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+\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
+