subset of types from
the concept ConvexHullTraits\_2 and their corresponding member the concept \ccc{ConvexHullTraits_2} and their corresponding member
%\ccIndexMainItem[c]{ConvexHullTraits_2} %\ccIndexMainItem[c]{ConvexHullTraits_2}
functions that return instances of these types: functions that return instances of these types:
\begin{itemize} \begin{itemize}