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diff --git a/Master/texmf-dist/doc/generic/pst-eucl/euclide-english.tex b/Master/texmf-dist/doc/generic/pst-eucl/euclide-english.tex deleted file mode 100644 index 6956dacb2cf..00000000000 --- a/Master/texmf-dist/doc/generic/pst-eucl/euclide-english.tex +++ /dev/null @@ -1,1177 +0,0 @@ -\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} |