songsenand
/
cgal
mirror of https://github.com/CGAL/cgal
1
0
Fork 0
Code Issues Packages Projects Releases Wiki Activity

fixed req. vs. precond.; fixed iterator name; made example an include of 

a program; added implementation section
This commit is contained in:
Susan Hert 2001-07-06 16:47:18 +00:00
parent 1c191a6abd
commit 5b0c8b87be
4 changed files with 58 additions and 148 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

56
Packages/Partition_2/doc_tex/Partition_2/Partition_2_ref/is_y_monotone_2.tex
View File

@ -11,17 +11,17 @@ Function for testing the $y$-monotonicity of a sequence of points.
\ccFunction{
template<class InputIterator, class Traits>
bool
is_y_monotone_2(InputIterator first, InputIterator last,
is_y_monotone_2(InputIterator first, InputIterator beyond,
const Traits& traits);
}
{
Determines if the sequence of points in the range
[\ccc{first}, \ccc{last}) define a $y$-monotone
[\ccc{first}, \ccc{beyond}) define a $y$-monotone
polygon or not. If so, the function returns \ccc{true}, otherwise it
returns \ccc{false}.
}
\ccHeading{Preconditions}
\ccHeading{Requirements}
\ccIndexSubitem[C]{is_y_monotone_2}{preconditions}
\begin{enumerate}
\item \ccc{Traits} is a model of the concept IsYMonotoneTraits\_2.%
@ -29,57 +29,31 @@ returns \ccc{false}.
\item \ccc{InputIterator::value_type} should be \ccc{Traits::Point_2}.
\end{enumerate}
The default traits class \ccc{Default_traits} is the \cgal\ \ccc{Kernel_traits_2}
class,
The default traits class \ccc{Default_traits} is the kernel in which the
type \ccc{InputIterator::value_type} is defined.%
\ccIndexTraitsClassDefault{is_y_monotone_2}
with the representation type determined by \ccc{InputIterator::value_type}.
\ccSeeAlso
\ccRefIdfierPage{CGAL::Is_y_monotone_2<Traits>} \\
\ccRefIdfierPage{CGAL::y_monotone_partition_2} \\
\ccRefIdfierPage{CGAL::y_monotone_partition_is_valid_2}
\ccImplementation
This function requires $O(n)$ time for a polygon with $n$ vertices.
\ccExample
The following code fragment computes a $y$-monotone partitioning
of the simple polygon \ccc{P} using the default
The following program computes a $y$-monotone partitioning
of a polygon using the default
traits class and stores the partition polygons in the list
\ccc{partition_polys}. It then asserts that each of the partition
polygons is, in fact, a $y$-monotone polygon. (Note that this
assertion is superfluous unless the postcondition checking done
polygons is, in fact, a $y$-monotone polygon and that the partition
is valid. (Note that the
assertions are superfluous unless the postcondition checking done
by \ccc{y_monotone_partition_2} has been turned off during compilation.)
\begin{verbatim}
#include <CGAL/basic.h>
#include <CGAL/Cartesian.h>
#include <CGAL/Partition_traits_2.h>
#include <CGAL/partition_2.h>
#include <CGAL/is_y_monotone_2.h>
#include <list>
typedef CGAL::Cartesian<double> R;
typedef CGAL::Polygon_traits_2<R> Traits;
typedef Traits::Point_2 Point_2;
typedef Traits::Polygon_2 Polygon_2
Polygon_2 P;
std::list<Polygon_2> partition_polys;
// ...
// insert vertices into P to create a simple CCW-oriented polygon
// ...
CGAL::y_monotone_partition_2(P.vertices_begin(),
P.vertices_end(),
std::back_inserter(partition_polys));
std::list<Polygon_2>::const_iterator poly_it;
for (poly_it = partition_polys.begin(); poly_it != partition_polys.end();
poly_it++)
{
assert(CGAL::is_y_monotone_2((*poly_it).vertices_begin(),
(*poly_it).vertices_end()));
}
\end{verbatim}
\ccIncludeExampleCode{Partition_2/y_monotone_ex.C}

47
Packages/Partition_2/doc_tex/Partition_2/Partition_2_ref/y_monotone_partition_2.tex
View File

@ -16,15 +16,17 @@ OutputIterator y_monotone_partition_2(InputIterator first,
const Traits& traits = Default_traits);
}
{
computes a partition of the simple, counterclockwise-oriented polygon defined
by the points in the range [\ccc{first}, \ccc{last}) into $y$-monotone
computes a partition of the polygon defined
by the points in the range [\ccc{first}, \ccc{beyond}) into $y$-monotone
polygons. The counterclockwise-oriented partition polygons are written to
the sequence starting at position \ccc{result}. The past-the-end iterator for
the resulting sequence of polygons is returned.
\ccPrecond The points in the range [\ccc{first}, \ccc{beyond}) define a
simple, counterclockwise-oriented polygon.
%\ccIndexSubitem[C]{y_monotone_partition_2}{preconditions}
}
\ccHeading{Requirements}
%\ccIndexSubitem[C]{y_monotone_partition_2}{preconditions}
\begin{enumerate}
\item \ccc{Traits} is a model of the concept YMonotonePartitionTraits\_2%
\ccIndexMainItem[c]{YMonotonePartitionTraits_2} and, for the purposes
@ -36,8 +38,6 @@ the resulting sequence of polygons is returned.
\item \ccc{InputIterator::value_type} should be \ccc{Traits::Point_2},
which should also be the type of the points stored in an object
of type \ccc{Traits::Polygon_2}.
\item Points in the range $[first, beyond)$ must define a simple polygon
whose vertices are oriented counterclockwise.
\end{enumerate}
The default traits class \ccc{Default_traits} is \ccc{Partition_traits_2},
@ -53,41 +53,22 @@ with the representation type determined by \ccc{InputIterator::value_type}.
\ccImplementation
This function implements the algorithm presented by de Bert \textit{et al.}
This function implements the algorithm presented by de Berg \textit{et al.}
\cite{bkos-cgaa-97} which requires $O(n \log n)$ time
and $O(n)$ space for a polygon with $n$ vertices.
\ccExample
The following code fragment will compute a $y$-monotone partitioning
of the simple polygon \ccc{P} using the default
traits class and store the partition polygons in the list
\ccc{partition_polys}.
The following program computes a $y$-monotone partitioning
of a polygon using the default
traits class and stores the partition polygons in the list
\ccc{partition_polys}. It then asserts that each partition polygon
produced is, in fact, $y$-monotone and that the partition is valid.
(Note that these assertions are superfluous unless the postcondition
checking for \ccc{y_monotone_partition_2} has been turned off.)
\begin{verbatim}
#include <CGAL/basic.h>
#include <CGAL/Cartesian.h>
#include <CGAL/Polygon_traits_2.h>
#include <CGAL/partition_2.h>
#include <list>
typedef CGAL::Cartesian<double> R;
typedef CGAL::Polygon_traits_2<R> Traits;
typedef Traits::Point_2 Point_2;
typedef std::list<Point_2> Container;
typedef CGAL::Polygon_2<Traits, Container> Polygon_2;
Polygon_2 P;
std::list<Polygon_2> partition_polys;
// ...
// insert vertices into P to create a simple CCW-oriented polygon
// ...
CGAL::y_monotone_partition_2(P.vertices_begin(),
P.vertices_end(),
std::back_inserter(partition_polys));
\end{verbatim}
\ccIncludeExampleCode{Partition_2/y_monotone_ex.C}

56
Packages/Partition_2/doc_tex/basic/Partition_2/Partition_2_ref/is_y_monotone_2.tex
View File

@ -11,17 +11,17 @@ Function for testing the $y$-monotonicity of a sequence of points.
\ccFunction{
template<class InputIterator, class Traits>
bool
is_y_monotone_2(InputIterator first, InputIterator last,
is_y_monotone_2(InputIterator first, InputIterator beyond,
const Traits& traits);
}
{
Determines if the sequence of points in the range
[\ccc{first}, \ccc{last}) define a $y$-monotone
[\ccc{first}, \ccc{beyond}) define a $y$-monotone
polygon or not. If so, the function returns \ccc{true}, otherwise it
returns \ccc{false}.
}
\ccHeading{Preconditions}
\ccHeading{Requirements}
\ccIndexSubitem[C]{is_y_monotone_2}{preconditions}
\begin{enumerate}
\item \ccc{Traits} is a model of the concept IsYMonotoneTraits\_2.%
@ -29,57 +29,31 @@ returns \ccc{false}.
\item \ccc{InputIterator::value_type} should be \ccc{Traits::Point_2}.
\end{enumerate}
The default traits class \ccc{Default_traits} is the \cgal\ \ccc{Kernel_traits_2}
class,
The default traits class \ccc{Default_traits} is the kernel in which the
type \ccc{InputIterator::value_type} is defined.%
\ccIndexTraitsClassDefault{is_y_monotone_2}
with the representation type determined by \ccc{InputIterator::value_type}.
\ccSeeAlso
\ccRefIdfierPage{CGAL::Is_y_monotone_2<Traits>} \\
\ccRefIdfierPage{CGAL::y_monotone_partition_2} \\
\ccRefIdfierPage{CGAL::y_monotone_partition_is_valid_2}
\ccImplementation
This function requires $O(n)$ time for a polygon with $n$ vertices.
\ccExample
The following code fragment computes a $y$-monotone partitioning
of the simple polygon \ccc{P} using the default
The following program computes a $y$-monotone partitioning
of a polygon using the default
traits class and stores the partition polygons in the list
\ccc{partition_polys}. It then asserts that each of the partition
polygons is, in fact, a $y$-monotone polygon. (Note that this
assertion is superfluous unless the postcondition checking done
polygons is, in fact, a $y$-monotone polygon and that the partition
is valid. (Note that the
assertions are superfluous unless the postcondition checking done
by \ccc{y_monotone_partition_2} has been turned off during compilation.)
\begin{verbatim}
#include <CGAL/basic.h>
#include <CGAL/Cartesian.h>
#include <CGAL/Partition_traits_2.h>
#include <CGAL/partition_2.h>
#include <CGAL/is_y_monotone_2.h>
#include <list>
typedef CGAL::Cartesian<double> R;
typedef CGAL::Polygon_traits_2<R> Traits;
typedef Traits::Point_2 Point_2;
typedef Traits::Polygon_2 Polygon_2
Polygon_2 P;
std::list<Polygon_2> partition_polys;
// ...
// insert vertices into P to create a simple CCW-oriented polygon
// ...
CGAL::y_monotone_partition_2(P.vertices_begin(),
P.vertices_end(),
std::back_inserter(partition_polys));
std::list<Polygon_2>::const_iterator poly_it;
for (poly_it = partition_polys.begin(); poly_it != partition_polys.end();
poly_it++)
{
assert(CGAL::is_y_monotone_2((*poly_it).vertices_begin(),
(*poly_it).vertices_end()));
}
\end{verbatim}
\ccIncludeExampleCode{Partition_2/y_monotone_ex.C}

47
Packages/Partition_2/doc_tex/basic/Partition_2/Partition_2_ref/y_monotone_partition_2.tex
View File

@ -16,15 +16,17 @@ OutputIterator y_monotone_partition_2(InputIterator first,
const Traits& traits = Default_traits);
}
{
computes a partition of the simple, counterclockwise-oriented polygon defined
by the points in the range [\ccc{first}, \ccc{last}) into $y$-monotone
computes a partition of the polygon defined
by the points in the range [\ccc{first}, \ccc{beyond}) into $y$-monotone
polygons. The counterclockwise-oriented partition polygons are written to
the sequence starting at position \ccc{result}. The past-the-end iterator for
the resulting sequence of polygons is returned.
\ccPrecond The points in the range [\ccc{first}, \ccc{beyond}) define a
simple, counterclockwise-oriented polygon.
%\ccIndexSubitem[C]{y_monotone_partition_2}{preconditions}
}
\ccHeading{Requirements}
%\ccIndexSubitem[C]{y_monotone_partition_2}{preconditions}
\begin{enumerate}
\item \ccc{Traits} is a model of the concept YMonotonePartitionTraits\_2%
\ccIndexMainItem[c]{YMonotonePartitionTraits_2} and, for the purposes
@ -36,8 +38,6 @@ the resulting sequence of polygons is returned.
\item \ccc{InputIterator::value_type} should be \ccc{Traits::Point_2},
which should also be the type of the points stored in an object
of type \ccc{Traits::Polygon_2}.
\item Points in the range $[first, beyond)$ must define a simple polygon
whose vertices are oriented counterclockwise.
\end{enumerate}
The default traits class \ccc{Default_traits} is \ccc{Partition_traits_2},
@ -53,41 +53,22 @@ with the representation type determined by \ccc{InputIterator::value_type}.
\ccImplementation
This function implements the algorithm presented by de Bert \textit{et al.}
This function implements the algorithm presented by de Berg \textit{et al.}
\cite{bkos-cgaa-97} which requires $O(n \log n)$ time
and $O(n)$ space for a polygon with $n$ vertices.
\ccExample
The following code fragment will compute a $y$-monotone partitioning
of the simple polygon \ccc{P} using the default
traits class and store the partition polygons in the list
\ccc{partition_polys}.
The following program computes a $y$-monotone partitioning
of a polygon using the default
traits class and stores the partition polygons in the list
\ccc{partition_polys}. It then asserts that each partition polygon
produced is, in fact, $y$-monotone and that the partition is valid.
(Note that these assertions are superfluous unless the postcondition
checking for \ccc{y_monotone_partition_2} has been turned off.)
\begin{verbatim}
#include <CGAL/basic.h>
#include <CGAL/Cartesian.h>
#include <CGAL/Polygon_traits_2.h>
#include <CGAL/partition_2.h>
#include <list>
typedef CGAL::Cartesian<double> R;
typedef CGAL::Polygon_traits_2<R> Traits;
typedef Traits::Point_2 Point_2;
typedef std::list<Point_2> Container;
typedef CGAL::Polygon_2<Traits, Container> Polygon_2;
Polygon_2 P;
std::list<Polygon_2> partition_polys;
// ...
// insert vertices into P to create a simple CCW-oriented polygon
// ...
CGAL::y_monotone_partition_2(P.vertices_begin(),
P.vertices_end(),
std::back_inserter(partition_polys));
\end{verbatim}
\ccIncludeExampleCode{Partition_2/y_monotone_ex.C}