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+\documentclass[12pt, draft]{report}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\usepackage{euclide}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\title{The \texttt{pst-euclide} Package}
+\author{\Version\\\\Dominique Rodriguez\thanks{domino.rodriguez@laposte.net}}
+\date{\Date}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{document}
+\maketitle
+\begin{abstract}
+ The \texttt{pst-eucl} package allow the drawing of Euclidean
+ geometric figures using \LaTeX\ macros for specifying mathematical
+ constraints. It is thus possible to build point using common
+ transformations or intersections. The use of coordinates is limited
+ to points which controlled the figure.
+
+ \vfill
+
+ \begin{center}\bfseries
+ Acknowledgements
+ \end{center}
+
+ I would like to thanks the following persons for the help they gave
+ me for development of this package:
+
+ \begin{itemize}
+ \item Denis Girou pour ses critiques pertinentes et ses
+ encouragement lors de la découverte de l'embryon initial et pour
+ sa relecture du présent manuel ;
+ \item Michael Vulis for his fast testing of the documentation using
+ V\TeX\ which leads to the correction of a bug in the \PostScript\ code;
+ \item Manuel Luque and Olivier Reboux for their remarks and their examples.
+ \item Alain Delplanque for its modification propositions on automatic
+ placing of points name and the ability of giving a list of points in
+ \com{pstGeonode}.
+ \end{itemize}
+\end{abstract}
+%%%%%%%%%%%%%%%%%%%%
+\renewcommand{\abstractname}{WARNING}
+\begin{abstract}
+ This is the first release put on \texttt{CTAN} archives.
+
+ \vfill
+
+ \begin{center}\bfseries
+ LICENSE
+ \end{center}
+
+ This program and its documentation can be redistributed and/or modified under the
+ terms of the ``\LaTeX{} Project Public License'' Distributed from \texttt{CTAN}
+ archives in directory \texttt{macros/latex/base/lppl.txt}. However, you may send me
+ an Email with a small commentary. Then you should consider making a
+ donation\footnote{especially if you use a purchased operating system!. Furthermore,
+ do not forget that \LaTeX{} is freely usable and that many users buy several
+ hundreds of euros (dollars, pounds) softwares of lower quality}:
+
+\begin{enumerate}
+\item directly to the \LaTeX3 team;
+\item and/or to me for the support of this package\footnote{1~\MonEuro, £1 ou \$1 is
+ OK, but I accept more.}.
+\end{enumerate}
+
+ A donation of time depending of competences is possible : correction of the
+ documentation (especially this one), test of functionnalities, propositions of
+ extensions, \ldots
+\end{abstract}
+\twocoltoc{}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\chapter{User's manual}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Special specifications}
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \subsection{\PStricks\ Options}
+
+The package activates the \com{SpecialCoor} mode. This mode extend the
+coordinates specification. Furthermore the plotting type is set to
+\texttt{dimen=middle}, which indicates that the position of the
+drawing is done according to the middle of the line. Please look at
+the user manual for more information about these setting.
+
+At last, the working axes are supposed to be (ortho)normed.
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \subsection{Conventions}
+
+For this manual, I used the geometric French conventions for naming
+the points:
+
+\begin{itemize}
+\item $O$ is a centre (circle, axes, symmetry, homothety, rotation);
+\item $I$ defined the unity of the abscissa axe, or a midpoint;
+\item $J$ defined the unity of the ordinate axe;
+\item $A$, $B$, $C$, $D$ are points ;
+\item $M'$ is the image of $M$ by a transformation ;
+\end{itemize}
+
+At last, although these are nodes in \PStricks, I treat them
+intentionally as points.
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Basic Objects}
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \subsection{Points}
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \subsubsection{default axes}
+
+\defcom[Creates a list of points using the common axis. \protect\ParamList{\param{PointName},
+ \param{PointNameSep}, \param{PosAngle}, \param{PointSymbol}, \param{PtNameMath}}]
+ {pstGeonode}{\OptArg{par}$(x_1,y_1)$\Arg{$A_1$}$(x_2,y_2)$\Arg{$A_2$}\ldots$(x_n,y_n)$\Arg{$A_n$}}
+
+This command defines one or more geometrical points associated with a node. Each
+point has a node name \Argsans{$A_i$} which defines the default label put on the
+picture. This label is managed by default in mathematical mode, the boolean parameter
+\param{PtNameMath} \DefaultVal{true} can modify this behavior and let manage the
+label in normal mode. It is placed at a distance of \cbstart\param{PointNameSep}
+\DefaultVal{1em}\cbend{} of the center of the node with a angle of
+\param{PosAngle}\DefaultVal{0}. It is possible to specify another label using the
+parameter \param{PointName} \DefaultVal{default}, and an empty label can be specified
+by selecting the value \texttt{none}, in that case the point will have no name on the
+picture.
+
+The point symbol is given by the parameter \param{PointSymbol} \DefaultVal{*}. The
+symbol is the same as used by the macro \com{pstdot}. This parameter can be set to
+\texttt{none}, which means that the point will not be drawn on the picture.
+
+Here are the possible values for this parameter:
+
+\begin{multicols}{3}
+ \begin{itemize}\psset{dotscale=2}
+ \item \param{*}: \psdots(.5ex,.5ex)
+ \item \param{o}: \psdots[dotstyle=o](.5ex,.5ex)
+ \item \param{+}: \psdots[dotstyle=+](.5ex,.5ex)
+ \item \param{x}: \psdots[dotstyle=x](.5ex,.5ex)
+ \item \param{asterisk} : \psdots[dotstyle=asterisk](.5ex,.5ex)
+ \item \param{oplus}: \psdots[dotstyle=oplus](.5ex,.5ex)
+ \item \param{otimes}: \psdots[dotstyle=otimes](.5ex,.5ex)
+ \item \param{triangle}: \psdots[dotstyle=triangle](.5ex,.5ex)
+ \item \param{triangle*}: \psdots[dotstyle=triangle*](.5ex,.5ex)
+ \item \param{square}: \psdots[dotstyle=square](.5ex,.5ex)
+ \item \param{square*}: \psdots[dotstyle=square*](.5ex,.5ex)
+ \item \param{diamond}: \psdots[dotstyle=diamond](.5ex,.5ex)
+ \item \param{diamond*}: \psdots[dotstyle=diamond*](.5ex,.5ex)
+ \item \param{pentagon}: \psdots[dotstyle=pentagon](.5ex,.5ex)
+ \item \param{pentagon*}: \psdots[dotstyle=pentagon*](.5ex,.5ex)
+ \item \param{|}: \psdots[dotstyle=|](.5ex,.5ex)
+ \end{itemize}
+\end{multicols}
+
+\cbstart Furthermore, these symbols can be controlled with some others \PStricks,
+several of these are :
+
+\begin{itemize}
+\item their scale with \param{dotscale}, the value of whom is either two numbers
+ defining the horizontal and vertical scale factor, or one single value being the
+ same for both,
+\item their angle with parameter \param{dotangle}.
+\end{itemize}
+
+Please consult the \PStricks documentation for further details.\cbend
+
+The parameters are specified explicitly in the \Argsans{par} part. The
+parameters \param{PosAngle}, \param{PointSymbol}, \param{PointName} and
+\param{PointNameSep} can be set to :
+
+\begin{itemize}
+\item either a single value, the same for all points ;
+\item or a list of values delimited by accolads \texttt{\{ ... \}} and
+ separated with comma \textit{without any blanks}, allowing to differenciate the
+ value for each point.
+\end{itemize}
+
+In the later case, the list can have less values than point which means that the
+last value is used for all the remaining points.
+
+\cbstart At least, the parameter \param{CurveType} \DefaultVal{none} can be used to
+draw a line between the points:
+
+\begin{itemize}
+\item opened \verb$polyline$ ;
+\item closed \verb$polygon$ ;
+\item open and curved \verb$curve$.
+\end{itemize}\cbend
+
+% EXEMPLE GEONODE
+\tabex{geonode}
+
+Obviously, the nodes appearing in the picture can be used as normal
+\PStricks nodes. Thus, it is possible to reference a point from
+\rnode{ici}{here}.
+\nccurve[arrowscale=2]{->}{ici}{B_1}
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \subsubsection{User defined axes}
+
+
+\defcom[Creates a list of points in the landmark $(O;I;J)$.
+ \protect\ParamList{\param{PointName}, \param{PointNameSep}, \param{PosAngle},
+ \param{PointSymbol}, \param{PtNameMath}}]
+ {pstOIJGeonode}
+ {\OptArg{par}$(x_1,y_1)$\Arg{$A_1$}\Arg{$O$}\Arg{$I$}\Arg{$J$}$(x_2,y_2)$\Arg{$A_2$}\ldots$(x_n,y_n)$\Arg{$A_n$}}
+
+This command allows the placement of points in any landmark(?) defined
+by the three points $(O;I;J)$.
+
+%% EXAMPLE
+\tabex{oij}
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \subsection{Segment mark}
+
+A segment can be drawn using the \com{ncline} command. However,
+for marking a segment there is the following command:
+
+\defcom[Marks segment \Segment{AB} in its middle with the mark given by
+ \protect\param{SegmentSymbol}. \protect\ParamList{\param{SegmentSymbol}}]
+ {pstMarkSegment}{\OptArg{par}\Arg{$A$}\Arg{$B$}}
+
+The symbol drawn on the segment is given by the parameter
+\param{SegmentSymbol}. Its value can be any valid command which can be
+used in math mode. Its default value is \texttt{pstslashh},
+which produced two slashes on the segment. The segment is drawn.
+
+Several commands are predefined for marking the segment:
+
+\begin{multicols}{3}
+ \psset{PointSymbol=none, PointName=none, unit=.8}
+ \newcommand{\Seg}[1]{%
+ \com{#1} : \begin{pspicture}[.3](2,1)
+ \pstGeonode(0.3,.5){A}(1.7,.5){B}\pstSegmentMark[SegmentSymbol=#1]{A}{B}
+ \end{pspicture}}%
+ \begin{itemize}
+ \item \Seg{pstslash} ;
+ \item \Seg{pstslashh} ;
+ \item \Seg{pstslashhh} ;
+ \item \Seg{MarkHash} ;
+ \item \Seg{MarkHashh} ;
+ \item \Seg{MarkHashhh} ;
+ \item \Seg{MarkCros} ;
+ \item \Seg{MarkCross} ;
+ \end{itemize}
+\end{multicols}
+
+The three commands of the family \texttt{MarkHash} draw a line whose inclination is
+controled by the parameter \param{MarkAngle} \DefaultVal{45}. Their width and colour
+depends of the width and color of the line when the drawing is done, ass shown is the
+next example.
+
+%% EXAMPLE
+\tabex{segmentmark}
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \subsection{Triangles}
+
+The more classical figure, it has its own macro for a quick definition:
+
+\defcom[Draws a triangle. \protect\ParamList{\param{PointName},
+ \param{PointNameSep}, \param{PointSymbol}, \param{PointNameA},
+ \param{PosAngleA}, \param{PointSymbolA}, \param{PointNameB},
+ \param{PosAngleB}, \param{PointSymbolB}, \param{PointNameC},
+ \param{PosAngleC}, \param{PointSymbolC}}]
+ {pstTriangle}{%
+ \OptArg{par}
+ $(x_A;y_A)$\Arg{$A$}$(x_B;y_B)$\Arg{$B$}$(x_C;y_C)$\Arg{$C$}}
+
+In order to accurately put the name of the points, there are three parameters
+\param{PosAngleA}, \param{PosAngleB} and \param{PosAngleC}, which are associated
+respectively to the nodes \Argsans{$A$}, \Argsans{$B$} et \Argsans{$C$}. Obviously
+they have the same meaning as the parameter \param{PosAngle}. If no angle
+is specified for a given point, its name is put on the bissector line.
+
+In the same way there are parameters for controlling the symbol used
+for each points: \param{PointSymbolA}, \param{PointSymbolB} and
+\param{PointSymbolC}. They are equivalent to the parameter
+\param{PointSymbol}. The management of the default value followed the
+same rule.
+
+\tabex{triangle}
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \subsection{Angles}
+
+Each angle is defined with three points. The vertex is the second
+point. Their order is important because it is assumed that the angle is
+specified in the direct order. The first command is the marking of a
+right angle:
+
+\defcom[Marks the rigth angle \protect\Angle{ABC} given in direct
+ order. \protect\ParamList{\param{RightAngleType}, \param{RightAngleSize},
+ \param{RightAngleSize}}]
+ {pstRightAngle}%
+ {\OptArg{par}\Arg{$A$}\Arg{$B$}\Arg{$C$}}
+
+\cbstart The symbol used is controlled by the parameter \param{RightAngleType}
+\DefaultVal{default}. Its possible values are :
+
+\begin{itemize}
+\item \verb$default$ : standard symbol ;
+\item \verb$german$ : german symbol (given by U. Dirr) ;
+\item \verb$suisseromand$ : swiss romand symbol (given P. Schnewlin).
+\end{itemize}\cbend
+
+The only parameter controlling this command, excepting the ones which
+controlled the line, is \param{RightAngleSize} which defines the size
+of the symbol\DefaultVal{0.28 unit}.
+
+For other angles, there is the command:
+
+\defcom[Marks the angle \protect\Angle{ABC} given in direct order.
+ \protect\ParamList{\param{MarkAngleRadius}, \param{LabelAngleOffset},
+ \param{Mark}}]
+ {pstMarkAngle}%
+ {\OptArg{par}\Arg{$A$}\Arg{$B$}\Arg{$C$}}
+
+
+The \param{label} can be any valid \TeX\ box, it is put at \param{LabelSep}
+\DefaultVal{1 unit} of the node in the direction of the bisector of the angle
+modified by \param{LabelAngleOffset}\DefaultVal{0} and positioned using
+\param{LabelRefPt} \DefaultVal{c}. Furthermore the arc used for marking has a radius
+of \param{MarkAngleRadius} \DefaultVal{.4~unit}. At least, it is possible to place
+an arrow using the parameter \param{arrows}.Finally, it is possible to mark
+the angle by specifying a \TeX{} command as argument of parameter \param{Mark}.
+
+\tabex{angle}
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \subsection{Lines, half-lines and segments}
+
+The classical line!
+
+\defcom[Draws line $(AB)$.]
+ {pstLineAB}{\OptArg{par}\Arg{$A$}\Arg{$B$}}
+
+In order to control its length\footnote{which is the comble for a
+line!}, the two parameters \param{nodesepA} et \param{nodesepB}
+specify the abscissa of the extremity of the drawing part of the line.
+A negative abscissa specify an outside point, while a positive
+abscissa specify an internal point. If these parameters have to be
+equal, \param{nodesep} can be used instead. The default value of these
+parameters is equal to 0.
+
+\tabex{droite}
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \subsection{Circles}
+
+A circle can be defined either with its center and a point of its
+circumference, or with two diameterly opposed points. There is two
+commands :
+
+\renewcommand{\ComUnDescr}{Draws the circle of center $O$ crossing $A$. \protect\ParamList{\param{Radius},
+ \param{Diameter}}.}
+\renewcommand{\ComDeuxDescr}{Draws the circle of diameter $AB$. \protect\ParamList{\param{Radius},
+ \param{Diameter}}.}
+\defcomdeux{pstCircleOA}{\OptArg{par}\Arg{$O$}\Arg{$A$}}%
+ {pstCircleAB}{\OptArg{par}\Arg{$A$}\Arg{$B$}}
+
+For the first macro, it is possible to omit the second point and then
+to specify a radius or a diameter using the parameters \param{Radius}
+and \param{Diameter}. The values of these parameters must be specified
+with one of the two following macros :
+
+\renewcommand{\ComUnDescr}{Specifies distance $AB$ for the parameters
+ \protect\param{Radius} and \protect\param{Diameter}. \protect\ParamList{\param{DistCoef}}.}
+\renewcommand{\ComDeuxDescr}{Specifies a numerical value for the parameters
+ \protect\param{Radius} and \protect\param{Diameter}. \protect\ParamList{\param{DistCoef}}.}
+\defcomdeux{pstDistAB}{\OptArg{par}\Arg{$A$}\Arg{$B$}}%
+ {pstDistVal}{\OptArg{par}\Arg{x}}
+
+The first specifies a distance between two points. The parameter
+\param{DistCoef} can be used to specify a coefficient to reduce or
+enlarge this distance. To be taken into account this last parameter
+must be specified before the distance. The second macro can be used to
+specify an explicit numeric value.
+
+We will see later how to draw the circle crossing three points.
+
+\vspace{1.1\baselineskip}
+\begin{minipage}[m]{.45\linewidth}
+ With this package, it becomes possible to draw:
+
+ \begin{itemize}
+ \item {\color{red} the circle of center $A$ crossing $B$;}
+ \item {\color{green} the circle of center $A$ whose radius is $AC$;}
+ \item {\color{blue} the circle of center $A$ whose radius is $BC$;}
+ \item {\color{Sepia} the circle of center $B$ whose radius is $AC$;}
+ \item {\color{Aquamarine} the circle of center $B$ of diameter $AC$;}
+ \item {\color{RoyalBlue} the circle whose diameter is $BC$.}
+ \end{itemize}
+\end{minipage}
+%
+\input{Exemples/cercle}
+
+\smallverbatiminput{Exemples/cercle_in}
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \subsection{Circle arcs}
+
+\renewcommand{\ComUnDescr}{Draws the circle arc of center $O$ and radius $OA$,
+ delimited by the angle $\protect\Angle{AOB}$ in direct order.}
+\renewcommand{\ComDeuxDescr}{Draws the circle arc of center $O$ and radius $OA$,
+ delimited by the angle $\protect\Angle{AOB}$ in indirect order.}
+\defcomdeux{pstArcOAB}{\OptArg{par}\Arg{$O$}\Arg{$A$}\Arg{$B$}}%
+ {pstArcnOAB}{\OptArg{par}\Arg{$O$}\Arg{$A$}\Arg{$B$}}
+
+These two macros draw circle arcs, $O$ is the center, the radius
+defined by $OA$, the beginning angle given by $A$ and the final angle
+by $B$. Finally, the first macro draws the arc in the direct way,
+whereas the second in the indirect way. It is not necessary that the
+two points are at the same distance of $O$.
+
+\tabex{arc}
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \subsection{Curved abscissa}
+
+A point can be positioned on a circle using its curved abscissa.
+
+\defcom[Puts a point on a circle using an curves abscissa.
+ \protect\ParamList{\param{PointSymbol}, \param{PosAngle},
+ \param{PointName}, \param{PointNameSep}, \param{PtNameMath}, \param{CurvAbsNeg}}]
+ {pstCurvAbsNode}{\OptArg{par}\Arg{$O$}\Arg{$A$}\Arg{$B$}\Arg{Abs}}
+
+The point \Argsans{$B$} is positioned on the circle of center
+\Argsans{$O$} crossing \Argsans{$A$}, with the curved abscissa
+\Argsans{Abs}. The origin is \Argsans{$A$} and the direction is
+anti-clockwise by default. The parameter \param{CurvAbsNeg}
+\DefaultVal{false} can change this behavior.
+
+If the parameter \param{PosAngle} is not specified, the point label is put
+automatically in oirder to be alined with the circle center and the point.
+
+\tabex{abscur}
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \subsection{Généric curve}
+
+It is possible to generate a set of points using a loop, and to give
+them a generic name defined by a radical and a number. The following
+command can draw a interpolated curve crossing all such kind of
+points.
+
+\defcom[Draws an interpolate curve using a points family whose name has a
+ naming convention using a prefix and a number.
+ \protect\ParamList{\param{GenCurvFirst}, \param{GenCurvInc},
+ \param{GenCurvLast}}]
+ {pstGenericCurve}{\OptArg{par}\Arg{Radical}\Arg{$n_1$}\Arg{$n_2$}}
+
+The curve is drawn on the points whose name is defined using the
+radical \Argsans{Radical} followed by a number from \Argsans{$n_1$} to
+\Argsans{$n_2$}. In order to manage side effect, the parameters
+\param{GenCurvFirst} et \param{GenCurvLast} can be used to specified
+special first or last point. The parameter \param{GenCurvInc} can be
+used to modify the increment from a point to the next one
+\DefaultVal{1}.
+
+\tabex{gencur}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Geometric Transformations}
+
+The geometric transformations are the ideal tools to construct geometric figures. All
+the classical transformations are available with the following macros \cbstart which
+share the same syntaxic scheme end two parameters.
+
+The common syntax put at the end two point lists whose second is optional or with a
+cardinal at least equal. These two lists contain the antecedent points and their
+respective images. In the case no image is given for some points the a default name
+is build appending a \verb$'$ to the antecedent name.
+
+The first shared parameter is \param{CodeFig} which draws the specific
+constructions lines. Its default value is \param{false}, and a
+\param{true} value activates this optional drawing.
+The drawing is done using the line style \param{CodeFigStyle}
+\DefaultVal{dashed}, with the color \param{CodeFigColor}
+\DefaultVal{cyan}.
+
+Their second shared parameter is \param{CurveType} which controls the drawing of a
+line crossing all images, and thus allow a quick description of a transformed figure.\cbend
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \subsection{Central symmetry}
+
+\defcom[Builds the symetric point $M'_i$ of $M_i$ in relation to point $O$.
+ \protect\ParamList{\param{PointSymbol}, \param{PosAngle},
+ \param{PointName}, \param{PointNameSep}, \param{PtNameMath},
+ \param{CodeFig}, \param{CodeFigColor}, \param{CodeFigStyle}}]{pstSymO}%
+ {\OptArg{par}\Arg{$O$}\Arg{$M_1, M_2, \cdots, M_n$}\OptArg{$M'_1, M'_2, \cdots, M'_p$}}
+
+Draw the symmetric point in relation to point $O$. The classical
+parameter of point creation are usable here, and also for all the
+following functions.
+
+\tabex{symcentrale}
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \subsection{Orthogonal (or axial) symmetry}
+
+\defcom[Builds the symetric point $M'_i$ of $M_i$ in relation to line $(AB)$.
+ \protect\ParamList{\param{PointSymbol}, \param{PosAngle},
+ \param{PointName}, \param{PointNameSep}, \param{PtNameMath},
+ \param{CodeFig}, \param{CodeFigColor}, \param{CodeFigStyle}}]{pstOrtSym}%
+ {\OptArg{par}\Arg{$A$}\Arg{$B$}\Arg{$M_1, M_2, \cdots, M_n$}\OptArg{$M'_1, M'_2, \cdots, M'_p$}}
+
+Draws the symmetric point in relation to line $(AB)$.
+
+\tabex{symorthogonale}
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \subsection{Rotation}
+
+\defcom[Builds the image $M'_i$ of $M_i$ using a rotation around $O$ of \protect\param{RotAngle}
+ degrees (direct).
+ \protect\ParamList{\param{PointSymbol}, \param{PosAngle},
+ \param{PointName}, \param{PointNameSep}, \param{PtNameMath}, \param{RotAngle}}]{pstRotation}%
+ {\OptArg{par}\Arg{$O$}\Arg{$M_1, M_2, \cdots, M_n$}\OptArg{$M'_1, M'_2, \cdots, M'_p$}}
+
+Draw the image of $M_i$ by the rotation of center $O$ and angle given by
+the parameter \param{RotAngle}. This later can be an angle specified
+by three points. In such a case, the following function must be used:
+
+\defcom[Specifies the measure of \protect\Angle{AOB} (direct) for the parameter
+ \protect\param{RotAngle}. \protect\ParamList{\param{AngleCoef}}]
+ {pstAngleABC}{\Arg{$A$}\Arg{$B$}\Arg{$C$}}
+
+Never forget to use the rotation for drawing a square or an equilateral
+triangle.\cbstart The parameter \param{CodeFig} puts a bow with an arrow between the
+point and its image, and if \param{TransformLabel} \DefaultVal{none}
+contain some text, it is put on the corresponding angle in mathematical mode.
+
+\tabex{rotation}\cbend
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \subsection{Translation}
+
+\defcom[Builds the translated $M'_i$ of $M_i$ using the vector \protect\Vecteur{AB}.
+ \protect\ParamList{\param{PointSymbol}, \param{PosAngle},
+ \param{PointName}, \param{PointNameSep}, \param{PtNameMath}, \param{DistCoef}}]
+ {pstTranslation}%
+ {\OptArg{par}\Arg{$A$}\Arg{$B$}\Arg{$M_1, M_2, \cdots, M_n$}\OptArg{$M'_1, M'_2, \cdots, M'_p$}}
+
+Draws the translated $M'_i$ of $M_i$ using the vector \Vecteur{AB}. Useful for drawing a
+parallel line.
+
+\tabex{translation}
+
+The parameter \param{DistCoef} can be used as a multiplicand
+coefficient to modify the translation vector.\cbstart The parameter \param{CodeFig}
+draws the translation vector le vecteur de translation between the
+point and its image, labeled in its middle defaultly with the vector name or by the
+text specified with \param{TransformLabel} \DefaultVal{none}.\cbend
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \subsection{Homothetie}
+
+\defcom[Builds the image $M'_i$ de $M_i$ using the homothetie of centre $O$ and coefficient
+ \protect\param{HomCoef}.
+ \protect\ParamList{\param{PointSymbol}, \param{PosAngle},
+ \param{PointName}, \param{PointNameSep}, \param{PtNameMath}, \param{HomCoef}}]
+ {pstHomO}%
+ {\OptArg{par}\Arg{$O$}\Arg{$M_1, M_2, \cdots, M_n$}\OptArg{$M'_1, M'_2, \cdots, M'_p$}}
+
+Draws $M'_i$ the image of $M_i$ by the homotethy of center $O$ and
+coefficient specified with the parameter \param{HomCoef}.
+
+\tabex{homothetie}
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \subsection{Orthogonal projection}
+
+\defcom[Build the projected point $M'_i$ of $M_i$ on line $(AB)$.
+ \protect\ParamList{\param{PointSymbol}, \param{PosAngle},
+ \param{PointName}, \param{PointNameSep}, \param{PtNameMath},
+ \param{CodeFig}, \param{CodeFigColor}, \param{CodeFigStyle}}]
+ {pstProjection}%
+ {\OptArg{par}\Arg{$A$}\Arg{$B$}\Arg{$M_1, M_2, \cdots, M_n$}\OptArg{$M'_1, M'_2, \cdots, M'_p$}}
+
+Projects orthogonally the point $M_i$ on the line $(AB)$. Useful for the altitude of a
+triangle. The name is aligned with the point and the projected point as
+shown in the exemple.
+
+\tabex{projection}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Special object}
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \subsection{Midpoint}
+
+\defcom[Build the middle $I$ of \Segment{AB}.
+ \protect\ParamList{\param{PointSymbol}, \param{PosAngle},
+ \param{PointName}, \param{PointNameSep}, \param{PtNameMath}, \param{SegmentSymbol},
+ \param{CodeFig}, \param{CodeFigColor}, \param{CodeFigStyle}}]
+ {pstMiddleAB}%
+ {\OptArg{par}\Arg{$A$}\Arg{$B$}\Arg{$I$}}
+
+Draw the midpoint $I$ of segment $[AB]$. By default, the point name is
+automatically put below the segment.
+
+\tabex{milieu}
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \subsection{Triangle center of gravity}
+
+\defcom[Builds the centre of gravity $G$ of triangle $ABC$.
+ \protect\ParamList{\param{PointName}, \param{PointNameSep}, \param{PosAngle},
+ \param{PointSymbol}, \param{PtNameMath}}]
+ {pstCGravABC}%
+ {\OptArg{par}\Arg{$A$}\Arg{$B$}\Arg{$C$}\Arg{$G$}}
+
+Draw the $ABC$ triangle centre of gravity $G$.
+
+\tabex{grav}
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \subsection{Centre of the circumcircle of a triangle}
+
+\defcom[Buids the center $O$ of the circumcircle of triangle $ABC$.
+ \protect\ParamList{\param{PointName}, \param{PointNameSep}, \param{PosAngle},
+ \param{PointSymbol}, \param{PtNameMath}, \param{DrawCirABC}, \param{CodeFig},
+ \param{CodeFigColor}, \param{CodeFigStyle}, \param{SegmentSymbolA},
+ \param{SegmentSymbolB}, \param{SegmentSymbolC}}]
+ {pstCircleABC}{\OptArg{par}\Arg{$A$}\Arg{$B$}\Arg{$C$}\Arg{$O$}}
+
+Draws the circle crossing three points (the circum circle) and put its center $O$.
+The effective drawing is controlled by the boolean parameter \param{DrawCirABC}
+\DefaultVal{true}.\cbstart Moreover the intermediate constructs (mediator lines) can
+be drawn by setting the boolean parameter \param{CodeFig}. In that case the middle
+points are marked on the segemnts using three different marks given by the parameters
+\param{SegmentSymbolA}, \param{SegmentSymbolB} et \param{SegmentSymbolC}.\cbend
+
+\tabex%
+ [@{}m{.35\linewidth}@{\hspace{.013\linewidth}}>{\small}m{.627\linewidth}@{}]%
+ {ccirc}
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \subsection{Perpendicular bisector of a segment}
+
+\defcom[Builds the perpendicular bisector of the segment \Segment{AB}, its middle $I$
+ and a point $M$ of the bisector wich is the image of $B$ using rotation.
+ \protect\ParamList{\param{PointName}, \param{PointNameSep}, \param{PosAngle},
+ \param{PointSymbol}, \param{PtNameMath}, \param{CodeFig},
+ \param{CodeFigColor}, \param{CodeFigStyle}, \param{SegmentSymbol}}]
+ {pstMediatorAB}{\OptArg{par}\Arg{$A$}\Arg{$B$}\Arg{$I$}\Arg{$M$}}
+
+The perpendicular bisector of a segment is a line perpendicular to
+this segment in its midpoint. The segment is $[AB]$, the midpoint $I$,
+and $M$ is a point belonging to the perpendicular bisector line. It is
+build by a rotation of $B$ of 90 degrees around $I$. This mean
+that the order of $A$ and $B$ is important, it controls the position
+of $M$. The command creates the two points $M$ end $I$. The
+construction is controlled by the following parameters:
+
+\begin{itemize}
+\item \param{CodeFig}, \param{CodeFigColor} et \param{SegmentSymbol}
+ for marking the right angle ;
+\item \param{PointSymbol} et \param{PointName} for controlling the
+ drawing of the two points, each of them can be specified
+ separately with the parameters \param{...A} et \param{...B} ;
+\item parameters controlling the line drawing.
+\end{itemize}
+
+\tabex%
+ [@{}m{.35\linewidth}@{\hspace{.013\linewidth}}>{\small}m{.627\linewidth}@{}]%
+ {mediator}
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \subsection{Bisectors of angles}
+
+\defcom[Builds the internal bisector of angle \protect\Angle{BAC} and one of its point
+ $M$, image of $B$ by rotation around $A$.
+ \protect\ParamList{\param{PointSymbol}, \param{PosAngle},
+ \param{PointName}, \param{PointNameSep}, \param{PtNameMath}}]
+ {pstBissectBAC}{\OptArg{par}\Arg{$B$}\Arg{$A$}\Arg{$C$}\Arg{$N$}}
+
+\defcom[Builds the external bisector of angle \protect\Angle{BAC} and one of its point
+ $M$, image of $B$ by rotation around $A$.
+ \protect\ParamList{\param{PointSymbol}, \param{PosAngle},
+ \param{PointName}, \param{PointNameSep}, \param{PtNameMath}}]
+ {pstOutBissectBAC}{\OptArg{par}\Arg{$B$}\Arg{$A$}\Arg{$C$}\Arg{$N$}}
+
+there are two bisectors for a given geometric angle: the inside one and
+the outside one; this is why there is two commands. The angle is
+specified by three points specified in the trigonometric direction
+(anti-clockwise). The result of the commands is the specific line and
+a point belonging to this line. This point is built by a rotation of
+point $B$.
+
+\tabex%
+ [@{}m{.35\linewidth}@{\hspace{.013\linewidth}}>{\small}m{.627\linewidth}@{}]%
+ {bissec}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Intersections}
+
+Points can be defined by intersections. Six intersection types are
+managed:
+
+\begin{itemize}
+\item line-line;
+\item line-circle;
+\item circle-circle;
+\item function-function;
+\item function-line;
+\item function-circle.
+\end{itemize}
+
+An intersection can not exist: case of parallel lines. In such a case,
+the point(s) are positioned at the origin. In fact, the user has to
+manage the existence of these points.
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \subsection{Line-Line}
+
+\defcom[Puts a point at the intersection of the two lines $(AB)$ et $(CD)$.
+ \protect\ParamList{\param{PointSymbol}, \param{PosAngle},
+ \param{PointName}, \param{PointNameSep}, \param{PtNameMath}}]
+ {pstInterLL}%
+ {\OptArg{par}\Arg{$A$}\Arg{$B$}\Arg{$C$}\Arg{$D$}\Arg{$M$}}
+
+Draw the intersection point between lines $(AB)$ and $(CD)$.
+
+\begin{description}
+\item[basique]
+
+ \tabex{interDD}
+
+\item[Horthocentre]
+
+ \tabex%
+ [@{}m{.35\linewidth}@{\hspace{.013\linewidth}}>{\small}m{.627\linewidth}@{}]
+ {orthocentre}
+
+\end{description}
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \subsection{Circle--Line}
+
+\defcom[Puts the intersection point(s) between $(AB)$ and the circle of
+ centre $O$ crossing $C$.
+ \protect\ParamList{\param{PointSymbol}, \param{PosAngle},
+ \param{PointName}, \param{PointNameSep}, \param{PtNameMath},
+ \param{PointSymbolA}, \param{PosAngleA}, \param{PointNameA},
+ \param{PointSymbolB}, \param{PosAngleB}, \param{PointNameB},
+ \param{Radius}, \param{Diameter}}]
+ {pstInterLC}%
+ {\OptArg{par}\Arg{$A$}\Arg{$B$}\Arg{$O$}\Arg{$C$}%
+ \Arg{$M_1$}\Arg{$M_2$}}
+
+Draw the one or two intersection point(s) between the line $(AB)$ and
+the circle of centre $O$ and with radius $OC$.
+
+The circle is specified with its center and either a point of its
+circumference or with a radius specified with parameter \param{radius}
+or its diameter specified with parameter \param{Diameter}. These two
+parameters can be modify by coefficient \param{DistCoef}.
+
+
+The position of the wo points is such that the vectors \Vecteur{AB} abd
+\Vecteur{M_1M_2} are in the same direction. Thus, if the points
+definig the line are switch, then the resulting points will be also
+switched. If the intersection is void, then the points are positionned
+at the center of the circle.
+
+
+\tabex
+ [@{}m{.4\linewidth}@{\hspace{.013\linewidth}}>{\small}m{.5777\linewidth}@{}]
+ {interDC}
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \subsection{Circle--Circle}
+
+\defcom[Put the intersection point(s) between the circle of centre $O_1$ passant
+ par $B$ et le cercle de centre $O_2$ passant par $C$.]
+ {pstInterCC}%
+ {\OptArg{par}\Arg{$O_1$}\Arg{$B$}\Arg{$O_2$}\Arg{$C$}%
+ \Arg{$M_1$}\Arg{$M_2$}}
+
+This function is similar to the last one. The boolean parameters
+\param{CodeFigA} et \param{CodeFigB} allow the drawing of the arcs
+at the intersection. In order to get a coherence \param{CodeFig} allow
+the drawing of both arcs. The boolean parameters \param{CodeFigAarc} and
+\param{CodeFigBarc} specified the direction of these optional arcs:
+trigonometric (by default) or clockwise. Here is a first example.
+
+\tabex{interCC}
+
+And a more complete one, which includes the special circle
+specification using radius and diameter. For such specifications it
+exists the parameters \param{RadiusA}, \param{RadiusB},
+\param{DiameterA} and \param{DiameterB}.
+
+\begin{center}
+ \rule[-.5cm]{0pt}{8cm}
+ \begin{pspicture}(-3,-4)(7,3)\psgrid
+ \input{Exemples/interCC_bis_in}
+ \end{pspicture}
+\end{center}
+
+\smallverbatiminput{Exemples/interCC_bis_in}
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \subsection{Function--function}
+
+\defcom[Puts an intersection point between two function curves.]
+ {pstInterFF}{\OptArg{par}\Arg{$f$}\Arg{$g$}\Arg{$x_0$}\Arg{$M$}}
+
+This function put a point at the intersection between two curves
+defined by a function. $x_0$ is an intersection approximated value of
+the abscissa. It is obviously possible to ise this function several
+time if more than one intersection is present. Each function is
+describerd in \PostScript in the same way as the description used by
+the \com{psplot} macro of \PStricks. A constant function can be
+specified, and then seaching function root is possible.
+
+The Newton algorithm is used for the research, and the intersection
+may not to be found. In such a case the point is positionned at the
+origin. On the other hand, the research can be trapped (in a local
+extremum near zero).
+
+\tabex{interFF}
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \subsection{Function--line}
+
+\defcom[Puts an intersection point between one function curve and the line $(AB)$.]
+ {pstInterFL}{\OptArg{par}\Arg{$f$}\Arg{$A$}\Arg{$B$}\Arg{$x_0$}\Arg{$M$}}
+
+Puts a point at the intersection between the function $f$ and the line
+$(AB)$.
+
+\tabex{interFL}
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \subsection{Function--circle}
+
+\defcom[Puts an intersection point between one function curve and a circle.]
+ {pstInterFC}{\OptArg{par}\Arg{$f$}\Arg{$O$}\Arg{$A$}\Arg{$x_0$}\Arg{$M$}}
+
+Puts a point at the intersection between the function $f$ and the circle
+of centre $O$ and radius $OA$.
+
+\tabex{interFC}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\chapter{Examples gallery}
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \section{Basic geometry}
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \subsection{Drawing of the bissector}
+ \nopagebreak[4]
+
+\tabex{gal_biss}
+
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \cbstart\subsection{Transformation de polygones et courbes}
+
+Here is an example of the use of \param{CurveType} with transformation.
+\nopagebreak[4]
+
+\begin{center}
+\input{Exemples/curvetype}
+\end{center}\nopagebreak[4]
+
+\smallverbatiminput{Exemples/curvetype_in}\cbend
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \subsection{Triangle lines}
+
+\begin{center}
+\psset{unit=2cm}
+\input{Exemples/remarq}
+\end{center}\nopagebreak[4]
+
+\smallverbatiminput{Exemples/remarq_in}
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \subsection{Euler circle}
+
+\begin{center}
+\psset{unit=2cm}
+\input{Exemples/euler}
+\end{center}\nopagebreak[4]
+
+\smallverbatiminput{Exemples/euler_in}
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \subsection{Orthocenter and hyperbola}
+
+The orthocenter of a triangle whose points are on the branches of the
+hyperbola ${\mathscr H} : y=a/x$ belong to this hyperbola.
+\nopagebreak[4]
+
+\begin{center}
+\psset{unit=.5cm}
+\input{Exemples/orthoethyper}
+\end{center}\nopagebreak[4]
+
+\smallverbatiminput{Exemples/orthoethyper_in}
+
+\pagebreak[4]
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \subsection{17 sides regular polygon}
+
+Striking picture created by K. F. Gauss.
+he also prooved that it is possible to build the regular polygons which
+have $2^{2^p}+1$ sides, the following one has 257 sides!
+\nopagebreak[4]
+
+\begin{center}
+\psset{unit=1.5cm, CodeFig=true, RightAngleSize=.14, CodeFigColor=red,
+ CodeFigB=true, linestyle=dashed, dash=2mm 2mm}
+\input{Exemples/gauss}
+\end{center}
+
+\pagebreak[4]
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \subsection{Circles \& tangents}
+
+The drawing of the circle tangents which crosses a given point.
+\nopagebreak[4]
+
+\begin{center}
+\input{Exemples/tg1c}
+\end{center}
+
+The drawing of the common tangent of two circles.
+\nopagebreak[4]
+
+\begin{center}
+\input{Exemples/tg2c}
+\end{center}
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \subsection{Fermat's point}
+
+Drawing of Manuel Luque.\nopagebreak[4]
+
+\begin{center}
+\input{Exemples/ptfermat}
+\end{center}
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \subsection{Escribed and inscribed circles of a triangle}
+
+%% cercles inscrit et exinscrits d'un triangle
+\begin{center}
+\psset{unit=1cm, dash=5mm 4mm}%, PointSymbolA=none, PointSymbolB=none}
+\input{Exemples/cinscex}
+\end{center}
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \section{Some locus points}
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \subsection{Parabola}
+
+\begin{minipage}[m]{.33\linewidth}
+The parabola is the set of points which are at the same distance
+between a point and a line.
+\end{minipage}
+\newcommand{\NbPt}{11}
+\input{Exemples/parabole}\nopagebreak[4]
+
+\smallverbatiminput{Exemples/parabole_in}
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \subsection{Hyperbola}
+
+\begin{minipage}[b]{.55\linewidth}
+The hyperbola is the set of points whose difference between their
+distance of two points (the focus) is constant.
+\begin{verbatim}
+%% QQ RAPPELS : a=\Sommet, c=\PosFoyer,
+%% b^2=c^2-a^2, e=c/a
+%% pour une hyperbole -> e>1, donc c>a,
+%% ici on choisi a=\sqrt{2}, c=2, e=\sqrt{2}
+%% M est sur H <=> |MF-MF'|=2a
+\end{verbatim}
+\end{minipage}
+%% QQ DEFINITIONS
+\input{Exemples/hyperbole}\nopagebreak[4]
+
+\smallverbatiminput{Exemples/hyperbole_in}
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \subsection{Cycloid}
+
+The wheel rolls from $M$ to $A$. The circle points are on a
+cycloid.\nopagebreak[4]
+
+\begin{center}
+\input{Exemples/cyclo}
+\end{center}\nopagebreak[4]
+
+\smallverbatiminput{Exemples/cyclo_in}
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \subsection{Hypocycloids (Astroid and Deltoid)}
+
+A wheel rolls inside a circle, and depending of the radius ratio, it
+is an astroid, a deltoid and in the general case hypo-cycloids.
+\nopagebreak[4]
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% ASTROIDE
+\input{Exemples/hypocyclo}
+%%%%%%%%%%%%%%%%%%%%
+\begin{center}
+\input{Exemples/astro}\input{Exemples/delto}
+\end{center}
+
+\smallverbatiminput{Exemples/hypocyclo}
+\smallverbatiminput{Exemples/astro_in}
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \section{Lines and circles envelope}
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \subsection{Conics}
+
+Let's consider a circle and a point $A$ not on the circle. The
+set of all the mediator lines of segments defined by $A$ and the
+circle points, create two conics depending of the position of $A$:
+
+\begin{itemize}
+\item inside the circle: an hyperbola;
+\item outside the circle: an ellipse.
+\end{itemize}
+
+(figure of O. Reboux).
+
+\begin{center}\input{Exemples/envellipse}\end{center}
+
+\smallverbatiminput{Exemples/envellipse_in}
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \subsection{Cardioid}
+
+The cardioid is defined by the circles centered on a circle and
+crossing a given point.
+
+%\begin{center}\input{Exemples/envcardi}\end{center}
+
+\tabex%
+ [@{}m{.5\linewidth}@{\hspace{.013\linewidth}}>{\small}m{.627\linewidth}@{}]%
+ {envcardi}
+
+%\smallverbatiminput{Exemples/envcardi_in}
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \section{Homotethy and fractals}
+
+\tabex{fracthom}
+
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ \section{hyperbolic geometry: a triangle and its altitudes}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%% Tracé de géodésique en géométrie hyperbolique
+%% Attention ne fonctionne que si les points ne sont pas alignés avec O
+%% Ceci est un cas particulier, je ne crois pas que les hauteurs
+%% soient concourantes pour tous les triangles hyperboliques.
+\input{Exemples/geohyper}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\appendix
+\chapter{Glossaire des commandes}%%\markboth{GLOSSAIRE DES COMMANDES}{\thepage}%
+%%\addcontentsline{toc}{chapter}{\protect\numberline{}Glossaire des commandes}%
+
+Here is the complete macros list defined by \texttt{pst-eucl}. Each is shown with a
+short description and its parameters which control it. It is obvious that some over
+\PStricks parameters can be used, especially the ones which control the drawing of
+the line (width, style, color).
+
+\input{euclide_english_macros.ind}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\chapter{The parameters of \texttt{pst-eucl}}
+
+\begin{longtable}{|l|l|p{10cm}|}
+ \hline
+ \multicolumn{1}{|c|}{\textbf{Paramètre}} &
+ \multicolumn{1}{c|}{\textbf{Défaut}} &
+ \multicolumn{1}{c|}{\textbf{Signification}} \\\hline\hline
+ \endfirsthead
+ \hline
+ \multicolumn{1}{|c|}{\textbf{Paramètre}} &
+ \multicolumn{1}{c|}{\textbf{Défaut}} &
+ \multicolumn{1}{c|}{\textbf{Signification}} \\\hline\hline
+ \endhead
+ \hline
+ \multicolumn{3}{|c|}{$\ldots$ à suivre $\ldots$}\\
+ \hline
+ \endfoot
+ \hline
+ \endlastfoot
+ \param{PointSymbol}&\verb$default$&Symbol used for drawing a point.\\\hline
+ \param{PointSymbolA}&\verb$default$&idem for the first point of several.\\\hline
+ \param{PointSymbolB}&\verb$default$&for the second\ldots\\\hline
+ \param{PointSymbolC}&\verb$default$&for the third\ldots\\\hline
+ \param{PointName}&\verb$default$&Point's label.\\\hline
+ \param{PointNameA}&\verb$default$&idem for the first point of several.\\\hline
+ \param{PointNameB}&\verb$default$&for the second\ldots\\\hline
+ \param{PointNameC}&\verb$default$&for the third\ldots\\\hline
+ \param{PtNameMath}&\verb$true$&boolean parameter for (de)-activate the math style
+ for the point name..\\\hline
+ \param{SegmentSymbol}&\verb$default$&Symbol used for marking a segment\\\hline
+ \param{SegmentSymbolA}&\verb$default$&idem for the first segment of a macro which
+ marks several.\\\hline
+ \param{SegmentSymbolB}&\verb$default$&for the second\ldots\\\hline
+ \param{SegmentSymbolC}&\verb$default$&for the third\ldots\\\hline
+ \param{Mark}&\verb$default$&the mark symbol for an angle.\\\hline
+ \param{MarkAngle}&\verb$default$&angle for the precedent symbol.\\\hline
+ \param{PointNameSep}&\verb$1em$&Distance from the label and a point.\\\hline
+ \param{PosAngle}&\verb$undef$&Label position around the point.\\\hline
+ \param{PosAngleA}&\verb$undef$&idem for the first point.\\\hline
+ \param{PosAngleB}&\verb$undef$&for the second\ldots\\\hline
+ \param{PosAngleC}&\verb$undef$&for the third\ldots\\\hline
+ \param{RightAngleSize}&\verb$.4$&size for the right angle symbol\\\hline
+ \param{RightAngleType}&\verb$default$&Right angle type, possible value:
+ \verb$german$ et \verb$suisseromand$\\\hline
+ \param{MarkAngleRadius}&\verb$.4$&Radius of the angle mark.\\\hline
+ \param{LabelAngleOffset}&\verb$0$&Angular offset for the angle label.\\\hline
+ \param{LabelSep}&\verb$1$&Distance from the label and the angle top and its label.\\\hline
+ \param{LabelRefPt}&\verb$c$&Reference point \TeX\ used for the angle label.\\\hline
+ \param{HomCoef}&\verb$.5$&Homothetie angle.\\\hline
+ \param{RotAngle}&\verb$60$&Rotation angle.\\\hline
+ \param{DrawCirABC}&\verb$true$&Boolean parameter driving the drawing of the circumcircle.\\\hline
+ \param{CodeFig}&\verb$false$&Boolean parameter driving the coding of the construct.\\\hline
+ \param{CodeFigA}&\verb$false$&idem for the first\ldots\\\hline
+ \param{CodeFigB}&\verb$false$&idem for the second\ldots\\\hline
+ \param{CodeFigColor}&\verb$cyan$&Line color for the coding.\\\hline
+ \param{CodeFigStyle}&\verb$dashed$&Line style for the coding.\\\hline
+ \param{CodeFigAarc}&\verb$true$&Boolean parameter driving the drawing of the bows
+ around the first intersection.\\\hline
+ \param{CodeFigBarc}&\verb$true$&idem for the second\ldots\\\hline
+ \param{Radius}&\verb$none$&Circle radius.\\\hline
+ \param{RadiusA}&\verb$undef$&For the first circle.\\\hline
+ \param{RadiusB}&\verb$undef$&For the second circle.\\\hline
+ \param{Diameter}&\verb$none$&Circle diameter.\\\hline
+ \param{DiameterA}&\verb$undef$&For the first circle.\\\hline
+ \param{DiameterB}&\verb$undef$&For the second circle.\\\hline
+ \param{DistCoef}&\verb$none$&Coefficient for modifying a distance/vector.\\\hline
+ \param{AngleCoef}&\verb$none$&Coefficient for modifying an angle.\\\hline
+ \param{CurvAbsNeg}&\verb$false$&Boolean parameter driving the direction of curved abscissa.\\\hline
+ \param{GenCurvFirst}&\verb$none$&Name of the first point of a generic curve (side effect).\\\hline
+ \param{GenCurvLast}&\verb$none$&Name of the last point of a generic curve (side effect).\\\hline
+ \param{GenCurvInc}&\verb$none$&Increment value for a generic curve.\\\hline
+ \cbstart%
+ \param{CurveType}&\verb$none$&Drawing mode for a list of points.\\\hline
+ \param{TransformLabel}&\verb$none$&Label to be used for the rotation or the translation.\\\hline
+\end{longtable}
+
+\cbend
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\cbstart\chapter{Compatibilité ascendantes de \texttt{pst-eucl}}
+
+Especially for this release, some macros have their syntax changed without changing
+their name, this mean that upward compatibility is not maintained. However, in order
+to help users it is possible to reactivate the old syntax by setting the option
+\texttt{old} when using the package \verb$\usepackage[old]{pst-eucl}$. For this
+release this concern the macros for geometric transformations. You must refer to the
+latter manual for the syntax.
+
+\cbend
+\end{document}