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authorKarl Berry <karl@freefriends.org>2006-07-03 00:28:54 +0000
committerKarl Berry <karl@freefriends.org>2006-07-03 00:28:54 +0000
commitdc497353a898123eb22a06a6d82bafab0c34fb4d (patch)
tree55517fb508911422e25ecd43f38e37e65d71713b /Master/texmf-dist/doc/latex/euclide
parenta2a6f251603241637013515bcd8feecb79d0e037 (diff)
delete obsolete euclide package
git-svn-id: svn://tug.org/texlive/trunk@1759 c570f23f-e606-0410-a88d-b1316a301751
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-rw-r--r--Master/texmf-dist/doc/latex/euclide/euclide.tex1322
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diff --git a/Master/texmf-dist/doc/latex/euclide/README b/Master/texmf-dist/doc/latex/euclide/README
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index 6812122750d..00000000000
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- Geometry and PsTricks
- the pst-eucl package
-
-
-VERSION 0.beta.5
-DATE march 2002
-
-LICENCE
--------
-
-This program can be redistributed and/or modified under the terms
-of the LaTeX Project Public License Distributed from CTAN
-archives in directory macros/latex/base/lppl.txt.
-
-However, you MUST send me an Email with a small commentary!
-
-Then you should consider making a donation:
-
- 1. directly to the LaTeX3 team;
- 2. and/or to me for the support of this package (choose one of the three)
- a. $1 or 1 euro (or more),
- b. some beautiful stamps (cancelled or not) of your country
- (for my children),
- c. a beautiful postcard with a beautiful stamp on it .
-
- my address:
- La Grand'Terre
- 07460 Saint André de Cruzières
- FRANCE
-
-INSTALLATION
-------------
-
- for teTeX :
- -----------
-
- If you want to just test it quickly, keep the files:
-
- pst-eucl.pro, pst-eucl.tex and pst-eucl.sty
-
- in the directory where you work.
-
- For a good integration:
-
- copy pst-eucl.pro to your local texmf directory :
-
- /usr/local/texmf.local/dvips/pstricks (for example)
-
- pst-eucl.tex and pst-eucl.sty to a directory referenced
- by the TEXCONFIG shell global variable, or in the local texmf
- directory :
-
- /usr/local/texmf.local/tex/generic/pstricks
-
- run `texhash`
-
- if you don't have a local texmf directory, you can create it or ask
- the root to create it by modifying the file:
-
- $(TEXMF)/web2c/texmf.cnf
-
- remove the original for the first line:
-
-% original texmf.cnf -- runtime path configuration file for kpathsea.
- ^^^^^^^^
-
- uncomment the line for declaring the local directory and
- choose where to store it:
-
-TEXMFLOCAL = /usr/local/texmf.local
-
- add this directory to the TEXMF directory list:
-
-TEXMF = {$TEXMFLOCAL,!!$TEXMFMAIN}
-
- normally it should work now!
-
- create the complete directory structure you want to use:
-
-mkdir /usr/local/texmf.local
-mkdir /usr/local/texmf.local/tex
-mkdir /usr/local/texmf.local/tex/generic
-mkdir /usr/local/texmf.local/tex/generic/pstricks
-mkdir /usr/local/texmf.local/dvips
-mkdir /usr/local/texmf.local/dvips/pstricks
-
- for Window$ : Ooops (I don't know)
- -----------
-
- If you use fpTeX, it should be similar as teTeX, look for the
- texmf.local directory at the root of the texmf directory.
-
- anyway, the simplest is to keep these three files in the
- directory where you work!
-
-DOCUMENTATION
--------------
-
- a ps and a dvi files are provided. In order to build them, just
- run LaTeX on euclide.tex (latex euclide). Depending of your TeX
- engine you may run out of memory...
-
-EXAMPLES
---------
-
- The directory Exemples contains all the exemples of the
- documentation. Each example is divided in two files:
-
- o <exemple>.tex which contains the pspicture declaration and an
- include to the second file,
- o <exemple>_in.tex which contains the exemple.
-
- In order to use them, you can concatenate both files and include
- them in a LaTeX file.
-
diff --git a/Master/texmf-dist/doc/latex/euclide/euclide.dvi b/Master/texmf-dist/doc/latex/euclide/euclide.dvi
deleted file mode 100644
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diff --git a/Master/texmf-dist/doc/latex/euclide/euclide.tex b/Master/texmf-dist/doc/latex/euclide/euclide.tex
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-%% This doc can be redistributed and/or modified under the terms
-%% of the LaTeX Project Public License Distributed from CTAN
-%% archives in directory macros/latex/base/lppl.txt.
-\documentclass[12pt, draft]{report}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\usepackage[T1]{fontenc}
-\usepackage[latin1]{inputenc}
-\usepackage[a4paper]{geometry}
-\usepackage[frenchb]{babel}
-\usepackage[usenames]{pstcol}
-\usepackage{pst-eucl}
-\usepackage{pst-plot}
-\usepackage{ifthen}
-\usepackage{calc}
-\usepackage{array}
-\usepackage{moreverb}
-\usepackage{multicol}
-\usepackage{mathrsfs}
-\usepackage[dvips]{changebar}
-\usepackage{xspace}
-\usepackage{fancyhdr}
-\expandafter\ifx\csname PDF\endcsname\relax\else
-\usepackage{pslatex}%for generating a pdf-file with ps2pdf
-\fi
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% QQ DEFINITIONS
-\newcommand{\Vecteur}[1]{\ensuremath{\overrightarrow{#1\hspace{.3em}}}}%
-\newcommand{\Angle}[1]{\ensuremath{\widehat{#1}}}%
-\makeatletter
-\newcommand{\Arg}[1]{{\normalfont$\{$\@Arg{#1}$\}$}}%
-\newcommand{\Argsans}[1]{\@Arg{#1}}%
-\newcommand{\OptArg}[1]{{\normalfont[{\@Arg{#1}}]}}%
-\newcommand{\@Arg}[1]%
- {$\protect\langle${\itshape\mdseries\rmfamily#1}$\protect\rangle$}%
-\makeatother
-%% le backslash \
-\newcommand{\bs}{\symbol{'134}}%
-\newcommand{\defcom}[2]%
- {\begin{trivlist}\item\fbox{\texttt{\upshape\bs#1}#2}\end{trivlist}}%
-\newcommand{\defcomdeux}[4]%
- {%
- \begin{center}%
- \begin{minipage}[t]{.45\linewidth}%
- \begin{trivlist}\item\fbox{\texttt{\upshape\bs#1}#2}\end{trivlist}%
- \end{minipage}%
- \hfill%
- \begin{minipage}[t]{.45\linewidth}%
- \begin{trivlist}\item\fbox{\texttt{\upshape\bs#3}#4}\end{trivlist}%
- \end{minipage}
- \end{center}}%end defcomdeux
-\newenvironment{tabexemple}[1]%
- [@{}m{.3\linewidth}@{\hspace{.013\linewidth}}>{\small}m{.677\linewidth}@{}]%
- {\vspace{1em}\noindent\small\begin{center}%
- \noindent\begin{tabular}{#1}}%
- {\mbox{}\vspace{-1.5em}\end{tabular}\end{center}}%
-\newcommand{\tabex}[2]%
- [@{}m{.3\linewidth}@{\hspace{.013\linewidth}}>{\small}m{.677\linewidth}@{}]%
-{%
- \begin{tabexemple}[#1]%
- \input{Exemples/#2}&\verbatiminput{Exemples/#2_in}%
- \end{tabexemple}%
-}%
-\newcommand{\param}[1]{\texttt{#1}}
-\newcommand{\com}[1]{\texttt{\bs #1}}
-\newcommand{\DefaultVal}[1]{(\texttt{#1} par défaut)}
-\newcommand{\PStricks}{\texttt{PSTricks}\xspace}
-\newcommand{\Postcript}{\textsf{PostScript}\xspace}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\title{Extension \texttt{pst-eucl}\\
- Géométrie euclidienne avec \PStricks}
-\author{Version $0.\beta.5$\\Dominique \textsc{Rodriguez}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\geometry{bottom=1cm, left=1cm, headheight=15.5pt}%, verbose}
-\psset{subgriddiv=0,griddots=5}
-\setlength{\changebarsep}{10pt}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% entête et pied de page
-\pagestyle{fancy}
-\renewcommand{\headrulewidth}{0.4pt}
-\renewcommand{\footrulewidth}{0.4pt}
-%\lhead{version $\beta.5$ -- Mars 2002}
-%\chead{}
-%\rhead{Extension \texttt{pst-eucl} -- D. \textsc{Rodriguez}}
-%\cfoot{\thepage}
-\lfoot{version $\beta.5$ -- Mars 2002}
-\rfoot{Extension \texttt{pst-eucl} -- D. \textsc{Rodriguez}}
-%%%%%%%%%%%%%%%%%%%%
-\newcounter{i}
-%%%%%%%%%%%%%%%%%%%%
-\makeatletter
-\newcommand{\twocoltoc}{%
- \chapter*{\contentsname
- \@mkboth{%
- \MakeUppercase\contentsname}{\MakeUppercase\contentsname}}%
- \begin{multicols}{2}
- \@starttoc{toc}%
- \end{multicols}}
-\makeatother
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{document}
-%%%%%%%%%%%%%%%%%%%%
-\maketitle
-%%%%%%%%%%%%%%%%%%%%
-\cbstart
-\begin{abstract}
- L'extension \texttt{pst-eucl} permet de dessiner des figures
- géométriques en spécifiant des contraintes mathématiques. Il est
- ainsi possible de définir des points au moyen de transformations ou
- d'intersection. L'emploi des coordonnées est donc limité aux points
- de départ qui paramètrent en quelque sorte le dessin.
-
- \vfill
-
- \begin{center}\bfseries
- Remerciements
- \end{center}
-
- Je tiens à remercier tout particulièrement les personnes suivantes
- pour leur aide dans l'élaboration de ce paquetage :
-
- \begin{itemize}
- \item Denis \textsc{girou} pour ses critiques pertinentes et ses
- encouragement lors de la découverte de l'embryon initial et pour
- sa relecture du présent manuel ;
- \item Manuel \textsc{Luque} et Olivier \textsc{Reboux} pour leurs
- remarques et leurs exemples.
- \end{itemize}
-\end{abstract}
-%%%%%%%%%%%%%%%%%%%%
-\renewcommand{\abstractname}{Avertissement}
-\begin{abstract}
- Ceci est une version $\beta$, elle est encore en cours de
- développement, le nom des fonctions peut et va changer sans
- maintient de la compatibilité ascendante.
-\end{abstract}
-\cbend
-\twocoltoc{}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\chapter{Manuel de l'utilisateur}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\section{Spécifications particulières}
-
-\cbstart
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Options de \PStricks}
-
-L'extension active le mode \com{SpecialCoor}. Ce mode permet d'étendre
-la manière dont les coordonnées sont spécifiées en plus des classiques
-coordonnées cartésiennes. D'autre part le mode de tracé est mis à
-\texttt{dimen=middle}, c'est-à-dire que le positionnement des tracés
-est fait par rapport à leur milieu. Pour ces deux modes, je vous
-renvoie au manuel de l'utilisateur.
-
-Enfin, il est supposé que le repère de travail est (ortho)normé.
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Conventions}
-
-Pour la rédaction de ce manuel, j'ai utilisé les conventions
-géométriques de nommage des points classiques en France :
-
-\begin{itemize}
-\item $O$ est un centre (cercle, repère, symétrie, homotéthie, rotation) ;
-\item $I$ est l'unité de l'axe des abscisses, ou un milieu ;
-\item $J$ est l'unité de l'axe des ordonnées ;
-\item $A$, $B$, $C$, $D$ sont des points ;
-\item $M$ est un point \emph{paramètre} ;
-\item $M'$ l'image de $M$ par une transformation ;
-\end{itemize}
-
-Enfin, bien que s'agissant de n\oe uds au sens de \PStricks,
-je les ai résolument confondus avec des points dans le texte.
-\cbend
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\section{Objets de base}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Les points}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsubsection{Repère par défaut}
-
-\defcom{pstGeonode}{\OptArg{par}$(x,y)$\Arg{$A$}}
-
-Cette commande définit un point géométrique associé avec un n\oe ud.
-Le point possède un nom de n\oe ud \Argsans{$A$}, qui définit par
-défaut l'étiquette placée sur le dessin. D'autre part, celle-ci est
-par défaut traitée en mode mathématique, le paramètre booléen
-\param{PtNameMath} permet de modifier ce traitement et de traiter
-l'étiquette en mode normal. Elle est positionnée à une distance de
-\texttt{1em} du n\oe ud, avec un angle de
-\param{PosAngle}\DefaultVal{0}. Il est également possible de proposer
-une étiquette différente du nom de n\oe ud avec le paramètre
-\param{PointName}, et une étiquette vide se spécifie en positionnant
-ce paramètre à \texttt{none} ; dans ce cas le point n'aura pas de nom
-sur le dessin.
-
-Le symbole du point est donné par le paramètre \param{PointSymbol}
-\DefaultVal{*}.
-\cbstart
-Le symbole est celui utilisé pour la commande \com{psdot}.
-\cbend Il peut être également positionné à \texttt{none}, auquel cas
-le point n'est pas affiché sur la figure y compris son étiquette.
-
-\cbstart
-Voici en rappel les valeurs possibles du symbole :
-
-\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}
-\cbend
-
-% EXEMPLE GEONODE
-\tabex{geonode}
-
-Il est évident que les n\oe uds ainsi définis sont utilisables par
-toutes les commandes utilisant les n\oe uds de \PStricks. Ainsi, il est
-possible de les réferencer \rnode{ici}{d'ici}.
-\nccurve[arrowscale=2]{->}{ici}{B_1}
-
-%l existe un bug lié à la définition de point, il faut impérativement
-%aire suivre la commande par un \verb$%$, sinon il se crée un décalage
-%es points sur le graphiques, comme le montre le dessin suivant :
-%
-% \begin{center}
-% \begin{pspicture}(-2,-2)(2,2)\psgrid
-% \pstGeonode(0,0){A}
-% \pstGeonode[PosAngle=-90, PointName=B_1](1,2){B1}
-% \pstGeonode[PointSymbol=pstSmallCircle, PointName=B_2,
-% linecolor=red](-2,1){B2}%
-% \end{pspicture}
-% \end{center}
-\cbstart
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsubsection{Repère personnalisé}
-
-\defcom{pstOIJGeonode}{\OptArg{par}$(x,y)$\Arg{$A$}\Arg{$O$}\Arg{$I$}\Arg{$J$}}
-
-Cette commande permet de placer des points dans un repère quelconque
-non forcément normé ni orthogonal, défini par le triplet $(O;I;J)$.
-
-%% EXEMPLE
-\tabex{oij}
-\cbend
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Marquage des segments}
-
-Il est possible de tracer des segments en utilisant la commande
-\texttt{\bs ncline}. Pour en plus marquer les segments afin d'associer
-ceux ayant la même longueur, il existe la commande :
-
-\defcom{pstSegmentMark}{\OptArg{par}\Arg{$A$}\Arg{$B$}}
-
-Le symbole placé sur le segment est donné par le paramètre
-\param{SegmentSymbol}. Il prend comme valeur une commande utilisable en
-mode mathématique. Par défaut, sa valeur est \texttt{pstslashslash},
-et produit deux barres sur le segment. Le segment est également tracé.
-
-%% EXEMPLE
-\tabex{segmentmark}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Triangles}
-
-Figures étudiées par excellence, elles possèdent leur macro pour les tracer
-rapidement :
-
-\defcom{pstTriangle}{%
- \OptArg{par}
- $(x_A;y_A)$\Arg{$A$}$(x_B;y_B)$\Arg{$B$}$(x_C;y_C)$\Arg{$C$}}
-
-Afin de pouvoir placer avec précision les noms des points, il existe
-trois paramètres \param{PosAngleA}, \param{PosAngleB} et
-\param{PosAngleC}, qui s'associent respectivement aux n\oe uds \Argsans{$A$},
-\Argsans{$B$} et \Argsans{$C$}. Ils ont le même rôle que le paramètre
-\param{PosAngle} vu précédemment. Si un ou plusieurs de ces paramètres
-ne sont pas spécifiés la valeur de \param{PosAngle} est prise.
-
-Il existe également des paramètres pour contrôler le symbole utilisé
-pour représenter les points : \param{PointSymbolA},
-\param{PointSymbolB} et \param{PointSymbolC}, et des paramètres pour
-le nom de chacun des points : \param{PointNameA}, \param{PointNameB}
-et \param{PointNameC}. Ces deux ensembles de paramètres sont liés à
-\param{PointSymbol} et \param{PointName}. La gestion de la valeur par
-défaut suit les mêmes règles que celles vues précédemment.
-
-\tabex{triangle}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Angles}
-
-Chaque angle est déterminé par trois points. Le sommet de l'angle est
-le second. L'ordre a de l'importance en sachant que le sens direct ou
-trigonométrique est le sens inverse des aiguilles d'une
-montre. Tout d'abord, il est possible de marquer un angle droit avec
-le symbole standard :
-
-\defcom{pstRightAngle}%
- {\OptArg{par}\Arg{$A$}\Arg{$B$}\Arg{$C$}}
-
-L'unique paramètre auquel est sensible cette commande, hormis bien
-entendu ceux de contrôle du trait, est \param{RightAngleSize} qui
-permet de contrôler la longueur du carré utilisé \DefaultVal{0.28 unit}.
-Le symbole est placé sur l'angle de sommet \Argsans{$B$}.
-
-Pour les autres angles, il y a la commande :
-
-\defcom{pstMarkAngle}%
- {\OptArg{par}\Arg{$A$}\Arg{$B$}\Arg{$C$}\Arg{label}}
-
-L'étiquette définie par le paramètre \param{label} peut être tout
-texte \TeX. Elle est placée à \param{LabelSep} \DefaultVal{1~unit}
-du point \cbstart dans la direction angulaire de la bissectrice
-intérieure modifié par \param{LabelAngleOffset} \DefaultVal{0} et
-positionnée par rapport à \param{LabelRefPt} \DefaultVal{c}. \cbend
-D'autre part l'arc de cercle utilisé pour le marquage a pour rayon
-\param{MarkAngleRadius} \DefaultVal{.4~unit}. Enfin, il est posible
-de placer une flèche en début ou fin d'arc en utilisant le paramètre
-\param{arrows}.
-
-\tabex{angle}
-
-\cbstart
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Droites, demi-droites et segments}
-\cbend
-
-Rien de plus utile qu'une droite !
-
-\defcom{pstLineAB}{\OptArg{par}\Arg{$A$}\Arg{$B$}}
-
-Afin de contrôler sa longueur\footnote{Ce qui est le comble pour une
- droite !}, les deux paramètres \param{nodesepA} et
-\param{nodesepB} indiquent l'abscisse des extrémités de la droite. Une
-abscisse négative spécifie un dépassement au-delà des points, tandis
-qu'une abscisse positive indique le contraire. Si les deux valeurs
-sont identiques, on peut utiliser alors le paramètre
-\param{nodesep}. La valeur par défaut de ces paramètres est nulle.
-
-\tabex{droite}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Cercles}
-
-Un cercle peut être défini soit par son centre et un point de sa
-circonférence, soit par deux points diamètralement opposés. Il existe
-donc deux fonctions :
-
-\defcomdeux{pstCircleOA}{\OptArg{par}\Arg{$O$}\Arg{$A$}}%
- {pstCircleAB}{\OptArg{par}\Arg{$A$}\Arg{$B$}}
-
-Pour la première fonction, il est également possible d'omettre le
-second point, et de spécifier un rayon ou un diamètre avec les
-paramètres \param{Radius} et \param{Diameter} au moyen des deux fonctions
-suivantes :
-
-\defcomdeux{pstDistAB}{\OptArg{par}\Arg{$A$}\Arg{$B$}}%
- {pstDistVal}{\OptArg{par}\Arg{x}}
-
-La première permet de spécifier une distance entre deux points. Le
-paramètre \param{DistCoef} permet de donner un coefficient
-multiplicatif à appliquer sur cette distance. Afin d'être pris en
-considération, ce paramètre doit être spécifié avant la distance. La
-seconde fonction permet de spécifier directement une valeur
-numérique qui peut être un calcul en code \Postcript.
-
-Nous verrons plus loin comment tracer le cercle passant par trois
-points.
-
-\vspace{1.1\baselineskip}
-\begin{minipage}[m]{.4\linewidth}
- Avec cette extension, il devient possible de tracer :
-
- \begin{itemize}
- \item {\color{red} le cercle de centre $A$ passant par $B$ ;}
- \item \cbstart{\color{green} le cercle de centre $A$ de rayon les deux tiers de $AC$ ;}\cbend
- \item {\color{blue} le cercle de centre $A$ de rayon $BC$ ;}
- \item {\color{Sepia} le cercle de centre $B$ de rayon $AC$ ;}
- \item {\color{Aquamarine} le cercle de centre $B$ de diamètre $AC$ ;}
- \item {\color{RoyalBlue} le cercle de diamètre $BC$ ;}
- \end{itemize}
-\end{minipage}
-\hfill%
-\input{Exemples/cercle}
-
-\verbatiminput{Exemples/cercle_in}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Arcs de cercles}
-
-\defcomdeux{pstArcOAB}{\OptArg{par}\Arg{$O$}\Arg{$A$}\Arg{$B$}}%
- {pstArcnOAB}{\OptArg{par}\Arg{$O$}\Arg{$A$}\Arg{$B$}}
-
-Ces deux fonctions tracent des arcs de cercle, le centre étant donné
-par $O$, le rayon par $OA$, l'angle de départ par $A$ et celui
-d'arrivée par $B$. Enfin la première trace l'arc dans le sens direct et la
-seconde dans le sens indirect. Il n'est pas nécessaire que les deux points
-soient à égales distances de $O$.
-
-\tabex{arc}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Abscisse curviligne}
-
-Un point peut être positionné sur un cercle au moyen d'une abscisse
-curviligne.
-
-\defcom{pstCurvAbsNode}{\OptArg{par}\Arg{$O$}\Arg{$A$}\Arg{$B$}\Arg{Abs}}
-
-Le point \Argsans{$B$} est placé sur le cercle de centre \Argsans{$O$}
-passant par \Argsans{$A$}, avec l'abscisse curviligne \Argsans{Abs}.
-L'origine est en \Argsans{$A$}, et le sens est par défaut le
-sens trigonométrique (inverse des aiguilles d'une montre). Le
-paramètre \param{CurvAbsNeg} \DefaultVal{false} permet de
-modifier le sens de parcours du cercle.
-
-\tabex{abscur}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Courbe générique}
-
-Il est tout à fait possible de générer des points au moyen d'une boucle
-et de leur donner à chacun un nom générique composé d'un radical et
-d'un nombre. La commande suivante permet de relier ces points au moyen
-d'une courbe interpolée.
-
-\defcom{pstGenericCurve}{\OptArg{par}\Arg{Radical}\Arg{$n_1$}\Arg{$n_2$}}
-
-La courbe est tracée sur les points dont le nom comporte le radical
-\Argsans{Radical}, et comme suffixe un nombre allant de
-\Argsans{$n_1$} à \Argsans{$n_2$}. Pour gérer les effets de bords, les
-paramètres \param{GenCurvFirst} et \param{GenCurvLast} permettent de
-désigner explicitement le premier et le dernier point. Le paramètre
-\param{GenCurvInc} permet de spécifier l'incrément de boucle pour
-passer d'un point à un autre \DefaultVal{1}.
-
-\tabex{gencur}
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\section{Transformations}
-
-Les transformations du plan permettent de coder facilement des
-propriétés géométriques. Il est donc possible de construire les images
-de points par toutes les transformations classiques du plan.
-
-Toutes ces commandes partagent le paramètre \param{CodeFig} qui permet
-de faire apparaître les propriétés caractéristiques liées à la
-tranformation et à la construction de l'image. Par défaut, ce
-paramètre a pour valeur \param{false}, il doit être mis à \param{true}
-pour activer ce tracé optionnel.
-
-Ce tracé se fait en utilisant le style \param{CodeFigStyle}
-\DefaultVal{dashed} et suivant la couleur \param{CodeFigColor}
-\DefaultVal{cyan}.
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Symétrie centrale}
-
-\defcom{pstSymO}%
- {\OptArg{par}\Arg{$O$}\Arg{$M$}\Arg{$M'$}}
-
-Construit le point symétrique par rapport au point\Argsans{$O$}. Les
-paramètres classiques de la création de point sont utilisables comme
-dans toutes les fonctions suivantes.
-
-Elle peut servir à la construction d'un parallélogramme de centre
-connu.
-
-\tabex{symcentrale}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Symétrie orthogonale}
-
-\defcom{pstOrtSym}%
- {\OptArg{par}\Arg{$A$}\Arg{$B$}\Arg{$M$}\Arg{$M'$}}
-
-Construit le point symétrique de $M$ par rapport à la droite $(AB)$.
-
-\tabex{symorthogonale}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Rotation}
-
-\defcom{pstRotation}%
- {\OptArg{par}\Arg{centre}\Arg{M}\Arg{M'}}
-
-Construit l'image d'un point par rotation. L'angle de rotation est
-donné par le paramètre \param{RotAngle} \DefaultVal{60}. Celui-ci
-peut-être un angle orienté défini par trois points. Il faut alors
-utiliser la fonction :
-
-\defcom{pstAngleABC}{\Arg{$A$}\Arg{$B$}\Arg{$C$}}
-
-Pensez à l'utiliser pour construire un carré ou un triangle équilatéral.
-
-\tabex{rotation}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Translation}
-
-\defcom{pstTranslation}%
- {\OptArg{par}\Arg{$A$}\Arg{$B$}\Arg{$M$}\Arg{$M'$}}
-
-Construit le translaté de vecteur \Vecteur{AB} du point
-\Argsans{$M$}. À utiliser pour construire la parallèle passant
-par un point.
-
-\tabex{translation}
-
-Il est également possible d'utiliser le paramètre \param{DistCoef}
-pour modifier le vecteur de translation avec un coefficient
-multiplicatif.
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Homothétie}
-
-\defcom{pstHomO}%
- {\OptArg{par}\Arg{$O$}\Arg{$M$}\Arg{$M'$}}
-
-Construit l'image d'un point par homothétie.
-Le coefficient se spécifie avec le paramètre
-\param{HomCoef}. Incontournable pour les situations de
-\textsc{Thalès}.
-
-\tabex{homothetie}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Projection orthogonale}
-
-\defcom{pstProjection}%
- {\OptArg{par}\Arg{$A$}\Arg{$B$}\Arg{$M$}\Arg{$M'$}}
-
-Projette orthogonalement le point $M$ sur la droite
-$(AB)$. Très important pour tracer les hauteurs d'un triangle.
-
-\tabex{projection}
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\section{Objets particuliers}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Milieu}
-
-\defcom{pstMiddleAB}%
- {\OptArg{par}\Arg{$A$}\Arg{$B$}\Arg{$I$}}
-
-Construit le milieu d'un segment.
-
-\tabex{milieu}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Centre de gravité d'un triangle}
-
-\defcom{pstCGravABC}%
- {\OptArg{par}\Arg{$A$}\Arg{$B$}\Arg{$C$}\Arg{$G$}}
-
-Construit le centre de gravité d'un triangle.
-
-\tabex{grav}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Cercle circonscrit d'un triangle et son centre}
-
-\defcom{pstCircleABC}{\OptArg{par}\Arg{$A$}\Arg{$B$}\Arg{$C$}\Arg{$O$}}
-
-Cette commande permet de tracer le cercle passant par trois points et
-de positionner le centre. Le tracé du cercle est contrôlé par le
-paramètre booléen \param{DrawCirABC} \DefaultVal{true}.
-La création du point est sensible à tous les paramètres classiques
-déjà vus.
-
-\tabex%
- [@{}m{.35\linewidth}@{\hspace{.013\linewidth}}>{\small}m{.627\linewidth}@{}]%
- {ccirc}
-
-\cbstart
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Médiatrice d'un segment}
-
-\defcom{pstMediatorAB}{\OptArg{par}\Arg{$A$}\Arg{$B$}\Arg{$I$}\Arg{$M$}}
-
-La médiatrice d'un segment est la droite perpendiculaire au milieu de
-ce segement. Le segment est $[AB]$, le milieu est $I$, et $M$ est un
-point de la médiatrice, construit par une rotation de $90$\degres\ du
-point point $B$ par rapport à $I$. L'ordre des deux points est
-important, il permet de contrôler la position de la médiatrice. La
-commande crée les points $M$ et $I$. La construction est sensible aux
-paramètres suivant :
-
-\begin{itemize}
-\item \param{CodeFig}, \param{CodeFigColor} et \param{SegmentSymbol}
- pour marquer l'angle droit et le milieu ;
-\item \param{PointSymbol} et \param{PointName} pour contrôler
- l'apparence des deux nouveaux points, chacun pouvant être spécifiés
- séparément au moyen des paramètres \param{...A} et \param{...B} ;
-\item les paramètres de tracés des droites.
-\end{itemize}
-
-\tabex%
- [@{}m{.35\linewidth}@{\hspace{.013\linewidth}}>{\small}m{.627\linewidth}@{}]%
- {mediator}
-\cbend
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Bissectrices d'un angle}
-
-\defcom{pstBissectBAC}{\OptArg{par}\Arg{$B$}\Arg{$A$}\Arg{$C$}\Arg{$M$}}
-
-\defcom{pstOutBissectBAC}{\OptArg{par}\Arg{$B$}\Arg{$A$}\Arg{$C$}\Arg{$M$}}
-
-Il existe deux bissectrices pour un angle géométrique donné :
-l'intérieure et l'extérieure ; donc il y a deux commandes. L'angle est
-spécifié dans le sens trigonométrique. Les résultats de ces deux
-commandes sont la bissectrice et un point de celle-ci qui est
-positionné par une rotation du point $B$.
-
-\tabex%
- [@{}m{.35\linewidth}@{\hspace{.013\linewidth}}>{\small}m{.627\linewidth}@{}]%
- {bissec}
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\section{Intersections}
-
-Un autre moyen de définir un point est de spécifier une intersection.
-Trois types d'intersections sont gérées :
-
-\begin{itemize}
-\item l'intersection droite-droite ;
-\item l'intersection droite-cercle ;
-\item l'intersection cercle-cercle.
-\end{itemize}
-
-Une intersection peut ne pas exister : cas des droites parallèles par
-exemple. Dans ce cas, le ou les points concernés se retrouvent placés
-à l'origine. En fait, il est supposé que l'utilisation de ces
-commandes implique l'existence de l'intersection.
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Droite-droite}
-\cbstart
-\defcom{pstInterLL}%
- {\OptArg{par}\Arg{$A$}\Arg{$B$}\Arg{$C$}\Arg{$D$}\Arg{$M$}}
-\cbend
-
-Construit le point d'intersection de la droite $(AB)$ avec la droite
-$(CD)$. Option essentielle de la construction de figures du triangle,
-elle permet de positionner les points remarquables. Les paragraphes
-suivants proposent différents exemples :
-
-\begin{description}
-\item[basique]
-
- \tabex{interDD}
-
-\item[orthocentre]
-
- \tabex%
- [@{}m{.35\linewidth}@{\hspace{.013\linewidth}}>{\small}m{.627\linewidth}@{}]
- {orthocentre}
-
-\end{description}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Cercle--droite}
-
-\defcom{pstInterLC}%
- {\OptArg{par}\Arg{$A$}\Arg{$B$}\Arg{$O$}\Arg{$C$}%
- \Arg{$M_1$}\Arg{$M_2$}}
-
-Construit le ou les points d'intersection de la droite $(AB)$ avec
-le cercle de centre $O$ et de rayon $OC$. L'intersection entre un
-cercle et une droite donne en cas d'existence un ou deux points. En
-fait le cas tangent représente un point double au sens des racines
-d'un polynôme.
-
-Le cercle est spécifié avec son centre et soit un point de sa
-circonférence, soit son rayon ou diamètre spécifié au moyen des
-paramètres \param{Radius} et \param{Diameter} et modulé par le
-paramètre coefficient multiplicatif \param{DistCoef}.
-
-\tabex
- [@{}m{.4\linewidth}@{\hspace{.013\linewidth}}>{\small}m{.5777\linewidth}@{}]
- {interDC}
-
-La position des points n'étant pas spécifiée, il faudra bien regarder si
-cela correspond à votre choix. Il arrive aussi, qu'après la
-modification de la position d'un point, un dessin ne représente plus
-la même figure à cause de l'échange entre les deux points d'une
-intersection droite-cercle comme le montre l'exemple suivant sur le
-léger déplacement du point $C$ :
-
-\hfill\rule[-\baselineskip]{0pt}{5cm+2\baselineskip}
-\begin{pspicture}(5,5)\psgrid
- \pstGeonode(2,2){O}\pstGeonode(3,1){A}%
- \pstGeonode(1,2){B}\pstGeonode(1.1,4){C}%
- \pstCircleOA{O}{A}%
- \pstInterLC{B}{C}{O}{A}{D}{E}
-\end{pspicture}
-\hfill
-\begin{pspicture}(5,5)\psgrid
- \pstGeonode(2,2){O}\pstGeonode(3,1){A}%
- \pstGeonode(1,2){B}\pstGeonode(.9,4){C}%
- \pstCircleOA{O}{A}%
- \pstInterLC{C}{B}{O}{A}{D}{E}
-\end{pspicture}
-\hspace*{\fill}
-
-Ce traitement se retrouve pour les points d'intersections entre deux
-cercles.
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Cercle--cercle}
-
-\defcom{pstInterCC}%
- {\OptArg{par}\Arg{$O_1$}\Arg{$B$}\Arg{$O_2$}\Arg{$C$}%
- \Arg{$M_1$}\Arg{$M_2$}}
-
-Fonction au comportement identique à la précédente. Les paramètres
-booléens \param{CodeFigA} et \param{CodeFigB} permettent de faire
-apparaître les arcs au niveau des intersections. Par cohérence
-\param{CodeFig} permet de faire apparaître les deux arcs. Afin de
-contrôler dans quel sens vont-être ces arcs, les paramètres booléens
-\param{CodeFigAarc} et \param{CodeFigBarc} permettent de choisir dans
-le sens direct ou indirect.
-
-\tabex{interCC}
-
-Et un deuxième exemple plus complet, intégrant les spécifications de
-cercle avec des rayons et des diamètres. Il existe dans ce cas des
-paramètres \param{RadiusA}, \param{RadiusB}, \param{DiameterA} et
-\param{DiameterB}.
-\cbstart
-Toutefois, même dans le cas où le diamètre est
-spécifié, il faut donner un centre. On ne peut pas spécifier un cercle
-avec deux points diamétralement opposé.
-\cbend
-
-\begin{center}
- \rule[-.5cm]{0pt}{8cm}
- \begin{pspicture}(-3,-4)(7,3)\psgrid
- \input{Exemples/interCC_bis_in}
- \end{pspicture}
-\end{center}
-
-\verbatiminput{Exemples/interCC_bis_in}
-\pagebreak[4]
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\chapter{Galerie d'exemples}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \section{Géométrie élémentaire}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Tracé de la bissectrice}
- \nopagebreak[4]
-
-\tabex{gal_biss}
-
-\cbstart
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Angle droit allemand}
-
-En Allemagne, on utilise une autre convention pour les angles
-droits (remarque de U. \textsc{Dirr}).
-\nopagebreak[4]
-
-\tabex{german_ra}
-
-\cbend
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Droites remarquables du triangle}\nopagebreak[4]
-
-\begin{center}
-\psset{unit=2cm}
-\input{Exemples/remarq}
-\end{center}\nopagebreak[4]
-
-\verbatiminput{Exemples/remarq_in}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Cercle d'\textsc{Euler}}
-
-\begin{center}
-\psset{unit=2cm}
-\input{Exemples/euler}
-\end{center}\nopagebreak[4]
-
-\verbatiminput{Exemples/euler_in}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Orthocentre et hyperbole}
-
-L'orthocentre d'un triangle dont les points sont situés sur les
-branches de l'hyperbole ${\mathscr H} : y=a/x$ appartient à cette hyperbole.
-\nopagebreak[4]
-
-\begin{center}
-\psset{unit=.5cm}
-\input{Exemples/orthoethyper}
-\end{center}\nopagebreak[4]
-
-\verbatiminput{Exemples/orthoethyper_in}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Polygone régulier à 17 côtés}
-
-Remarquable construction due à K. F. \textsc{Gauss}.
-Il a démontré qu'il était possible de construire les polygones à
-$2^{2^p}+1$ côtés, le suivant est donc à 257 côtés !
-\nopagebreak[4]
-
-%% Polygone à 17 côtés
-\begin{center}
-\psset{unit=1.5cm, CodeFig=true, RightAngleSize=.14, CodeFigColor=red,
- CodeFigB=true, linestyle=dashed, dash=2mm 2mm}
-\begin{pspicture}(-5.5,-5.5)(5.5,6)%\psgrid
- \pstGeonode[PosAngle=-90](0,0){O}
- %% picture correct for x>0 and y<=0 for P_1!!
- \pstGeonode[PosAngle=0](5,0){P_1}
- \pstCircleOA{O}{P_1}
- \pstSymO[PointSymbol=none, CodeFig=false]{O}{P_1}{PP_1}
- \ncline[linestyle=solid]{PP_1}{P_1}
- \pstRotation[RotAngle=90, PosAngle=90]{O}{P_1}{B}
- \pstRightAngle[linestyle=solid]{B}{O}{PP_1}\ncline[linestyle=solid]{O}{B}
- \pstHomO[HomCoef=.25]{O}{B}{J}
- \ncline{J}{P_1}
- \pstBissectBAC[PointSymbol=none]{O}{J}{P_1}{PE1}
- \pstBissectBAC[PointSymbol=none]{O}{J}{PE1}{PE2}
- \pstInterLL[PosAngle=-90]{O}{P_1}{J}{PE2}{E}
- \pstRotation[PosAngle=-90, RotAngle=-45, PointSymbol=none]{J}{E}{PF1}
- \pstInterLL[PosAngle=-90]{O}{P_1}{J}{PF1}{F}
- \pstMiddleAB[PointSymbol=none]{F}{P_1}{MFP1}
- \pstCircleOA{MFP1}{P_1}
- \pstInterLC[PointSymbolB=none]{O}{B}{MFP1}{P_1}{K}{H}
- \pstCircleOA{E}{K}
- \pstInterLC{O}{P_1}{E}{K}{N_4}{N_6}
- \pstRotation[RotAngle=90, PointSymbol=none]{N_6}{E}{PP_6}{}
- \pstInterLC[PosAngleA=90, PosAngleB=-90, PointNameB=P_{13}]
- {N_6}{PP_6}{O}{P_1}{P_6}{P_13}
- \pstSegmentMark[SegmentSymbol=wedge]{N_6}{P_6}
- \pstSegmentMark[SegmentSymbol=wedge]{P_13}{N_6}
- \pstRotation[RotAngle=90, PointSymbol=none]{N_4}{E}{PP_4}{}
- \pstInterLC[PosAngleA=90, PosAngleB=-90, PointNameB=P_{15}]
- {N_4}{PP_4}{O}{P_1}{P_4}{P_15}
- \pstSegmentMark[SegmentSymbol=cup]{N_4}{P_4}
- \pstSegmentMark[SegmentSymbol=cup]{P_15}{N_4}
- \pstRightAngle[linestyle=solid]{P_1}{N_6}{P_6}
- \pstRightAngle[linestyle=solid]{P_1}{N_4}{P_4}
- \pstBissectBAC[PosAngle=90, linestyle=none]{P_4}{O}{P_6}{P_5}
- \pstOrtSym[PosAngle=-90, PointName=P_{14}]{O}{P_1}{P_5}{P_14}
- \pstInterCC[PosAngleB=90, PointSymbolA=none,
- PointNameA=none]{O}{P_1}{P_4}{P_5}{H}{P_3}
- \pstOrtSym[PosAngle=-90, SegmentSymbol=pstslash, PointName=P_{16}]
- {O}{P_1}{P_3}{P_16}
- \pstInterCC[PosAngleB=90, PointSymbolA=none]{O}{P_1}{P_3}{P_4}{H}{P_2}
- \pstOrtSym[PosAngle=-90, SegmentSymbol=pstslashslashslash,
- PointName=P_{17}]{O}{P_1}{P_2}{P_17}
- \pstInterCC[PosAngleA=90, PointSymbolB=none]{O}{P_1}{P_6}{P_5}{P_7}{H}
- \pstOrtSym[PosAngle=-90, SegmentSymbol=circ,
- PointName=P_{12}]{O}{P_1}{P_7}{P_12}
- \pstInterCC[PosAngleA=100, PointSymbolB=none]{O}{P_1}{P_7}{P_6}{P_8}{H}
- \pstOrtSym[PosAngle=-100, SegmentSymbol=times,
- PointName=P_{11}]{O}{P_1}{P_8}{P_11}
- \pstInterCC[PosAngleA=135, PointSymbolB=none]{O}{P_1}{P_8}{P_7}{P_9}{H}
- \pstOrtSym[PosAngle=-135, SegmentSymbol=equiv,
- PointName=P_{10}]{O}{P_1}{P_9}{P_10}
- \pspolygon[linecolor=green, linestyle=solid, linewidth=2\pslinewidth]
- (P_1)(P_2)(P_3)(P_4)(P_5)(P_6)(P_7)(P_8)(P_9)
- (P_10)(P_11)(P_12)(P_13)(P_14)(P_15)(P_16)(P_17)
-\end{pspicture}
-\end{center}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Tangentes de cercles}
-
-Construction des tangentes à un cercle passant par un point donné.
-\nopagebreak[4]
-
-\begin{center}
-\begin{pspicture}(15,10)%\psgrid
- \pstGeonode(5, 5){O}
- \pstCircleOA[Radius=\pstDistVal{4}]{O}{}
- \pstGeonode(14,2){M}
- \pstMiddleAB[PointSymbol=none]{O}{M}{O'}
- \pstInterCC[RadiusA=\pstDistVal{4}, DiameterB=\pstDistAB{O}{M},
- CodeFigB=true, CodeFigColor=magenta, PosAngleB=45]
- {O}{}{O'}{}{A}{B}
- \psset{linecolor=red, linewidth=1.3\pslinewidth, nodesep=-2}
- \pstLineAB{M}{A}\pstLineAB{M}{B}
-\end{pspicture}
-\end{center}
-
-Construction des tangentes à deux cercles.
-\nopagebreak[4]
-
-\begin{center}
-\begin{pspicture}(-2,0)(13,9)%\psgrid
- %% tangente à deux cercles
- \pstGeonode(9,3){O}\pstGeonode(3,6){O'}\psset{PointSymbol=none}
- \pstCircleOA[Radius=\pstDistVal{3}]
- {O}{}\pstCircleOA[Radius=\pstDistVal{1}]{O'}{}
- \pstInterLC[Radius=\pstDistVal{3}]{O}{O'}{O}{}{M}{toto}
- \pstInterLC[Radius=\pstDistVal{1}]{O}{O'}{O'}{}{M'}{toto}
- \pstRotation[RotAngle=30]{O}{M}{N}
- \pstRotation[RotAngle=30]{O'}{M'}{N'}
- \pstInterLL[PointName=\Omega]{O}{O'}{N}{N'}{Omega}
- \pstMiddleAB{O}{Omega}{I}
- \pstInterCC{I}{O}{O}{M}{A}{B}
- \psset{nodesepA=-1, nodesepB=-3, linecolor=blue, linewidth=1.3\pslinewidth}
- \pstLineAB[nodesep=-2]{A}{Omega}\pstLineAB[nodesep=-2]{B}{Omega}
- \pstRotation[RotAngle=-150]{O'}{M'}{N''}
- \pstInterLL[PointName=\Omega']{O}{O'}{N}{N''}{Omega'}
- \pstMiddleAB{O}{Omega'}{J}
- \pstInterCC{J}{O}{O}{M}{A'}{B'}
- \psset{nodesepA=-1, nodesepB=-3, linecolor=red}
- \pstLineAB{A'}{Omega'}\pstLineAB{B'}{Omega'}
-\end{pspicture}
-\end{center}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Point de \textsc{Fermat} d'un triangle}
-
-Figure de Manuel \textsc{Luque}.\nopagebreak[4]
-
-\begin{pspicture}(-7,-6)(5,5)%\psgrid
- \psset{PointSymbol=none}
- \pstTriangle[PosAngleA=-160, PosAngleB=90, PosAngleC=-25]%
- (-3,-2){B}(0,3){A}(2,-1){C}%
- \psset{RotAngle=-60}
- \pstRotation[PosAngle=-90]{B}{C}{A'}
- \pstRotation{C}{A}{B'}
- \pstRotation[PosAngle=160]{A}{B}{C'}
- \pstLineAB{A}{B'}
- \pstLineAB{C}{B'}
- \pstLineAB{B}{A'}
- \pstLineAB{C}{A'}
- \pstLineAB{B}{C'}
- \pstLineAB{A}{C'}
- \pstCircleABC[linecolor=red]{A}{B}{C'}{O_1}
- \pstCircleABC[linecolor=blue]{A}{C}{B'}{O_2}
- \pstCircleABC[linecolor=Aquamarine]{A'}{C}{B}{O_3}
- \pstInterCC[PointSymbolA=none]{O_1}{A}{O_2}{A}{E}{F}
-\end{pspicture}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Cercles ex-insrits et inscrit d'un triangle}
-
-Les centres de ces cercles sont les intersections des bissectrices
-intérieures et extérieures.
-
-%% cercles inscrit et exinscrits d'un triangle
-\bgroup\centering
-\psset{unit=1cm, dash=5mm 4mm}%, PointSymbolA=none, PointSymbolB=none}
-\begin{pspicture}(-6,-5)(11,15)%\psgrid
- \psframe(-6,-5)(11,15)
- \pstTriangle[linewidth=2\pslinewidth, PosAngleA=-75, PosAngleB=180,
- PosAngleC=45, linecolor=red]
- (4,1){A}(0,3){B}(5,5){C}
- \psset{linecolor=blue}
- \pstBissectBAC[PointSymbol=none]{C}{A}{B}{AB}
- \pstBissectBAC[PointSymbol=none]{A}{B}{C}{BB}
- \pstBissectBAC[PointSymbol=none]{B}{C}{A}{CB}
- \pstInterLL{A}{AB}{B}{BB}{I}
- \psset{linecolor=magenta, linestyle=dashed}
- \pstProjection[PosAngle=-90]{A}{B}{I}{I_C}
- \pstLineAB{I}{I_C}\pstRightAngle[linestyle=solid]{A}{I_C}{I}
- \pstProjection{A}{C}{I}{I_B}
- \pstLineAB{I}{I_B}\pstRightAngle[linestyle=solid]{C}{I_B}{I}
- \pstProjection[PosAngle=80]{C}{B}{I}{I_A}
- \pstLineAB{I}{IA}\pstRightAngle[linestyle=solid]{B}{I_A}{I}
- \pstCircleOA[linecolor=yellow, linestyle=solid]{I}{I_A}
- %% BISSECTRICES EXTÉRIEURES
- \psset{linecolor=magenta, linestyle=none}
- \pstOutBissectBAC[PointSymbol=none]{C}{A}{B}{AOB}
- \pstOutBissectBAC[PointSymbol=none]{A}{B}{C}{BOB}
- \pstOutBissectBAC[PointSymbol=none]{B}{C}{A}{COB}
- \pstInterLL[PosAngle=-90]{A}{AOB}{B}{BOB}{I_1}
- \pstInterLL{A}{AOB}{C}{COB}{I_2}
- \pstInterLL[PosAngle=90]{C}{COB}{B}{BOB}{I_3}
- \psset{linecolor=magenta, linestyle=dashed}
- \pstProjection[PosAngle=50, PointName=I_{1C}]{A}{B}{I_1}{I1C}
- \pstLineAB{I_1}{I1C}\pstRightAngle[linestyle=solid]{I_1}{I1C}{A}
- \pstProjection[PointName=I_{1B}]{A}{C}{I_1}{I1B}
- \pstLineAB{I_1}{I1B}\pstRightAngle[linestyle=solid]{A}{I1B}{I_1}
- \pstProjection[PosAngle=110, PointName=I_{1A}]{C}{B}{I_1}{I1A}
- \pstLineAB{I_1}{I1A}\pstRightAngle[linestyle=solid]{I_1}{I1A}{C}
- \pstProjection[PointName=I_{2B}]{A}{C}{I_2}{I2B}
- \pstLineAB{I_2}{I2B}\pstRightAngle[linestyle=solid]{A}{I2B}{I_2}
- \pstProjection[PosAngle=-90, PointName=I_{2C}]{A}{B}{I_2}{I2C}
- \pstLineAB{I_2}{I2C}\pstRightAngle[linestyle=solid]{I_2}{I2C}{A}
- \pstProjection[PosAngle=90, PointName=I_{2A}]{B}{C}{I_2}{I2A}
- \pstLineAB{I_2}{I2A}\pstRightAngle[linestyle=solid]{C}{I2A}{I_2}
- \pstProjection[PosAngle=130, PointName=I_{3A}]{C}{B}{I_3}{I3A}
- \pstLineAB{I_3}{I3A}\pstRightAngle[linestyle=solid]{C}{I3A}{I_3}
- \pstProjection[PosAngle=-90, PointName=I_{3C}]{A}{B}{I_3}{I3C}
- \pstLineAB{I_3}{I3C}\pstRightAngle[linestyle=solid]{A}{I3C}{I_3}
- \pstProjection[PointName=I_{3B}]{C}{A}{I_3}{I3B}
- \pstLineAB{I_3}{I3B}\pstRightAngle[linestyle=solid]{I_3}{I3B}{A}
- \psset{linecolor=yellow, linestyle=solid}
- \pstCircleOA{I_1}{I1C}
- \pstCircleOA{I_2}{I2B}
- \pstCircleOA{I_3}{I3A}
- \psset{linecolor=red, linestyle=solid, nodesepA=-1, nodesepB=-1}
- \pstLineAB{I1B}{I3B}\pstLineAB{I1A}{I2A}\pstLineAB{I2C}{I3C}
-\end{pspicture}
-\egroup
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \section{Quelques lieux de points}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Parabole}
-
-\begin{minipage}[m]{.33\linewidth}
-La parabole est l'ensemble des points situés à égale distance d'un
-point : le foyer, et d'une droite : la directrice.
-\end{minipage}
-\newcommand{\NbPt}{11}
-\input{Exemples/parabole}\nopagebreak[4]
-
-\verbatiminput{Exemples/parabole_in}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Hyperbole}
-
-\begin{minipage}[m]{.33\linewidth}
-L'hyperbole est composée des points dont la différence des distances
-avec les foyers est constant.
-\end{minipage}
-%% QQ DEFINITIONS
-%% RAPPELS : a=\Sommet, c=\PosFoyer, b^2=c^2-a^2, e=c/a
-%% pour une hyperbole -> e>1, donc c>a
-%% a=\sqrt{2}, c=2, e=\sqrt{2}
-%% M est sur H <=> MF-MF'=2a ou MF'-MF=2a
-\newcommand{\Sommet}{1.4142135623730951}\newcommand{\PosFoyer}{2}
-\newcommand{\HypAngle}{0}
-\setcounter{i}{1}\newcounter{CoefDiv}\setcounter{CoefDiv}{20}
-\newcounter{Inc}\setcounter{Inc}{2}\newcounter{n}\setcounter{n}{2}
-%% rayon des cercles successifs utilisés pour trouver les points de H
-%% on choisi \Rii=\Ri+2\Sommet (définition de l'hyperbole)
-\newcommand{\Ri}{%
- \PosFoyer\space\Sommet\space%
- sub \arabic{i}\space\arabic{CoefDiv}\space%
- div add}
-\newcommand{\Rii}{\Ri\space\Sommet\space 2 mul add}% .001 add}
-\begin{pspicture}[.5](-4,-4)(4,4)%\psgrid
- \pstGeonode[PosAngle=90](0,0){O}
- \pstGeonode(\PosFoyer;\HypAngle){F}
- \pstSymO[PosAngle=180]{O}{F}{F'}
- \pstLineAB{F}{F'}
- %% TRACÉ DES ASYMPTOTES
- %\psset{PointSymbol=none}
- \pstCircleOA{O}{F}
- %% positionnement des deux sommets de H
- \pstGeonode[PosAngle=-135](\Sommet;\HypAngle){S}
- \pstGeonode[PosAngle=-45](-\Sommet;\HypAngle){S'}
- %% l'intersection de la droite perpendiculaire à (FF')
- %% passant par S, coupe les asymptotes sur le cercle
- %% de diamètre [FF'] (cette droite est une tangente)
- \pstRotation[RotAngle=90, PointSymbol=none]{S}{O}{B}
- \pstInterLC[PosAngleA=90, PosAngleB=-90]{S}{B}{O}{F}{A_1}{A_2}
- \pstLineAB[nodesepA=-3,nodesepB=-5]{A_1}{O}
- \pstLineAB[nodesepA=-3,nodesepB=-5]{A_2}{O}
- %% cos(\Psi)=OS/OF (c-a-d \Sommet/\PosFoyer)
- %% ici \sqrt(2)/2, donc \Psi=45 => hyperbole équilatère
- \pstMarkAngle[LabelSep=.8, MarkAngleRadius=.7,
- arrows=->, LabelSep=1.1]{F}{O}{A_1}{$\Psi$}
- \ncline[linecolor=red]{A_1}{A_2}
- \pstRightAngle[RightAngleSize=.15]{A_1}{S}{O}
- \psset{PointName=none}
- \whiledo{\value{n}<8}{%
- \psset{RadiusA=\pstDistVal{\Ri},RadiusB=\pstDistVal{\Rii},PointSymbol=none}
- \pstInterCC{F}{}{F'}{}{M\arabic{n}}{P\arabic{n}}
- \pstInterCC{F'}{}{F}{}{M'\arabic{n}}{P'\arabic{n}}
- %% bcp de points au début, moins ensuite
- %% n -> numéro du point, i -> taille des cercles
- %% Inc -> incrément variable de i (2^n)
- \stepcounter{n}\addtocounter{i}{\value{Inc}}
- \addtocounter{Inc}{\value{Inc}}}%% fin de whiledo
- \psset{linecolor=blue}
- %% tracé de l'hyperbole
- \pstGenericCurve[GenCurvFirst=S]{M}{2}{7}
- \pstGenericCurve[GenCurvFirst=S]{P}{2}{7}
- \pstGenericCurve[GenCurvFirst=S']{M'}{2}{7}
- \pstGenericCurve[GenCurvFirst=S']{P'}{2}{7}
- %% pour vérif le trace paramètrique
- %\parametricplot[linecolor=black, linewidth=.25pt]{-1}{1}
- % {t dup tx@EcldDict begin sh exch ch end \Sommet\space mul exch
- % \PosFoyer\space dup mul \Sommet\space dup mul sub sqrt mul}
- %\parametricplot[linecolor=black, linewidth=.25pt]{-1}{1}
- % {t dup tx@EcldDict begin sh exch ch end neg \Sommet\space mul exch
- % \PosFoyer\space dup mul \Sommet\space dup mul sub sqrt mul}
-\end{pspicture}
-\pagebreak
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Cycloïde}
-
-La roue roule de $M$ à $A$. Les points du cercle parcourent
-des cycloïdes. L'intérêt de cet exemple est de faire coïncider les
-points de rebroussement avec des points calculés.
-\nopagebreak[4]
-
-\begin{center}
-\input{Exemples/cyclo}
-\end{center}\nopagebreak[4]
-
-\verbatiminput{Exemples/cyclo_in}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Hypocycloïdes (astroïde et deltoïde)}
-
-Une roue roule à l'intérieure d'un cercle et selon le rapport
-des rayons, on obtient une astroïde, une deltoïde et dans le cas
-générale des hypocycloïdes.\nopagebreak[4]
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% ASTROÏDE
-\input{Exemples/hypocyclo}
-%%%%%%%%%%%%%%%%%%%%
-\begin{center}
-\input{Exemples/astro}\input{Exemples/delto}
-\end{center}
-
-\verbatiminput{Exemples/hypocyclo}
-\verbatiminput{Exemples/astro_in}
-
-\cbstart
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \section{Enveloppes de droites et de cercles}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Coniques}
-
-On considère un cercle et un point $A$ extérieur à ce cercle.
-L'ensemble des médiatrices des segments formés par $A$ et les points
-du cercle forme les deux coniques selon la place de $A$ : s'il est à
-l'intérieur du cercle l'ellipse, à l'extérieur l'hyperbole. $A$ et le
-centre du cercle en sont les foyers (figure d'O. \textsc{Reboux}).
-
-\begin{center}\input{Exemples/envellipse}\end{center}
-
-\verbatiminput{Exemples/envellipse_in}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Cardioïde}
-
-La cardioïde est l'enveloppe des cercles centrés sur un cercle et
-passant par un point fixé de ce cercle.
-
-\begin{center}\input{Exemples/envcardi}\end{center}
-
-\verbatiminput{Exemples/envcardi_in}
-
-\cbend
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \section{Homothéties et fractales}\nopagebreak[4]
-
-\tabex{fracthom}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \section{Géométrie hyperbolique : triangle et ses hauteurs}
-
-Le comble pour de la géométrie euclidienne !
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% 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.
-\begin{pspicture}(-5,-5)(5,5)
- \psclip{\pscircle(0,0){4}}%\psgrid
- %\newlength{\radius}\setlength{\radius}{0cm}
- %\newcounter{rapport}\setcounter{i}{1}
- %\whiledo{\value{i}<100}{
- % \setlength{\radius}{4cm*\value{i}}
- % \setcounter{rapport}{\value{i}+1}
- % \divide\radius by \arabic{rapport}
- % \pscircle[linestyle=dotted, linecolor=gray]%
- % (0, 0){\radius}
- % \setcounter{i}{\value{i}*2}
- % }
- \pstGeonode(1, 2){M}\pstGeonode(-2,2){N}\pstGeonode(0,-2){P}%
- \psset{DrawCirABC=false, PointSymbol=none}%
- \pstGeonode(0,0){O}\pstGeonode(4,0){A}\pstCircleOA{O}{A}%
- \pstHomO[HomCoef=\pstDistAB{O}{A} 2 mul \pstDistAB{O}{M} sub
- \pstDistAB{O}{M} div]{O}{M}{M'}%
- \pstHomO[HomCoef=\pstDistAB{O}{A} 2 mul \pstDistAB{O}{P} sub
- \pstDistAB{O}{P} div]{O}{P}{P'}%
- \pstHomO[HomCoef=\pstDistAB{O}{A} 2 mul \pstDistAB{O}{N} sub
- \pstDistAB{O}{N} div]{O}{N}{N'}%
- \psset{linecolor=green, linewidth=1.5\pslinewidth}%
- \pstCircleABC{M}{N}{M'}{OmegaMN}\pstArcOAB{OmegaMN}{N}{M}%
- \pstCircleABC{M}{P}{M'}{OmegaMP}\pstArcOAB{OmegaMP}{M}{P}%
- \pstCircleABC{N}{P}{P'}{OmegaNP}\pstArcOAB{OmegaNP}{P}{N}%
- \psset{linecolor=blue}
- %% la hauteur issue de M
- \pstHomO[HomCoef=\pstDistAB{OmegaNP}{N} 2 mul \pstDistAB{OmegaNP}{M} sub
- \pstDistAB{OmegaNP}{M} div]{OmegaNP}{M}{MH'}
- \pstCircleABC{M}{M'}{MH'}{OmegaMH}\pstArcOAB{OmegaMH}{MH'}{M}
- %% la hauteur issue de N
- \pstHomO[HomCoef=\pstDistAB{OmegaMP}{M} 2 mul \pstDistAB{OmegaMP}{N} sub
- \pstDistAB{OmegaMP}{N} div]{OmegaMP}{N}{NH'}
- \pstCircleABC{N}{N'}{NH'}{OmegaNH}\pstArcOAB{OmegaNH}{N}{NH'}
- %% la hauteur issue de P
- \pstHomO[HomCoef=\pstDistAB{OmegaMN}{M} 2 mul \pstDistAB{OmegaMN}{P} sub
- \pstDistAB{OmegaMN}{P} div]{OmegaMN}{P}{PH'}
- \pstCircleABC{P}{P'}{PH'}{OmegaPH}\pstArcOAB{OmegaPH}{P}{PH'}
- \endpsclip
-\end{pspicture}
-\end{document}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \section{Une figure fractale : le flocon de \textsc{von Koch}}
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% TENTATIVE DE FLOCON DE VON KOCH
-\newcounter{nbvk}%
-%%%%%%%%%%%%%
-%% PILE LIFO%
-\newcounter{lifon}\setcounter{lifon}{1}%%
-\newcommand{\Push}[1]{%%
- \expandafter\edef\csname lifocmd\roman{lifon}\endcsname{#1}%%
- \addtocounter{lifon}{1}%%
- }%
-\newcommand{\Pop}{\csname lifocmd\roman{lifon}\endcsname}%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\newcounter{nombre}\setcounter{nombre}{0}%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\newcommand{\vonkoch}[3]{%%
- \setcounter{nbvk}{#1}%%
- \edef\Pointi{#2}\edef\Pointii{#3}%%
- \ifnum\value{nbvk}=1%
- \ncline{\Pointi}{\Pointii}%
- \else % ELSE%
- \addtocounter{nombre}{1}%
- %% position des nouveauX points%
- \pstHomO[HomCoef=1 3 div]{\Pointi}{\Pointii}{P\arabic{nombre}1}%
- \pstHomO[HomCoef=2 3 div]{\Pointi}{\Pointii}{P\arabic{nombre}2}%
- \pstRotation[RotAngle=60]{P\arabic{nombre}1}{P\arabic{nombre}2}{P\arabic{nombre}3}%
- \addtocounter{nbvk}{-1}%%
- \Push{\Pointi}\Push{\Pointii}\Push{\arabic{nombre}}\Push{\arabic{nbvk}}%
- \vonkoch{\value{nbvk}}{\Pointi}{P\arabic{nombre}1}%
- \addtocounter{lifon}{-1}\edef\nbvklocal{\Pop}%
- \addtocounter{lifon}{-1}\edef\nombrelocal{\Pop}%
- \addtocounter{lifon}{-1}\edef\Pointii{\Pop}%
- \addtocounter{lifon}{-1}\edef\Pointi{\Pop}%
- \addtocounter{lifon}{4}%
- \vonkoch{\nbvklocal}{P\nombrelocal1}{P\nombrelocal3}%
- \addtocounter{lifon}{-1}\edef\nbvklocal{\Pop}%
- \addtocounter{lifon}{-1}\edef\nombrelocal{\Pop}%
- \addtocounter{lifon}{-1}\edef\Pointii{\Pop}%
- \addtocounter{lifon}{-1}\edef\Pointi{\Pop}%
- \addtocounter{lifon}{4}%
- \vonkoch{\nbvklocal}{P\nombrelocal3}{P\nombrelocal2}%
- \addtocounter{lifon}{-1}\edef\nbvklocal{\Pop}%
- \addtocounter{lifon}{-1}\edef\nombrelocal{\Pop}%
- \addtocounter{lifon}{-1}\edef\Pointii{\Pop}%
- \addtocounter{lifon}{-1}\edef\Pointi{\Pop}%
- \addtocounter{lifon}{4}%
- \vonkoch{\nbvklocal}{P\nombrelocal2}{\Pointii}%
- \addtocounter{lifon}{-4}%
- \fi%
-}%
-\psset{unit=2.5cm}%
-\begin{pspicture}(-2,-2)(2,2)%
- \psset{PointSymbol=none}
- \pstGeonode(-2,-2){A}\pstGeonode(2,2){B}%
- \pstRotation[RotAngle=60]{B}{A}{C}%
- \vonkoch{5}{A}{B}\setcounter{nombre}{0}%%%
- \vonkoch{4}{B}{C}\setcounter{nombre}{0}%%%
- \vonkoch{4}{C}{A}%%
-\end{pspicture}%
-%
-\end{document}%
-
-\begin{pspicture*}(-4,-5)(4,5)%\psgrid
- \pstGeonode[PosAngle=-135](0,0){O}
- \pstGeonode[PosAngle=-90](1,0.5){I}
- \pstGeonode[PosAngle=-180](0.5,2){J}
- \pstLineAB[nodesep=100]{O}{I}
- \pstLineAB[nodesep=100]{O}{J}
- \multips(-5,-2.5)(1,0.5){11}{\psline(0,-.15)(0,.15)}%
- \multips(-5,-2.5)(1,0.5){11}{\psline[linestyle=dotted](-10,-40)(10,40)}%
- \multips(-2,-8)(0.5,2){9}{\psline(-.15,0)(.15,0)}%
- \multips(-2,-8)(0.5,2){9}{\psline[linestyle=dotted](-10,-5)(10,5)}%
- %% huit points
- \psset{PointSymbol=x}
- \pstOIJGeonode(1,2){A}{O}{I}{J}
- \pstOIJGeonode(-2,1){B}{O}{I}{J}
- \pstOIJGeonode(-1,-1.5){C}{O}{I}{J}
- \pstOIJGeonode(2,-1){D}{O}{I}{J}
-\end{pspicture*}
-%
diff --git a/Master/texmf-dist/doc/latex/euclide/euclide_english.dvi b/Master/texmf-dist/doc/latex/euclide/euclide_english.dvi
deleted file mode 100644
index 0a543ac8849..00000000000
--- a/Master/texmf-dist/doc/latex/euclide/euclide_english.dvi
+++ /dev/null
Binary files differ
diff --git a/Master/texmf-dist/doc/latex/euclide/euclide_english.tex b/Master/texmf-dist/doc/latex/euclide/euclide_english.tex
deleted file mode 100644
index 4c0f2a98b99..00000000000
--- a/Master/texmf-dist/doc/latex/euclide/euclide_english.tex
+++ /dev/null
@@ -1,1177 +0,0 @@
-\documentclass[12pt, draft]{article}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\usepackage[T1]{fontenc}
-\usepackage[latin1]{inputenc}
-\usepackage[a4paper]{geometry}
-\usepackage[usenames]{pstcol}
-\usepackage{pst-eucl}
-\usepackage{pst-plot}
-\usepackage{multido}
-\usepackage{ifthen}
-\usepackage{calc}
-\usepackage{array}
-\usepackage{moreverb}
-\usepackage{multicol}
-\usepackage{mathrsfs}
-\usepackage[dvips]{changebar}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% QQ DEFINITIONS
-\newcommand{\Vecteur}[1]{\ensuremath{\overrightarrow{#1}}}%
-\newcommand{\Angle}[1]{\ensuremath{\widehat{#1}}}%
-\makeatletter
-\newcommand{\Arg}[1]{{\normalfont$\{$\@Arg{#1}$\}$}}%
-\newcommand{\Argsans}[1]{\@Arg{#1}}%
-\newcommand{\OptArg}[1]{{\normalfont[{\@Arg{#1}}]}}%
-\newcommand{\@Arg}[1]%
- {$\protect\langle${\itshape\mdseries\rmfamily#1}$\protect\rangle$}%
-\makeatother
-%% le backslash \
-\newcommand{\bs}{\symbol{'134}}%
-\newcommand{\defcom}[2]%
- {\begin{trivlist}\item\fbox{\texttt{\upshape\bs#1}#2}\end{trivlist}}%
-\newcommand{\defcomdeux}[4]%
- {%
- \begin{center}%
- \begin{minipage}[t]{.45\linewidth}%
- \begin{trivlist}\item\fbox{\texttt{\upshape\bs#1}#2}\end{trivlist}%
- \end{minipage}%
- \hfill%
- \begin{minipage}[t]{.45\linewidth}%
- \begin{trivlist}\item\fbox{\texttt{\upshape\bs#3}#4}\end{trivlist}%
- \end{minipage}
- \end{center}}%
-\newenvironment{tabexemple}[1]%
- [@{}m{.3\linewidth}@{\hspace{.013\linewidth}}>{\small}m{.677\linewidth}@{}]%
- {\vspace{1em}\noindent\small\begin{center}%
- \noindent\begin{tabular}{#1}}%
- {\mbox{}\vspace{-1.5em}\end{tabular}\end{center}}%
-\newcommand{\tabex}[2]%
- [@{}m{.3\linewidth}@{\hspace{.013\linewidth}}>{\small}m{.677\linewidth}@{}]%
-{%
- \begin{tabexemple}[#1]%
- \input{Exemples/#2}&\verbatiminput{Exemples/#2_in}%
- \end{tabexemple}%
-}%
-\newcommand{\param}[1]{\texttt{#1}}
-\newcommand{\com}[1]{\texttt{\bs #1}}
-\newcommand{\DefaultVal}[1]{(\texttt{#1} by default)}
-\newcommand{\PStricks}{\texttt{PStricks}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\title{The \texttt{pst-euclide.sty} Package}
-\author{Version $0.\beta.5$\\Dominique Rodriguez}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\geometry{bottom=1cm, left=1cm, right=1cm}
-\psset{subgriddiv=0,griddots=5}
-%%%%%%%%%%%%%%%%%%%%
-%%%%%%%%%%%%%%%%%%%%
-%%%%%%%%%%%%%%%%%%%%
-\newcounter{i}
-%%%%%%%%%%%%%%%%%%%%
-%%%%%%%%%%%%%%%%%%%%
-%%%%%%%%%%%%%%%%%%%%
-\begin{document}
-\renewcommand{\abstractname}{WARNING}
-\maketitle
-\cbstart
-\begin{abstract}
- This is a $\beta$-version, it is still in development, the macros
- name can and will change without upward-compatibility.
-\end{abstract}
-\cbend
-\begin{multicols}{2}
-\tableofcontents{}
-\end{multicols}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\section{Special specifications}
-
-\cbstart
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \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.
-\cbend
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\section{Basic Objects}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Points}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsubsection{default axes}
-
-\defcom{pstGeonode}{\OptArg{par}\Arg{$A$}}
-
-This command defines a geometrical point associated with a node. This
-point has a node name \Argsans{$A$} which defines the default label put on
-the picture. This label is managed by default in mathematical mode,
-the boolean parameter \param{PtNameMath} can modify this behavior and
-let manage the label in normal mode. It is put at a distance of
-\texttt{1em} 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}, 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 neither the point nor its label will 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}
-
-% 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{->}{ici}{B_1}
-
-% There is a bug linked to the definition of a point, so a mandatory
-% \verb$%$ symbol must be put at the end of each such command. If it is
-% forgotten, a shift appear on the picture as it can be seen on the
-% following diagram:
-
-% \begin{center}
-% \begin{pspicture}(-2,-2)(2,2)\psgrid
-% \pstGeonode(0,0){A}{A}
-% \pstGeonode[PosAngle=-90](1,2){B1}{B_1}
-% \pstGeonode[PointSymbol=pstSmallCircle,
-% linecolor=red](-2,1){B2}{B_2}%
-% \end{pspicture}
-% \end{center}
-
-\cbstart
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsubsection{User defined axes}
-
-\defcom{pstOIJGeonode}{\OptArg{par}$(x,y)$\Arg{$A$}\Arg{$O$}\Arg{$I$}\Arg{$J$}}
-
-This command allows the placement of points in any landmark(?) defined
-by the three points $(O;I;J)$.
-
-%% EXAMPLE
-\tabex{oij}
-\cbend
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Segment mark}
-
-A segment can be drawn using the \texttt{\bs ncline} command. However,
-for marking a segment there is the following command:
-
-\defcom{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{pstSlashsSlash},
-which produced two slashes on the segment. The segment is drawn.
-
-%% EXAMPLE
-\tabex{segmentmark}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Triangles}
-
-The more classical figure, it has its own macro for a quick definition:
-
-\defcom{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.
-
-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{pstRightAngle}%
- {\OptArg{par}\Arg{$A$}\Arg{$B$}\Arg{$C$}}
-
-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{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
-\cbstart the bisector of the angle modified by
-\param{LabelAngleOffset}\DefaultVal{0} and positioned using
-\param{LabelRefPt} \DefaultVal{c}. \cbend 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}.
-
-\tabex{angle}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Lines, half-lines and segments}
-
-The classical line!
-
-\defcom{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 :
-
-\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 :
-
-\defcomdeux{pstDistAB}{\OptArg{par}\Arg{$A$}\Arg{$B$}}%
- {pstDistVal}{\OptArg{par}\Arg{x}}
-
-The first specifies a distance between two points. The parameter
-\param{DistCoef} can be used to specify a coefficient to reduce or
-enlarge this distance. To be taken into account this last parameter
-must be specified before the distance. The second macro can be used to
-specify an explicit numeric value.
-
-We will see later how to draw the circle crossing three points.
-
-\vspace{1.1\baselineskip}
-\begin{minipage}[m]{.45\linewidth}
- With this package, it becomes possible to draw:
-
- \begin{itemize}
- \item {\color{red} the circle of center $A$ crossing $B$ ;}
- \item {\color{green} the circle of center $A$ whose radius is $AC$ ;}
- \item {\color{blue} the circle of center $A$ whose radius is $BC$ ;}
- \item {\color{Sepia} the circle of center $B$ whose radius is $AC$ ;}
- \item {\color{Aquamarine} the circle of center $B$ of diameter $AC$ ;}
- \item {\color{RoyalBlue} the circle whose diameter is $BC$ ;}
- \end{itemize}
-\end{minipage}
-%
-\input{Exemples/cercle}
-
-\verbatiminput{Exemples/cercle_in}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Circle arcs}
-
-\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{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.
-
-\tabex{abscur}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Généric curve}
-
-It is possible to generate a set of point 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{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 transformation are the ideal tools to construct
-geometric figures. All the classical transformation are accessible
-with the following macros.
-
-They share the parameter \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}.
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Central symmetry}
-
-\defcom{pstSymO}%
- {\OptArg{par}\Arg{$O$}\Arg{$M$}\Arg{$M'$}}
-
-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{pstOrtSym}%
- {\OptArg{par}\Arg{$A$}\Arg{$B$}\Arg{$M$}\Arg{$M'$}}
-
-Draw the symmetric point in relation to line $(AB)$.
-
-\tabex{symorthogonale}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Rotation}
-
-\defcom{pstRotation}%
- {\OptArg{par}\Arg{$O$}\Arg{$M$}\Arg{$M'$}}
-
-Draw the image of $M$ 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{pstAngleABC}{\Arg{$A$}\Arg{$B$}\Arg{$C$}}
-
-Never forget to use the rotation for a square or a equilateral
-triangle.
-
-\tabex{rotation}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Translation}
-
-\defcom{pstTranslation}%
- {\OptArg{par}\Arg{$A$}\Arg{$B$}\Arg{$M$}\Arg{$M'$}}
-
-Draw the translated of vector \Vecteur{AB} of the point
-\Argsans{$M$}. Useful for drawing a parallel line.
-
-\tabex{translation}
-
-The parameter \param{DistCoef} can be used as a multiplicand
-coefficient to modify the translation vector.
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Homothetie}
-
-\defcom{pstHomO}%
- {\OptArg{par}\Arg{$O$}\Arg{$M$}\Arg{$M'$}}
-
-Draw $M'$ the image of $M$ by the homotethy of center $O$ and
-coefficient specified with the parameter \param{HomCoef}.
-
-\tabex{homothetie}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Orthogonal projection}
-
-\defcom{pstProjection}%
- {\OptArg{par}\Arg{$A$}\Arg{$B$}\Arg{$M$}\Arg{$M'$}}
-
-Project orthogonally the point $M$ on the line
-$(AB)$. Useful for the altitude of a triangle.
-
-\tabex{projection}
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\section{Special object}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Midpoint}
-
-\defcom{pstMiddleAB}%
- {\OptArg{par}\Arg{$A$}\Arg{$B$}\Arg{$I$}}
-
-Draw the midpoint $I$ of segment $[AB]$.
-
-\tabex{milieu}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Triangle center of gravity}
-
-\defcom{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{pstCircleABC}{\OptArg{par}\Arg{$A$}\Arg{$B$}\Arg{$C$}\Arg{$O$}}
-
-It's obvious.
-
-\tabex%
- [@{}m{.35\linewidth}@{\hspace{.013\linewidth}}>{\small}m{.627\linewidth}@{}]%
- {ccirc}
-
-\cbstart
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Perpendicular bisector of a segment}
-
-\defcom{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}
-\cbend
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Bissectors of angles}
-
-\defcom{pstBissectBAC}{\OptArg{par}\Arg{$B$}\Arg{$A$}\Arg{$C$}\Arg{$N$}}
-
-\defcom{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. Three intersection types are
-managed:
-
-\begin{itemize}
-\item line-line;
-\item line-circle;
-\item circle-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{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{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}.
-
-\tabex
- [@{}m{.4\linewidth}@{\hspace{.013\linewidth}}>{\small}m{.5777\linewidth}@{}]
- {interDC}
-
-In the case of a two points intersection, their position is not
-specified, the user will have to check the result. It can arise that
-after a modification the name of points can be swapped leading to a
-wrong figure as shown in the following example:
-
-\hfill\rule[-\baselineskip]{0pt}{5cm+2\baselineskip}
-\begin{pspicture}(5,5)\psgrid
- \pstGeonode(2,2){O}\pstGeonode(3,1){A}%
- \pstGeonode(1,2){B}\pstGeonode(1.1,4){C}%
- \pstCircleOA{O}{A}%
- \pstInterLC{B}{C}{O}{A}{D}{E}
-\end{pspicture}
-\hfill
-\begin{pspicture}(5,5)\psgrid
- \pstGeonode(2,2){O}\pstGeonode(3,1){A}%
- \pstGeonode(1,2){B}\pstGeonode(.9,4){C}%
- \pstCircleOA{O}{A}%
- \pstInterLC{B}{C}{O}{A}{D}{E}
-\end{pspicture}
-\hspace*{\fill}
-
-This management is the same for the circle-circle intersection.
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Circle--Circle}
-
-\defcom{pstInterCC}%
- {\OptArg{par}\Arg{$O_1$}\Arg{$B$}\Arg{$O_2$}\Arg{$C$}%
- \Arg{$M_1$}\Arg{$M_2$}}
-
-This function is similar to the last one. The boolean parameters
-\param{CodeFigA} et \param{CodeFigB} allow the drawing of the arcs
-at the intersection. In order to get a coherence \param{CodeFig} allow
-the drawing of both arcs. The boolean parameters \param{CodeFigAarc} and
-\param{CodeFigBarc} specified the direction of these optional arcs:
-trigonometric (by default) or clockwise. Here is a first example.
-
-\tabex{interCC}
-
-And a more complete one, which includes the special circle
-specification using radius and diameter. For such specifications it
-exists the parameters \param{RadiusA}, \param{RadiusB},
-\param{DiameterA} and \param{DiameterB}.
-
-\begin{center}
- \rule[-.5cm]{0pt}{8cm}
- \begin{pspicture}(-3,-4)(7,3)\psgrid
- \input{Exemples/interCC_bis_in}
- \end{pspicture}
-\end{center}
-
-\verbatiminput{Exemples/interCC_bis_in}
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\section{Examples gallery}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Basic geometry}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsubsection{Drawing of the bissector}
- \nopagebreak[4]
-
-\tabex{gal_biss}
-
-
-\cbstart
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsubsection{German right angle}
-
-In Germany, there is another convention for the right angle (remark
-of U. Dirr).
-\nopagebreak[4]
-
-\tabex{german_ra}
-
-\cbend
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsubsection{Triangle lines}
-
-\begin{center}
-\psset{unit=2cm}
-\input{Exemples/remarq}
-\end{center}\nopagebreak[4]
-
-\verbatiminput{Exemples/remarq_in}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsubsection{Euler circle}
-
-\begin{center}
-\psset{unit=2cm}
-\input{Exemples/euler}
-\end{center}\nopagebreak[4]
-
-\verbatiminput{Exemples/euler_in}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsubsection{Orthocenter and hyperbola}
-
-The orthocenter of a triangle whose points are on the branches of the
-hyperbola ${\mathscr H} : y=a/x$ belong to this hyperbola.
-\nopagebreak[4]
-
-\begin{center}
-\psset{unit=.5cm}
-\input{Exemples/orthoethyper}
-\end{center}\nopagebreak[4]
-
-\verbatiminput{Exemples/orthoethyper_in}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsubsection{17 sides regular polygon}
-
-Striking picture created by K. F. Gauss.
-he also demonstrates that it is possible to build the polygons which
-have $2^{2^p}+1$ sides, the following one has 257 sides!
-\nopagebreak[4]
-
-%% Polygone à 17 côtés
-\bgroup\centering
-\psset{unit=1.5cm, CodeFig=true, RightAngleSize=.14, CodeFigColor=red,
- CodeFigB=true, linestyle=dashed, dash=2mm 2mm}
-\begin{pspicture}(-5.5,-5.5)(5.5,6)%\psgrid
- \pstGeonode[PosAngle=-90](0,0){O}%
- %% picture correct for x>0 and y<=0 for P_1!!
- \pstGeonode[PosAngle=0](5,0){P_1}%
- \pstCircleOA{O}{P_1}%
- \pstSymO[PointSymbol=none, CodeFig=false]{O}{P_1}{PP_1}%
- \ncline[linestyle=solid]{PP_1}{P_1}%
- \pstRotation[RotAngle=90, PosAngle=90]{O}{P_1}{B}%
- \pstRightAngle{B}{O}{PP_1}\ncline[linestyle=solid]{O}{B}%
- \pstHomO[HomCoef=.25]{O}{B}{J}{J}%
- \ncline{J}{P_1}%
- \pstBissectBAC[PointSymbol=none]{O}{J}{P_1}{PE1}%
- \pstBissectBAC[PointSymbol=none]{O}{J}{PE1}{PE2}%
- \pstInterLL[PosAngle=-90]{O}{P_1}{J}{PE2}{E}%
- \pstRotation[PosAngle=-90, RotAngle=-45, PointSymbol=none]{J}{E}{PF1}%
- \pstInterLL[PosAngle=-90]{O}{P_1}{J}{PF1}{F}%
- \pstMiddleAB[PointSymbol=none]{F}{P_1}{MFP1}
- \pstCircleOA{MFP1}{P_1}%
- \pstInterLC[PointSymbolB=none]{O}{B}{MFP1}{P_1}{K}{H}%
- \pstCircleOA{E}{K}%
- \pstInterLC{O}{P_1}{E}{K}{N_4}{N_6}%
- \pstRotation[RotAngle=90, PointSymbol=none]{N_6}{E}{PP_6}{}%
- \pstInterLC[PosAngleA=90, PosAngleB=-90, PointNameB=P_{13}]%
- {N_6}{PP_6}{O}{P_1}{P_6}{P_13}%
- \pstSegmentMark[SegmentSymbol=wedge]{N_6}{P_6}%
- \pstSegmentMark[SegmentSymbol=wedge]{P_13}{N_6}%
- \pstRotation[RotAngle=90, PointSymbol=none]{N_4}{E}{PP_4}{}%
- \pstInterLC[PosAngleA=90, PosAngleB=-90, PointNameB=P_{15}]%
- {N_4}{PP_4}{O}{P_1}{P_4}{P_15}%
- \pstSegmentMark[SegmentSymbol=cup]{N_4}{P_4}%
- \pstSegmentMark[SegmentSymbol=cup]{P_15}{N_4}%
- \pstRightAngle{P_1}{N_6}{P_6}\pstRightAngle{P_1}{N_4}{P_4}%
- \pstBissectBAC[PosAngle=90, linestyle=none]{P_4}{O}{P_6}{P_5}%
- \pstOrtSym[PosAngle=-90, PointName=P_{14}]{O}{P_1}{P_5}{P_14}%
- \pstInterCC[PosAngleB=90, PointSymbolA=none,
- PointNameA=none]{O}{P_1}{P_4}{P_5}{H}{P_3}%
- \pstOrtSym[PosAngle=-90, SegmentSymbol=pstslash, PointName=P_{16}]%
- {O}{P_1}{P_3}{P_16}%
- \pstInterCC[PosAngleB=90, PointSymbolA=none]{O}{P_1}{P_3}{P_4}{H}{P_2}%
- \pstOrtSym[PosAngle=-90, SegmentSymbol=pstslashslashslash,
- PointName=P_{17}]{O}{P_1}{P_2}{P_17}%
- \pstInterCC[PosAngleA=90, PointSymbolB=none]{O}{P_1}{P_6}{P_5}{P_7}{H}
- \pstOrtSym[PosAngle=-90, SegmentSymbol=circ,
- PointName=P_{12}]{O}{P_1}{P_7}{P_12}%
- \pstInterCC[PosAngleA=100, PointSymbolB=none]{O}{P_1}{P_7}{P_6}{P_8}{H}
- \pstOrtSym[PosAngle=-100, SegmentSymbol=times,
- PointName=P_{11}]{O}{P_1}{P_8}{P_11}%
- \pstInterCC[PosAngleA=135, PointSymbolB=none]{O}{P_1}{P_8}{P_7}{P_9}{H}
- \pstOrtSym[PosAngle=-135, SegmentSymbol=equiv,
- PointName=P_{10}]{O}{P_1}{P_9}{P_10}%
- \psline[linecolor=green, linestyle=solid]%
- (P_1)(P_2)(P_3)(P_4)(P_5)(P_6)(P_7)(P_8)(P_9)%
- (P_10)(P_11)(P_12)(P_13)(P_14)(P_15)(P_16)(P_17)(P_1)%
-\end{pspicture}
-\egroup
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsubsection{Circles tangents}
-
-The drawing of the circle tangents which crosses a given point.
-\nopagebreak[4]
-
-\begin{pspicture}(15,9)%\psgrid
- %%% tangente à un cercle passant par un point
- \pstGeonode(5, 5){O}%
- \pstCircleOA[Radius=\pstDistVal{4}]{O}{}%
- \pstGeonode(14,2){M}%
- \pstMiddleAB[PointSymbol=none]{O}{M}{O'}
- \pstInterCC[RadiusA=\pstDistVal{4}, DiameterB=\pstDistAB{O}{M}]%
- {O}{}{O'}{}{A}{B}%
- \psset{linecolor=red, linewidth=1.3pt, nodesep=-2}
- \pstLineAB{M}{A}\pstLineAB{M}{B}
-\end{pspicture}
-
-The drawing of the common tangent of two circles.
-\nopagebreak[4]
-
-\begin{pspicture}(-2,0)(13,9)%\psgrid
- %% tangente à deux cercles
- \pstGeonode(9,3){O}\pstGeonode(3,6){O'}\psset{PointSymbol=none}%
- \pstCircleOA[Radius=\pstDistVal{3}]{O}{}\pstCircleOA[Radius=\pstDistVal{1}]{O'}{}
- \pstInterLC[Radius=\pstDistVal{3}]{O}{O'}{O}{}{M}{toto}
- \pstInterLC[Radius=\pstDistVal{1}]{O}{O'}{O'}{}{M'}{toto}
- \pstRotation[RotAngle=30]{O}{M}{N}%
- \pstRotation[RotAngle=30]{O'}{M'}{N'}%
- \pstInterLL[PointName=\Omega]{O}{O'}{N}{N'}{Omega}
- \pstMiddleAB[PointSymbol=none]{O}{Omega}{I}
- \pstInterCC{I}{O}{O}{M}{A}{B}
- \psset{nodesepA=-1, nodesepB=-3, linecolor=blue, linewidth=1.3pt}
- \pstLineAB[nodesep=-2]{A}{Omega}\pstLineAB[nodesep=-2]{B}{Omega}
- \pstRotation[RotAngle=-150]{O'}{M'}{N''}%
- \pstInterLL[PointName=\Omega']{O}{O'}{N}{N''}{Omega'}
- \pstMiddleAB[PointSymbol=none]{O}{Omega'}{J}
- \pstInterCC{J}{O}{O}{M}{A'}{B'}
- \psset{nodesepA=-1, nodesepB=-3, linecolor=red}
- \pstLineAB{A'}{Omega'}\pstLineAB{B'}{Omega'}
-\end{pspicture}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsubsection{Fermat's point}
-
-Drawing of Manuel Luque.\nopagebreak[4]
-
-\begin{pspicture}(-7,-6)(5,5)%\psgrid
- \psset{PointSymbol=none}
- \pstTriangle[PosAngleA=-160, PosAngleB=90, PosAngleC=-25]%
- (-3,-2){B}(0,3){A}(2,-1){C}%
- \psset{RotAngle=-60}
- \pstRotation[PosAngle=-90]{B}{C}{A'}
- \pstRotation{C}{A}{B'}
- \pstRotation[PosAngle=160]{A}{B}{C'}
- \pstLineAB{A}{B'}
- \pstLineAB{C}{B'}
- \pstLineAB{B}{A'}
- \pstLineAB{C}{A'}
- \pstLineAB{B}{C'}
- \pstLineAB{A}{C'}
- \pstCircleABC[linecolor=red]{A}{B}{C'}{O_1}
- \pstCircleABC[linecolor=blue]{A}{C}{B'}{O_2}
- \pstCircleABC[linecolor=Aquamarine]{A'}{C}{B}{O_3}
- \pstInterCC[PointSymbolA=none]{O_1}{A}{O_2}{A}{E}{F}
-\end{pspicture}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsubsection{Escribed and inscribed circles of a triangle}
-
-%% cercles inscrit et exinscrits d'un triangle
-\bgroup\centering
-\psset{unit=1cm, dash=5mm 4mm, PointSymbolA=none, PointSymbolB=none}
-\begin{pspicture}(-6,-5)(11,15)%\psgrid
- \psframe(-6,-5)(11,15)
- \pstTriangle[linewidth=2pt, PosAngleA=-75, PosAngleB=180,
- PosAngleC=45, linecolor=red]%
- (4,1){A}(0,3){B}(5,5){C}%
- \psset{linecolor=blue}
- \pstBissectBAC[PointSymbol=none]{C}{A}{B}{AB}
- \pstBissectBAC[PointSymbol=none]{A}{B}{C}{BB}
- \pstBissectBAC[PointSymbol=none]{B}{C}{A}{CB}
- \pstInterLL{A}{AB}{B}{BB}{I}
- \psset{linecolor=magenta, linestyle=dashed}
- \pstProjection[PosAngle=-90]{A}{B}{I}{I_C}
- \pstLineAB{I}{I_C}\pstRightAngle[linestyle=solid]{A}{I_C}{I}
- \pstProjection{A}{C}{I}{I_B}
- \pstLineAB{I}{I_B}\pstRightAngle[linestyle=solid]{C}{I_B}{I}
- \pstProjection[PosAngle=80]{C}{B}{I}{I_A}
- \pstLineAB{I}{IA}\pstRightAngle[linestyle=solid]{B}{I_A}{I}
- \pstCircleOA[linecolor=yellow, linestyle=solid]{I}{I_A}
- %% BISSECTRICES EXTÉRIEURES
- \psset{linecolor=magenta, linestyle=none}
- \pstOutBissectBAC[PointSymbol=none]{C}{A}{B}{AOB}
- \pstOutBissectBAC[PointSymbol=none]{A}{B}{C}{BOB}
- \pstOutBissectBAC[PointSymbol=none]{B}{C}{A}{COB}
- \pstInterLL[PosAngle=-90]{A}{AOB}{B}{BOB}{I_1}
- \pstInterLL{A}{AOB}{C}{COB}{I_2}
- \pstInterLL[PosAngle=90]{C}{COB}{B}{BOB}{I_3}
- \psset{linecolor=magenta, linestyle=dashed}
- \pstProjection[PosAngle=50, PointName=I_{1C}]{A}{B}{I_1}{I1C}
- \pstLineAB{I_1}{I1C}\pstRightAngle[linestyle=solid]{I_1}{I1C}{A}
- \pstProjection[PointName=I_{1B}]{A}{C}{I_1}{I1B}
- \pstLineAB{I_1}{I1B}\pstRightAngle[linestyle=solid]{A}{I1B}{I_1}
- \pstProjection[PosAngle=110, PointName=I_{1A}]{C}{B}{I_1}{I1A}
- \pstLineAB{I_1}{I1A}\pstRightAngle[linestyle=solid]{I_1}{I1A}{C}
- \pstProjection[PointName=I_{2B}]{A}{C}{I_2}{I2B}
- \pstLineAB{I_2}{I2B}\pstRightAngle[linestyle=solid]{A}{I2B}{I_2}
- \pstProjection[PosAngle=-90, PointName=I_{2C}]{A}{B}{I_2}{I2C}
- \pstLineAB{I_2}{I2C}\pstRightAngle[linestyle=solid]{I_2}{I2C}{A}
- \pstProjection[PosAngle=90, PointName=I_{2A}]{B}{C}{I_2}{I2A}
- \pstLineAB{I_2}{I2A}\pstRightAngle[linestyle=solid]{C}{I2A}{I_2}
- \pstProjection[PosAngle=130, PointName=I_{3A}]{C}{B}{I_3}{I3A}
- \pstLineAB{I_3}{I3A}\pstRightAngle[linestyle=solid]{C}{I3A}{I_3}
- \pstProjection[PosAngle=-90, PointName=I_{3C}]{A}{B}{I_3}{I3C}
- \pstLineAB{I_3}{I3C}\pstRightAngle[linestyle=solid]{A}{I3C}{I_3}
- \pstProjection[PointName=I_{3B}]{C}{A}{I_3}{I3B}
- \pstLineAB{I_3}{I3B}\pstRightAngle[linestyle=solid]{I_3}{I3B}{A}
- \psset{linecolor=yellow, linestyle=solid}
- \pstCircleOA{I_1}{I1C}
- \pstCircleOA{I_2}{I2B}
- \pstCircleOA{I_3}{I3A}
- \psset{linecolor=red, linestyle=solid, nodesepA=-1, nodesepB=-1}
- \pstLineAB{I1B}{I3B}\pstLineAB{I1A}{I2A}\pstLineAB{I2C}{I3C}
-\end{pspicture}
-\egroup
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Some locus points}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsubsection{Parabola}
-
-\begin{minipage}[m]{.33\linewidth}
-The parabola is the set of points which is at the same distance
-between a point and a line.
-\end{minipage}
-\newcommand{\NbPt}{11}
-\input{Exemples/parabole}\nopagebreak[4]
-
-\verbatiminput{Exemples/parabole_in}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsubsection{Hyperbola}
-
-\begin{minipage}[m]{.33\linewidth}
-The hyperbola is the set of points whose difference between their
-distance of two points (the focus) is constant.
-\end{minipage}
-%% QQ DEFINITIONS
-\newcommand{\Sommet}{1.4142135623}\newcommand{\PosFoyer}{2}
-\newcommand{\HypAngle}{0}
-\setcounter{i}{0}\newcounter{CoefDiv}\setcounter{CoefDiv}{20}
-\newcounter{Inc}\setcounter{Inc}{1}\newcounter{n}\setcounter{n}{1}
-\newcommand{\Ri}{%
- \PosFoyer\space\Sommet\space%
- sub \arabic{i}\space\arabic{CoefDiv}\space%
- div add}
-\newcommand{\Rii}{\Ri\space \Sommet\space 2 mul add .001 add}
-\begin{pspicture}[.5](-4,-4)(4,4)%\psgrid
- \pstGeonode[PosAngle=90](0,0){O}%
- \pstGeonode(\PosFoyer;\HypAngle){F}%
- \pstSymO[PosAngle=180]{O}{F}{F'}%
- \pstLineAB{F}{F'}
- %% TRACÉ DES ASYMPTOTES
- %\psset{PointSymbol=none}
- \pstCircleOA{O}{F}
- \pstGeonode[PosAngle=-135](\Sommet;\HypAngle){S}
- \pstRotation[RotAngle=90, PointSymbol=none]{S}{O}{B}
- \pstInterLC[PosAngleA=90, PosAngleB=-90]{S}{B}{O}{F}{A_1}{A_2}
- \pstLineAB[nodesepA=-3,nodesepB=-5]{A_1}{O}
- \pstLineAB[nodesepA=-3,nodesepB=-5]{A_2}{O}
- \pstMarkAngle[LabelSep=.8, MarkAngleRadius=.7, arrows=->]{F}{O}{A_1}{$\Psi$}
- \ncline[linecolor=red]{A_1}{A_2}
- \pstRightAngle[RightAngleSize=.15]{A_1}{S}{O}
- \psset{PointName=none}
- \whiledo{\value{n}<8}{%
- \psset{RadiusA=\pstDistVal{\Ri},RadiusB=\pstDistVal{\Rii},PointSymbol=none}
- \pstInterCC{F}{}{F'}{}{M\arabic{n}}{P\arabic{n}}
- \pstInterCC{F'}{}{F}{}{M'\arabic{n}}{P'\arabic{n}}
- \stepcounter{n}\addtocounter{i}{\value{Inc}}\addtocounter{Inc}{\value{Inc}}
- } %% fin de whiledo
- \psset{linecolor=blue}
- \pstGenericCurve[GenCurvFirst=P1]{M}{1}{7}\pstGenericCurve{P}{1}{7}
- \pstGenericCurve[GenCurvFirst=P'1]{M'}{1}{7}\pstGenericCurve{P'}{1}{7}
-\end{pspicture}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsubsection{Cycloid}
-
-The wheel rolls from $M$ to $A$. The circle points are on a
-cycloids.\nopagebreak[4]
-
-\begin{center}
-\input{Exemples/cyclo}
-\end{center}\nopagebreak[4]
-
-\verbatiminput{Exemples/cyclo_in}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsubsection{Hypocycloids (Astroid and Deltoid)}
-
-A wheel rolls inside a circle, and depending of the radius ratio, it
-is an astroid, a deltoid and in the general case hypo-cycloids.
-\nopagebreak[4]
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% ASTROIDE
-\input{Exemples/hypocyclo}
-%%%%%%%%%%%%%%%%%%%%
-\begin{center}
-\input{Exemples/astro}\input{Exemples/delto}
-\end{center}
-
-\verbatiminput{Exemples/hypocyclo}
-\verbatiminput{Exemples/astro_in}
-
-\cbstart
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Lines and circles envelope}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsubsection{Conics}
-
-Let's consider a circle and a point $A$ not on the circle. The
-set of all the mediator lines of segments defined by $A$ and the
-circle points, create two conics depending of the position of $A$:
-
-\begin{itemize}
-\item inside the circle: an hyperbola;
-\item outside the circle: an ellipse.
-\end{itemize}
-
-(figure of O. Reboux).
-
-\begin{center}\input{Exemples/envellipse}\end{center}
-
-\verbatiminput{Exemples/envellipse_in}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsubsection{Cardioid}
-
-The cardioid is defined by the circles centred on a circle and
-crossing a given point.
-
-\begin{center}\input{Exemples/envcardi}\end{center}
-
-\verbatiminput{Exemples/envcardi_in}
-
-\cbend
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Homotethy and fractals}
-
-\tabex{fracthom}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{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.
-\begin{pspicture}(-5,-5)(5,5)
- \psclip{\pscircle(0,0){4}}%\psgrid
- %\newlength{\radius}\setlength{\radius}{0cm}
- %\newcounter{rapport}\setcounter{i}{1}
- %\whiledo{\value{i}<100}{
- % \setlength{\radius}{4cm*\value{i}}
- % \setcounter{rapport}{\value{i}+1}
- % \divide\radius by \arabic{rapport}
- % \pscircle[linestyle=dotted, linecolor=gray]%
- % (0, 0){\radius}
- % \setcounter{i}{\value{i}*2}
- % }
- \pstGeonode(1, 2){M}\pstGeonode(-2,2){N}\pstGeonode(0,-2){P}%
- \psset{DrawCirABC=false, PointSymbol=none}%
- \pstGeonode(0,0){O}\pstGeonode(4,0){A}\pstCircleOA{O}{A}%
- \pstHomO[HomCoef=\pstDistAB{O}{A} 2 mul \pstDistAB{O}{M} sub
- \pstDistAB{O}{M} div]{O}{M}{M'}%
- \pstHomO[HomCoef=\pstDistAB{O}{A} 2 mul \pstDistAB{O}{P} sub
- \pstDistAB{O}{P} div]{O}{P}{P'}%
- \pstHomO[HomCoef=\pstDistAB{O}{A} 2 mul \pstDistAB{O}{N} sub
- \pstDistAB{O}{N} div]{O}{N}{N'}%
- \psset{linecolor=green, linewidth=1.5pt}%
- \pstCircleABC{M}{N}{M'}{OmegaMN}\pstArcOAB{OmegaMN}{N}{M}%
- \pstCircleABC{M}{P}{M'}{OmegaMP}\pstArcOAB{OmegaMP}{M}{P}%
- \pstCircleABC{N}{P}{P'}{OmegaNP}\pstArcOAB{OmegaNP}{P}{N}%
- \psset{linecolor=blue}
- %% la hauteur issue de M
- \pstHomO[HomCoef=\pstDistAB{OmegaNP}{N} 2 mul \pstDistAB{OmegaNP}{M} sub
- \pstDistAB{OmegaNP}{M} div]{OmegaNP}{M}{MH'}
- \pstCircleABC{M}{M'}{MH'}{OmegaMH}\pstArcOAB{OmegaMH}{MH'}{M}
- %% la hauteur issue de N
- \pstHomO[HomCoef=\pstDistAB{OmegaMP}{M} 2 mul \pstDistAB{OmegaMP}{N} sub
- \pstDistAB{OmegaMP}{N} div]{OmegaMP}{N}{NH'}
- \pstCircleABC{N}{N'}{NH'}{OmegaNH}\pstArcOAB{OmegaNH}{N}{NH'}
- %% la hauteur issue de P
- \pstHomO[HomCoef=\pstDistAB{OmegaMN}{M} 2 mul \pstDistAB{OmegaMN}{P} sub
- \pstDistAB{OmegaMN}{P} div]{OmegaMN}{P}{PH'}
- \pstCircleABC{P}{P'}{PH'}{OmegaPH}\pstArcOAB{OmegaPH}{P}{PH'}
- \endpsclip
-\end{pspicture}
-
-\end{document}
-
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- \subsection{Une figure fractale : le flocon de \textsc{von Koch}}
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%% TENTATIVE DE FLOCON DE VON KOCH
-\newcounter{nbvk}%
-%%%%%%%%%%%%%
-%% PILE LIFO%
-\newcounter{lifon}\setcounter{lifon}{1}%%
-\newcommand{\Push}[1]{%%
- \expandafter\edef\csname lifocmd\roman{lifon}\endcsname{#1}%%
- \addtocounter{lifon}{1}%%
- }%
-\newcommand{\Pop}{\csname lifocmd\roman{lifon}\endcsname}%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\newcounter{nombre}\setcounter{nombre}{0}%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\newcommand{\vonkoch}[3]{%%
- \setcounter{nbvk}{#1}%%
- \edef\Pointi{#2}\edef\Pointii{#3}%%
- \ifnum\value{nbvk}=1%
- \ncline{\Pointi}{\Pointii}%
- \else % ELSE%
- \addtocounter{nombre}{1}%
- %% position des nouveauX points%
- \pstHomO[HomCoef=1 3 div]{\Pointi}{\Pointii}{P\arabic{nombre}1}%
- \pstHomO[HomCoef=2 3 div]{\Pointi}{\Pointii}{P\arabic{nombre}2}%
- \pstRotation[RotAngle=60]{P\arabic{nombre}1}{P\arabic{nombre}2}{P\arabic{nombre}3}%
- \addtocounter{nbvk}{-1}%%
- \Push{\Pointi}\Push{\Pointii}\Push{\arabic{nombre}}\Push{\arabic{nbvk}}%
- \vonkoch{\value{nbvk}}{\Pointi}{P\arabic{nombre}1}%
- \addtocounter{lifon}{-1}\edef\nbvklocal{\Pop}%
- \addtocounter{lifon}{-1}\edef\nombrelocal{\Pop}%
- \addtocounter{lifon}{-1}\edef\Pointii{\Pop}%
- \addtocounter{lifon}{-1}\edef\Pointi{\Pop}%
- \addtocounter{lifon}{4}%
- \vonkoch{\nbvklocal}{P\nombrelocal1}{P\nombrelocal3}%
- \addtocounter{lifon}{-1}\edef\nbvklocal{\Pop}%
- \addtocounter{lifon}{-1}\edef\nombrelocal{\Pop}%
- \addtocounter{lifon}{-1}\edef\Pointii{\Pop}%
- \addtocounter{lifon}{-1}\edef\Pointi{\Pop}%
- \addtocounter{lifon}{4}%
- \vonkoch{\nbvklocal}{P\nombrelocal3}{P\nombrelocal2}%
- \addtocounter{lifon}{-1}\edef\nbvklocal{\Pop}%
- \addtocounter{lifon}{-1}\edef\nombrelocal{\Pop}%
- \addtocounter{lifon}{-1}\edef\Pointii{\Pop}%
- \addtocounter{lifon}{-1}\edef\Pointi{\Pop}%
- \addtocounter{lifon}{4}%
- \vonkoch{\nbvklocal}{P\nombrelocal2}{\Pointii}%
- \addtocounter{lifon}{-4}%
- \fi%
-}%
-\psset{unit=2.5cm}%
-\begin{pspicture}(-2,-2)(2,2)%
- \psset{PointSymbol=none}
- \pstGeonode(-2,-2){A}\pstGeonode(2,2){B}%
- \pstRotation[RotAngle=60]{B}{A}{C}%
- \vonkoch{5}{A}{B}\setcounter{nombre}{0}%%%
- \vonkoch{4}{B}{C}\setcounter{nombre}{0}%%%
- \vonkoch{4}{C}{A}%%
-\end{pspicture}%
-%
-\end{document}%
-
-\begin{pspicture*}(-4,-5)(4,5)%\psgrid
- \pstGeonode[PosAngle=-135](0,0){O}
- \pstGeonode[PosAngle=-90](1,0.5){I}
- \pstGeonode[PosAngle=-180](0.5,2){J}
- \pstLineAB[nodesep=100]{O}{I}
- \pstLineAB[nodesep=100]{O}{J}
- \multips(-5,-2.5)(1,0.5){11}{\psline(0,-.15)(0,.15)}%
- \multips(-5,-2.5)(1,0.5){11}{\psline[linestyle=dotted](-10,-40)(10,40)}%
- \multips(-2,-8)(0.5,2){9}{\psline(-.15,0)(.15,0)}%
- \multips(-2,-8)(0.5,2){9}{\psline[linestyle=dotted](-10,-5)(10,5)}%
- %% huit points
- \psset{PointSymbol=x}
- \pstOIJGeonode(1,2){A}{O}{I}{J}
- \pstOIJGeonode(-2,1){B}{O}{I}{J}
- \pstOIJGeonode(-1,-1.5){C}{O}{I}{J}
- \pstOIJGeonode(2,-1){D}{O}{I}{J}
-\end{pspicture*}
-%