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-\documentclass[12pt]{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}[shift=.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{PosAngle}, \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 one or more of such
-parameters is omitted, the value of \param{PosAngle} is taken. If no angle
-is specified, points name are placed 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{Examples/cercle}
-
-\smallverbatiminput{Examples/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{Examples/interCC_bis_in}
- \end{pspicture}
-\end{center}
-
-\smallverbatiminput{Examples/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{Examples/curvetype}
-\end{center}\nopagebreak[4]
-
-\smallverbatiminput{Examples/curvetype_in}\cbend
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Triangle lines}
-
-\begin{center}
-\psset{unit=2cm}
-\input{Examples/remarq}
-\end{center}\nopagebreak[4]
-
-\smallverbatiminput{Examples/remarq_in}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Euler circle}
-
-\begin{center}
-\psset{unit=2cm}
-\input{Examples/euler}
-\end{center}\nopagebreak[4]
-
-\smallverbatiminput{Examples/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{Examples/orthoethyper}
-\end{center}\nopagebreak[4]
-
-\smallverbatiminput{Examples/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{Examples/gauss}
-\end{center}
-
-\pagebreak[4]
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Circles \& tangents}
-
-The drawing of the circle tangents which crosses a given point.
-\nopagebreak[4]
-
-\begin{center}
-\input{Examples/tg1c}
-\end{center}
-
-The drawing of the common tangent of two circles.
-\nopagebreak[4]
-
-\begin{center}
-\input{Examples/tg2c}
-\end{center}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Fermat's point}
-
-Drawing of Manuel Luque.\nopagebreak[4]
-
-\begin{center}
-\input{Examples/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{Examples/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{Examples/parabole}\nopagebreak[4]
-
-\smallverbatiminput{Examples/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{Examples/hyperbole}\nopagebreak[4]
-
-\smallverbatiminput{Examples/hyperbole_in}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Cycloid}
-
-The wheel rolls from $M$ to $A$. The circle points are on a
-cycloid.\nopagebreak[4]
-
-\begin{center}
-\input{Examples/cyclo}
-\end{center}\nopagebreak[4]
-
-\smallverbatiminput{Examples/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{Examples/hypocyclo}
-%%%%%%%%%%%%%%%%%%%%
-\begin{center}
-\input{Examples/astro}\input{Examples/delto}
-\end{center}
-
-\smallverbatiminput{Examples/hypocyclo}
-\smallverbatiminput{Examples/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{Examples/envellipse}\end{center}
-
-\smallverbatiminput{Examples/envellipse_in}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Cardioid}
-
-The cardioid is defined by the circles centered on a circle and
-crossing a given point.
-
-%\begin{center}\input{Examples/envcardi}\end{center}
-
-\tabex%
- [@{}m{.5\linewidth}@{\hspace{.013\linewidth}}>{\small}m{.627\linewidth}@{}]%
- {envcardi}
-
-%\smallverbatiminput{Examples/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{Examples/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.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}