Initial revision

.gitignore

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+Packages/Distance_2/web/lis

Packages/Distance_2/description.txt

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+Squared distance computations for simple 2D objects.

Packages/Distance_2/doc_tex/Distance_2/main.tex

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+
+\cleardoublepage
+\chapter{Squared Distances}
+
+There is a family of functions called \ccStyle{CGAL_squared_distance} that
+compute the square of the Euclidean distance between two geometric objects.
+
+The squared distance between two two-dimensional points \ccStyle{p1} and
+\ccStyle{p2} is defined as $d_{x}^{2} + d_{y}^{2}$, where $d_{x}$
+\ccTexHtml{$\equiv$}{==}
+\ccStyle{p2.x()-p1.x()} and $d_{y}$\ccTexHtml{$\equiv$}{==} \ccStyle{p2.y()-p1.y()}.
+
+For arbitrary two-dimensional geometric objects \ccStyle{obj1} and
+\ccStyle{obj2} the squared distance is defined as the minimal
+\ccStyle{CGAL_squared_distance(p1, p2)}, where \ccStyle{p1} is a point of
+\ccStyle{obj1} and \ccStyle{p2} is a point of \ccStyle{obj2}.
+Note that for objects like triangles and polygons that have an inside (a
+bounded region), this inside is part of the object.
+So, the squared distance from a point inside a triangle to that triangle is
+zero, not the squared distance to the closest edge of the triangle.
+
+The general format of the functions is:
+
+\ccUnchecked{
+\ccGlobalFunctionTemplate{R}
+{R::FT CGAL_squared_distance(Type1<R> obj1, Type2<R> obj2);}
+}
+
+\noindent
+where the types \ccStyle{Type1} and \ccStyle{Type2} can be any of the
+following:
+\begin{itemize}
+\item \ccStyle{CGAL_Point_2}
+\item \ccStyle{CGAL_Line_2}
+\item \ccStyle{CGAL_Ray_2}
+\item \ccStyle{CGAL_Segment_2}
+\item \ccStyle{CGAL_Triangle_2}
+%\item \ccStyle{CGAL_Iso_Rectangle_2}
+%\item \ccStyle{CGAL_Polygon_2}
+\end{itemize}
+
+Those routines are defined in the header file
+\ccStyle{CGAL/squared_distance.h}.
+
+\subsection{Why the square?}
+
+There are routines that compute the square of the Euclidean distance, but no
+routines that compute the distance itself. Why?
+
+First of all, the two values can be derived from each other quite easily (by
+taking the square root or taking the square). So, supplying only the one and
+not the other is only a minor inconvenience for the user.
+
+Second, often either value can be used. This is for example the case when
+(squared) distances are compared.
+
+Third, the library wants to stimulate the use of the squared distance instead
+of the distance. The squared distance can be computed in more cases and the
+computation is cheaper.
+We do this by not providing the perhaps more natural routine,
+
+The problem of a distance routine is that it needs the \ccStyle{sqrt}
+operation.
+This has two drawbacks.
+\begin{itemize}
+\item
+The \ccStyle{sqrt} operation can be costly. Even if it is not very costly for
+a specific number type and platform, avoiding it is always cheaper.
+\item
+There are number types on which no \ccStyle{sqrt} operation is defined,
+especially integer types and rationals.
+\end{itemize}

Packages/Distance_2/doc_tex/kernel/Distance_2/main.tex

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+
+\cleardoublepage
+\chapter{Squared Distances}
+
+There is a family of functions called \ccStyle{CGAL_squared_distance} that
+compute the square of the Euclidean distance between two geometric objects.
+
+The squared distance between two two-dimensional points \ccStyle{p1} and
+\ccStyle{p2} is defined as $d_{x}^{2} + d_{y}^{2}$, where $d_{x}$
+\ccTexHtml{$\equiv$}{==}
+\ccStyle{p2.x()-p1.x()} and $d_{y}$\ccTexHtml{$\equiv$}{==} \ccStyle{p2.y()-p1.y()}.
+
+For arbitrary two-dimensional geometric objects \ccStyle{obj1} and
+\ccStyle{obj2} the squared distance is defined as the minimal
+\ccStyle{CGAL_squared_distance(p1, p2)}, where \ccStyle{p1} is a point of
+\ccStyle{obj1} and \ccStyle{p2} is a point of \ccStyle{obj2}.
+Note that for objects like triangles and polygons that have an inside (a
+bounded region), this inside is part of the object.
+So, the squared distance from a point inside a triangle to that triangle is
+zero, not the squared distance to the closest edge of the triangle.
+
+The general format of the functions is:
+
+\ccUnchecked{
+\ccGlobalFunctionTemplate{R}
+{R::FT CGAL_squared_distance(Type1<R> obj1, Type2<R> obj2);}
+}
+
+\noindent
+where the types \ccStyle{Type1} and \ccStyle{Type2} can be any of the
+following:
+\begin{itemize}
+\item \ccStyle{CGAL_Point_2}
+\item \ccStyle{CGAL_Line_2}
+\item \ccStyle{CGAL_Ray_2}
+\item \ccStyle{CGAL_Segment_2}
+\item \ccStyle{CGAL_Triangle_2}
+%\item \ccStyle{CGAL_Iso_Rectangle_2}
+%\item \ccStyle{CGAL_Polygon_2}
+\end{itemize}
+
+Those routines are defined in the header file
+\ccStyle{CGAL/squared_distance.h}.
+
+\subsection{Why the square?}
+
+There are routines that compute the square of the Euclidean distance, but no
+routines that compute the distance itself. Why?
+
+First of all, the two values can be derived from each other quite easily (by
+taking the square root or taking the square). So, supplying only the one and
+not the other is only a minor inconvenience for the user.
+
+Second, often either value can be used. This is for example the case when
+(squared) distances are compared.
+
+Third, the library wants to stimulate the use of the squared distance instead
+of the distance. The squared distance can be computed in more cases and the
+computation is cheaper.
+We do this by not providing the perhaps more natural routine,
+
+The problem of a distance routine is that it needs the \ccStyle{sqrt}
+operation.
+This has two drawbacks.
+\begin{itemize}
+\item
+The \ccStyle{sqrt} operation can be costly. Even if it is not very costly for
+a specific number type and platform, avoiding it is always cheaper.
+\item
+There are number types on which no \ccStyle{sqrt} operation is defined,
+especially integer types and rationals.
+\end{itemize}

Packages/Distance_2/make_release

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+#!/bin/sh
+
+if [ ! -d include ]
+then
+    mkdir include
+    mkdir include/CGAL
+fi
+
+
+cd web
+if [ ! -d lis ]
+then
+    mkdir lis
+fi
+
+make xsrcs
+
+echo "Now adapt version and description.txt and run make_zip"
+
+
+

Packages/Distance_2/make_zip

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+#!/bin/sh
+
+zip -r Distance_2.zip version description.txt include test doc_tex

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