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diff --git a/obsolete/macros/latex/contrib/tkz/tkz-fct/doc/latex/TKZdoc-fct-param.tex b/obsolete/macros/latex/contrib/tkz/tkz-fct/doc/latex/TKZdoc-fct-param.tex new file mode 100644 index 0000000000..102ff07534 --- /dev/null +++ b/obsolete/macros/latex/contrib/tkz/tkz-fct/doc/latex/TKZdoc-fct-param.tex @@ -0,0 +1,179 @@ +\section{Courbes avec équations paramétrées} + \hypertarget{tfpa}{} +\begin{NewMacroBox}{tkzFctPar}{\oarg{local options}\marg{$x(t)$}\marg{$y(t)$}} + {$x(t)$ et $y(t)$ sont des expressions utilisant la syntaxe de \tkzname{gnuplot}. La variable est $t$.} + +\medskip +\begin{tabular}{lll} + \toprule + options & exemple & explication \\ + \midrule +\TAline{$x(t)$,$y(t)$}{\tkzcname{tkzFctPar[0:1]}\{\tkzcname{t**3}\}\{\tkzcname{t**2}\}}{$x(t)=t^3$,$y(t)=t^2$ } + \bottomrule +\end{tabular} + +Les options sont celles de \TIKZ. + +\begin{tabular}{lll} +\toprule +options & défaut & définition \\ +\midrule +\TOline{domain}{-5:5}{domaine de la fonction} +\TOline{samples}{200}{nombre de points utilisés} +\TOline{id} {tkzfonct}{permet d'identifier les noms des fichiers auxiliaires} +\TOline{color}{black}{couleur de la ligne} +\TOline{line width} {0.4pt}{épaisseur de la ligne} +\TOline{style} {solid}{style de la ligne} +\bottomrule +\end{tabular} + \end{NewMacroBox} + +\subsection{Courbe paramétrée exemple 1} + +\begin{align*} +x(t) &=t- \sin(t)\\ +y(t) &=1-\cos(t)\\ +\end{align*} + +\begin{center} +\begin{tkzexample}[] +\begin{tikzpicture} + \tkzInit[ymax=2.25,ystep=.5] \tkzGrid + \tkzAxeXY + \tkzFctPar[samples=400,domain=0:2*pi]{(t-sin(t))}{(1-cos(t))} +\end{tikzpicture} +\end{tkzexample} +\end{center} + + +\newpage +\subsection{Courbe paramétrée exemple 2} + +\begin{align*} +x(t) &=t\times \sin(t)\\ +y(t) &=t\times \cos(t)\\ +\end{align*} + +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}[scale=1.25] + \tkzInit[xmin=-50,xmax=50,xstep=10, + ymin=-50,ymax=50,ystep=10] + \tkzGrid + \tkzAxeXY + \tkzFctPar[smooth,samples=200,domain=0:50]{t*sin(t)}{t*cos(t)} +\end{tikzpicture} +\end{tkzexample} +\end{center} + + +\newpage +\subsection{Courbe paramétrée exemple 3} +\begin{align*} +x(t) &=\exp(t)\times \sin(t)\\ +y(t) &=\exp(t)\times \cos(t)\\ +\end{align*} + +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}[scale=1.5] + \tkzInit[xmin=-2,xmax=10,xstep=2,ymin=-10,ymax=4,ystep=2] + \tkzGrid[sub] + \tkzAxeX[step=2] + \tkzAxeY[step=2] + \tkzFctPar[samples=400,domain=-pi:pi]{exp(t)*sin(t)}{exp(t)*cos(t)} +\end{tikzpicture} +\end{tkzexample} +\end{center} + + +\newpage + +\subsection{Courbe paramétrée exemple 4} +\begin{align*} +x(t) &=\cos^3(t)\\ +y(t) &=\sin^3(t)\\ +\end{align*} + +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}[scale=1.25] + \tkzInit[xmin=-1,xmax=1,xstep=.2, + ymin=-1,ymax=1,ystep=.2] + \tkzFctPar[color=red, + line width=2pt, + fill=orange, + opacity=.4, + samples=400, + domain=0:2*pi]{(cos(t))**3}{(sin(t))**3} +\end{tikzpicture} +\end{tkzexample} +\end{center} + + +\newpage +\subsection{Courbe paramétrée exemple 5} +Saint Valentin version 1 +\begin{align*} +x(t) &=\sin^3(t)\\ +y(t) &=\cos(t)-\cos^4(t)\\ +\end{align*} + + +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}[scale=4] + \tkzInit[xmin=-1,xmax=1,ymin=-2,ymax=1] + \tkzClip + \tkzFctPar[samples=500,smooth,domain=-pi:pi, + ball color=red,shading=ball]% + {(sin(t))**3}{cos(t)-(cos(t))**4} +\end{tikzpicture} +\end{tkzexample} +\end{center} + + +\newpage +\subsection{Courbe paramétrée exemple 6} +Saint Valentin version 2 from \url{http://mathworld.wolfram.com/HeartCurve.html} + +\begin{align*} +x(t) &=\sin(t)\cos(t)\log(|t|)\\ +y(t) &=\sqrt{(|t|)\cos(t)}\\ +\end{align*} + + +\begin{center} +\begin{tkzexample}[vbox] +\begin{tikzpicture}[scale=1.5] + \tkzInit[xmin=-.4,xmax=.4,xstep=.1,ymin=0,ymax=.7,ystep=.1] + \tkzClip + \tkzFctPar[samples=2000,smooth,domain=-1:1, + ball color=red,shading=ball]% + {sin(t)*cos(t)*log(abs(t))}{sqrt(abs(t))*cos(t)} +\end{tikzpicture} +\end{tkzexample} +\end{center} + + + \newpage +\subsection{Courbe paramétrée exemple 7} +Saint Valentin version 3 from \url{http://en.wikipedia.org/wiki/Heart_(symbol)} + +\begin{align*} +x(t) &=16\sin^3(t)\\ +y(t) &=13\cos(t)-5\cos(2t)-2cos(3t)-cos(4t)\\ +\end{align*} + + +\begin{tkzexample}[vbox] +\begin{tikzpicture}[scale=1.75] + \tkzInit[xmin=-20,xmax=20,xstep=5,ymin=-25,ymax=15,ystep=5] + \tkzClip + \tkzFctPar[samples=400,smooth,domain=0:6.28, + ball color=red,shading=ball]% + {16*(sin(t))**3}{13*cos(t)-5*cos(2*t)-2*cos(3*t)-cos(4*t)} +\end{tikzpicture} +\end{tkzexample} +\endinput + |