\input arma.tex

\def\pav #1|{\par\vskip 12pt\noindent{\bftwelve #1.}~~\vskip5pt\penalty500}

\font\pench=cmssi10
\long\def\theo#1|#2|#3|#4\fintha{\par\vskip12pt\noindent
        {\pench #1}{\bf #2}{\rm #3\pointir}{\sl #4}\par\vskip 5pt}
\def\remark#1|#2|{\par\vskip12pt\noindent{{\pench #1}{\bf #2}\pointir}}
\def\proof{\par{\sl Proof}\pointir}

\vphantom{}
\def\rmo{{\rm O}}
\def\ov{\overline}
\def\rb{{\Bbb R}}
\def\cb{{\Bbb C}}
\def\hr{{\cal H}}
\def\as{A\wedge \sigma }
\def\ata{A\wedge \tau  }
\def\eo{E_{\restriction\Omega}}
\def\ec{\eo\to \Omega \times \cb}
\def\ci{C^\infty}
\def\bu{{\scriptstyle\bullet}}
\def\wh{\widehat}
\def\wt{\widetilde}

%\input mizenpaj

\font\bffourt=cmbx10 at 14.4pt

% figures inserted as PostScript files
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\def\ab{\Bbb A}
\def\gb{\Bbb G}
\def\hb{\Bbb H}
\def\kb{\Bbb K}
\def\sb{\Bbb S}

\def\pom{{\partial\Omega}}
\def\dem{{\sl D\'emonstration}\pointir}

\centerline{\bffourt Noyau de Szeg\"o et calcul num\'erique}
\medskip
\centerline{\bffourt de l'application conforme de Riemann}
\vskip15pt
\centerline{\bftwelve d'apr\`es Norberto Kerzman et Manfred Trummer}
\vskip30pt

\remark Notations||Soit $P$ une partie de $\rb^n$ et $I$ un intervalle 
ferm\'e born\'e de $\rb$. A toute fonction continue $K(t,s)$ sur $P\times I$, 
on associe un op\'erateur $\kb$ de $L^1(I)$ \`a valeurs dans l'espace $C(P)$
des fonctions continues sur $P$, d\'efini par
$$\kb u(t)=\int_I~~K(t,s)\,u(s)\,ds,~~~~t\in P.$$
La fonction $K$ sera appel\'ee {\sl noyau de l'op\'erateur} $\kb$.
Pour $P=I$ et $u,v\in L^2(I)$, le th\'eor\`eme de Fubini donne
$$\langle\kb u,v\rangle=\int_{I\times I}K(t,s)u(s)\ov v(t)\,ds\,dt$$
et l'in\'egalit\'e de Cauchy-Schwarz implique
$$|\langle \kb u,v\rangle|\le ||K||_{L^2(I\times I)}\,||u||_2\,||v||_2.$$
Par cons\'equent $||\kb||\le ||K||_2$, et un argument de densit\'e montre
que $\kb$ d\'efinit un op\'erateur continu $L^2(I)\to L^2(I)$ pour tout
noyau $K\in L^2(I\times I)$.

Soit $\Omega$ un ouvert connexe born\'e du plan complexe $\cb$ dont la
fronti\`ere $\pom$ est une r\'eunion de courbes ferm\'ees de classe
$C^k$, $k\ge 2$.

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\noindent On d\'esigne par $H(\Omega)$ l'espace des fonctions holomorphes
sur $\Omega$, muni de la topologie de la convergence uniforme sur les
compacts.  Par ailleurs, on note $ds$ la mesure de longueur d'arc sur
$\pom$ et $s$ l'abscisse curviligne sur chaque composante connexe,
calcul\'ee \`a partir d'une origine quelconque.  Enfin $L^p(\pom)$
d\'esigne l'espace des fonctions $L^p$ \`a valeurs complexes sur
$\pom$ muni de la mesure $ds$. 
\vfill\eject

\pav 1. Transformation de Hilbert|

Si $f$ est une fonction continue sur $\ov\Omega$ et holomorphe dans
$\Omega$, la formule de Cauchy donne 
$$f(w)={1\over2i\pi}\int_\pom{f(z)\over z-w}\,dz,~~~~w\in\Omega.$$ 
Notons $z=\gamma(s)$ la param\'etrisation de $\pom$ par l'abscisse
curviligne.  On a $dz=\tau(z)\,ds$ o\`u $\tau(z)=\gamma'(s)$ est le
vecteur unitaire tangent \`a $\pom$ au point $z$.  Par suite
$$\eqalign{
f(w)&=\int_\pom H(w,z)\,f(z)\,ds~~~~{\rm avec}\cr
H(w,z)&={1\over 2i\pi}\,{\tau(z)\over z-w},~~~~w\in\Omega,~~z\in\pom.\cr}$$

\theo D\'efinition| 1.1||La fonction $H(w,z)$ est appel\'ee noyau de Cauchy
de $\Omega$. Si $u$ est une fonction sur $\pom$, la transform\'ee de Hilbert
de $u$ est d\'efinie par
$$\hb u(w)=\int_\pom H(w,z)\,u(z)\,ds,~~~~w\in\Omega.$$\fintha

\noindent Comme le noyau $H$ est continu sur $\Omega\times\pom$, $\hb u$ est
bien d\'efinie d\`es que $u\in L^1(\pom)$, et donc aussi si
$u\in L^p(\pom)\subset L^1(\pom)$, $p\ge 1$. 

\theo Proposition| 1.2||Pour tout $u\in L^1(\pom)$, $\hb u$ est holomorphe sur
$\Omega$, et l'op\'erateur
$\hb:L^p(\pom)\to H(\Omega)$ est continu.\fintha

\dem Le noyau $H(w,z)$ est diff\'erentiable par rapport \`a $w$ et on a
$${\partial H\over\partial w}(w,z)={1\over 2i\pi}\,{\tau(z)\over(z-w)^2},
~~~~{\partial H\over\partial\ov w}(w,z)=0.$$
Les d\'eriv\'ees partielles $\partial H/\partial w$ et 
$\partial H/\partial\ov w$ sont donc continues sur $\Omega\times\partial
\Omega$. D'apr\`es le th\'eor\`eme de d\'erivation sous le signe somme,
on en d\'eduit que $\hb u$ est diff\'erentiable et que 
$${\partial\over\partial w}\hb u(w)=
\int_\pom{1\over 2i\pi}\,{\tau(z)\over(z-w)^2}\,u(z)\,ds,~~~~
{\partial\over\partial\ov w}\hb u(w)=0,$$
donc $\hb u$ est holomorphe sur $\Omega$. On a par ailleurs
$$|H(w,z)|=\big(2\pi|z-w|\big)^{-1}\le\big(2\pi d(w,\pom)\big)^{-1}.$$
Si $K$ est une partie compacte de $\Omega$, on obtient
$$\sup_{w\in K}\big|\hb u(w)\big|\le\big(2\pi d(K,\pom)\big)^{-1}||u||_1,$$
donc $\hb:L^1(\pom)\to H(\Omega)$ est continu. Le r\'esultat
est vrai aussi pour $L^p(\pom)$ puisque l'inclusion
$L^p(\pom)\to L^1(\pom)$ est continue.\hfill\finpr

\theo Formule| 1.3||Si $u\in C^1(\pom)$, on d\'efinit la d\'eriv\'ee de $u$ 
le long de $\pom$ par 
$$u'\big(\gamma(s)\big)={1\over\gamma'(s)}\,{d\over ds}
\big[u\big(\gamma(s)\big)\big].$$
Alors $(\hb u)'=\hb(u')$ sur $\Omega$.\fintha

\noindent En effet, comme $dz/ds=\gamma'(s)=\tau(z)$ le long de
$\pom$, le calcul ci-dessus suivi d'une int\'egration par parties montre que
$$\eqalign{
(\hb u)'(w)&=\int_\pom{1\over 2i\pi}\,{\tau(z)\over(z-w)^2}\,u(z)\,ds
 =\int_\pom{1\over 2i\pi}\,{d\over ds(z)}\Big[{-1\over z-w}\Big]
\,u\big(\gamma(s)\big)\,ds\cr
&=\int_\pom{1\over 2i\pi}\,{1\over z-w}
\,{d\over ds}\big[u\big(\gamma(s)\big)\big]\,ds
 =\int_\pom H(w,z)\,u'(z)\,ds=\hb(u')(w).\cr}$$

\remark Exemple| 1.4|$\Omega=\hbox{disque unit\'e}~~D=\{w\in\cb\,;\,|w|<1\}$.

\noindent La param\'etrisation de $\partial D$ par l'abscisse curviligne 
s'\'ecrit
$$z=\gamma(s)=e^{is},~~~~s\in[0,2\pi].$$
On a $\gamma'(s)=ie^{is}=iz$, donc le noyau de Cauchy de $D$ est donn\'e par
$$H^D(w,z)={1\over 2\pi}\,{e^{is}\over e^{is}-w}=
{1\over 2\pi}\,{1\over 1-w\,e^{-is}}={1\over 2\pi}\,{1\over 1-w\ov z}.$$
Puisque $|w|<1$, $H^D(w,z)$ est d\'eveloppable en s\'erie enti\`ere
normalement convergente sur tout compact de $D\times\partial D\,$:
$$H^D(w,z)={1\over 2\pi}\sum_{n=0}^{+\infty}w^n\,e^{-ins}.$$
On peut donc \'ecrire
$$\hb^D u(w)=\sum_{n=0}^{+\infty}\wh u(n)\,w^n~~~~\hbox{o\`u}~~~
\wh u(n)={1\over 2\pi}\int_0^{2\pi}u(e^{is})\,e^{-ins}\,ds,~~~n\in\zb$$
est le $n$-i\`eme coefficient de Fourier de $u$. Si $u\in L^2(\partial D)$,
la fonction $u$ s'\'ecrit elle-m\^eme comme somme d'une s\'erie de Fourier
$L^2$-convergente
$$u(e^{is})=\sum_{n\in\zb}\wh u(n)\,e^{ins}$$
et d'apr\`es la formule de Parseval, la transformation de Fourier
est une isom\'etrie d'espaces de Hilbert:
$$\eqalignno{
L^2(\partial D)&\la l^2(\zb)\cr
\hfill u&\longmapsto\sqrt{2\pi}\big(\wh u(n)\big)_{n\in\zb}.&\finpr\cr}$$

Revenons au cas g\'en\'eral. On consid\`ere pour tout $\varepsilon>0$
assez petit la courbe de classe $C^{k-1}$
$$\gamma_\varepsilon(s)=\gamma(s)+\varepsilon i\gamma'(s)=z+\varepsilon 
i\tau(z),~~~~z=\gamma(s)\in\pom,$$
o\`u $i\gamma'(s)$ est le vecteur normal rentrant \`a $\pom$.\vfill\eject
$~$

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\noindent Notre objectif est d'\'etudier le comportement de $\hb u$
sur la courbe $\gamma_\varepsilon$ lorsque $\varepsilon$ tend vers $0$.
Pour cela, on d\'efinit un op\'erateur $\hb_\varepsilon$ sur
$L^2(\pom)$ \`a valeurs dans $C^{k-1}(\pom)\subset L^2(\pom)$ par
$$\hb_\varepsilon u(w)=\hb u\big(w+\varepsilon i\tau(w)\big)~~~~\ie~~
\hb_\varepsilon u\big(\gamma(s)\big)=\hb u\big(\gamma_\varepsilon(s)\big).$$
L'op\'erateur $\hb_\varepsilon$ est associ\'e au noyau
$$H_\varepsilon(w,z)=H(w+\varepsilon i\tau(w),z)=
{1\over 2i\pi}\,{\tau(z)\over z-w-\varepsilon i\tau(w)}.$$

\theo Th\'eor\`eme| 1.5||{\rm(a)} Si $u\in L^2(\pom)$, alors $\hb_\varepsilon u$
converge dans $L^2(\pom)$ vers une limite not\'ee $\hb_0 u$, o\`u
$\hb_0$ est un op\'erateur continu sur $L^2(\pom)$. De plus, il
existe une constante $C>0$ ind\'ependante de $\varepsilon$, $u$ telle que
$$||\hb_\varepsilon u||_2\le C||u||_2.$$
{\rm(b)} Si $u\in C^q(\partial\Omega)$, $1\le q\le k$, alors $\hb u$ se
prolonge en une fonction de classe $C^{q-1}$ sur $\ov\Omega$.\fintha

\dem On montre d'abord le th\'eor\`eme lorsque $\Omega=D$.

(a) On a par d\'efinition $\gamma_\varepsilon(s)=(1-\varepsilon)e^{is}$, d'o\`u
$$\hb^D_\varepsilon u(e^{is})=\hb^D u\big((1-\varepsilon)e^{is}\big)
=\sum_{n=0}^{+\infty}(1-\varepsilon)^n\,\wh u(n)\,e^{ins}.$$
Si $\hb_0^D$ est l'op\'erateur obtenu en faisant $\varepsilon=0$
dans la formule ci-dessus, l'\'egalit\'e de Parseval montre que 
$||\hb^D_\varepsilon u||_2\le ||u||_2$ pour tout $\varepsilon$ et
$$||\hb^D_0 u-\hb^D_\varepsilon u||_2^2=
2\pi\sum_{n=0}^{+\infty}\big[1-(1-\varepsilon)^n\big]^2\,|\wh u(n)|^2$$
converge vers $0$ quand $\varepsilon$ tend vers $0$.

(b) La formule $(\hb u)'=\hb(u')$ montre qu'il suffit de consid\'erer
le cas $q=1$. Alors, comme $u'$ est continue, la suite des coefficients de
Fourier $in\,\wh u(n)$ de $u'$ est dans $l^2(\zb)$. Par suite
$\big(\wh u(n)\big)\in l^1(\zb)$ gr\^ace \`a l'in\'egalit\'e de Cauchy-Schwarz;
il en r\'esulte que la s\'erie $\sum \wh u(n)\,w^n$ converge normalement
sur $\ov D$, d'o\`u $\hb^D u\in C^0(\ov D)$.

On se place maintenant dans le cas d'un ouvert quelconque $\Omega$.
Si le bord $\pom$ est une r\'eunion de courbes $\gamma_j$, alors
$$\hb u(w)=\sum_j\int_{\gamma_j}H(w,z)\,u(z)\,ds$$
et le terme d'indice $j$ est holomorphe (donc $\ci$) sur 
$\cb\setminus\{\gamma_j\}$. On peut donc supposer que $\pom$ est
compos\'e d'une seule courbe ferm\'ee, et apr\`es homoth\'etie on se ram\`ene
au cas o\`u $\pom$ est de longueur $2\pi$. On a alors
$$\hb u(w)={1\over 2i\pi}\int_0^{2\pi}{u\big(\gamma(s)\big)\gamma'(s)\over
\gamma(s)-w}\,ds.$$
\indent(a) Posons $w=\gamma(t)\in\pom$. Il vient
$$\hb_\varepsilon u(w)=
{1\over 2i\pi}\int_0^{2\pi}{u\big(\gamma(s)\big)\gamma'(s)
\over\gamma(s)-\gamma(t)-\varepsilon i\gamma'(t)}\,ds.$$
Comme $\gamma$ est de classe $C^k$, $k\ge 2$, la formule de Taylor avec reste
int\'egral donne
$$\gamma(s)-\gamma(t)=(s-t)\gamma'(t)+(s-t)^2\varphi_1(t,s)$$
o\`u $\varphi_1,\varphi_2,\ldots$ sont des fonctions dans 
$C^{k-2}(\pom\times\pom)$. On en d\'eduit
$$\eqalign{
\gamma(s)-\gamma(t)-\varepsilon i\gamma'(t)&=\big[s-t-\varepsilon i+
(s-t)^2\varphi_2(t,s)\big]\gamma'(t)\cr
&=-i\big[e^{i(s-t)}-1+\varepsilon+(s-t)^2\varphi_3(t,s)\big]\gamma'(t)\cr
&=-i\big[e^{is}-(1-\varepsilon)e^{it}+(s-t)^2\varphi_4(t,s)\big]\,
e^{-it}\gamma'(t),\cr
\hb_\varepsilon u(w)=\int_0^{2\pi}\kern40pt&\kern-40pt
{u\big(\gamma(s)\big)\gamma'(s)e^{it}\over\big(e^{is}-(1-\varepsilon)e^{it}
\big)\gamma'(t)}\Big[1-{(s-t)^2\varphi_4(t,s)\over e^{is}-(1-\varepsilon)e^{it}+
(s-t)^2\varphi_4(t,s)}\Big]\,{ds\over2\pi}.\cr}$$
Comme $e^{i(t-s)}\gamma'(s)/\gamma'(t)=1+(s-t)\varphi_5(t,s)$, on peut \'ecrire
$$\hb_\varepsilon u(w)={1\over 2\pi}\int_0^{2\pi}{e^{is}\,u\big(\gamma(s)\big)
\over e^{is}-(1-\varepsilon)e^{it}}\,ds
+\int_\pom R_\varepsilon(t,s)\,u\big(\gamma(s)\big)\,ds$$
o\`u $R_\varepsilon(t,s)$ est de la forme
$$R_\varepsilon(t,s)={s-t\over e^{is}-(1-\varepsilon)e^{it}}
\Big[\varphi_5(t,s)+{s-t\over \gamma(s)-\gamma_\varepsilon(t)}\varphi_6(t,s)
\Big].$$
Nous pouvons interpr\'eter cette d\'ecomposition sous la forme
$$(\hb_\varepsilon u)\circ\gamma=\hb^D_\varepsilon(u\circ\gamma)+
\rb_\varepsilon(u\circ\gamma),$$
o\`u $\hb^D$ est la transformation de Hilbert sur le disque. Il est 
facile de v\'erifier qu'on a des minorations 
$$\big|e^{is}-(1-\varepsilon)e^{it}\big|\ge C_1\big(|s-t|+\varepsilon\big),
~~~~\big|\gamma(s)-\gamma_\varepsilon(t)\big|\ge C_2\big(|s-t|+\varepsilon\big).$$
Par suite on a une majoration uniforme $|R_\varepsilon(t,s)|\le C_3$ lorsque
$\varepsilon$ tend vers $0$ et l'op\'erateur $\rb_\varepsilon$ est de
norme uniform\'ement born\'ee. Le th\'eor\`eme de convergence domin\'ee
montre que l'op\'erateur $\rb_\varepsilon$ converge en norme vers 
l'op\'erateur $\rb_0$ associ\'e au noyau $R_0$. Comme
l'application $u\mapsto u\circ\gamma$ est une isom\'etrie de
$L^2(\partial\Omega)$ sur $L^2([0,2\pi])\simeq L^2(\partial D)$, il 
en r\'esulte, modulo cette isom\'etrie, que $\hb_\varepsilon$
converge vers $\hb_0=\hb^D_0+\rb_0$. On notera que 
$R_0\in C^{k-2}(\pom\times\pom)$.

(b) On peut encore supposer $q=1$ ici. Si $u\in C^1(\pom)$,
on sait d'apr\`es la premi\`ere partie que $(\varepsilon,s)\mapsto
\hb^D_\varepsilon(u\circ\gamma)(s)$ s'\'etend continument \`a 
$[0,\varepsilon_0]\times[0,2\pi]$. Il en est de m\^eme pour 
$\rb_\varepsilon(u\circ\gamma)(s)$ d'apr\`es le th\'eor\`eme de
convergence domin\'ee, d'o\`u $\hb u\in C^0(\ov\Omega)$.\hfill\finpr

\pav 2. Espace de Hardy $\hr^2(\pom)$|

A toute fonction holomorphe $f\in H(\Omega)$,
on associe les fonctions $f_\varepsilon$ sur $\pom$ d\'efinies par
$$f_\varepsilon\big(\gamma(s)\big)=f\big(\gamma_\varepsilon(s)\big).$$

\theo Th\'eor\`eme| 2.1||Si $f\in H(\Omega)$, il y a 
\'equivalence entre les propri\'et\'es suivantes:

\noindent{\rm(a)}~~$f_\varepsilon$ converge dans $L^2(\pom)$ vers
une fonction $f_0$.\hfill\break
\noindent{\rm(b)}~~La norme $||f_\varepsilon||_2$ reste born\'ee
quand $\varepsilon$ tend vers $0$.\hfill\break
\noindent{\rm(c)}~~$\,$Il existe une suite $\varepsilon_p>0$ tendant vers
$0$ telle que la suite $||f_{\varepsilon_p}||_2$ soit born\'ee.
\noindent{\rm(d)}~~$f$ est la transform\'ee de Hilbert $\hb u$ d'une fonction
$u\in L^2(\pom)$.

\noindent On a alors $f=\hb f_0$.\fintha

\dem Il est \'evident que $(a)\Longrightarrow(b)\Longrightarrow(c)$ et
l'implication $(d)\Longrightarrow(a)$ r\'esulte du th\'eor\`eme 1.5,
avec $f_0=\hb_0 u$.

Pour d\'emontrer l'implication restante $(c)\Longrightarrow(d)$, nous aurons
besoin du lemme suivant.

\theo Lemme| 2.2||Soit $E$ un espace de Hilbert s\'eparable et
$(x_n)$ une suite born\'ee de $E$. Alors il existe une sous-suite
$(x_{n(p)})$ qui converge faiblement vers un \'el\'ement $\xi\in E$,
c'est-\`a-dire telle que
$$\lim_{p\to+\infty}\langle x_{n(p)},y\rangle=\langle\xi,y\rangle,
~~~~\forall y\in E.$$
En outre, si $(y_p)$ converge en norme vers $y$, alors
$\langle x_{n(p)},y_p\rangle$ converge vers $\langle\xi,y\rangle$.\fintha

\dem Soit $(e_l)_{l\in\nb}$ une base hilbertienne de $E$, 
$x_n=\sum x_{n,l}e_l$ et $M$ un majorant de $||x_n||$. 
Chaque suite $(x_{n,l})_{n\in\nb}$ est born\'ee
dans $\cb\,$; il existe donc une partie $I_0\subset\nb$ telle que la sous-suite
$(x_{n,0})_{n\in I_0}$ ait une limite $\xi_0$, puis une partie 
$I_1\subset I_0$ telle que $(x_{n,1})_{n\in I_1}$ converge vers une limite
$\xi_1$ et ainsi de suite. Soit $n(p)$ le $p$-i\`eme \'el\'ement de $I_p$.
La sous-suite diagonale $x_{n(p)}$ a la propri\'et\'e que chaque
coordonn\'ee $x_{n(p),l}$ tend vers une limite $\xi_l$, et on voit
facilement que $\sum|\xi_l|^2\le M^2$, de sorte que le vecteur
$\xi=\sum\xi_le_l$ est bien d\'efini. Comme
$$\big|\sum_{l\ge L}x_{n(p),l}~\ov y_l\big|\le M\Big(\sum_{l\ge L}|y_l|^2\Big)
^{1/2}$$
o\`u le second membre converge vers $0$ quand $L$ tend vers $+\infty$,
il est \'el\'ementaire de v\'erifier que $\langle x_{n(p)},y\rangle$ converge 
vers $\langle\xi,y\rangle$ pour tout $y\in E$. La derni\`ere affirmation 
r\'esulte de ce que
$$\big|\langle x_{n(p)},y-y_p\rangle\big|\le M||y-y_p||.\eqno\finpr$$

{\sl D\'emonstration de $(c)\Longrightarrow(d)$}\pointir Quitte
\`a extraire une sous-suite de $(f_{\varepsilon_p})$, on peut
supposer que $(f_{\varepsilon_p})$ converge faiblement vers
un \'el\'ement $u\in L^2(\pom)$. Pour $w\in\Omega$ fix\'e, la formule 
de Cauchy appliqu\'ee au chemin $\gamma_\epsilon$ donne
$$f(w)={1\over2i\pi}\int_{\gamma_\varepsilon}{f(z)\over z-w}\,dz
={1\over2i\pi}\int_\pom f_\varepsilon\big(\gamma(s)\big)
{\gamma'_\varepsilon(s)\over\gamma_\varepsilon(s)-w}\,ds$$
Pour $\varepsilon=\varepsilon_p$, ceci peut s'interpr\'eter comme un 
produit scalaire $\langle f_{\varepsilon_p},g_p\rangle$
o\`u $(f_{\varepsilon_p})$ converge faiblement vers $u$ et o\`u
$(g_p)$ converge uniform\'ement (donc en norme $L^2$) vers
$s\mapsto \ov H\big(w,\gamma(s)\big)$. A la limite, on
obtient par cons\'equent
$$f(w)=\langle u,\ov H\big(w,\bu\big)\rangle=\hb u(w),$$
soit $f=\hb u$. En outre, si (a) est v\'erifi\'e, on peut
prendre $u=f_0$ dans (c), donc $f=\hb f_0$.\hfill\finpr

\theo D\'efinition| 2.3||L'ensemble des applications
$f\in H(\Omega)$ v\'erifiant l'une des propri\'et\'es \'equivalentes
{\rm 2.1 (a), (b), (c), (d)}, muni de la norme $||f||_2=||f_0||_2$,\break
est not\'e $\hr^2(\pom)$.\fintha

L'application $f\mapsto f_0$ d\'efinit donc une isom\'etrie de
$\hr^2(\pom)$ sur un sous-espace $\hr^2_0(\pom)$ de l'espace de Hilbert 
$L^2(\pom)$. La formule $f=\hb f_0$ implique $f_0=\hb_0f_0$
pour tout $f_0\in\hr^2_0(\pom)$, et comme $\hb_0 u=(\hb u)_0\in\hr^2_0(\pom)$
pour tout $u\in L^2(\pom)$ on voit que l' op\'erateur
$$\hb_0:L^2(\pom)\la\hr^2_0(\pom)$$
est un projecteur continu. Il en r\'esulte que
$\hr^2_0(\pom)=\Ker(1-\hb_0)$ est un sous-espace ferm\'e de
$L^2(\pom)$. Pour simplifier les notations, on conviendra
dans la suite d'identifier $\hr^2(\pom)$ et son image
$\hr^2_0(\pom)$, une fonction $f\in\hr^2(\pom)$ et sa limite
au bord $f_0$, l'op\'erateur $\hb$ et sa limite au bord $\hb_0$.

\remark Exemple| 2.4|Si $\Omega=D$, les calculs faits en 1.4 donnent
pour tout $u\in L^2(\pom)\,$:
$$u(e^{is})=\sum_{n\in\zb}\wh u(n)\,e^{ins},~~~~
\hb u(e^{is})=\sum_{n\in\nb}\wh u(n)\,e^{ins}.$$
La transformation de Fourier donne donc
un isomorphisme $L^2(\partial D)\simeq l^2(\zb)$ par
lequel $\hr^2(\partial D)$ s'identifie au sous-espace $l^2(\nb)$
des fonctions dont les coefficients de Fourier $\wh u(n)$, $n<0$,
sont nuls. Dans ce cas, $\hb$ est la projection orthogonale 
$l^2(\zb)\to l^2(\nb)$.\hfill\finpr

Dans le cas g\'en\'eral, une condition n\'ecessaire pour qu'une
fonction $u$ de $L^2(\pom)$ soit dans $\hr^2(\pom)$ est que
$\int_{\pom}u(z)f(z)dz=0$ pour toute fonction $f\in\hr^2(\partial\Omega)$,
en particulier pour $f(z)=z^n$, $n\ge 0$. Ceci r\'esulte du th\'eor\`eme
de Cauchy appliqu\'e sur $\gamma_\varepsilon$ lorsque $\varepsilon$
tend vers $0$, compte tenu du fait que $u_\varepsilon\to u_0$ et
$f_\varepsilon\to f_0$ dans $L^2$. Comme nous le verrons plus loin,
le projecteur $\hb$ n'est orthogonal que si $\Omega$ est un disque.

\theo Th\'eor\`eme| 2.5||L'ensemble des fonctions holomorphes sur
un voisinage de $\ov\Omega$ est dense dans $\hr^2(\pom)$.\fintha

\dem Si $f\in\hr^2(\pom)$, on a la repr\'esentation de Cauchy
$$f(w)={1\over2i\pi}\int_\pom{f_0\big(\gamma(s)\big)\over \gamma(s)-w}\,
\gamma'(s)\,ds.$$
Soit, pour $\varepsilon>0$ assez petit, 
$\wt\gamma_\varepsilon(s)=\gamma(s)-\varepsilon i\gamma'(s)$
la courbe des points de $\complement\Omega$ situ\'es \`a la distance 
$\varepsilon$ de $\pom$. Il est clair que 
$$\wt f_\varepsilon(w)={1\over2i\pi}\int_\pom{f_0\big(\gamma(s)\big)\over 
\wt\gamma_\varepsilon(s)-w}\,\gamma'(s)\,ds$$
est holomorphe sur l'ouvert des points situ\'es \`a une distance
$<\varepsilon$ de $\ov\Omega$. Des calculs analogues \`a ceux faits 
dans la d\'emonstration du th\'eor\`eme 1.5 montrent que $\wt f_\varepsilon$
converge vers $f$ dans $\hr^2(\pom)\,$: on v\'erifie d'abord le
r\'esultat pour $\Omega=D\,$; on voit ensuite que $(\wt f_\varepsilon
)_{\restriction\pom}$ converge dans $\hr^2(\pom)$ par un d\'eveloppement
de Taylor du noyau, et la limite est $f$ dans $H(\Omega)$.\finpr

\pav 3. Adjoint de l'op\'erateur $\hb$|

Si $I$ est un intervalle ferm\'e born\'e de $\rb$ et si $\kb$
est l'op\'erateur sur $L^2(I)$ associ\'e \`a un noyau $K\in L^2(I\times I)$,
il est facile de voir que l'op\'erateur adjoint $\kb^\star$ est d\'efini par
le noyau
$$K^\star(t,s)=\ov K(s,t).$$
Cette formule ne peut toutefois \^etre appliqu\'ee directement \`a
$\hb$, car le noyau $H$ ne se prolonge pas en un \'element de
$L^2(\pom\times\pom)$ ni m\^eme de $L^1(\pom\times\pom)$. Pour
contourner cette difficult\'e, on cherche \`a \'evaluer
l'op\'erateur diff\'erence $\hb^\star-\hb$,
qui, comme on le verra plus loin, a le m\'erite d'\^etre associ\'e 
\`a un vrai noyau. On consid\`ere les op\'erateurs
approch\'es $\hb_\varepsilon$, $\hb^\star_\varepsilon$ d\'efinis par 
les noyaux continus
$$\eqalign{
H_\varepsilon(w,z)&={1\over 2i\pi}\,{\tau(z)\over z-w-\varepsilon i\tau(w)},\cr
H^\star_\varepsilon(w,z)&=\ov H_\varepsilon(z,w)=
{1\over 2i\pi}\,{\ov\tau(w)\over \ov z-\ov w-\varepsilon i\ov\tau(z)},\cr}$$
et l'op\'erateur diff\'erence $\ab_\varepsilon=\hb^\star_\varepsilon-
\hb_\varepsilon$ associ\'e au noyau
$$A_\varepsilon(w,z)={1\over 2i\pi}\,
{(z-w)\ov\tau(w)-(\ov z-\ov w)\tau(z)\over\big(z-w-\varepsilon i\tau(w)\big)
\big(\ov z-\ov w-\varepsilon i\ov\tau(z)\big)}.$$
Pour $z=\gamma(s)$, $w=\gamma(t)$ assez voisins, on voit comme dans
1.5 qu'il existe des fonctions $\varphi_j\in C^{k-2}(\pom\times\pom)$
telles que
$$\eqalign{
z-w&=(s-t)\gamma'(t)+(s-t)^2\varphi_1(t,s),\cr
|z-w|^2&=(s-t)^2\big[1+(s-t)\varphi_2(t,s)\big].\cr}$$
En substituant $\gamma'(t)=\tau(w)$ et $(s-t)^2$ en fonction de $|z-w|^2$
dans la premi\`ere ligne, il vient
$$z-w=(s-t)\tau(w)+|z-w|^2\varphi_3(w,z).$$
En \'echangeant les r\^oles de $z$ et $w$, on obtient
$$\eqalign{
z-w&=(s-t)\tau(z)-|z-w|^2\varphi_3(z,w),~~~~\hbox{d'o\`u}\cr
A_\varepsilon(w,z)&={|z-w|^2\,A(w,z)\over\big(z-w-\varepsilon i\tau(w)\big)
\big(\ov z-\ov w-\varepsilon i\ov\tau(z)\big)}~~~~~\hbox{avec}\cr
A(w,z)&={1\over 2i\pi}\big(\varphi_3(w,z)\ov\tau(w)+\ov\varphi_3(z,w)\tau(z)\big).\cr}$$
On obtient $\lim_{\varepsilon\to 0}A_\varepsilon(w,z)=A(w,z)$ pour $w\ne z$,
avec $A(w,z)\in C^{k-2}(\pom\times\pom)$, et de plus on a une majoration
uniforme $|A_\varepsilon(w,z)|\le C|A(w,z)|$. Ceci entra\^\i ne que
$\ab_\varepsilon$ converge en norme vers l'op\'erateur $\ab$ de noyau
$A$. Pour tout $u,v\in L^2(\pom)$ on obtient donc
$$\langle \hb u,v\rangle=
\lim~\langle\hb_\varepsilon u,v\rangle=
\lim~\langle u,\hb_\varepsilon^\star v\rangle=
\lim~\langle u,\hb_\varepsilon v+\ab_\varepsilon v\rangle=
\langle u,(\hb+\ab)v\rangle$$
ce qui prouve bien que $\hb^\star=\hb+\ab$. On a d'autre part
$$\eqalign{
\varphi_3(w,w)&=\varphi_1(t,t)={1\over 2}\gamma''(t),~~~~\hbox{d'o\`u}\cr
A(w,w)&={1\over 4i\pi}\big(\gamma''(t)\ov\gamma'(t)+\ov\gamma''(t)\gamma'(t)
\big)={1\over 4i\pi}{d\over dt}\big|\gamma'(t)\big|^2=0\cr}$$
car $|\gamma'(t)|=1$. On peut donc \'enoncer:

\theo Th\'eor\`eme| 3.1||L'op\'erateur $\ab=\hb^\star-\hb$ est associ\'e
\`a un noyau $A\in C^{k-2}(\pom\times\pom)$ d\'efini par
$$A(w,z)={1\over 2i\pi}\Big({\ov\tau(w)\over\ov z-\ov w}-{\tau(z)\over
z-w}\Big),~~~~w,z\in\pom.$$
Ce noyau $A$ est antisym\'etrique, c'est-\`a-dire que
$\ov A(z,w)=-A(w,z)$, et de plus $A(w,w)\equiv 0$.\fintha

Pour que le projecteur $\hb$ soit orthogonal, il faut et il suffit
que $\hb^\star=\hb$, ce qui \'equivaut \`a dire que $A\equiv 0$.

\theo Corollaire| 3.2||Le projecteur $\hb$ est orthogonal si et
seulement si $\Omega$ est un disque.\fintha

\dem Si $A\equiv 0$, on a n\'ecessairement 
$${\rm angle}\big([z,w],\tau(z)\big)=-{\rm angle}\big([z,w],\tau(w)\big)~~~~
\forall w,z\in\pom,$$
car les membres de gauche et de droite repr\'esentent les arguments 
respectifs des termes $\tau(z)/(z-w)$ et $\ov\tau(w)/(\ov z-\ov w)$ 
intervenant dans $A(w,z)$.

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\medskip

\noindent En d\'epla\c cant la corde $[z,w]$
parall\`element \`a une direction fix\'ee, on en d\'eduit que
$\pom$ doit \^etre invariant par sym\'etrie autour de la m\'ediatrice
de chacune de ses cordes. Consid\'erons deux cordes faisant entre elles
un angle irrationnel, et le point d'intersection $P$ de leurs
m\'ediatrices. Les deux sym\'etries correspondantes
engendrent un groupe dense de rotations de centre $P$. Comme $\pom$
est ferm\'e, $\pom$ est n\'ecessairement une r\'eunion de cercles de 
centre $P$, \`a savoir un cercle si $\Omega$ est un disque, ou deux cercles
si $\Omega$ est une couronne. Mais une couronne n'est invariante que
par les sym\'etries autour des m\'ediatrices des cordes dont les extr\^emit\'es
sont sur un m\^eme cercle. Par cons\'equent $\Omega$ est un 
disque.\hfill\finpr

\pav 4. Noyau de Szeg\"o|

Le {\sl projecteur de Szeg\"o} est par d\'efinition le projecteur
orthogonal $\sb$ de $L^2(\pom)$ sur $\hr^2(\pom)$. On cherche ici
\`a montrer que $\sb$ est, en un certain sens, associ\'e \`a un
noyau $S$. Rappelons que $\hb$ est orthogonal dans le cas du disque, 
par suite $\sb^D=\hb^D$.

Soit $(\psi_j)_{j\in\nb}$ une base hilbertienne de $\hr^2(\pom)$.
L'image d'une fonction $u\in L^2(\pom)$ par le projecteur $\sb$ est alors 
donn\'ee par la s\'erie $L^2$-convergente
$$\sb u(w)=\sum_{j\in\nb}\langle u,\psi_j\rangle~\psi_j(w)=
\sum_{j\in\nb}\psi_j(w)\int_{\pom}u(z)\,\ov\psi_{j,0}(z)\,ds,$$
o\`u $\psi_{j,0}$ d\'esigne la limite au bord de $\psi_j$.
Ceci sugg\`ere d'introduire le noyau
$$S(w,z)=\sum_{j\in\nb}\psi_j(w)\ov\psi_j(z),~~~~w,z\in\Omega,$$
qui sera appel\'e {\sl noyau de Szeg\"o} de $\Omega$.

\theo Lemme| 4.1||La s\'erie $\sum_{j\in\nb}|\psi_j(w)|^2$ converge
uniform\'ement sur tout compact de $\Omega$. Le noyau
$S(w,z)$ est de classe $\ci$ sur $\Omega\times\Omega$,
holomorphe en $w$ et antiholomorphe en $z$. De plus, on a la 
majoration
$$S(w,z)=\sum_{j\in\nb}|\psi_j(w)|^2\le{1\over4\pi^2}\int_\pom
{1\over|z-w|^2}\,ds.$$\fintha

\dem Comme $\psi_j\in\hr^2(\pom)$, on a
$$\psi_j(w)=\hb\psi_j(w)=\langle\psi_j,\ov H(w,\bu)\rangle=
\langle\psi_j,\sb\ov H(w,\bu)\rangle.$$
Par cons\'equent, $\big(\psi_j(w)\big)$ est la suite des coordonn\'ees
de la fonction $\sb\ov H(w,\bu)$ dans la base $(\psi_j)$, ce qui donne
$$\sum_j|\psi_j(w)|^2=||\sb\ov H(w,\bu)||^2\le||H(w,\bu)||^2=
{1\over4\pi^2}\int_\pom{1\over|z-w|^2}\,ds.$$
L'application $w\mapsto\ov H(w,\bu)$ \'etant continue de $\Omega$
dans $L^2(\pom)$, on voit que la fonction $w\mapsto||\sb H(w,\bu)||^2$
est continue sur $\Omega$. Le lemme de Dini entra\^\i ne
alors la convergence uniforme sur tout compact de la s\'erie de fonctions
continues $\sum|\psi_j(w)|^2$. L'in\'egalit\'e de Cauchy-Schwarz montre que
pour $N$ tendant vers $+\infty$,
$$\Big(\sum_{j\ge N}\big|\psi_j(w)\ov\psi_j(z)\big|\Big)^2\le
\sum_{j\ge N}|\psi_j(w)|^2\sum_{j\ge N}|\psi_j(z)|^2$$
converge uniform\'ement vers $0$ lorsque $(w,z)$ d\'ecrit un compact
quelconque de $\Omega\times\Omega$. Comme $\sum\psi_j(w)\ov{\psi_j(z)}$ 
est une s\'erie de fonctions holomorphes en $(w,\ov z)$, on en d\'eduit que
$S$ est holomorphe en $(w,\ov z)$, en particulier
de classe $\ci$ sur $\Omega\times\Omega$.\hfill\finpr

\theo Lemme| 4.2||Pour $w\in\Omega$ fix\'e et pour $\varepsilon$ tendant
vers $0$, la fonction 
$$S_\varepsilon(w,\bu)=\sum_{j\in\nb}\psi_j(w)\ov\psi_{j,\varepsilon}$$
converge vers $S_0(w,\bu)=\sum_{j\in\nb}\psi_j(w)\ov\psi_{j,0}$
dans $L^2(\pom)$. De plus
$$\sb u(w)=\int_\pom S_0(w,z)\,u(z)\,ds,~~~~\forall u\in L^2(\pom).$$\fintha

\dem Comme $\hb:L^2(\pom)\to H(\Omega)$ est continu, 
$\hb$ envoie une s\'erie $L^2$-convergente sur une s\'erie de fonctions
holomorphes convergeant uniform\'ement sur tout compact, d'o\`u
$$\eqalign{
\hb\Big(\sum_{j\in\nb}\ov\psi_j(w)\psi_{j,0}\Big)
&=\sum_{j\in\nb}\ov\psi_j(w)\,\hb\psi_{j,0}
=\sum_{j\in\nb}\ov\psi_j(w)\,\psi_j=\ov{S(w,\bu)},\cr
\hb_\varepsilon\Big(\sum_{j\in\nb}\ov\psi_j(w)\psi_{j,0}\Big)
&=\ov{S_\varepsilon(w,\bu)}.\cr}$$
Le th\'eor\`eme 1.5 entra\^\i ne que le membre de gauche converge dans
$L^2(\pom)$ vers $\hb_0\big(\sum_{j\in\nb}\ov\psi_j(w)\psi_{j,0}\big)=
\sum_{j\in\nb}\ov\psi_j(w)\psi_{j,0}$ $\big($cet \'el\'ement est dans 
$\hr^2(\pom)\big)$. La formule int\'egrale
r\'esulte imm\'ediatement des consid\'erations du d\'ebut
du~\S$\,$4.\hfill\finpr

L'espace $\hr^2(\partial D)$ du disque admet la base hilbertienne
$(w^n/\sqrt{2\pi})_{n\in\nb}$, ce qui donne l'expression
$$S^D(w,z)={1\over 2\pi}\sum_{n\in\nb}w^n\ov z^n=
{1\over 2\pi}\,{1\over 1-w\ov z},~~~~\forall(w,z)\in D\times D.$$
On voit que $S^D_0(w,z)$ co\"\i ncide bien avec $H^D(w,z)$ pour
$(w,z)\in D\times\partial D$.

\pav 5. Formule int\'egrale reliant $S$ et $H$|

L'id\'ee centrale introduite par N. Kerzman est que l'on peut
retrouver le projecteur orthogonal $\sb$ \`a partir du projecteur
oblique $\hb$ (qui est connu explicitement). Comme $\sb$ et $\hb$
co\"\i ncident avec l'application identique sur $\hr^2(\pom)$,
on a en effet
$$\sb\hb=\hb,~~~~~\hb\sb=\sb.$$
Prenons les adjoints dans la seconde \'egalit\'e. Comme $\sb^\star=\sb$, on 
trouve $\sb\hb^\star=\sb$. Soustrayons maintenant la premi\`ere \'egalit\'e
et introduisons l'op\'erateur $\ab=\hb^\star-\hb$. Il vient
$$\sb\ab=\sb\hb^\star-\sb\hb=\sb-\hb,$$
soit encore $\sb(1-\ab)=\hb$. 

\theo Lemme| 5.1||L'op\'erateur $1-\ab$ est un isomorphisme
de $L^2(\pom)$ et on a $||(1-\ab)^{-1}||\le 1$.\fintha

\dem Comme $\ab$ est antisym\'etrique, le produit scalaire
$\langle\ab u,u\rangle$ est purement imaginaire pour
tout $u\in L^2(\pom)$, ce qui implique
$$||u||_2^2\le|\langle(1-\ab)u,u\rangle|\le||(1-\ab)u||_2\,||u||_2$$
et en particulier $||(1-\ab)u||_2\ge ||u||_2$. L'op\'erateur 
$1-\ab$ est donc injectif et d'image ferm\'ee. 
L'orthogonal de $\im(1-\ab)$ est \'egal au noyau de l'adjoint
$(1-\ab)^\star=1+\ab$, et cet op\'erateur est injectif pour les m\^emes 
raisons que pr\'ec\'edemment.
Par suite $\im(1-\ab)=L^2(\pom)$ et $1-\ab$ est donc un isomorphisme 
topologique de $L^2(\pom)$. Comme $1-\ab$ accro\^\i t la norme de tout 
vecteur, on voit que $(1-\ab)^{-1}$ est contractant.\hfill\finpr

Le lemme montre qu'on peut calculer $\sb$ \`a partir de $\hb$ par la formule
$$\sb=\hb(1-\ab)^{-1}.$$
C'est cette id\'ee qu'on va exploiter dans la suite pour \'evaluer
le noyau de Szeg\"o $S$, en \'etablissant une formule int\'egrale
reliant $S$ et $H$.

Pour tout $u\in L^2(\pom)$ et $w\in\Omega$, on a en effet
$$\sb\ab u(w)=\int_\pom S_0(w,\xi)\,\ab u(\xi)\,ds(\xi)=
\int_\pom S_0(w,\xi)\,ds(\xi)\int_\pom A(\xi,z)\,u(z)\,ds(z).$$
Le th\'eor\`eme de Fubini montre que $\sb\ab$ est associ\'e au noyau
$$\Omega\times\pom\ni(w,z)\longmapsto\int_\pom S_0(w,\xi)\,A(\xi,z)\,ds(\xi).$$
L'\'egalit\'e $\sb=\hb+\sb\ab$ fournit alors l'\'egalit\'e de noyaux:

\theo Formule| 5.2||Pour tous $(w,z)\in\Omega\times\pom$ on a
$$S_0(w,z)=H(w,z)+\int_\pom S_0(w,\xi)\,A(\xi,z)\,ds(\xi).$$\fintha

\pav 6. R\'egularit\'e au bord du noyau de Szeg\"o|

Nous nous proposons ici de montrer que $S$ s'\'etend en une fonction
de classe $C^{k-2}$ sur $\ov\Omega\times\ov\Omega$ en dehors de
la diagonale $\Delta_\pom$ de $\pom\times\pom$. On utilise
pour cela la relation $\sb=\hb+\sb\ab$ d\'emontr\'ee au \S 5,
ce qui donne
$$\eqalign{
\sb&=\hb+(\hb+\sb\ab)\ab=\hb(\hb+\ab)+\sb\ab^2=\hb\hb^\star+\sb\ab^2,\cr
\sb\ab&=\sb-\hb=(\sb-\hb^\star)^\star=(\sb-\hb-\ab)^\star=(\sb\ab-\ab)^\star
=\ab-\ab\sb.\cr}$$
La deuxi\`eme \'egalit\'e implique $\sb\ab^2=\ab^2-\ab\sb\ab$, d'o\`u
$$\sb=\hb\hb^\star+\ab^2-\ab\sb\ab.\leqno(6.1)$$
Comme $A\in C^{k-2}(\pom\times\pom)$, il est clair que $\ab^2$
poss\`ede un noyau de classe $C^{k-2}$ sur $\pom\times\pom$.
L'op\'erateur $\sb\ab$ est associ\'e au noyau $\sb A(\bu,z)$ et
$\ab\sb\ab$ au noyau
$$\int_\pom A(w,\bu)\,\sb A(\bu,z)\,ds=\langle A(w,\bu),\ov{\sb A(\bu,z)}
\rangle.$$
Les applications $w\mapsto A(w,\bu)$ et $z\mapsto A(\bu,z)$
sont dans $C^{k-2}\big(\pom,L^2(\pom)\big)$. Il en est de m\^eme pour
l'application $z\mapsto \sb A(\bu,z)$, puisque $\sb$
est un op\'erateur continu sur $L^2(\pom)$, donc $\ab\sb\ab$ a lui
aussi un noyau dans $C^{k-2}(\pom\times\pom)$. Il reste \`a \'etudier
le noyau de $\hb\hb^\star$.

\theo Lemme| 6.2||La fonction
$$G(w,z)=\int_\pom H(w,\xi)\,\ov{H(z,\xi)}\,ds(\xi)=
{1\over4\pi^2}\int_\pom{ds(\xi)\over(\xi-w)(\ov\xi-\ov z)},~~~~(w,z)\in
\Omega\times\Omega$$
se prolonge en une fonction $G\in C^{k-2}(\ov\Omega\times\ov\Omega
\setminus\Delta_\pom)$, et l'op\'erateur d\'efini par 
$G_{\restriction\Omega\times\pom}$ est $\gb=\hb\hb^\star$.\fintha

Avant de d\'emontrer le lemme 6.2, nous aurons besoin d'un r\'esultat
pr\'eliminaire g\'en\'eralisant le th\'eor\`eme 1.5 (b).

\theo Lemme| 6.3||Soit $E$ une partie ouverte ou un domaine \`a bord de
classe $C^1$ dans $\rb^n$. Soit $u:\pom\times E\to\cb$ une fonction
continue.

\noindent{\rm(a)}~~Si $u$ est de classe $C^q$, $1\le q\le k$, alors la
transform\'ee $\hb u$ d\'efinie par
$$\hb u(w,x)=\int_\pom H(w,z)\,u(z,x)\,ds(z),~~~~(w,x)\in\Omega\times E$$
se prolonge en une fonction de classe $C^{q-1}$ sur $\ov\Omega\times E$.

\noindent{\rm(b)}~~Si $u$ est de classe $C^q$, $0\le q\le k$ et si 
$u(\bu,x)\in\hr^2(\pom)$ pour tout $x\in\Omega$, alors $\hb u$ se 
prolonge en une fonction de classe $C^q$ sur $\ov\Omega\times E$.\fintha

\dem (a) Gr\^ace \`a la formule 1.3 suivie d'une d\'erivation sous le signe 
somme en $x$, on obtient
$${\partial^l\over\partial x^l}\,{\partial^m\over\partial w^m}\,\hb u(w,x)=
\hb\Big({\partial^l\over\partial x^l}\,{\partial^m\over\partial z^m}\,
u(z,x)\Big),$$
de sorte qu'il suffit de regarder le cas $q=1$. La d\'emonstration
du th\'eor\`eme 1.5 montre que $\hb$ est continu de $C^1(\pom)$
dans $C^0(\ov\Omega)$. On en d\'eduit
$$||\hb u(\bu,x)-\hb u(\bu,x_0)||_{C^0(\ov\Omega)}\le C
||u(\bu,x)-u(\bu,x_0)||_{C^1(\pom)}$$
et le second membre tend vers $0$ quand $x$ tend xers $x_0$ dans $E$.
On sait d'autre part que $w\mapsto H(w,x)$ s'\'etend continument \`a
$\ov\Omega$ pour tout $x\in E$ fix\'e. Ceci entra\^\i ne facilement la
continuit\'e de $\hb u$ sur $\ov\Omega\times E$ gr\^ace \`a
l'in\'egalit\'e triangulaire
$$\big|\hb u(w,x)-\hb u(w_0,x_0)\big|\le
\big|\hb u(w,x)-\hb u(w,x_0)\big|+\big|\hb u(w,x_0)-\hb u(w_0,x_0)\big|.$$

(b) On est facilement ramen\'e au cas $q=0$, \`a condition de v\'erifier 
que toutes les d\'eriv\'ees de $u$ en $(z,x)$ d'ordre inf\'erieur
ou \'egal \`a $q$ sont encore dans $\hr^2(\pom)$. Par r\'ecurrence, il
suffit de v\'erifier ce resultat pour $u'_x$ et $u'_z$. Pour $u'_x$,
on observe simplement que
$$u'_x(\bu,x_0)=\lim_{x\to x_0}{u(\bu,x)-u(\bu,x_0)\over x-x_0}~~~~{\rm dans}~~
\hr^2(\pom).$$
D'autre part, la fonction holomorphe $v=\hb u(\bu,x)$ est continue
sur $\ov\Omega$ d'apr\`es (a), et v\'erifie par
hypoth\`ese $v_{\restriction\pom}=u(\bu,x)$. Comme $v'=\hb u'_z$,
le th\'eor\`eme 1.5 montre que $(v')_\varepsilon$ converge vers $\hb_0 u'_z$ 
dans $L^2(\pom)$, et par suite dans $L^1(\pom)$. Pour tout arc 
${\buildo\frown\over{ab}}\subset\pom$ on obtient donc
$$\eqalign{
\int_a^b (\hb_0 u'_z)(w,x)\,dw&=\lim\int_a^b (v')_\varepsilon(w)\,dw=
\lim v\big(b+\varepsilon i\tau(b)\big)-v\big(a+\varepsilon i\tau(a)\big)\cr
&=v(b)-v(a)=u(b,x)-u(a,x)\cr}$$
donc $\hb_0 u'_z=u'_z$ et $u'_z(\bu,x)\in\hr^2(\pom)$. Comme dans (a),
le cas $q=0$ se r\'eduit \`a voir que $\hb$ 
envoie $C^0(\pom)\cap\hr^2(\pom)$ dans $C^0(\ov\Omega)$, continument
par rapport aux normes uniformes. Si $\Omega=D$, ceci
r\'esulte du fait que $\hb u$ est, pour $u\in C^0(\partial D)\cap
\hr^2(\partial D)$, la solution du probl\`eme de Dirichlet (\cf W. Rudin). 
Le cas g\'en\'eral r\'esulte de l'\'ecriture $\hb_\varepsilon=
\hb^D_\varepsilon+\rb_\varepsilon$ obtenue dans la d\'emonstration du 
th\'eor\`eme~1.5.\hfill\finpr

{\sl D\'emonstration du lemme 6.2}\pointir Soit
$(\theta_j)$ une partition de l'unit\'e de classe $C^k$ sur $\pom$,
et $T_j={\rm Supp}\,\theta_j$. Ecrivons $G=\sum G_j$ avec
$$G_j(w,z)=\int_\pom H(w,\xi)\,\ov{H(z,\xi)}\,\theta_j(\xi)\,ds(\xi),$$
c'est-\`a-dire $G_j(\bu,z)=\hb\big(\ov H(\bu,z)\theta_j\big)$. Comme 
$\ov{H(z,\xi)}\theta_j(\xi)$ est de classe $C^{k-1}$ pour 
$(\xi,z)\in\pom\times(\ov\Omega\setminus T_j)$, le lemme 6.3 (a) montre que 
$G_j$ est de classe $C^{k-2}$ sur $\ov\Omega\times(\ov\Omega\setminus T_j)$,
et donc aussi sur $(\ov\Omega\setminus T_j)\times\ov\Omega$ apr\`es
conjugaison et \'echange des r\^oles de $w,z$. Par
cons\'equent $G_j\in C^{k-2}\big(\ov\Omega\times\ov\Omega\setminus
T_j\times T_j\big)$, et $G=\sum G_j$ est de classe $C^{k-2}$ sur 
$\ov\Omega\times\ov\Omega$ en dehors de $\bigcup_j T_j\times T_j$, 
qui est un voisinage arbitrairement petit de $\Delta_\pom$ si les 
diam\`etres des $T_j$ sont choisis assez petits.

Pour tout $u\in L^2(\pom)$, on a d'autre part
$$\hb\hb^\star u=\lim_{\varepsilon\to 0}~~\hb\hb^\star_\varepsilon u=
\lim_{\varepsilon\to 0}~~\gb_\varepsilon u,$$
o\`u $\gb_\varepsilon$ est l'op\'erateur associ\'e au noyau
$$G_\varepsilon(w,z)=\int_\pom H(w,\xi)\,\ov{H_\varepsilon(z,\xi)}\,ds(\xi)
=G\big(w,z+\varepsilon i\tau(z)\big).$$
Comme ce noyau converge vers $G_{\restriction\Omega\times\pom}$ uniform\'ement
sur tout compact, on en d\'eduit bien $\hb\hb^\star=\gb$.\hfill\finpr

\theo Th\'eor\`eme| 6.4||Le noyau de Szeg\"o $S(w,z)$ se prolonge en une
fonction dans $C^{k-2}(\ov\Omega\times\ov\Omega\setminus\Delta_\pom)$, 
et plus pr\'ecis\'ement, en la somme du noyau $G$ et d'une fonction de classe
$C^{k-2}$ sur $\ov\Omega\times\ov\Omega$.
Quand $z\in\Omega$ tend vers le bord $\pom$, on a
$$S(z,z)\sim{1\over 4\pi^2}\int_\pom {ds(\xi)\over|\xi-z|^2}
\sim{1\over 4\pi\,d(z,\pom)}.$$\fintha

\dem Consid\'erons le noyau $K(w,z)=S_0(w,z)-G_0(w,z)$ sur
$\Omega\times\pom$, associ\'e \`a l'op\'erateur 
$$\sb-\hb\hb^\star=\ab^2-\ab\sb\ab:L^2(\pom)\la\hr^2(\pom).$$
On sait que cet op\'erateur est d\'efini par un 
noyau $K_0\in C^{k-2}(\pom\times\pom)$, ce qui implique
$K_0(\bu,z)\in\hr^2(\pom)$ pour tout $z$ et $K=\hb K_0$.
Le lemme 6.3 (b) donne alors $K\in C^{k-2}(\ov\Omega\times\pom)$.
Par \'echange de $w,z$ on voit que $\big(S(\bu,z)-G(\bu,z)\big)_0$ 
est de classe $C^{k-2}$ sur $\pom\times\ov\Omega$, et une nouvelle 
application du lemme 6.3 (b) donne $S-G\in C^{k-2}(\ov\Omega\times\ov\Omega)$.
On en d\'eduit en particulier
$$S(z,z)\sim G(z,z)={1\over 4\pi^2}\int_\pom {ds(\xi)\over|\xi-z|^2}$$
quand $z$ tend vers $\pom$. Soit $\delta=d(z,\pom)$ et
$\gamma(t)$ le point de $\pom$ tel que $|z-\gamma(t)|=\delta$.
Le point $z$ est sur la normale \`a $\pom$ au point $\gamma(t)$,
donc $z=\gamma(t)+\delta i\gamma'(t)$. Quand $\delta$ et $|s-t|$
tendent vers $0$, on a
$$\gamma(s)-z=\gamma(s)-\gamma(t)-\delta i\gamma'(t)=
\gamma'(t)\big(s-t-i\delta+{\rm O}((s-t)^2)\big),$$
par suite $|\gamma(s)-z|^2\sim (s-t)^2+\delta^2$ et
$$\eqalignno{
\int_\pom{ds\over|\gamma(s)-z|^2}
&\sim\int_{|s-t|<\delta^{1/3}}{ds\over(s-t)^2+\delta^2}
+\int_{|s-t|>\delta^{1/3}}{ds\over|\gamma(s)-z|^2}\cr
&={2\over\delta}{\rm arctan}(\delta^{-2/3})+{\rm O}(\delta^{-2/3})
\sim{\pi\over\delta}.&\finpr\cr}$$

\pav 7. Relation avec l'application conforme de Riemann|

On suppose ici que $\Omega$ est un ouvert simplement connexe \`a fronti\`ere
de classe $C^k$, $k\ge 2$. Pour tout point $a\in\Omega$ fix\'e, il
existe alors une unique application conforme bijective
$$R:\Omega\to D$$
telle que $R(a)=0$ et $R'(a)>0$.

\theo Th\'eor\`eme| 7.1||L'application $R$ s'\'etend en un diff\'eomorphisme
de classe $C^{k-1}$ de $\ov\Omega$ sur $\ov D$.\fintha

La d\'emonstration de ce th\'eor\`eme sera donn\'ee plus loin. Nous
admettons le r\'esultat provisoirement. Le changement de variable 
$z=R(w)$ donne alors
$$\int_{\partial D}|u(z)|^2\,|dz|=\int_\pom|u\circ R(w)|^2\,|R'(w)|\,|dw|$$
pour toute fonction $u\in L^2(\pom)$. On voit donc qu'on a une isom\'etrie
$$\eqalign{
L^2(\partial D)&\la L^2(\pom)\cr
\hfill u&\longmapsto u\circ R\,(R')^{1/2}\cr}$$
o\`u $(R')^{1/2}$ est la d\'etermination de la racine carr\'ee complexe
telle que $R'(a)^{1/2}>0$\break (on notera que $R'$ ne s'annule pas sur
$\Omega$). L'isom\'etrie envoie $H(D)\cap C^0(\ov D)$
sur $H(\Omega)\cap C^0(\ov\Omega)$ et, par densit\'e (th\'eor\`eme 2.5),
elle envoit donc $\hr^2(\partial D)$ sur $\hr^2(\pom)$.
Si $(\psi_j)$ est une base orthonorm\'ee de $\hr^2(\partial D)$,
on en d\'eduit que $\big(\psi_j\circ R\,(R')^{1/2}\big)$ est une base
orthonorm\'ee de $\hr^2(\pom)$. Par cons\'equent
$$\eqalign{
S(w,z)&=S^D\big(R(w),R(z)\big)\,R'(w)^{1/2}\,\ov{R'(z)}{}^{1/2},\cr
S(w,z)&={1\over 2\pi}\,{R'(w)^{1/2}\,\ov{R'(z)}{}^{1/2}\over
1-R(w)\ov{R(z)}}.\cr}$$
En substituant $z=a$, $R(a)=0$, on obtient en particulier
$$S(w,a)={1\over 2\pi}R'(w)^{1/2}R'(a)^{1/2},~~~~
S(a,a)={1\over 2\pi}R'(a),$$
d'o\`u on d\'eduit aussit\^ot les

\theo Formules| 7.2||L'application conforme $R$ et sa d\'eriv\'ee sont 
donn\'ees par

\noindent{\rm(a)}~~~$\displaystyle
R'(w)=2\pi\,{S(w,a)^2\over S(a,a)},~~~~\forall w\in\ov\Omega$,

\noindent{\rm(b)}~~~$\displaystyle
R(w)=-i\tau(w){S(w,a)^2\over|S(w,a)|^2},~~~~\forall w\in\pom$.\fintha

\dem La relation (a) est imm\'ediate \`a partir de ce qui pr\'ec\`ede.
On a par ailleurs $|R(w)|^2=1$ sur $\pom$. En prenant la d\'eriv\'ee
$d/ds$ le long de $\pom$, on voit que $dR(w)/ds=R'(w)dw/ds=R'(w)\tau(w)$ 
doit \^etre orthogonal \`a $R(w)$.
Quand $w$ tourne dans le sens positif sur $\pom$, il en est de
m\^eme pour $R(w)$ sur $\partial D$ (une application holomorphe
pr\'eserve l'orientation), donc l'argument de $R'(w)\tau(w)$
est \'egal \`a celui de $iR(w)$. Ceci donne
$iR(w)=R'(w)\tau(w)/|R'(w)|$ et (b) se d\'eduit alors de~(a).\hfill\finpr
\vskip6pt
Il nous reste \`a d\'emontrer la r\'egularit\'e jusqu'au bord de 
l'application conforme de Riemann. Pour cela, on va montrer d'abord la
r\'egularit\'e analytique lorsque $\partial\Omega$ est r\'eelle
analytique, puis on passera au cas g\'en\'eral par un argument
d'approximation en norme $C^k$ de $\partial\Omega$.

\theo Lemme| 7.3||Soient $\Omega_1$, $\Omega_2$ des ouverts simplement
connexes born\'es de $\cb$ ayant des fronti\`eres $\rb$-analytiques et
$F:\Omega_1\to\Omega_2$ une application biholomorphe. Alors $F$ s'\'etend 
en une application biholomorphe d'un voisinage
de $\ov\Omega_1$ sur un voisinage de $\ov\Omega_2$.\fintha

\dem Quitte \`a remplacer $F$ par $F^{-1}:\Omega_2\to\Omega_1$, il suffit de 
voir que $F$ s'\'etend holomorphiquement \`a un voisinage de $\ov\Omega_1$.
D'apr\`es Rudin (th\'eor\`eme 14.19), $F$
se prolonge en un hom\'eomorphisme de $\ov\Omega_1$ sur $\ov\Omega_2$.
Soit $x_1\in\pom_1$ un point quelconque et $x_2=F(x_1)\in\pom_2$.
Au voisinage de $x_j$, $\pom_j$ est donn\'e par une courbe
$\rb$-analytique $s\mapsto\gamma_j(s)$ d\'efinie pour $s\in\rb$ voisin
de $0$.\break Celle-ci se prolonge en une application holomorphe
$\wt\gamma_j$ de la variable $z=s+it$ au voisinage de $0$ dans $\cb$.
Soit $\Pi^+=\{z=s+it\,;\,t>0\}$ le demi-plan sup\'erieur. Il existe un
disque $U_j\subset\cb$ de centre $0$ et un voisinage $V_j\subset\cb$ de $x_j$
tels que $\wt\gamma_j$ d\'efinit un biholomorphisme de
$\Pi^+\cap U_j$ sur $\Omega_j\cap V_j$. Si on choisit en outre $V_1$
assez petit pour que $F(\Omega_1\cap V_1)\subset V_2$, on en d\'eduit une 
application holomorphe $G=\wt\gamma_2^{-1}\circ F\circ\wt\gamma_1:\Pi^+\cap U_1
\to\Pi^+\cap U_2$ qui se prolonge continument en une application
de $\ov\Pi^+\cap U_1$ dans $\ov\Pi^+\cap U_2$ telle que
$G(\rb\cap U_1)\subset\rb\cap U_2$. Le principe de r\'eflexion de Schwarz
(W. Rudin, th\'eor\`eme 11.17) montre que $G$ se prolonge en une application 
holomorphe $\wt G$ de $U_1$ dans $U_2$, d'o\`u un prolongement local
$\wt F=\wt\gamma_2\circ\wt G\circ\wt\gamma_1^{-1}$ de $V_1$
dans~$V_2$.\hfill\finpr

{\sl D\'emonstration du th\'eor\`eme 7.1}\pointir Si $\Omega$ est \`a
fronti\`ere $\rb$-analytique, le lemme 7.3 montre que $R$ est en 
particulier un $\ci$-diff\'eomorphisme de $\ov\Omega$ sur $\ov D$,
donc les formules 7.2 sont bien vraies. Si $\pom$ est seulement de
classe $C^k$, on peut approximer la courbe fronti\`ere $\gamma$
par une courbe $\rb$-analytique obtenue par convolution:
$$\gamma_\delta(s)=\int_\rb\gamma(t)\exp\Big({-(s-t)^2\over\delta^2}\Big)\,
{dt\over\delta\sqrt{2\pi}}.$$
On notera que $\gamma_\delta$ est une fonction ayant la m\^eme p\'eriodicit\'e
que $\gamma$ et que $||\gamma_\delta-\gamma||_{C^k}$ converge vers $0$
avec $\delta$. Pour $\delta$ assez petit, cette courbe est la fronti\`ere
d'un ouvert $\Omega_\delta$ pour lequel on a un noyau de Szeg\"o $S_\delta$
et une application de Riemann $R_\delta:\Omega_\delta\to D$. D'apr\`es
ce qui pr\'ec\`ede, $R'_\delta$ est li\'e \`a $S_\delta$ par
la formule 7.2 (a). La~d\'emonstration que nous avons donn\'ee de
la r\'egularit\'e de $S$ fournit en outre la
continuit\'e de l'application $\gamma\mapsto S$, lorsqu'on prend
la norme $C^k$ sur l'espace des courbes $\gamma$ et la norme
$C^{k-2}$ pour $S$ (sur un compact de $\ov\Omega\times\ov\Omega$ ne
rencontrant pas $\Delta_\pom$). Il en r\'esulte que $R_\delta$ 
converge uniform\'ement vers une application holomorphe $R_0$ qui v\'erifie
encore 7.2 (a). En particulier $R_0'\in C^{k-2}(\ov\Omega)$,
donc $R_0\in C^{k-1}(\ov\Omega)$. De~plus $R_0$ envoie $\pom$ sur 
$\partial D$. Comme une limite d'applications holomorphes injectives est ou 
bien injective ou bien constante (cons\'equence du th\'eor\`eme de Rouch\'e),
et comme $R_0(a)=0$, $R_0'(a)=2\pi S(a,a)>0$, on en d\'eduit que $R_0$
co\"\i ncide avec l'application conforme $R:\Omega\to D$ cherch\'ee. Il reste 
\`a d\'emontrer que la d\'eriv\'ee $R'$ ne peut s'annuler en aucun point 
$z_0\in\pom$. Un calcul facile montre que pour $\varepsilon>0$ assez petit
l'image conforme de $\Omega$ par l'application $z\mapsto 1/\big(z-z_0+
\varepsilon i\tau(z_0)\big)$ est strictement convexe au voisinage du point 
image de $z_0$. On peut donc supposer que $\Omega$ est convexe au voisinage
de $z_0$. Dans ce cas, on peut modifier la courbe $\partial\Omega$
en dehors d'un petit voisinage de $z_0$ de sorte qu'elle soit la
fronti\`ere $\partial\wt\Omega$ d'un ouvert arbitrairement proche d'un disque 
en norme $C^2$. Alors l'application conforme $\wt R:\wt\Omega\to D$ est voisine
de l'application identique en norme $C^1$, donc $\wt R$ est un 
$C^1$-diff\'eomorphisme jusqu'au bord. Comme $R\circ \wt R^{-1}$
envoie $\partial D$ sur $\partial D$ au voisinage de $\wt R(z_0)$, la 
d\'emonstration du lemme 7.3 montre que $R\circ \wt R^{-1}$ s'\'etend en une
application biholomorphe au voisinage de $\wt R(z_0)$, par suite
$R'(z_0)\ne 0$.\hfill\finpr\vskip6pt

\remark Remarque| 7.4|Lorsque $\partial\Omega$ est de classe $C^1$,
il n'est pas vrai en g\'en\'eral que $R$ s'\'etend en une application de
classe $C^1$ sur $\ov\Omega$, et m\^eme si c'est le cas, il se peut que la
d\'eriv\'ee $R'$ s'annule au bord. Un exemple de cette situation est
donn\'e par l'ouvert $\Omega$ obtenu en prenant l'image conforme d'un petit 
disque $\Delta=\{|z-\varepsilon|<\varepsilon\}$ par l'application 
$Q(z)=z/\log(1/z)$ (resp. $Q(z)=z\log(1/z)$). La fronti\'ere de 
$\partial\Omega$ est de classe $C^1$ au voisinage de $0$ parce que $\log(1/z)$ 
a un argument qui tend vers $0$ quand $z$ tend vers $0$ le long de 
$\partial\Delta$. L'application conforme est donn\'ee par $R=Q^{-1}
/\varepsilon-1$ et on a donc $R'(0)=1/\big(\varepsilon Q'(0)\big)=\infty$ 
(resp $R'(0)=0$). De m\^eme, pour $k\ge 2$, on peut v\'erifier que l'image
de $\Delta$ par $Q(z)=z+z^k\log\log(1/z)$ a une fronti\`ere de classe $C^k$, 
mais $Q$ et $R$ ne sont pas de classe $C^k$ au voisinage de $0$.

\pav 8. Calcul num\'erique de l'application conforme|

La formule int\'egrale 5.2 donne
$$S(a,w)=H(a,w)+\int_\pom S(a,z)\,A(z,w)\,ds,~~~~w\in\pom.$$
Comme $\ov{A(z,w)}=-A(w,z)$, on trouve apr\`es conjugaison:
$$S(w,a)+\int_\pom A(w,z)\,S(z,a)\,ds=\ov{H(a,w)},~~~~w\in\pom,\leqno(8.1)$$
ce qui permet d'obtenir $S(w,a)$ en fonction des noyaux $H$ et $A$ 
explicitement connus. Les formules 7.2~(a), (b) peuvent alors \^etre 
utilis\'ees pour calculer l'application de Riemann $R$ \`a partir de $S$.

Les int\'egrales $\int_\alpha^\beta f(t)\,dt$ mises en jeu seront \'evalu\'ees
par la m\'ethode des trap\`ezes relative \`a une subdivision
$t_i=\alpha+ih$, $0\le i\le n$, de pas constant $h=(\beta-\alpha)/n\,$:
$$\int_\alpha^\beta f(t)\,dt\simeq h\Big(f(t_0)+f(t_1)+\ldots+f(t_{n-1})
+{f(\beta)-f(\alpha)\over 2}\Big).$$
Si $f$ est de classe $C^{2l}$, l'erreur d'approximation $\varepsilon$
est donn\'ee par la formule d'Euler-Mac Laurin
$$\varepsilon=\sum_{m=1}^l{b_{2m}h^{2m}\over(2m)!}\,\big(f^{(2m-1)}(\beta)-
f^{(2m-1)}(\alpha)\big)-h^{2l}\,\int_\alpha^\beta
{B_{2l}\big((t-\alpha)/h\big)\over(2l)!}\,f^{(2l)}(t)\,dt,$$
o\`u $b_{2m}$ et $B_{2m}$ sont respectivement les nombres et les
polyn\^omes de Bernoulli. Ceci montre que l'erreur est en g\'en\'eral 
de l'ordre de ${\rm O}(h^2)={\rm O}(n^{-2})$.
N\'eanmoins, pour une fonction $f$ p\'eriodique de p\'eriode $\beta-\alpha$
et de classe $C^{2l}$, l'erreur est major\'ee par ${\rm O}(h^{2l})\,$; 
dans ce cas, on a en effet $f^{(m)}(\beta)=f^{(m)}(\alpha)$ pour tout $m$.

Comme les int\'egrales \`a \'evaluer sont des
int\'egrales de fonctions p\'eriodiques, la convergence de la m\'ethode
des trap\`ezes est donc extr\^ement rapide, tout au moins dans le cas de 
fonctions $\ci$. Cette remarque montre que l'on n'a pas int\'er\^et
\`a calculer $R$ par int\'egration \`a partir de 7.2~(a), mais
plut\^ot \`a partir de 7.2~(b) et de la formule de Cauchy
$$R(w)={1\over 2i\pi}\int_\pom{R(z)\,dz\over z-w}.$$

Supposons donn\'ee une param\'etrisation quelconque 
$[\alpha,\beta]\ni t\mapsto z(t)$ de la courbe $\pom$.
En multipliant (8.1) par $|z'(t)|^{1/2}$ apr\`es avoir substitu\'e
$w=z(t)$, $z=z(u)$, on obtient la relation \'equivalente
$$\sigma(t)+\int_\alpha^\beta a(t,u)\,\sigma(u)\,du=g(t),\leqno(8.2)$$
avec les notations
$$\eqalign{
\sigma(t)&=|z'(t)|^{1/2}\,S\big(z(t),a\big),\cr
g(t)&=|z'(t)|^{1/2}\,\ov{H\big(a,z(t)\big)},\cr
a(t,u)&=|z'(t)|^{1/2}\,|z'(u)|^{1/2}\,A\big(z(t),z(u)\big).\cr}$$
Cette \'ecriture a l'avantage de pr\'eserver le caract\`ere hermitien
antisym\'etrique du noyau $a(t,u)$. Les fonctions $g(t)$ et $a(t,u)$ 
sont donn\'ees par les formules explicites
$$\eqalign{
g(t)&={1\over 2i\pi}\,\ov{z'(t)\over a-z(t)}\,|z'(t)|^{-1/2},\cr
h(t,u)&={1\over 2i\pi}\,{z'(u)\over z(u)-z(t)}\,|z'(t)|^{1/2}\,|z'(u)|^{-1/2},\cr
a(t,u)&=\cases{\ov{h(u,t)}-h(t,u)&si~~$t\ne u$\cr 0&si~~$t=u$.\cr}\cr}$$
L'utilisation de la m\'ethode des trap\`ezes conduit \`a r\'esoudre le 
syst\`eme lin\'eaire
$$\sigma(t_i)+h\sum_{0\le j<n}a(t_i,t_j)\,\sigma(t_j)=g(t_i),~~~~0\le i<n.$$
Ce syst\`eme est de rang $n$, car la matrice antisym\'etrique
$\big(a(t_i,t_j)\big)$ a toutes ses valeurs propres imaginaires.
La r\'esolution du syst\`eme fournit les valeurs $\sigma(t_j)$ cherch\'ees,
par exemple \`a l'aide de la m\'ethode d'\'elimination de Gauss.
Dans cette situation, il existe en fait des sch\'emas de r\'esolution
it\'eratifs plus efficaces (voir\break M.R. Trummer). Une fois les valeurs
$\sigma(t_j)$ connues, on obtient
$$R\big(z(t_j)\big)
=-i\,{z'(t_j)\over|z'(t_j)|}\,{\sigma(t_j)^2\over|\sigma(t_j)|^2},$$
et une int\'egration approch\'ee de la formule de Cauchy donne
$$R(w)\simeq{h\over 2i\pi}\sum_{0\le j<n}{z'(t_j)\over z(t_j)-w}\,
R\big(z(t_j)\big).\leqno(8.3)$$
Tous ces calculs sont imm\'ediats d\`es lors que la fonction $z(t)$ et sa 
d\'eriv\'ee $z'(t)$ sont connues aux points $t=t_j$. L'application de 
Riemann inverse
$$Q=R^{-1}:D\to\Omega,~~~~Q(0)=a,$$
peut \^etre \'evalu\'ee comme suit. La formule des r\'esidus implique
$$\eqalign{
Q'(w)&={1\over R'\big(R^{-1}(w)\big)}={1\over 2i\pi}
\int_\pom{dz\over R(z)-w},\cr
Q(w)&=a+\int_0^w Q'(v)\,dv=a-{1\over 2i\pi}\int_\pom
\log\big(1-w\ov{R(z)}\big)\,dz.\cr}$$
L'approximation des trap\`ezes fournit alors
$$Q(w)\simeq a-{h\over 2i\pi}\sum_{0\le j<n}\log\big(1-w\ov{R(z(t_j))}
\big)\,z'(t_j).\leqno(8.4)$$
Dans la pratique, les formules (8.3) et (8.4) sont un peu instables
lorsqu'on s'approche du bord, \`a cause des p\^oles de la fonction \`a
int\'egrer. Un moyen de r\'esoudre cette difficult\'e est de consid\'erer
que $R(z)$ est affine par morceaux sur le bord entre les points
$z(t_j)$ et $z(t_{j+1})$. Pour la fonction~$Q$, ceci donne par exemple
$$Q(w)\simeq a+{1/w\over 2\pi i}\sum_{0\le j<n}{z(t_{j+1})-z(t_j)\over
\ov{R(z(t_{j+1}))}-\ov{R(z(t_j))}}\Big[\zeta\log\zeta-\zeta\Big
]_{\zeta=1-w\ov{R(z(t_j))}}^{\zeta=1-w\ov{R(z(t_{j+1}))}}.\leqno(8.4')$$
L'approximation obtenue est alors tout \`a fait bonne, m\^eme au voisinage
du bord.
\vskip40pt

\centerline{\bf Bibliographie}
\vskip30pt
\article 1|N. Kerzman {\rm and} E.M. Stein|The Cauchy kernel, the Szeg\"o
kernel and the Riemann mapping function|Math. Ann.|236|1978|85-93|
\article 2|N. Kerzman {\rm and} M.R. Trummer|Numerical conformal mapping
via the Szeg\"o kernel|J. Comp. Appl. Math.|14|1986|111-123|
\livre 3|W. Rudin|Analyse r\'eelle et complexe|Mc Graw-Hill, {\oldstyle 1966}
et Masson, Paris|1975|
\article 4|M.R. Trummer|An efficient implementation of a conformal mapping
method based on the Szeg\"o kernel|Siam J. Numer. Anal.|23|1986|\break
853-872|
\vfill\eject
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 59.254  71.233   64.554  67.738   70.377  64.843   76.643  62.666 
 83.235  61.311   90.000  60.851   96.765  61.311  103.357  62.666 
109.623  64.843  115.446  67.739  120.746  71.233  125.483  75.209 
129.645  79.558  133.238  84.189  136.282  89.029  138.802  94.018 
140.824  99.114  142.369 104.282  143.459 109.498  144.106 114.742 
144.321 120.000  ] scurve
154.428 120.000 moveto
[ 154.428 120.000  154.207 126.042  153.540 132.085  152.411 138.126 
150.799 144.161  148.668 150.176  145.977 156.148  142.673 162.043 
138.697 167.801  133.988 173.339  128.491 178.538  122.172 183.241 
115.042 187.250  107.178 190.344   98.745 192.309   90.000 192.983 
 81.255 192.309   72.822 190.344   64.958 187.250   57.828 183.241 
 51.510 178.538   46.013 173.339   41.303 167.801   37.327 162.043 
 34.023 156.149   31.332 150.176   29.201 144.161   27.589 138.127 
 26.460 132.085   25.793 126.043   25.572 120.000   25.793 113.958 
 26.460 107.915   27.588 101.874   29.201  95.839   31.331  89.824 
 34.023  83.851   37.327  77.957   41.303  72.199   46.012  66.661 
 51.509  61.462   57.828  56.759   64.958  52.750   72.822  49.656 
 81.255  47.691   90.000  47.016   98.745  47.691  107.178  49.656 
115.042  52.750  122.172  56.760  128.491  61.462  133.988  66.662 
138.697  72.199  142.673  77.957  145.977  83.852  148.668  89.824 
150.799  95.839  152.411 101.873  153.540 107.915  154.207 113.958 
154.428 120.000  ] scurve
162.644 120.000 moveto
[ 162.644 120.000  162.427 126.613  161.773 133.240  160.662 139.894 
159.065 146.583  156.938 153.310  154.223 160.071  150.843 166.842 
146.707 173.583  141.706 180.213  135.723 186.608  128.651 192.571 
120.424 197.825  111.076 202.011  100.804 204.740   90.000 205.692 
 79.196 204.740   68.924 202.011   59.576 197.825   51.349 192.571 
 44.277 186.608   38.294 180.214   33.293 173.583   29.157 166.843 
 25.777 160.071   23.062 153.311   20.935 146.583   19.338 139.894 
 18.227 133.241   17.572 126.613   17.356 120.000   17.572 113.387 
 18.227 106.760   19.338 100.106   20.935  93.417   23.062  86.689 
 25.777  79.929   29.157  73.157   33.293  66.417   38.294  59.786 
 44.277  53.392   51.349  47.428   59.576  42.175   68.924  37.988 
 79.196  35.259   90.000  34.308  100.805  35.259  111.076  37.989 
120.424  42.175  128.651  47.429  135.723  53.392  141.706  59.787 
146.707  66.418  150.843  73.158  154.223  79.929  156.938  86.690 
159.065  93.417  160.662 100.106  161.773 106.759  162.427 113.387 
162.644 120.000  ] scurve
169.610 120.000 moveto
[ 169.610 120.000  169.553 123.524  169.400 127.043  169.144 130.578 
168.774 134.120  168.302 137.670  167.715 141.245  167.007 144.832 
166.181 148.442  165.221 152.079  164.123 155.737  162.880 159.426 
161.475 163.141  159.903 166.884  158.144 170.653  156.185 174.444 
154.007 178.254  151.590 182.072  148.912 185.889  145.949 189.688 
142.675 193.447  139.064 197.137  135.091 200.722  130.732 204.153 
125.971 207.371  120.803 210.307  115.236 212.880  109.303 215.006 
103.059 216.599   96.590 217.588   90.000 217.923   83.411 217.588 
 76.941 216.599   70.698 215.005   64.764 212.880   59.198 210.307 
 54.029 207.371   49.269 204.153   44.910 200.722   40.936 197.138 
 37.325 193.447   34.051 189.688   31.088 185.890   28.410 182.073 
 25.993 178.254   23.815 174.445   21.856 170.654   20.097 166.884 
 18.525 163.141   17.120 159.427   15.877 155.737   14.779 152.079 
 13.819 148.442   12.993 144.832   12.285 141.245   11.698 137.671 
 11.226 134.120   10.856 130.579   10.600 127.044   10.446 123.524 
 10.390 120.000   10.446 116.476   10.600 112.957   10.855 109.422 
 11.226 105.880   11.698 102.330   12.284  98.755   12.993  95.168 
 13.818  91.558   14.779  87.921   15.876  84.263   17.120  80.574 
 18.524  76.859   20.097  73.116   21.856  69.346   23.815  65.555 
 25.993  61.746   28.410  57.927   31.088  54.110   34.051  50.311 
 37.325  46.552   40.936  42.862   44.909  39.278   49.268  35.847 
 54.029  32.629   59.198  29.693   64.764  27.119   70.698  24.994 
 76.941  23.401   83.411  22.412   90.000  22.077   96.590  22.412 
103.060  23.401  109.303  24.994  115.236  27.120  120.803  29.693 
125.971  32.629  130.732  35.848  135.091  39.278  139.064  42.863 
142.675  46.553  145.949  50.312  148.912  54.111  151.590  57.928 
154.007  61.746  156.185  65.556  158.144  69.347  159.903  73.116 
161.475  76.859  162.880  80.574  164.123  84.263  165.221  87.921 
166.181  91.558  167.007  95.168  167.715  98.755  168.302 102.330 
168.774 105.880  169.144 109.421  169.400 112.957  169.553 116.476 
169.610 120.000  ] scurve
175.795 120.000 moveto
[ 175.795 120.000  175.646 122.586  175.457 124.938  175.436 127.263 
175.441 129.809  175.166 132.439  174.779 134.849  174.545 137.189 
174.371 139.728  173.944 142.396  173.368 144.870  172.926 147.265 
172.535 149.852  171.895 152.559  171.125 155.083  170.478 157.573 
169.813 160.268  168.884 162.999  167.913 165.569  167.027 168.217 
165.974 171.033  164.730 173.747  163.535 176.434  162.244 179.285 
160.728 182.100  159.201 184.870  157.559 187.770  155.704 190.632 
153.797 193.485  151.699 196.416  149.431 199.283  147.026 202.188 
144.390 205.061  141.592 207.907  138.550 210.714  135.303 213.451 
131.800 216.103  128.061 218.639  124.059 221.020  119.805 223.218 
115.304 225.181  110.568 226.871  105.626 228.243  100.518 229.256 
 95.290 229.878   90.000 230.087   84.710 229.877   79.482 229.256 
 74.374 228.242   69.433 226.870   64.697 225.181   60.195 223.217 
 55.941 221.020   51.940 218.639   48.200 216.103   44.697 213.451 
 41.451 210.714   38.408 207.907   35.610 205.061   32.974 202.189 
 30.570 199.283   28.301 196.417   26.204 193.486   24.296 190.632 
 22.441 187.770   20.800 184.870   19.272 182.101   17.756 179.285 
 16.465 176.434   15.270 173.747   14.026 171.033   12.974 168.217 
 12.087 165.570   11.116 162.999   10.187 160.268    9.522 157.573 
  8.875 155.083    8.105 152.559    7.465 149.853    7.074 147.266 
  6.632 144.870    6.056 142.397    5.629 139.728    5.455 137.190 
  5.221 134.849    4.834 132.440    4.559 129.809    4.563 127.263 
  4.543 124.938    4.353 122.586    4.205 120.000    4.353 117.414 
  4.543 115.062    4.563 112.737    4.559 110.192    4.834 107.561 
  5.221 105.151    5.455 102.811    5.629 100.272    6.055  97.604 
  6.631  95.130    7.074  92.735    7.464  90.148    8.104  87.441 
  8.875  84.917    9.522  82.427   10.187  79.732   11.115  77.001 
 12.087  74.431   12.973  71.783   14.026  68.967   15.269  66.253 
 16.464  63.566   17.755  60.715   19.272  57.899   20.799  55.130 
 22.441  52.229   24.296  49.368   26.203  46.514   28.301  43.583 
 30.569  40.717   32.974  37.811   35.610  34.939   38.408  32.092 
 41.450  29.285   44.697  26.548   48.200  23.896   51.940  21.361 
 55.941  18.979   60.195  16.782   64.697  14.818   69.433  13.129 
 74.374  11.757   79.483  10.744   84.710  10.122   90.001   9.912 
 95.291  10.122  100.519  10.744  105.627  11.757  110.568  13.130 
115.304  14.819  119.805  16.783  124.059  18.980  128.061  21.362 
131.800  23.897  135.303  26.549  138.550  29.286  141.592  32.093 
144.390  34.939  147.026  37.812  149.431  40.717  151.699  43.584 
153.797  46.515  155.704  49.368  157.559  52.230  159.201  55.130 
160.728  57.900  162.244  60.715  163.535  63.566  164.730  66.253 
165.974  68.967  167.026  71.783  167.913  74.431  168.884  77.001 
169.813  79.732  170.478  82.427  171.125  84.917  171.895  87.441 
172.535  90.148  172.926  92.735  173.368  95.130  173.944  97.603 
174.371 100.272  174.545 102.811  174.779 105.151  175.166 107.560 
175.441 110.191  175.436 112.737  175.457 115.062  175.646 117.414 
175.795 120.000  ] scurve
 10.000  16.000 moveto
  1.000 nbpt mul rm  (Ellipse) show currentpoint
clear
 10.000   7.000 moveto
  1.000 nbpt mul it  (x ) show currentpoint
  1.000 nbpt mul rm  (= 3 cos ) show currentpoint
  1.000 nbpt mul it  (t) show currentpoint
clear
 10.000   0.000 moveto
  1.000 nbpt mul it  (y ) show currentpoint
  1.000 nbpt mul rm  (= 4 sin ) show currentpoint
  1.000 nbpt mul it  (t) show currentpoint
clear
144.000   0.000 moveto
  1.000 nbpt mul rm  (Centre ) show <28> show (0,0) show <29> show currentpoint
clear
}
\EndFig
\vskip30pt
\centerline{\bf Fig.\ 1}
\vfill\eject


\InsertFig 0.000 184.000  {
%%EPS file  z2.eps
0.72 dup scale
1 mm unit  /nbpt 14 def
  0.000   0.000 translate
  0.452 setlinewidth
180.000 120.000 moveto
[ 180.000 120.000  179.945 124.188  179.781 128.371  179.507 132.543 
179.124 136.701  178.633 140.838  178.033 144.949  177.327 149.031 
176.514 153.076  175.595 157.082  174.572 161.042  173.447 164.953 
172.219 168.808  170.891 172.605  169.465 176.337  167.942 180.000 
166.324 183.590  164.613 187.103  162.812 190.534  160.921 193.879 
158.944 197.135  156.883 200.296  154.741 203.359  152.519 206.321 
150.222 209.177  147.851 211.925  145.410 214.561  142.901 217.082 
140.327 219.485  137.693 221.766  135.000 223.923  132.252 225.954 
129.453 227.855  126.606 229.625  123.715 231.262  120.782 232.763 
117.812 234.127  114.807 235.351  111.773 236.435  108.712 237.378 
105.628 238.177  102.526 238.832   99.408 239.343   96.278 239.708 
 93.141 239.927   90.000 240.000   86.859 239.927   83.722 239.708 
 80.592 239.343   77.474 238.832   74.372 238.177   71.288 237.378 
 68.227 236.435   65.193 235.351   62.188 234.127   59.218 232.763 
 56.285 231.262   53.394 229.625   50.547 227.855   47.748 225.954 
 45.000 223.923   42.307 221.766   39.673 219.485   37.099 217.082 
 34.590 214.561   32.149 211.925   29.778 209.177   27.481 206.321 
 25.259 203.359   23.117 200.296   21.056 197.135   19.079 193.879 
 17.188 190.534   15.387 187.103   13.676 183.590   12.058 180.000 
 10.535 176.337    9.109 172.605    7.781 168.808    6.553 164.953 
  5.428 161.042    4.405 157.082    3.486 153.076    2.673 149.031 
  1.967 144.949    1.367 140.838    0.876 136.701    0.493 132.543 
  0.219 128.371    0.055 124.188    0.000 120.000    0.055 115.812 
  0.219 111.629    0.493 107.457    0.876 103.299    1.367  99.162 
  1.967  95.051    2.673  90.969    3.486  86.924    4.405  82.918 
  5.428  78.958    6.553  75.047    7.781  71.192    9.109  67.395 
 10.535  63.663   12.058  60.000   13.676  56.410   15.387  52.897 
 17.188  49.466   19.079  46.121   21.056  42.866   23.117  39.704 
 25.259  36.641   27.481  33.679   29.778  30.823   32.149  28.075 
 34.590  25.439   37.099  22.918   39.673  20.516   42.307  18.234 
 45.000  16.077   47.748  14.046   50.547  12.145   53.394  10.375 
 56.285   8.738   59.218   7.237   62.188   5.873   65.193   4.649 
 68.227   3.565   71.288   2.622   74.372   1.823   77.474   1.168 
 80.592   0.657   83.722   0.292   86.859   0.073   90.000   0.000 
 93.141   0.073   96.278   0.292   99.408   0.657  102.526   1.168 
105.628   1.823  108.712   2.622  111.773   3.565  114.807   4.649 
117.812   5.873  120.782   7.237  123.715   8.738  126.606  10.375 
129.453  12.145  132.252  14.046  135.000  16.077  137.693  18.234 
140.327  20.515  142.901  22.918  145.410  25.439  147.851  28.075 
150.222  30.823  152.519  33.679  154.741  36.641  156.883  39.704 
158.944  42.865  160.921  46.121  162.812  49.466  164.613  52.897 
166.324  56.410  167.942  60.000  169.465  63.663  170.891  67.395 
172.219  71.192  173.447  75.047  174.572  78.958  175.595  82.918 
176.514  86.923  177.327  90.969  178.033  95.051  178.633  99.162 
179.124 103.299  179.507 107.457  179.781 111.629  179.945 115.812 
180.000 120.000  ] scurve
  0.113 setlinewidth
120.000 150.000 moveto
[ 120.000 150.000  115.763 150.040  111.355 150.164  106.773 150.384 
102.020 150.708   97.097 151.146   92.008 151.706   86.759 152.397 
 81.358 153.226   75.815 154.198   70.141 155.316   64.349 156.583 
 58.454 157.996   52.472 159.552   46.417 161.246   40.308 163.069 
 34.160 165.010   27.991 167.057   21.815 169.195   15.645 171.434 
  9.729 174.268  ] scurve
120.000 150.000 moveto
[ 120.000 150.000  116.008 148.555  111.827 147.062  107.449 145.525 
102.864 143.950   98.063 142.345   93.037 140.720   87.779 139.086 
 82.283 137.458   76.545 135.855   70.562 134.297   64.338 132.806 
 57.877 131.407   51.192 130.128   44.297 128.994   37.216 128.033 
 29.976 127.270   22.609 126.724   15.153 126.412    7.660 126.333 
  0.122 126.250  ] scurve
120.000 150.000 moveto
[ 120.000 150.000  116.767 147.253  113.421 144.346  109.956 141.270 
106.360 138.020  102.622 134.590   98.726 130.972   94.654 127.163 
 90.386 123.157   85.895 118.953   81.152 114.552   76.120 109.957 
 70.758 105.179   65.016 100.236   58.840  95.157   52.170  89.988 
 44.944  84.793   37.106  79.663   28.613  74.715   19.448  70.094 
  9.747  65.684  ] scurve
120.000 150.000 moveto
[ 120.000 150.000  117.934 146.311  115.890 142.426  113.870 138.336 
111.877 134.027  109.911 129.484  107.976 124.689  106.073 119.623 
104.203 114.259  102.368 108.569  100.569 102.515   98.807  96.054 
 97.083  89.128   95.398  81.669   93.752  73.584   92.146  64.755 
 90.579  55.018   89.048  44.145   87.549  31.801   86.065  17.459 
 84.534   0.222  ] scurve
120.000 150.000 moveto
[ 120.000 150.000  119.348 145.846  118.839 141.561  118.484 137.141 
118.298 132.583  118.293 127.885  118.488 123.043  118.902 118.055 
119.560 112.919  120.488 107.635  121.719 102.205  123.291  96.635 
125.248  90.937  127.639  85.131  130.521  79.246  133.956  73.330 
138.006  67.450  142.728  61.700  148.166  56.202  154.329  51.104 
161.044  46.332  ] scurve
120.000 150.000 moveto
[ 120.000 150.000  120.815 145.906  121.822 141.807  123.029 137.710 
124.443 133.626  126.072 129.567  127.924 125.547  130.004 121.581 
132.319 117.689  134.873 113.892  137.668 110.212  140.702 106.676 
143.970 103.311  147.462 100.146  151.163  97.209  155.051  94.527 
159.101  92.126  163.281  90.025  167.557  88.235  171.881  86.672 
176.048  84.831  ] scurve
120.000 150.000 moveto
[ 120.000 150.000  122.151 146.461  124.449 143.040  126.890 139.748 
129.469 136.595  132.179 133.592  135.011 130.748  137.955 128.074 
140.999 125.580  144.129 123.272  147.332 121.158  150.590 119.244 
153.888 117.530  157.208 116.019  160.534 114.708  163.847 113.595 
167.133 112.674  170.379 111.940  173.588 111.405  176.860 111.201 
179.796 111.933  ] scurve
120.000 150.000 moveto
[ 120.000 150.000  123.201 147.422  126.438 145.026  129.701 142.814 
132.978 140.784  136.258 138.936  139.531 137.268  142.786 135.774 
146.011 134.451  149.198 133.292  152.336 132.291  155.418 131.440 
158.436 130.730  161.384 130.152  164.257 129.698  167.050 129.359 
169.763 129.122  172.400 128.972  174.986 128.861  177.604 128.584 
179.813 127.740  ] scurve
120.000 150.000 moveto
[ 120.000 150.000  123.859 148.663  127.631 147.485  131.310 146.460 
134.892 145.578  138.372 144.830  141.748 144.207  145.018 143.700 
148.180 143.298  151.235 142.994  154.183 142.778  157.025 142.642 
159.762 142.578  162.396 142.579  164.931 142.637  167.367 142.748 
169.709 142.910  171.957 143.132  174.110 143.465  176.109 144.077 
178.023 145.017  ] scurve
120.000 150.000 moveto
[ 120.000 150.000  124.067 150.036  127.967 150.140  131.705 150.303 
135.285 150.516  138.712 150.774  141.992 151.069  145.130 151.396 
148.133 151.749  151.007 152.124  153.757 152.517  156.390 152.923 
158.910 153.341  161.324 153.766  163.637 154.197  165.851 154.631 
167.968 155.066  169.973 155.500  171.821 155.927  173.392 156.332 
175.633 156.925  ] scurve
120.000 150.000 moveto
[ 120.000 150.000  123.813 151.394  127.456 152.735  130.938 154.023 
134.268 155.258  137.452 156.439  140.500 157.569  143.417 158.648 
146.212 159.677  148.891 160.659  151.459 161.595  153.923 162.488 
156.287 163.339  158.558 164.150  160.740 164.922  162.837 165.657 
164.852 166.351  166.786 166.988  168.629 167.520  170.322 167.820 
172.438 168.148  ] scurve
120.000 150.000 moveto
[ 120.000 150.000  123.129 152.593  126.160 155.038  129.097 157.343 
131.945 159.514  134.708 161.557  137.389 163.480  139.991 165.287 
142.517 166.986  144.968 168.582  147.347 170.081  149.656 171.488 
151.897 172.808  154.072 174.047  156.182 175.209  158.231 176.298 
160.224 177.318  162.178 178.271  164.149 179.155  166.362 179.912 
168.110 179.612  ] scurve
120.000 150.000 moveto
[ 120.000 150.000  122.085 153.504  124.186 156.832  126.301 159.990 
128.426 162.987  130.558 165.828  132.695 168.518  134.832 171.065 
136.966 173.473  139.095 175.747  141.214 177.891  143.321 179.912 
145.413 181.814  147.485 183.600  149.537 185.277  151.564 186.850 
153.563 188.323  155.526 189.708  157.415 191.032  159.084 192.356 
160.901 193.913  ] scurve
120.000 150.000 moveto
[ 120.000 150.000  120.786 154.024  121.697 157.920  122.726 161.691 
123.864 165.337  125.106 168.860  126.445 172.259  127.875 175.536 
129.390 178.690  130.984 181.722  132.652 184.630  134.387 187.415 
136.184 190.077  138.037 192.615  139.939 195.029  141.884 197.320 
143.866 199.488  145.881 201.535  147.940 203.480  150.145 205.453 
151.743 207.309  ] scurve
120.000 150.000 moveto
[ 120.000 150.000  119.371 154.081  118.921 158.142  118.645 162.177 
118.538 166.183  118.595 170.153  118.813 174.085  119.187 177.972 
119.716 181.812  120.397 185.600  121.228 189.330  122.206 192.998 
123.330 196.598  124.599 200.124  126.010 203.569  127.560 206.926 
129.248 210.188  131.068 213.346  133.011 216.395  134.989 219.335 
136.903 222.417  ] scurve
120.000 150.000 moveto
[ 120.000 150.000  118.000 153.648  116.153 157.397  114.461 161.239 
112.924 165.165  111.544 169.172  110.321 173.252  109.256 177.401 
108.351 181.616  107.606 185.894  107.025 190.232  106.610 194.627 
106.366 199.080  106.298 203.587  106.411 208.149  106.715 212.763 
107.220 217.429  107.936 222.142  108.880 226.899  110.089 231.693 
112.016 236.354  ] scurve
120.000 150.000 moveto
[ 120.000 150.000  116.844 152.758  113.742 155.695  110.702 158.806 
107.730 162.088  104.832 165.538  102.013 169.152   99.276 172.928 
 96.622 176.862   94.054 180.953   91.572 185.200   89.173 189.604 
 86.858 194.166   84.623 198.889   82.465 203.779   80.378 208.843 
 78.359 214.090   76.398 219.534   74.489 225.192   72.623 231.088 
 71.065 237.314  ] scurve
120.000 150.000 moveto
[ 120.000 150.000  116.059 151.505  112.044 153.183  107.962 155.040 
103.820 157.080   99.625 159.305   95.385 161.717   91.106 164.315 
 86.793 167.097   82.451 170.060   78.084 173.199   73.693 176.508 
 69.278 179.981   64.837 183.609   60.367 187.382   55.863 191.290 
 51.318 195.320   46.724 199.458   42.070 203.690   37.336 207.988 
 32.203 211.985  ] scurve
133.086 150.378 moveto
[ 133.086 150.378  132.956 151.644  132.714 152.888  132.364 154.103 
131.907 155.280  131.347 156.414  130.686 157.496  129.928 158.518 
129.076 159.473  128.135 160.353  127.109 161.149  126.002 161.854 
124.822 162.459  123.575 162.954  122.271 163.332  120.918 163.585 
119.527 163.704  118.111 163.683  116.684 163.515  115.260 163.196 
113.857 162.723  112.493 162.095  111.185 161.312  109.953 160.379 
108.816 159.300  107.793 158.086  106.903 156.748  106.163 155.302 
105.588 153.763  105.192 152.153  104.984 150.494  104.974 148.811 
105.164 147.127  105.555 145.471  106.143 143.869  106.921 142.347 
107.876 140.929  108.993 139.640  110.252 138.498  111.632 137.521 
113.108 136.722  114.655 136.110  116.246 135.688  117.856 135.457 
119.460 135.414  121.035 135.552  122.561 135.859  124.020 136.325 
125.397 136.936  126.679 137.676  127.856 138.531  128.921 139.486 
129.870 140.526  130.698 141.636  131.404 142.804  131.986 144.017 
132.446 145.264  132.784 146.533  133.003 147.814  133.102 149.099 
133.086 150.378  ] scurve
148.953 151.852 moveto
[ 148.953 151.852  148.549 154.344  147.981 156.784  147.254 159.173 
146.367 161.508  145.320 163.786  144.110 166.003  142.735 168.154 
141.190 170.231  139.468 172.225  137.565 174.125  135.473 175.914 
133.187 177.576  130.703 179.088  128.017 180.423  125.131 181.552 
122.049 182.441  118.784 183.051  115.355 183.343  111.789 183.276 
108.125 182.811  104.411 181.913  100.706 180.554   97.074 178.716 
 93.589 176.392   90.324 173.589   87.356 170.326   84.755 166.635 
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 86.876 124.674   90.383 120.744   94.432 117.377   98.912 114.672 
103.684 112.696  108.598 111.479  113.501 111.008  118.259 111.233 
122.760 112.076  126.927 113.441  130.712 115.231  134.094 117.350 
137.071 119.715  139.655 122.255  141.870 124.913  143.739 127.642 
145.291 130.408  146.551 133.185  147.544 135.953  148.293 138.700 
148.816 141.415  149.132 144.091  149.252 146.724  149.190 149.312 
148.953 151.852  ] scurve
156.934 153.011 moveto
[ 156.934 153.011  156.367 155.976  155.643 158.882  154.761 161.733 
153.722 164.534  152.520 167.288  151.149 169.996  149.601 172.657 
147.863 175.270  145.924 177.829  143.766 180.326  141.374 182.747 
138.726 185.075  135.803 187.285  132.584 189.346  129.052 191.217 
125.192 192.846  120.997 194.171  116.473 195.121  111.641 195.615 
106.544 195.568  101.250 194.898   95.848 193.537   90.451 191.431 
 85.186 188.556   80.181 184.915   75.563 180.536   71.449 175.472 
 67.942 169.787   65.133 163.559   63.106 156.870   61.939 149.812 
 61.707 142.484   62.488 135.004   64.354 127.513   67.368 120.188 
 71.564 113.246   76.923 106.947   83.344 101.574   90.621  97.400 
 98.438  94.625  106.416  93.327  114.177  93.438  121.414  94.766 
127.931  97.056  133.640 100.040  138.538 103.486  142.675 107.209 
146.125 111.071  148.969 114.977  151.288 118.863  153.152 122.690 
154.623 126.434  155.755 130.083  156.589 133.633  157.163 137.083 
157.504 140.437  157.636 143.701  157.577 146.880  157.339 149.981 
156.934 153.011  ] scurve
162.545 153.991 moveto
[ 162.545 153.991  161.863 157.228  161.036 160.404  160.065 163.527 
158.947 166.607  157.673 169.652  156.237 172.667  154.624 175.658 
152.820 178.625  150.806 181.570  148.560 184.490  146.055 187.376 
143.261 190.216  140.143 192.988  136.663 195.662  132.782 198.195 
128.461 200.528  123.666 202.582  118.374 204.256  112.585 205.430 
106.334 205.964   99.696 205.716   92.797 204.554   85.804 202.381 
 78.914 199.150   72.327 194.868   66.226 189.591   60.764 183.407 
 56.062 176.417   52.218 168.723   49.316 160.421   47.440 151.599 
 46.683 142.347   47.159 132.763   49.006 122.977   52.385 113.174 
 57.459 103.627   64.349  94.736   73.046  87.031   83.299  81.122 
 94.533  77.530  105.933  76.464  116.682  77.714  126.219  80.757 
134.312  84.987  140.982  89.885  146.382  95.078  150.703 100.327 
154.134 105.492  156.837 110.498  158.946 115.309  160.567 119.916 
161.785 124.321  162.666 128.536  163.262 132.574  163.613 136.451 
163.749 140.185  163.695 143.791  163.469 147.285  163.082 150.681 
162.545 153.991  ] scurve
166.905 154.845 moveto
[ 166.905 154.845  166.145 158.255  165.242 161.619  164.207 164.913 
163.054 168.184  161.740 171.435  160.279 174.656  158.655 177.886 
156.833 181.111  154.813 184.342  152.551 187.586  150.025 190.834 
147.190 194.088  144.004 197.328  140.411 200.533  136.353 203.663 
131.763 206.660  126.573 209.438  120.724 211.876  114.177 213.814 
106.938 215.052   99.079 215.367   90.760 214.544   82.222 212.415 
 73.758 208.908   65.662 204.049   58.183 197.945   51.504 190.746 
 45.746 182.607   40.987 173.660   37.288 164.010   34.714 153.733 
 33.357 142.887   33.346 131.523   34.872 119.714   38.198 107.586 
 43.664  95.387   51.655  83.580   62.466  72.967   76.000  64.724 
 91.370  60.091  106.906  59.639  120.926  62.794  132.551  68.292 
141.721  74.938  148.783  81.937  154.171  88.853  158.267  95.480 
161.374 101.737  163.718 107.611  165.468 113.118  166.750 118.287 
167.654 123.155  168.253 127.751  168.596 132.117  168.722 136.270 
168.668 140.252  168.436 144.079  168.068 147.766  167.558 151.360 
166.905 154.845  ] scurve
170.430 155.602 moveto
[ 170.430 155.602  170.062 157.324  169.697 159.096  169.251 160.910 
168.703 162.684  168.123 164.371  167.578 166.016  167.060 167.694 
166.499 169.439  165.832 171.198  165.091 172.892  164.354 174.530 
163.643 176.184  162.906 177.903  162.071 179.660  161.145 181.380 
160.197 183.054  159.254 184.745  158.264 186.497  157.167 188.278 
155.984 190.027  154.770 191.761  153.513 193.537  152.152 195.352 
150.682 197.157  149.141 198.951  147.518 200.776  145.767 202.619 
143.894 204.449  141.910 206.281  139.781 208.118  137.496 209.936 
135.056 211.734  132.435 213.502  129.625 215.221  126.613 216.877 
123.384 218.445  119.928 219.902  116.237 221.216  112.307 222.351 
108.140 223.270  103.744 223.928   99.137 224.284   94.349 224.294 
 89.418 223.922   84.389 223.136   79.317 221.918   74.259 220.257 
 69.269 218.159   64.400 215.638   59.696 212.716   55.195 209.421 
 50.924 205.784   46.904 201.836   43.151 197.608   39.671 193.124 
 36.472 188.409   33.555 183.481   30.923 178.356   28.578 173.045 
 26.522 167.558   24.760 161.898   23.298 156.070   22.147 150.074 
 21.318 143.909   20.831 137.573   20.708 131.065   20.979 124.381 
 21.681 117.521   22.860 110.488   24.574 103.290   26.892  95.946 
 29.898  88.488   33.690  80.970   38.378  73.481   44.077  66.157 
 50.892  59.200   58.880  52.887   68.002  47.568   78.065  43.622 
 88.689  41.358   99.360  40.905  109.556  42.145  118.884  44.769 
127.142  48.387  134.292  52.634  140.403  57.221  145.589  61.944 
149.980  66.665  153.695  71.300  156.843  75.799  159.513  80.135 
161.782  84.297  163.713  88.282  165.358  92.095  166.756  95.740 
167.951  99.226  168.960 102.570  169.812 105.763  170.543 108.831 
171.144 111.793  171.629 114.625  172.047 117.344  172.391 119.997 
172.626 122.567  172.791 125.017  172.938 127.383  173.045 129.724 
173.057 132.023  172.993 134.216  172.926 136.315  172.873 138.391 
172.769 140.483  172.563 142.536  172.302 144.486  172.062 146.357 
171.851 148.226  171.607 150.138  171.261 152.045  170.840 153.866 
170.430 155.602  ] scurve
173.141 156.263 moveto
[ 173.141 156.263  172.955 157.236  172.896 158.298  172.912 159.545 
172.817 161.069  172.327 162.659  171.612 163.935  170.989 164.950 
170.529 165.868  170.221 166.791  170.039 167.791  169.942 168.954 
169.792 170.376  169.304 171.954  168.509 173.282  167.763 174.314 
167.183 175.232  166.760 176.156  166.463 177.168  166.237 178.354 
165.926 179.798  165.261 181.348  164.349 182.619  163.528 183.632 
162.884 184.580  162.388 185.583  161.986 186.737  161.548 188.132 
160.815 189.692  159.788 191.039  158.818 192.118  158.028 193.136 
157.380 194.244  156.772 195.554  155.987 197.091  154.862 198.569 
153.687 199.766  152.679 200.870  151.801 202.081  150.901 203.514 
149.728 205.081  148.331 206.448  147.028 207.644  145.854 208.916 
144.623 210.396  143.109 211.934  141.467 213.263  139.931 214.539 
138.384 215.975  136.589 217.484  134.650 218.821  132.765 220.131 
130.766 221.563  128.530 222.926  126.261 224.173  123.903 225.481 
121.323 226.718  118.675 227.843  115.880 228.964  112.912 229.945 
109.848 230.840  106.601 231.613  103.250 232.230   99.746 232.702 
 96.140 232.977   92.415 233.064   88.615 232.928   84.736 232.566 
 80.823 231.964   76.881 231.113   72.951 230.020   69.047 228.673 
 65.194 227.095   61.421 225.277   57.729 223.247   54.157 221.008 
 50.689 218.577   47.365 215.973   44.160 213.199   41.111 210.287 
 38.186 207.224   35.424 204.052   32.783 200.747   30.309 197.352 
 27.947 193.843   25.758 190.251   23.668 186.568   21.754 182.794 
 19.936 178.956   18.283 175.008   16.741 171.022   15.338 166.912 
 14.076 162.769   12.924 158.504   11.942 154.191   11.056 149.773 
 10.355 145.275    9.758 140.691    9.351 136.000    9.072 131.230 
  8.987 126.334    9.060 121.353    9.344 116.238    9.819 111.022 
 10.536 105.671   11.487 100.200   12.726  94.596   14.262  88.857 
 16.145  82.991   18.416  76.995   21.124  70.884   24.332  64.678 
 28.112  58.410   32.542  52.133   37.708  45.929   43.697  39.915 
 50.581  34.261   58.390  29.188   67.080  24.970   76.490  21.891 
 86.328  20.184   96.204  19.948  105.714  21.108  114.543  23.444 
122.508  26.661  129.554  30.473  135.712  34.638  141.059  38.977 
145.691  43.364  149.706  47.715  153.184  51.974  156.212  56.121 
158.849  60.111  161.157  63.983  163.165  67.666  164.967  71.245 
166.481  74.664  167.892  77.898  169.125  81.116  170.116  84.123 
171.115  86.950  172.028  89.836  172.656  92.590  173.257  95.064 
173.973  97.510  174.549 100.093  174.827 102.509  175.113 104.627 
175.571 106.671  176.067 108.889  176.261 111.193  176.239 113.208 
176.315 114.964  176.583 116.670  176.961 118.544  177.133 120.638 
176.956 122.577  176.753 124.187  176.713 125.628  176.861 127.066 
177.132 128.670  177.274 130.543  177.023 132.391  176.634 133.905 
176.366 135.187  176.275 136.394  176.350 137.643  176.535 139.066 
176.613 140.771  176.293 142.515  175.775 143.934  175.354 145.097 
175.098 146.160  175.001 147.225  175.043 148.384  175.149 149.752 
175.077 151.395  174.594 153.000  173.975 154.263  173.477 155.302 
173.141 156.263  ] scurve
 10.000  16.000 moveto
  1.000 nbpt mul rm  (Ellipse) show currentpoint
clear
 10.000   7.000 moveto
  1.000 nbpt mul it  (x ) show currentpoint
  1.000 nbpt mul rm  (= 3 cos ) show currentpoint
  1.000 nbpt mul it  (t) show currentpoint
clear
 10.000   0.000 moveto
  1.000 nbpt mul it  (y ) show currentpoint
  1.000 nbpt mul rm  (= 4 sin ) show currentpoint
  1.000 nbpt mul it  (t) show currentpoint
clear
144.000   0.000 moveto
  1.000 nbpt mul rm  (Centre ) show <28> show (1,1) show <29> show currentpoint
clear
}
\EndFig
\vskip30pt
\centerline{\bf Fig.\ 2}
\vfill\eject


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  0.000 200.000 moveto
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 29.555 115.604   25.361 115.641   21.296 115.671   17.369 115.695 
 13.589 115.714    9.962 115.728    6.510 115.745    3.357 115.802 
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 30.785  54.206   26.057  49.836   20.763  44.992   14.443  39.087 
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101.143  57.236  102.802  51.839  104.487  46.268  106.182  40.478 
107.857  34.395  109.452  27.908  110.822  20.833  111.552  12.942 
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110.188  86.799  113.737  83.396  117.407  80.018  121.208  76.663 
125.146  73.331  129.228  70.025  133.454  66.750  137.815  63.513 
142.289  60.325  146.838  57.204  151.404  54.170  155.865  51.242 
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101.806 107.380  106.019 105.664  110.245 104.042  114.485 102.522 
118.742 101.115  123.021  99.828  127.324  98.673  131.653  97.658 
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153.855  95.241  158.428  95.487  163.011  96.106  167.443  97.163 
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103.248 115.257  107.646 115.427  111.962 115.650  116.190 115.931 
120.322 116.276  124.351 116.689  128.271 117.172  132.074 117.728 
135.754 118.357  139.303 119.060  142.715 119.834  145.983 120.674 
149.101 121.574  152.061 122.525  154.833 123.517  157.276 124.531 
159.950 125.828  ] scurve
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[  85.000 115.000   89.180 117.015   93.309 119.006   97.378 120.967 
101.379 122.890  105.303 124.770  109.144 126.600  112.892 128.377 
116.541 130.096  120.084 131.755  123.516 133.351  126.831 134.882 
130.026 136.349  133.098 137.749  136.046 139.085  138.870 140.357 
141.571 141.565  144.151 142.704  146.609 143.741  148.920 144.526 
151.485 145.177  ] scurve
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108.220 141.914  111.157 144.815  114.102 147.578  117.049 150.192 
119.993 152.649  122.925 154.943  125.836 157.069  128.713 159.023 
131.546 160.808  134.328 162.426  137.072 163.884  139.948 165.208 
142.515 165.681  ] scurve
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 89.470 132.919   90.736 137.325   92.087 141.707   93.538 146.064 
 95.104 150.396   96.803 154.700   98.652 158.972  100.674 163.203 
102.889 167.384  105.326 171.496  108.010 175.515  110.970 179.401 
114.230 183.101  117.800 186.537  121.663 189.617  125.812 192.293 
129.783 194.782  ] scurve
 85.000 115.000 moveto
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 81.202 133.279   80.358 137.928   79.555 142.639   78.793 147.426 
 78.072 152.309   77.392 157.306   76.753 162.438   76.155 167.729 
 75.594 173.201   75.060 178.881   74.537 184.794   73.991 190.962 
 73.361 197.399   72.553 204.093   71.432 210.981   69.871 217.902 
 68.129 224.774  ] scurve
 85.000 115.000 moveto
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 73.501 129.862   70.614 133.666   67.693 137.506   64.722 141.383 
 61.682 145.298   58.554 149.250   55.317 153.241   51.950 157.271 
 48.428 161.344   44.723 165.465   40.803 169.646   36.629 173.912 
 32.145 178.309   27.267 182.931   21.848 187.986   15.635 194.055 
  9.539 203.469  ] scurve
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 50.976 131.623   46.643 133.568   42.291 135.426   37.923 137.180 
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 16.142 143.659   11.917 144.370    7.806 144.869    3.936 145.198 
  0.000 145.441  ] scurve
100.487 115.177 moveto
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100.487 115.177  ] scurve
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121.464 116.385  ] scurve
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105.002  63.304  110.638  66.246  115.764  69.860  120.290  74.028 
124.161  78.626  127.348  83.533  129.842  88.628  131.663  93.792 
132.857  98.917  133.497 103.922  133.662 108.757  133.431 113.401 
132.866 117.855  ] scurve
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135.186 137.261  133.255 141.419  131.120 145.532  128.752 149.625 
126.107 153.724  123.126 157.843  119.730 161.988  115.814 166.138 
111.245 170.236  105.873 174.150   99.568 177.636   92.320 180.335 
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110.303  51.442  117.487  55.391  123.866  60.253  129.347  65.783 
133.919  71.796  137.568  78.153  140.264  84.704  142.009  91.251 
142.896  97.593  143.093 103.597  142.776 109.223  142.081 114.493 
141.103 119.456  ] scurve
147.536 121.109 moveto
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131.714 157.317  128.838 161.906  125.566 166.653  121.763 171.592 
117.228 176.732  111.662 182.003  104.668 187.133   95.937 191.438 
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151.539  97.305  151.066 104.099  150.133 110.250  148.925 115.881 
147.536 121.109  ] scurve
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141.166 150.696  140.078 152.976  138.927 155.303  137.713 157.639 
136.468 160.000  135.174 162.433  133.787 164.928  132.317 167.471 
130.768 170.098  129.093 172.827  127.275 175.649  125.297 178.593 
123.105 181.675  120.649 184.902  117.854 188.289  114.610 191.827 
110.770 195.471  106.147 199.082  100.588 202.353   94.170 204.822 
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  9.124 115.732    9.127 112.561    9.178 109.371    9.274 106.172 
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 38.500  38.600   43.385  36.250   48.172  34.286   52.866  32.609 
 57.493  31.152   62.083  29.872   66.669  28.740   71.288  27.742 
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 96.286  24.991  102.005  25.198  108.038  25.943  114.265  27.457 
120.372  29.898  125.975  33.146  130.898  36.879  135.192  40.826 
138.982  44.847  142.381  48.892  145.474  52.958  148.317  57.064 
150.943  61.245  153.357  65.546  155.533  70.020  157.392  74.707 
158.801  79.591  159.632  84.533  159.885  89.318  159.695  93.790 
159.224  97.911  158.585 101.712  157.851 105.237  157.063 108.543 
156.228 111.659  155.377 114.606  154.521 117.432  153.636 120.154 
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156.882 124.351 moveto
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154.394 131.214  153.532 132.679  152.876 134.037  152.403 135.472 
151.976 137.122  151.318 138.943  150.400 140.567  149.562 141.925 
148.931 143.225  148.465 144.634  148.019 146.278  147.314 148.084 
146.366 149.680  145.516 151.036  144.869 152.365  144.370 153.838 
143.842 155.567  143.016 157.403  142.020 158.999  141.166 160.424 
140.504 161.903  139.920 163.605  139.145 165.542  138.092 167.377 
137.087 169.006  136.267 170.665  135.514 172.563  134.544 174.680 
133.348 176.686  132.241 178.589  131.248 180.666  130.108 183.015 
128.714 185.364  127.339 187.687  125.956 190.258  124.304 193.040 
122.482 195.875  120.513 198.974  118.163 202.332  115.404 205.931 
111.966 209.838  107.475 213.865  101.530 217.364   94.650 219.253 
 88.082 219.575   82.224 219.076   76.960 218.216   72.141 217.157 
 67.624 216.021   63.344 214.782   59.228 213.533   55.202 212.188 
 51.286 210.824   47.349 209.380   43.463 207.843   39.498 206.232 
 35.483 204.439   31.349 202.486   27.061 200.210   22.605 197.496 
 18.069 194.024   13.929 189.510   10.931 184.319    9.067 179.262 
  7.897 174.671    7.058 170.498    6.493 166.660    6.013 163.165 
  5.603 159.793    5.378 156.650    5.103 153.759    4.799 150.859 
  4.698 148.041    4.614 145.498    4.372 143.016    4.178 140.406 
  4.210 137.912    4.200 135.669    4.006 133.446    3.819 131.043 
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  3.661 119.938    3.830 117.770    3.879 115.785    3.736 113.739 
  3.607 111.457    3.743 109.151    3.920 107.069    3.911 105.050 
  3.776 102.844    3.811 100.435    4.038  98.153    4.154  96.009 
  4.096  93.743    4.114  91.219    4.356  88.711    4.543  86.323 
  4.577  83.798    4.706  81.009    5.017  78.220    5.247  75.420 
  5.452  72.349    5.856  69.090    6.301  65.732    6.820  62.041 
  7.600  58.049    8.649  53.680   10.285  48.838   12.948  43.707 
 16.923  39.046   21.556  35.550   26.109  33.037   30.406  31.112 
 34.403  29.555   38.220  28.188   41.852  27.047   45.308  25.948 
 48.752  24.960   52.032  24.099   55.251  23.182   58.528  22.374 
 61.670  21.652   64.814  20.841   68.065  20.127   71.224  19.488 
 74.428  18.750   77.780  18.103   81.097  17.514   84.532  16.845 
 88.144  16.280   91.818  15.737   95.744  15.196   99.895  14.783 
104.358  14.441  109.257  14.342  114.678  14.665  120.592  15.887 
126.374  18.423  131.236  21.861  135.168  25.504  138.458  29.042 
141.348  32.467  143.913  35.730  146.328  38.893  148.521  42.000 
150.629  44.969  152.674  47.980  154.557  50.931  156.469  53.836 
158.318  56.863  160.066  59.862  161.879  62.943  163.603  66.217 
165.283  69.605  166.908  73.343  168.178  77.464  168.870  81.832 
168.857  86.092  168.396  89.958  167.665  93.471  166.803  96.535 
166.060  99.332  165.280 102.084  164.348 104.585  163.542 106.799 
162.912 109.006  162.195 111.313  161.271 113.428  160.446 115.255 
159.841 117.037  159.318 118.976  158.583 121.017  157.663 122.807 
156.882 124.351  ] scurve
  0.000 237.000 moveto
  1.000 nbpt mul rm  (Domaine polygonal convexe) show currentpoint
clear
}
\EndFig
\vskip30pt
\centerline{\bf Fig.\ 3}
\vfill\eject


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1 mm unit  /nbpt 14 def
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 37.747 114.715   33.974 114.670   30.292 114.627   26.710 114.587 
 23.236 114.550   19.878 114.518   16.639 114.490   13.525 114.468 
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 26.115  95.875   22.584  94.823   19.096  93.906   15.664  93.133 
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104.431  78.846  108.230  76.258  112.365  73.807  116.921  71.547 
122.001  69.570  127.714  68.027  134.113  67.134  141.042  67.118 
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101.567 114.578  105.099 114.429  108.488 114.250  111.722 114.040 
114.790 113.795  117.685 113.512  120.400 113.186  122.934 112.809 
125.289 112.368  127.477 111.834  129.526 111.133  131.445 110.032 
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114.504 131.348  118.102 131.773  121.634 131.990  125.078 131.996 
128.411 131.794  131.605 131.391  134.615 130.776  137.309 129.838 
140.112 128.313  ] scurve
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106.115 152.588  110.246 155.507  114.742 158.335  119.687 161.011 
125.184 163.430  131.331 165.398  138.166 166.590  145.536 166.550 
153.291 165.215  ] scurve
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 78.095 148.471   79.259 153.017   80.448 157.696   81.647 162.530 
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 61.801 148.248   60.540 152.627   59.202 157.062   57.787 161.551 
 56.299 166.090   54.750 170.669   53.156 175.280   51.543 179.907 
 49.944 184.531   48.393 189.124   46.931 193.659   45.649 198.197 
 45.329 202.591  ] scurve
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 59.493 127.887   56.770 131.078   53.991 134.242   51.149 137.373 
 48.235 140.465   45.240 143.514   42.156 146.515   38.970 149.466 
 35.667 152.365   32.227 155.209   28.621 157.996   24.808 160.719 
 20.725 163.362   16.279 165.880   11.331 168.159    5.737 169.950 
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 68.498 129.020   67.020 128.777   65.580 128.376   64.194 127.822 
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 56.348 117.793   56.141 116.361   56.080 114.917   56.166 113.474 
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 74.415 101.766   75.772 102.315   77.060 103.003   78.264 103.820 
 79.372 104.755   80.373 105.795   81.258 106.929   82.021 108.142 
 82.654 109.423   83.155 110.758   83.519 112.134   83.744 113.539 
 83.828 114.960  ] scurve
102.572 114.539 moveto
[ 102.572 114.539  102.583 117.646  102.356 120.790  101.868 123.972 
101.092 127.182   99.995 130.401   98.542 133.595   96.704 136.714 
 94.460 139.696   91.808 142.463   88.768 144.934   85.384 147.031 
 81.721 148.692   77.858 149.873   73.878 150.553   69.860 150.728 
 65.878 150.411   61.997 149.621   58.277 148.388   54.770 146.746 
 51.521 144.737   48.570 142.409   45.942 139.813   43.652 137.004 
 41.705 134.031   40.094 130.940   38.809 127.765   37.837 124.536 
 37.164 121.273   36.780 117.991   36.679 114.702   36.859 111.417 
 37.323 108.145   38.078 104.900   39.136 101.698   40.507  98.564 
 42.204  95.528   44.236  92.629   46.601  89.915   49.292  87.435 
 52.284  85.241   55.546  83.382   59.033  81.898   62.697  80.822 
 66.483  80.181   70.335  79.992   74.190  80.266   77.983  81.006 
 81.643  82.202   85.099  83.828   88.286  85.840   91.152  88.176 
 93.666  90.765   95.818  93.536   97.620  96.425   99.098  99.382 
100.283 102.376  101.203 105.389  101.883 108.418  102.338 111.466 
102.572 114.539  ] scurve
112.387 113.991 moveto
[ 112.387 113.991  112.582 117.697  112.591 121.523  112.368 125.500 
111.849 129.650  110.954 133.982  109.583 138.478  107.621 143.082 
104.952 147.682  101.493 152.102   97.238 156.112   92.286 159.485 
 86.823 162.059   81.068 163.769   75.212 164.633   69.396 164.710 
 63.715 164.065   58.239 162.750   53.033 160.809   48.170 158.278 
 43.732 155.215   39.797 151.702   36.417 147.851   33.600 143.783 
 31.316 139.602   29.512 135.383   28.132 131.170   27.121 126.984 
 26.440 122.828   26.059 118.697   25.963 114.579   26.148 110.460 
 26.622 106.327   27.405 102.172   28.530  97.991   30.042  93.794 
 31.996  89.612   34.446  85.500   37.438  81.547   40.985  77.868 
 45.054  74.584   49.573  71.797   54.450  69.575   59.594  67.952 
 64.927  66.949   70.386  66.587   75.906  66.896   81.402  67.922 
 86.753  69.705   91.789  72.248   96.321  75.480  100.194  79.240 
103.336  83.311  105.782  87.481  107.638  91.598  109.035  95.582 
110.096  99.418  110.915 103.129  111.551 106.759  112.039 110.362 
112.387 113.991  ] scurve
119.126 113.347 moveto
[ 119.126 113.347  119.560 117.269  119.899 121.397  120.080 125.789 
120.028 130.500  119.639 135.588  118.763 141.099  117.181 147.047 
114.597 153.342  110.691 159.706  105.288 165.609   98.584 170.430 
 91.114 173.802   83.431 175.741   75.873 176.474   68.579 176.235 
 61.575 175.182   54.857 173.391   48.441 170.866   42.401 167.581 
 36.899 163.533   32.140 158.831   28.258 153.713   25.240 148.448 
 22.958 143.226   21.261 138.136   20.020 133.199   19.143 128.399 
 18.565 123.708   18.248 119.089   18.170 114.503   18.327 109.912 
 18.730 105.277   19.406 100.562   20.402  95.732   21.793  90.762 
 23.684  85.649   26.215  80.438   29.537  75.257   33.743  70.340 
 38.782  65.968   44.464  62.346   50.567  59.535   56.931  57.504 
 63.477  56.206   70.180  55.617   77.049  55.775   84.072  56.804 
 91.135  58.908   97.928  62.282  103.951  66.920  108.729  72.457 
112.110  78.298  114.298  83.936  115.657  89.109  116.533  93.780 
117.168  98.041  117.693 102.018  118.175 105.824  118.651 109.564 
119.126 113.347  ] scurve
124.115 112.601 moveto
[ 124.115 112.601  124.834 116.560  125.526 120.799  126.150 125.386 
126.631 130.399  126.894 135.941  126.790 142.162  126.052 149.226 
124.189 157.258  120.383 166.083  113.774 174.692  104.632 181.322 
 94.577 185.157   84.862 186.771   75.834 186.951   67.424 186.183 
 59.472 184.696   51.826 182.547   44.391 179.665   37.184 175.858 
 30.472 170.901   24.816 164.837   20.622 158.239   17.731 151.738 
 15.751 145.600   14.377 139.844   13.414 134.410   12.755 129.223 
 12.326 124.213   12.096 119.308   12.040 114.459   12.156 109.594 
 12.456 104.668   12.961  99.608   13.726  94.355   14.825  88.832 
 16.404  82.968   18.689  76.723   22.036  70.188   26.811  63.776 
 32.973  58.199   39.956  53.878   47.249  50.716   54.654  48.483 
 62.127  47.020   69.713  46.204   77.570  46.017   85.896  46.649 
 94.774  48.557  103.875  52.470  112.015  58.880  117.737  66.969 
120.827  75.111  122.080  82.298  122.400  88.283  122.434  93.255 
122.524  97.567  122.723 101.536  123.007 105.277  123.463 108.893 
124.115 112.601  ] scurve
127.976 111.687 moveto
[ 127.976 111.687  128.538 113.646  129.033 115.705  129.500 117.789 
130.011 119.918  130.571 122.171  131.110 124.583  131.589 127.106 
132.058 129.713  132.554 132.472  133.029 135.443  133.442 138.623 
133.809 142.030  134.108 145.740  134.275 149.810  134.250 154.302 
133.917 159.310  133.075 164.915  131.399 171.144  128.413 177.819 
123.688 184.324  117.365 189.694  110.293 193.365  103.302 195.519 
 96.763 196.621   90.735 197.051   85.166 197.047   79.977 196.756 
 75.092 196.258   70.451 195.607   65.993 194.827   61.681 193.934 
 57.467 192.937   53.319 191.822   49.209 190.587   45.098 189.203 
 40.968 187.637   36.793 185.839   32.568 183.724   28.327 181.186 
 24.184 178.088   20.392 174.367   17.247 170.172   14.855 165.834 
 13.097 161.617   11.788 157.630   10.794 153.879   10.024 150.358 
  9.395 147.029    8.891 143.843    8.500 140.810    8.161 137.914 
  7.857 135.091    7.632 132.323    7.478 129.656    7.328 127.074 
  7.176 124.504    7.082 121.927    7.063 119.398    7.053 116.933 
  7.018 114.463    7.010 111.938    7.083 109.395    7.197 106.882 
  7.295 104.358    7.401 101.752    7.582  99.067    7.832  96.355 
  8.098  93.592    8.399  90.708    8.796  87.696    9.293  84.578 
  9.880  81.312   10.615  77.847   11.563  74.176   12.791  70.275 
 14.432  66.133   16.663  61.831   19.641  57.587   23.341  53.746 
 27.494  50.541   31.803  47.963   36.103  45.881   40.340  44.162 
 44.522  42.721   48.660  41.508   52.783  40.493   56.892  39.683 
 60.958  39.050   64.994  38.536   69.039  38.099   73.164  37.721 
 77.439  37.425   81.916  37.247   86.663  37.238   91.747  37.485 
 97.242  38.122  103.194  39.383  109.534  41.627  115.885  45.283 
121.442  50.464  125.483  56.569  127.978  62.750  129.307  68.544 
129.800  73.807  129.683  78.453  129.218  82.436  128.632  85.850 
128.013  88.815  127.422  91.375  126.963  93.597  126.696  95.611 
126.605  97.542  126.616  99.480  126.625 101.424  126.595 103.291 
126.596 105.024  126.712 106.652  126.987 108.248  127.424 109.898 
127.976 111.687  ] scurve
131.120 110.279 moveto
[ 131.120 110.279  131.953 111.729  132.437 113.468  132.593 115.045 
132.734 116.382  133.007 117.589  133.469 118.774  134.147 120.072 
134.952 121.682  135.527 123.633  135.759 125.509  135.967 127.147 
136.349 128.679  136.973 130.281  137.772 132.180  138.405 134.445 
138.745 136.688  139.126 138.774  139.744 140.914  140.523 143.399 
141.115 146.226  141.570 149.065  142.189 152.028  142.879 155.436 
143.391 159.213  143.889 163.332  144.285 168.100  144.366 173.603 
143.875 180.116  142.067 187.814  137.666 196.149  130.206 202.903 
121.797 206.535  114.226 207.999  107.702 208.419  102.032 208.348 
 96.956 208.013   92.416 207.528   88.184 207.017   84.248 206.350 
 80.640 205.731   77.084 205.141   73.697 204.372   70.588 203.666 
 67.463 203.085   64.303 202.331   61.398 201.488   58.588 200.822 
 55.610 200.174   52.650 199.283   49.910 198.402   47.121 197.688 
 44.113 196.878   41.169 195.834   38.328 194.857   35.281 193.933 
 32.053 192.756   28.867 191.427   25.486 190.049   21.832 188.309 
 18.052 186.109   14.157 183.171   10.772 179.234    8.489 174.868 
  7.090 170.779    6.142 167.012    5.600 163.597    5.149 160.616 
  4.634 157.750    4.336 154.876    4.281 152.321    4.128 150.086 
  3.776 147.892    3.435 145.509    3.429 143.129    3.565 141.095 
  3.546 139.307    3.306 137.545    2.944 135.593    2.791 133.404 
  2.988 131.375    3.196 129.679    3.221 128.152    3.032 126.618 
  2.694 124.899    2.475 122.879    2.648 120.867    2.947 119.181 
  3.105 117.710    3.057 116.287    2.816 114.760    2.506 112.956 
  2.471 110.895    2.777 109.008    3.070 107.415    3.179 105.948 
  3.079 104.444    2.822 102.731    2.658 100.683    2.878  98.580 
  3.233  96.756    3.437  95.102    3.422  93.419    3.249  91.504 
  3.195  89.243    3.499  86.955    3.861  84.897    4.032  82.886 
  4.023  80.659    4.108  78.059    4.515  75.373    4.949  72.781 
  5.247  70.001    5.662  66.797    6.416  63.362    7.361  59.680 
  8.800  55.499   11.235  51.136   14.719  47.264   18.711  44.335 
 22.674  42.262   26.317  40.667   29.828  39.281   33.192  38.226 
 36.263  37.264   39.316  36.233   42.458  35.403   45.392  34.761 
 48.200  34.002   51.205  33.186   54.361  32.675   57.324  32.421 
 60.075  32.155   62.847  31.796   65.636  31.571   68.238  31.323 
 70.872  30.839   73.792  30.324   76.779  30.003   79.713  29.611 
 82.890  29.090   86.325  28.715   89.836  28.376   93.666  27.980 
 97.866  27.739  102.456  27.591  107.675  27.684  113.679  28.253 
120.713  29.872  128.430  33.739  134.782  40.519  138.104  48.205 
139.379  54.972  139.794  60.674  139.840  65.703  139.609  70.234 
139.183  74.535  138.150  78.623  136.613  81.863  135.279  84.277 
134.343  86.372  133.595  88.481  132.662  90.567  131.564  92.228 
130.666  93.469  130.059  94.511  129.705  95.480  129.565  96.442 
129.617  97.452  129.832  98.595  130.097  99.995  130.100 101.626 
129.758 103.082  129.392 104.216  129.158 105.155  129.077 105.995 
129.146 106.788  129.367 107.564  129.756 108.356  130.336 109.220 
131.120 110.279  ] scurve
  0.000 237.000 moveto
  1.000 nbpt mul rm  (Domaine polygonal non convexe) show currentpoint
clear
}
\EndFig
\vskip30pt
\centerline{\bf Fig.\ 4}
\vfill\eject


\InsertFig -5.000 154.000  {
%%EPS file  z5.eps
0.72 dup scale
1 mm unit  /nbpt 14 def
  0.000   0.000 translate
  0.452 setlinewidth
 39.600  90.000 moveto
[  39.600  90.000   39.333  88.231   38.544  86.402   37.265  84.457 
 35.550  82.347   33.471  80.032   31.116  77.484   28.584  74.687 
 25.983  71.644   23.426  68.369   21.023  64.895   18.882  61.266 
 17.099  57.542   15.761  53.791   14.937  50.088   14.678  46.513 
 15.017  43.146   15.965  40.063   17.512  37.334   19.629  35.020 
 22.268  33.166   25.366  31.803   28.846  30.944   32.622  30.584 
 36.603  30.697   40.696  31.242   44.808  32.157   48.855  33.369 
 52.760  34.789   56.458  36.322   59.900  37.865   63.052  39.318 
 65.896  40.579   68.432  41.558   70.677  42.174   72.660  42.360 
 74.426  42.067   76.026  41.266   77.521  39.950   78.975  38.133 
 80.452  35.850   82.011  33.157   83.707  30.130   85.585  26.858 
 87.676  23.444   90.000  20.000   92.562  16.641   95.351  13.483 
 98.341  10.637  101.496   8.205  104.763   6.277  108.083   4.926 
111.390   4.208  114.615   4.157  117.688   4.785  120.543   6.083 
123.122   8.020  125.376  10.545  127.268  13.589  128.778  17.070 
129.900  20.891  130.647  24.952  131.047  29.146  131.145  33.369 
131.001  37.521  130.686  41.512  130.282  45.263  129.874  48.709 
129.553  51.804  129.406  54.519  129.514  56.844  129.950  58.787 
130.774  60.376  132.030  61.650  133.744  62.666  135.922  63.487 
138.549  64.186  141.592  64.837  144.995  65.514  148.687  66.289 
152.580  67.223  156.574  68.369  160.560  69.767  164.425  71.444 
168.056  73.409  171.344  75.657  174.187  78.168  176.498  80.909 
178.203  83.832  179.248  86.883  179.600  90.000  179.248  93.117 
178.203  96.168  176.498  99.091  174.187 101.832  171.344 104.343 
168.056 106.591  164.425 108.556  160.560 110.233  156.574 111.631 
152.580 112.777  148.687 113.711  144.995 114.486  141.592 115.163 
138.549 115.814  135.922 116.513  133.744 117.334  132.030 118.350 
130.774 119.624  129.950 121.213  129.514 123.156  129.406 125.481 
129.553 128.196  129.874 131.291  130.282 134.737  130.686 138.488 
131.001 142.479  131.145 146.631  131.047 150.854  130.647 155.048 
129.900 159.109  128.778 162.930  127.268 166.411  125.376 169.455 
123.122 171.980  120.543 173.917  117.688 175.215  114.615 175.843 
111.390 175.792  108.083 175.074  104.763 173.723  101.496 171.795 
 98.341 169.363   95.351 166.517   92.562 163.359   90.000 160.000 
 87.676 156.556   85.585 153.142   83.707 149.870   82.011 146.843 
 80.452 144.150   78.975 141.867   77.521 140.050   76.026 138.734 
 74.426 137.933   72.660 137.640   70.677 137.826   68.432 138.442 
 65.896 139.421   63.052 140.682   59.900 142.135   56.458 143.678 
 52.760 145.211   48.855 146.631   44.808 147.843   40.696 148.758 
 36.603 149.303   32.622 149.416   28.846 149.056   25.366 148.197 
 22.268 146.834   19.629 144.980   17.512 142.666   15.965 139.937 
 15.017 136.854   14.678 133.487   14.937 129.912   15.761 126.209 
 17.099 122.458   18.882 118.734   21.023 115.105   23.426 111.631 
 25.983 108.356   28.584 105.313   31.116 102.516   33.471  99.968 
 35.550  97.653   37.265  95.543   38.544  93.598   39.333  91.769 
 39.600  90.000  ] scurve
 90.000  90.000 moveto
  0.113 setlinewidth
[  90.000  90.000   87.069  89.999   84.139  89.999   81.209  90.000 
 78.281  90.001   75.355  90.002   72.432  90.003   69.518  90.005 
 66.618  90.008   63.740  90.010   60.899  90.013   58.110  90.016 
 55.395  90.018   52.780  90.020   50.294  90.022   47.968  90.023 
 45.828  90.024   43.897  90.023   42.170  90.023   40.547  90.026 
 39.600  90.070  ] scurve
 90.000  90.000 moveto
[  90.000  90.000   87.360  88.728   84.719  87.457   82.078  86.186 
 79.437  84.916   76.795  83.648   74.149  82.382   71.497  81.121 
 68.833  79.866   66.149  78.623   63.432  77.398   60.665  76.201 
 57.825  75.049   54.881  73.965   51.796  72.988   48.522  72.177 
 45.016  71.631   41.250  71.501   37.275  72.001   33.361  73.349 
 29.804  76.050  ] scurve
 90.000  90.000 moveto
[  90.000  90.000   88.173  87.708   86.345  85.417   84.517  83.126 
 82.688  80.834   80.860  78.543   79.033  76.248   77.210  73.949 
 75.394  71.640   73.592  69.313   71.813  66.960   70.070  64.564 
 68.382  62.110   66.778  59.574   65.297  56.934   63.998  54.167 
 62.958  51.265   62.279  48.245   62.081  45.166   62.551  42.098 
 64.029  39.762  ] scurve
 90.000  90.000 moveto
[  90.000  90.000   89.348  87.142   88.696  84.284   88.043  81.426 
 87.389  78.568   86.734  75.711   86.077  72.857   85.418  70.010 
 84.756  67.176   84.088  64.363   83.411  61.583   82.724  58.855 
 82.022  56.200   81.302  53.644   80.563  51.218   79.805  48.955 
 79.033  46.888   78.261  45.050   77.518  43.475   76.885  42.223 
 76.237  41.115  ] scurve
 90.000  90.000 moveto
[  90.000  90.000   90.653  87.142   91.305  84.284   91.958  81.425 
 92.610  78.565   93.262  75.702   93.912  72.835   94.561  69.961 
 95.207  67.072   95.848  64.161   96.480  61.211   97.098  58.205 
 97.693  55.112   98.252  51.894   98.750  48.492   99.146  44.827 
 99.359  40.782   99.228  36.191   98.397  30.849   96.092  24.679 
 90.706  19.029  ] scurve
 90.000  90.000 moveto
[  90.000  90.000   91.828  87.709   93.657  85.417   95.486  83.124 
 97.316  80.832   99.147  78.540  100.981  76.250  102.819  73.966 
104.667  71.692  106.528  69.436  108.412  67.208  110.327  65.025 
112.287  62.908  114.303  60.887  116.388  58.998  118.547  57.290 
120.775  55.817  123.048  54.636  125.306  53.784  127.406  53.217 
129.471  52.902  ] scurve
 90.000  90.000 moveto
[  90.000  90.000   92.641  88.729   95.284  87.458   97.926  86.187 
100.569  84.915  103.211  83.643  105.851  82.369  108.484  81.092 
111.106  79.810  113.708  78.517  116.279  77.210  118.800  75.882 
121.251  74.524  123.604  73.130  125.825  71.694  127.875  70.216 
129.713  68.700  131.298  67.160  132.592  65.602  133.528  63.955 
133.605  62.600  ] scurve
 90.000  90.000 moveto
[  90.000  90.000   92.931  90.001   95.863  90.003   98.795  90.004 
101.729  90.007  104.664  90.010  107.603  90.013  110.550  90.017 
113.510  90.021  116.495  90.026  119.517  90.031  122.599  90.038 
125.769  90.046  129.073  90.056  132.573  90.069  136.368  90.086 
140.612  90.111  145.580  90.150  151.817  90.217  160.723  90.364 
179.522  91.468  ] scurve
 90.000  90.000 moveto
[  90.000  90.000   92.640  91.273   95.281  92.546   97.921  93.820 
100.561  95.095  103.199  96.371  105.834  97.650  108.462  98.931 
111.079 100.219  113.674 101.517  116.237 102.829  118.751 104.163 
121.193 105.524  123.537 106.920  125.748 108.356  127.788 109.831 
129.616 111.340  131.194 112.870  132.482 114.415  133.409 116.043 
133.522 117.440  ] scurve
 90.000  90.000 moveto
[  90.000  90.000   91.827  92.292   93.653  94.585   95.478  96.878 
 97.304  99.171   99.129 101.463  100.957 103.753  102.789 106.037 
104.629 108.311  106.482 110.568  108.357 112.797  110.264 114.982 
112.215 117.101  114.224 119.127  116.303 121.021  118.458 122.736 
120.685 124.218  122.960 125.409  125.225 126.270  127.334 126.841 
129.474 127.145  ] scurve
 90.000  90.000 moveto
[  90.000  90.000   90.651  92.858   91.302  95.715   91.951  98.572 
 92.600 101.430   93.249 104.289   93.895 107.152   94.539 110.021 
 95.180 112.904   95.814 115.809   96.439 118.751   97.047 121.748 
 97.631 124.830   98.176 128.037   98.657 131.423   99.029 135.068 
 99.211 139.084   99.036 143.630   98.143 148.895   95.770 154.911 
 90.381 160.528  ] scurve
 90.000  90.000 moveto
[  90.000  90.000   89.347  92.857   88.693  95.713   88.040  98.569 
 87.386 101.424   86.731 104.276   86.075 107.125   85.417 109.966 
 84.756 112.793   84.090 115.598   83.417 118.368   82.733 121.085 
 82.035 123.729   81.321 126.273   80.589 128.688   79.839 130.939 
 79.078 132.996   78.317 134.827   77.587 136.397   76.966 137.645 
 76.229 138.879  ] scurve
 90.000  90.000 moveto
[  90.000  90.000   88.172  92.291   86.344  94.581   84.517  96.871 
 82.691  99.160   80.865 101.450   79.042 103.742   77.224 106.039 
 75.415 108.346   73.620 110.670   71.849 113.021   70.116 115.413 
 68.440 117.864   66.848 120.395   65.382 123.029   64.098 125.786 
 63.073 128.674   62.405 131.675   62.214 134.727   62.685 137.755 
 64.209 140.157  ] scurve
 90.000  90.000 moveto
[  90.000  90.000   87.359  91.271   84.719  92.542   82.080  93.812 
 79.440  95.083   76.800  96.352   74.158  97.620   71.510  98.884 
 68.850 100.142   66.170 101.389   63.458 102.620   60.696 103.823 
 57.861 104.984   54.921 106.078   51.838 107.068   48.564 107.894 
 45.052 108.460   41.272 108.612   37.268 108.131   33.314 106.781 
 29.729 104.034  ] scurve
 99.271  90.005 moveto
[  99.271  90.005   99.220  90.974   99.067  91.933   98.815  92.870 
 98.466  93.776   98.025  94.640   97.496  95.453   96.884  96.206 
 96.198  96.892   95.443  97.502   94.629  98.029   93.764  98.469 
 92.859  98.816   91.921  99.066   90.963  99.217   89.995  99.267 
 89.026  99.215   88.069  99.062   87.133  98.811   86.228  98.463 
 85.364  98.022   84.551  97.494   83.798  96.884   83.113  96.198 
 82.503  95.444   81.975  94.631   81.535  93.767   81.188  92.862 
 80.937  91.925   80.785  90.968   80.734  90.000   80.785  89.032 
 80.936  88.074   81.186  87.137   81.534  86.231   81.973  85.367 
 82.501  84.553   83.112  83.799   83.797  83.112   84.551  82.502 
 85.365  81.973   86.229  81.532   87.135  81.184   88.072  80.932 
 89.031  80.780   90.000  80.729   90.969  80.779   91.928  80.931 
 92.866  81.182   93.773  81.530   94.638  81.971   95.452  82.500 
 96.206  83.111   96.892  83.798   97.503  84.553   98.031  85.367 
 98.472  86.232   98.819  87.139   99.070  88.076   99.221  89.035 
 99.271  90.005  ] scurve
112.756  90.020 moveto
[ 112.756  90.020  112.621  92.418  112.225  94.781  111.581  97.077 
110.706  99.281  109.616 101.375  108.325 103.344  106.845 105.174 
105.186 106.852  103.356 108.358  101.368 109.672   99.242 110.770 
 97.002 111.631   94.683 112.241   92.317 112.594   89.939 112.691 
 87.576 112.540   85.252 112.151   82.985 111.534   80.791 110.695 
 78.685 109.639   76.689 108.368   74.827 106.888   73.126 105.210 
 71.614 103.352   70.315 101.339   69.246  99.202   68.415  96.973 
 67.824  94.682   67.471  92.353   67.353  90.007   67.467  87.661 
 67.816  85.331   68.403  83.038   69.231  80.806   70.297  78.666 
 71.595  76.648   73.106  74.785   74.808  73.101   76.672  71.616 
 78.671  70.341   80.780  69.281   82.980  68.439   85.253  67.820 
 87.583  67.430   89.952  67.280   92.337  67.379   94.708  67.736 
 97.032  68.351   99.275  69.218  101.403  70.322  103.392  71.642 
105.221  73.155  106.880  74.839  108.357  76.675  109.644  78.649 
110.731  80.748  111.601  82.956  112.239  85.255  112.628  87.620 
112.756  90.020  ] scurve
121.012  90.034 moveto
[ 121.012  90.034  120.787  93.398  120.149  96.666  119.158  99.769 
117.881 102.680  116.372 105.405  114.661 107.964  112.747 110.376 
110.613 112.645  108.230 114.749  105.577 116.638  102.662 118.238 
 99.531 119.475   96.268 120.296   92.970 120.697   89.720 120.713 
 86.563 120.398   83.512 119.807   80.557 118.972   77.679 117.901 
 74.868 116.578   72.136 114.969   69.523 113.039   67.101 110.771 
 64.956 108.186   63.162 105.346   61.755 102.341   60.729  99.260 
 60.045  96.164   59.657  93.082   59.530  90.014   59.651  86.946 
 60.032  83.863   60.710  80.766   61.729  77.680   63.128  74.670 
 64.917  71.821   67.059  69.226   69.481  66.947   72.096  65.006 
 74.834  63.387   77.653  62.056   80.540  60.978   83.507  60.139 
 86.570  59.545   89.740  59.231   93.003  59.251   96.312  59.660 
 99.584  60.492  102.720  61.741  105.637  63.353  108.289  65.253 
110.670  67.366  112.802  69.644  114.712  72.064  116.421  74.631 
117.924  77.364  119.194  80.285  120.176  83.396  120.801  86.668 
121.012  90.034  ] scurve
127.895  90.052 moveto
[ 127.895  90.052  127.511  94.407  126.477  98.502  124.994 102.208 
123.253 105.534  121.375 108.568  119.397 111.417  117.289 114.174 
114.973 116.892  112.333 119.566  109.250 122.108  105.660 124.334 
101.631 126.014   97.380 126.989   93.176 127.268   89.203 127.002 
 85.511 126.375   82.053 125.528   78.741 124.529   75.478 123.379 
 72.188 122.022   68.840 120.346   65.479 118.214   62.257 115.507 
 59.410 112.213   57.160 108.487   55.582 104.585   54.595 100.729 
 54.039  97.027   53.767  93.478   53.685  90.020   53.761  86.562 
 54.026  83.014   54.573  79.312   55.548  75.455   57.111  71.546 
 59.349  67.807   62.188  64.495   65.410  61.768   68.777  59.618 
 72.135  57.928   75.436  56.559   78.711  55.400   82.039  54.392 
 85.514  53.539   89.227  52.911   93.223  52.650   97.448  52.943 
101.713  53.939  105.747  55.641  109.334  57.886  112.411  60.441 
115.046  63.125  117.358  65.851  119.464  68.615  121.440  71.474 
123.316  74.519  125.051  77.860  126.523  81.583  127.537  85.692 
127.895  90.052  ] scurve
134.393  90.077 moveto
[ 134.393  90.077  133.691  95.681  131.944 100.624  129.720 104.731 
127.418 108.176  125.204 111.223  123.090 114.107  120.994 117.007 
118.768 120.055  116.182 123.308  112.933 126.682  108.738 129.843 
103.605 132.189   98.071 133.244   92.846 133.107   88.266 132.263 
 84.287 131.141   80.713 129.979   77.326 128.860   73.931 127.763 
 70.360 126.590   66.487 125.143   62.294 123.116   58.003 120.134 
 54.178 116.013   51.443 111.100   49.935 106.097   49.305 101.482 
 49.129  97.350   49.119  93.590   49.129  90.023   49.116  86.457 
 49.120  82.701   49.286  78.576   49.899  73.966   51.381  68.960 
 54.088  64.028   57.899  59.873   62.195  56.857   66.402  54.806 
 70.290  53.344   73.874  52.159   77.283  51.051   80.685  49.919 
 84.281  48.744   88.289  47.614   92.907  46.772   98.171  46.657 
103.726  47.750  108.859  50.136  113.041  53.323  116.274  56.712 
118.850  59.970  121.071  63.021  123.165  65.926  125.283  68.817 
127.501  71.878  129.805  75.345  132.020  79.483  133.739  84.458 
134.393  90.077  ] scurve
141.184  90.115 moveto
[ 141.184  90.115  139.787  97.536  136.754 103.303  133.495 107.477 
130.580 110.706  128.096 113.494  125.970 116.201  124.051 119.064 
122.156 122.297  119.964 126.079  116.956 130.477  112.335 135.120 
105.651 138.647   98.184 139.594   91.787 138.492   86.826 136.691 
 82.862 134.923   79.448 133.425   76.222 132.237   72.917 131.291 
 69.276 130.484   65.031 129.568   59.960 128.086   54.148 125.180 
 48.712 119.982   45.453 113.205   44.486 106.780   44.645 101.497 
 45.088  97.175   45.449  93.460   45.576  90.024   45.450  86.589 
 45.087  82.882   44.638  78.573   44.461  73.309   45.384  66.898 
 48.582  60.095   53.993  54.828   59.826  51.868   64.927  50.361 
 69.194  49.433   72.850  48.618   76.166  47.660   79.404  46.456 
 82.838  44.936   86.837  43.145   91.857  41.332   98.327  40.259 
105.834  41.283  112.499  44.880  117.082  49.553  120.062  53.958 
122.239  57.738  124.127  60.967  126.049  63.828  128.184  66.538 
130.682  69.338  133.613  72.594  136.879  76.818  139.879  82.655 
141.184  90.115  ] scurve
149.157  90.185 moveto
[ 149.157  90.185  148.226  95.845  146.042 100.543  143.403 104.094 
140.803 106.752  138.414 108.801  136.304 110.435  134.479 111.843 
132.859 113.125  131.421 114.293  130.197 115.411  129.149 116.575 
128.197 117.817  127.313 119.109  126.531 120.471  125.846 121.989 
125.175 123.727  124.450 125.676  123.666 127.863  122.744 130.396 
121.501 133.322  119.727 136.635  117.086 140.244  113.190 143.728 
108.018 146.242  102.361 147.076   97.248 146.436   93.083 145.027 
 89.771 143.387   87.094 141.761   84.892 140.269   82.991 138.975 
 81.271 137.836   79.714 136.832   78.272 136.012   76.843 135.374 
 75.369 134.850   73.869 134.403   72.337 134.074   70.690 133.883 
 68.842 133.776   66.779 133.681   64.478 133.603   61.816 133.506 
 58.688 133.237   55.033 132.598   50.827 131.255   46.321 128.709 
 42.287 124.645   39.675 119.552   38.651 114.482   38.674 110.070 
 39.194 106.398   39.904 103.338   40.635 100.776   41.272  98.562 
 41.820  96.569   42.291  94.774   42.622  93.147   42.786  91.588 
 42.827  90.023   42.787  88.458   42.627  86.900   42.299  85.277 
 41.830  83.489   41.282  81.504   40.645  79.299   39.913  76.752 
 39.196  73.713   38.660  70.068   38.601  65.685   39.559  60.632 
 42.087  55.508   46.073  51.360   50.590  48.733   54.833  47.340 
 58.524  46.678   61.682  46.399   64.366  46.300   66.681  46.222 
 68.754  46.126   70.612  46.017   72.265  45.826   73.799  45.495 
 75.300  45.042   76.776  44.508   78.210  43.858   79.658  43.024 
 81.222  42.005   82.952  40.845   84.872  39.524   87.108  38.007 
 89.833  36.361   93.209  34.714   97.453  33.329  102.634  32.759 
108.308  33.692  113.447  36.283  117.294  39.807  119.893  43.431 
121.635  46.746  122.853  49.669  123.759  52.194  124.533  54.374 
125.251  56.317  125.918  58.049  126.602  59.561  127.385  60.918 
128.273  62.206  129.231  63.445  130.288  64.607  131.524  65.727 
132.974  66.901  134.609  68.191  136.455  69.611  138.588  71.273 
140.995  73.363  143.604  76.078  146.225  79.709  148.343  84.488 
149.157  90.185  ] scurve
160.427  90.358 moveto
[ 160.427  90.358  158.855  97.251  155.605 102.341  152.142 105.735 
148.917 108.106  146.082 109.662  143.795 110.905  141.672 112.076 
139.624 112.872  138.010 113.388  136.762 113.967  135.651 114.707 
134.452 115.503  133.229 116.060  132.275 116.457  131.572 116.905 
131.032 117.480  130.563 118.228  130.006 119.126  129.329 119.936 
128.765 120.617  128.389 121.314  128.184 122.128  128.103 123.170 
127.944 124.517  127.554 125.905  127.199 127.197  127.042 128.581 
127.048 130.310  126.896 132.536  126.421 134.930  125.937 137.530 
125.283 140.773  123.942 144.622  121.648 149.021  117.571 153.665 
111.252 157.048  104.208 157.581   98.435 156.009   94.201 153.773 
 90.986 151.453   88.659 149.267   86.776 147.503   85.005 145.860 
 83.616 144.168   82.626 142.803   81.688 141.802   80.640 140.980 
 79.508 140.093   78.593 139.103   77.917 138.315   77.273 137.782 
 76.559 137.443   75.705 137.226   74.680 136.975   73.695 136.579 
 72.871 136.246   72.092 136.092   71.260 136.136   70.257 136.369 
 68.944 136.637   67.499 136.697   66.157 136.740   64.805 136.987 
 63.206 137.499   61.094 138.059   58.678 138.353   56.098 138.664 
 52.912 139.055   48.910 139.031   44.109 138.304   38.458 136.059 
 33.138 131.277   30.257 124.737   29.881 118.680   30.673 113.902 
 31.882 110.093   33.238 107.185   34.329 104.832   35.347 102.626 
 36.528 100.781   37.515  99.413   38.172  98.206   38.628  96.948 
 39.122  95.593   39.780  94.414   40.319  93.525   40.625  92.746 
 40.727  91.960   40.669  91.079   40.591  90.025   40.663  88.965 
 40.726  88.077   40.633  87.289   40.336  86.512   39.807  85.633 
 39.147  84.471   38.642  83.117   38.189  81.856   37.542  80.651 
 36.569  79.298   35.388  77.477   34.366  75.284   33.285  72.950 
 31.935  70.088   30.709  66.336   29.877  61.641   30.125  55.676 
 32.773  49.111   37.954  44.108   43.659  41.665   48.561  40.856 
 52.637  40.793   55.897  41.181   58.511  41.512   60.939  41.804 
 63.084  42.356   64.709  42.884   66.068  43.149   67.406  43.200 
 68.847  43.252   70.176  43.512   71.191  43.751   72.027  43.803 
 72.803  43.657   73.619  43.327   74.590  42.922   75.617  42.653 
 76.478  42.428   77.193  42.083   77.837  41.540   78.515  40.739 
 79.438  39.740   80.565  38.846   81.602  38.002   82.536  36.958 
 83.557  35.533   85.011  33.826   86.793  32.183   88.700  30.352 
 91.146  28.113   94.471  25.817   98.848  23.618  104.753  22.208 
111.779  22.971  117.959  26.464  121.936  31.123  124.170  35.521 
125.461  39.366  126.079  42.590  126.546  45.179  127.000  47.573 
127.126  49.782  127.113  51.490  127.271  52.863  127.626  54.151 
128.011  55.538  128.163  56.876  128.243  57.910  128.449  58.717 
128.827  59.408  129.392  60.084  130.073  60.888  130.636  61.781 
131.111  62.525  131.659  63.096  132.374  63.539  133.346  63.937 
134.580  64.508  135.776  65.306  136.899  66.033  138.178  66.601 
139.845  67.131  141.921  67.982  144.043  69.173  146.380  70.429 
149.276  72.073  152.508  74.548  155.968  78.084  159.111  83.360 
160.427  90.358  ] scurve
 20.000   7.000 moveto
  1.000 nbpt mul rm  (Courbe d') show
(e) <c2> acc
(quation polaire) show currentpoint
clear
 20.000   0.000 moveto
  1.000 nbpt mul it  (r ) show currentpoint
  1.000 nbpt mul rm  (= 1 + 0.28 cos 5) show currentpoint  
  1.000 nbpt mul symb  (q) show currentpoint
clear
140.000   0.000 moveto
  1.000 nbpt mul rm  (Centre ) show <28> show (0,0) show <29> show currentpoint
clear
}
\EndFig
\vskip30pt
\centerline{\bf Fig.\ 5}
\vfill\eject



\InsertFig 0.000 154.000  {
%%EPS file  z6.eps
0.72 dup scale
1 mm unit  /nbpt 14 def
  0.000   0.000 translate
  0.452 setlinewidth
 20.000  90.000 moveto
[  20.000  90.000   19.951  89.998   19.806  89.986   19.564  89.954 
 19.229  89.892   18.803  89.789   18.290  89.637   17.694  89.425 
 17.021  89.146   16.276  88.790   15.466  88.350   14.599  87.818 
 13.682  87.187   12.723  86.451   11.732  85.604   10.718  84.641 
  9.691  83.558    8.661  82.352    7.639  81.019    6.636  79.559 
  5.662  77.969    4.730  76.250    3.849  74.403    3.031  72.428 
  2.288  70.329    1.631  68.109    1.070  65.771    0.617  63.321 
  0.280  60.764    0.072  58.108    0.000  55.359    0.075  52.526 
  0.304  49.617    0.696  46.642    1.258  43.612    1.997  40.536 
  2.918  37.427    4.027  34.296    5.328  31.155    6.825  28.018 
  8.520  24.896   10.416  21.804   12.512  18.755   14.809  15.762 
 17.305  12.839   20.000  10.000   22.889   7.258   25.970   4.628 
 29.236   2.122   32.683  -0.247   36.304  -2.465   40.091  -4.521 
 44.036  -6.403   48.129  -8.098   52.361  -9.596   56.720 -10.887 
 61.195 -11.961   65.774 -12.809   70.443 -13.424   75.190 -13.797 
 80.000 -13.923   84.859 -13.796   89.751 -13.410   94.662 -12.764 
 99.576 -11.853  104.477 -10.676  109.349  -9.232  114.177  -7.523 
118.943  -5.548  123.633  -3.311  128.229  -0.815  132.718   1.935 
137.082   4.935  141.307   8.177  145.379  11.655  149.282  15.359 
153.004  19.281  156.530  23.410  159.849  27.735  162.948  32.245 
165.817  36.927  168.445  41.767  170.823  46.752  172.942  51.867 
174.794  57.098  176.372  62.427  177.672  67.841  178.688  73.321 
179.416  78.853  179.854  84.418  180.000  90.000  179.854  95.582 
179.416 101.147  178.688 106.679  177.672 112.159  176.372 117.573 
174.794 122.902  172.942 128.133  170.823 133.248  168.445 138.233 
165.817 143.073  162.948 147.755  159.849 152.265  156.530 156.590 
153.004 160.719  149.282 164.641  145.379 168.345  141.307 171.823 
137.082 175.065  132.718 178.065  128.229 180.815  123.633 183.311 
118.943 185.548  114.177 187.523  109.349 189.232  104.477 190.676 
 99.576 191.853   94.662 192.764   89.751 193.410   84.859 193.796 
 80.000 193.923   75.190 193.797   70.443 193.424   65.774 192.809 
 61.195 191.961   56.720 190.887   52.361 189.596   48.129 188.098 
 44.036 186.403   40.091 184.521   36.304 182.465   32.683 180.247 
 29.236 177.878   25.970 175.372   22.889 172.742   20.000 170.000 
 17.305 167.161   14.809 164.238   12.512 161.245   10.416 158.196 
  8.520 155.104    6.825 151.982    5.328 148.845    4.027 145.704 
  2.918 142.573    1.997 139.464    1.258 136.388    0.696 133.358 
  0.304 130.383    0.075 127.474    0.000 124.641    0.072 121.892 
  0.280 119.236    0.617 116.679    1.070 114.229    1.631 111.891 
  2.288 109.671    3.031 107.572    3.849 105.597    4.730 103.750 
  5.662 102.031    6.636 100.441    7.639  98.981    8.661  97.648 
  9.691  96.442   10.718  95.359   11.732  94.396   12.723  93.549 
 13.682  92.813   14.599  92.182   15.466  91.650   16.276  91.210 
 17.021  90.854   17.694  90.575   18.290  90.363   18.803  90.211 
 19.229  90.108   19.564  90.046   19.806  90.014   19.951  90.002 
 20.000  90.000  ] scurve
 90.000  90.000 moveto
  0.113 setlinewidth
[  90.000  90.000   85.265  89.999   80.547  89.999   75.855  89.998 
 71.200  89.998   66.595  89.997   62.054  89.997   57.594  89.996 
 53.233  89.996   48.991  89.996   44.892  89.995   40.964  89.995 
 37.236  89.995   33.744  89.995   30.526  89.995   27.628  89.995 
 25.100  89.996   23.002  89.996   21.398  89.997   20.369  89.998 
 20.000  90.000  ] scurve
 90.000  90.000 moveto
[  90.000  90.000   85.550  88.382   81.110  86.777   76.684  85.192 
 72.276  83.639   67.892  82.129   63.535  80.674   59.211  79.290 
 54.922  77.994   50.674  76.805   46.469  75.745   42.310  74.837 
 38.200  74.112   34.138  73.599   30.124  73.335   26.155  73.358 
 22.225  73.715   18.325  74.454   14.442  75.632   10.557  77.311 
  6.603  79.507  ] scurve
 90.000  90.000 moveto
[  90.000  90.000   86.370  86.958   82.736  83.930   79.093  80.925 
 75.434  77.949   71.751  75.012   68.034  72.119   64.272  69.281 
 60.452  66.503   56.558  63.794   52.574  61.160   48.480  58.605 
 44.255  56.136   39.875  53.755   35.313  51.461   30.541  49.255 
 25.527  47.132   20.239  45.084   14.640  43.099    8.689  41.167 
  2.251  39.615  ] scurve
 90.000  90.000 moveto
[  90.000  90.000   87.627  85.898   85.243  81.802   82.837  77.711 
 80.401  73.622   77.926  69.530   75.401  65.432   72.818  61.320 
 70.167  57.187   67.438  53.024   64.625  48.819   61.718  44.560 
 58.711  40.233   55.598  35.822   52.376  31.312   49.041  26.682 
 45.594  21.916   42.035  16.991   38.368  11.888   34.574   6.583 
 30.217   1.421  ] scurve
 90.000  90.000 moveto
[  90.000  90.000   89.173  85.332   88.336  80.660   87.485  75.975 
 86.620  71.268   85.738  66.532   84.840  61.756   83.928  56.933 
 83.005  52.052   82.073  47.105   81.138  42.084   80.206  36.979 
 79.283  31.784   78.378  26.491   77.499  21.094   76.657  15.589 
 75.861   9.970   75.122   4.234   74.451  -1.620   73.796  -7.611 
 72.465 -13.614  ] scurve
 90.000  90.000 moveto
[  90.000  90.000   90.821  85.330   91.639  80.651   92.460  75.957 
 93.289  71.242   94.133  66.502   94.997  61.735   95.890  56.937 
 96.818  52.106   97.787  47.242   98.805  42.344   99.879  37.414 
101.015  32.452  102.219  27.462  103.499  22.447  104.858  17.408 
106.302  12.352  107.836   7.281  109.466   2.195  111.210  -3.022 
112.521  -8.141  ] scurve
 90.000  90.000 moveto
[  90.000  90.000   92.370  85.892   94.744  81.779   97.129  77.661 
 99.532  73.539  101.960  69.418  104.417  65.298  106.908  61.185 
109.438  57.081  112.010  52.991  114.626  48.917  117.290  44.866 
120.003  40.839  122.765  36.843  125.579  32.880  128.444  28.955 
131.359  25.071  134.324  21.232  137.323  17.444  140.206  13.753 
143.146   9.703  ] scurve
 90.000  90.000 moveto
[  90.000  90.000   93.632  86.951   97.270  83.902  100.915  80.859 
104.569  77.828  108.234  74.814  111.911  71.823  115.601  68.860 
119.302  65.929  123.014  63.034  126.737  60.178  130.470  57.365 
134.211  54.598  137.959  51.878  141.713  49.209  145.471  46.591 
149.232  44.026  152.994  41.513  156.766  39.032  160.610  36.383 
163.520  33.135  ] scurve
 90.000  90.000 moveto
[  90.000  90.000   94.456  88.378   98.914  86.758  103.370  85.145 
107.820  83.545  112.262  81.961  116.691  80.396  121.106  78.855 
125.502  77.339  129.878  75.851  134.232  74.392  138.561  72.963 
142.864  71.566  147.138  70.202  151.382  68.871  155.594  67.573 
159.775  66.309  163.925  65.078  168.073  63.872  172.446  62.618 
176.113  61.475  ] scurve
 90.000  90.000 moveto
[  90.000  90.000   94.742  90.001   99.484  90.001  104.219  90.002 
108.942  90.002  113.646  90.003  118.328  90.003  122.983  90.004 
127.609  90.004  132.201  90.005  136.758  90.005  141.277  90.006 
145.756  90.006  150.193  90.007  154.587  90.007  158.938  90.007 
163.244  90.008  167.508  90.008  171.764  90.009  176.255  90.011 
180.000  90.025  ] scurve
 90.000  90.000 moveto
[  90.000  90.000   94.456  91.623   98.913  93.244  103.369  94.858 
107.819  96.459  112.260  98.045  116.689  99.610  121.103 101.152 
125.499 102.669  129.875 104.158  134.229 105.618  138.558 107.048 
142.860 108.446  147.134 109.811  151.377 111.143  155.590 112.441 
159.770 113.706  163.920 114.938  168.068 116.146  172.440 117.403 
176.099 118.573  ] scurve
 90.000  90.000 moveto
[  90.000  90.000   93.632  93.050   97.268  96.100  100.912  99.144 
104.566 102.176  108.231 105.190  111.907 108.182  115.596 111.146 
119.296 114.078  123.008 116.974  126.731 119.830  130.463 122.644 
134.204 125.413  137.951 128.133  141.705 130.804  145.463 133.422 
149.223 135.988  152.985 138.501  156.756 140.983  160.597 143.634 
163.506 146.886  ] scurve
 90.000  90.000 moveto
[  90.000  90.000   92.369  94.108   94.742  98.222   97.126 102.341 
 99.528 106.463  101.955 110.585  104.411 114.705  106.901 118.819 
109.430 122.924  112.001 127.015  114.617 131.089  117.280 135.141 
119.991 139.168  122.753 143.166  125.566 147.130  128.430 151.056 
131.345 154.940  134.309 158.780  137.308 162.568  140.191 166.259 
143.135 170.307  ] scurve
 90.000  90.000 moveto
[  90.000  90.000   90.820  94.670   91.637  99.350   92.457 104.044 
 93.285 108.759   94.127 113.499   94.991 118.266   95.882 123.065 
 96.808 127.896   97.777 132.761   98.793 137.659   99.866 142.589 
101.001 147.551  102.204 152.542  103.482 157.558  104.840 162.597 
106.283 167.654  107.816 172.726  109.445 177.813  111.186 183.031 
112.477 188.157  ] scurve
 90.000  90.000 moveto
[  90.000  90.000   89.172  94.667   88.334  99.340   87.482 104.025 
 86.615 108.731   85.732 113.467   84.833 118.243   83.920 123.066 
 82.995 127.946   82.062 132.893   81.126 137.914   80.192 143.019 
 79.268 148.214   78.361 153.507   77.481 158.903   76.637 164.409 
 75.839 170.028   75.099 175.764   74.426 181.618   73.769 187.608 
 72.439 193.611  ] scurve
 90.000  90.000 moveto
[  90.000  90.000   87.626  94.101   85.241  98.196   82.834 102.287 
 80.397 106.376   77.921 110.467   75.395 114.564   72.811 118.675 
 70.159 122.807   67.429 126.970   64.614 131.175   61.706 135.433 
 58.698 139.759   55.584 144.168   52.360 148.678   49.024 153.306 
 45.575 158.071   42.014 162.995   38.344 168.097   34.549 173.401 
 30.188 178.559  ] scurve
 90.000  90.000 moveto
[  90.000  90.000   86.369  93.041   82.734  96.068   79.091  99.073 
 75.431 102.047   71.748 104.984   68.030 107.875   64.267 110.713 
 60.446 113.489   56.552 116.198   52.568 118.831   48.473 121.384 
 44.248 123.851   39.867 126.231   35.305 128.523   30.533 130.727 
 25.519 132.848   20.230 134.894   14.630 136.876    8.679 138.804 
  2.242 140.354  ] scurve
 90.000  90.000 moveto
[  90.000  90.000   85.550  91.617   81.109  93.221   76.683  94.805 
 72.275  96.357   67.890  97.866   63.533  99.319   59.208 100.702 
 54.920 101.998   50.671 103.186   46.467 104.245   42.308 105.152 
 38.198 105.876   34.137 106.388   30.124 106.652   26.156 106.627 
 22.228 106.270   18.330 105.530   14.449 104.350   10.568 102.670 
  6.614 100.475  ] scurve
104.987  90.002 moveto
[ 104.987  90.002  104.905  91.565  104.662  93.111  104.260  94.624 
103.703  96.089  102.996  97.489  102.146  98.808  101.162 100.034 
100.054 101.151   98.834 102.147   97.514 103.010   96.110 103.730 
 94.635 104.298   93.108 104.708   91.545 104.953   89.965 105.031 
 88.386 104.940   86.826 104.683   85.303 104.261   83.836 103.681 
 82.441 102.951   81.133 102.079   79.927 101.076   78.835  99.955 
 77.868  98.729   77.035  97.413   76.345  96.021   75.802  94.569 
 75.411  93.071   75.175  91.542   75.097  89.998   75.176  88.455 
 75.412  86.926   75.803  85.428   76.346  83.975   77.037  82.584 
 77.870  81.268   78.837  80.042   79.929  78.922   81.136  77.919 
 82.444  77.047   83.839  76.317   85.307  75.738   86.829  75.317 
 88.389  75.059   89.969  74.969   91.549  75.048   93.112  75.293 
 94.639  75.703   96.113  76.271   97.517  76.992   98.837  77.855 
100.057  78.852  101.165  79.969  102.148  81.194  102.998  82.514 
103.704  83.914  104.261  85.379  104.663  86.893  104.906  88.439 
104.987  90.002  ] scurve
126.437  90.004 moveto
[ 126.437  90.004  126.251  93.744  125.695  97.452  124.773 101.093 
123.488 104.635  121.848 108.044  119.864 111.285  117.547 114.325 
114.914 117.128  111.985 119.658  108.784 121.882  105.341 123.766 
101.690 125.278   97.872 126.389   93.931 127.074   89.920 127.316 
 85.894 127.100   81.913 126.424   78.036 125.295   74.326 123.729 
 70.839 121.755   67.628 119.412   64.735 116.748   62.190 113.817 
 60.013 110.676   58.209 107.381   56.769 103.981   55.680 100.519 
 54.922  97.023   54.477  93.512   54.330  89.996   54.477  86.480 
 54.924  82.969   55.682  79.473   56.772  76.011   58.212  72.612 
 60.018  69.317   62.196  66.176   64.741  63.246   67.635  60.582 
 70.847  58.240   74.334  56.267   78.045  54.702   81.922  53.574 
 85.904  52.899   89.930  52.685   93.940  52.927   97.880  53.613 
101.698  54.725  105.349  56.238  108.791  58.123  111.991  60.347 
114.920  62.879  117.552  65.682  119.868  68.722  121.852  71.964 
123.491  75.373  124.775  78.915  125.697  82.557  126.252  86.264 
126.437  90.004  ] scurve
138.968  90.006 moveto
[ 138.968  90.006  138.731  94.963  138.022  99.883  136.842 104.728 
135.194 109.460  133.083 114.037  130.514 118.419  127.496 122.560 
124.044 126.416  120.174 129.936  115.910 133.070  111.283 135.766 
106.331 137.972  101.103 139.636   95.660 140.709   90.072 141.150 
 84.423 140.925   78.807 140.014   73.328 138.415   68.092 136.144 
 63.207 133.245   58.772 129.786   54.869 125.858   51.553 121.574 
 48.850 117.054   46.746 112.419   45.195 107.773   44.121 103.191 
 43.439  98.710   43.068  94.324   42.952  89.995   43.069  85.666 
 43.440  81.280   44.123  76.798   45.198  72.216   46.751  67.570 
 48.856  62.936   51.560  58.416   54.877  54.132   58.782  50.206 
 63.218  46.748   68.104  43.850   73.340  41.581   78.820  39.983 
 84.436  39.074   90.085  38.850   95.672  39.293  101.115  40.368 
106.342  42.033  111.294  44.240  115.920  46.937  120.183  50.072 
124.052  53.593  127.504  57.449  130.520  61.591  133.088  65.973 
135.198  70.551  136.845  75.282  138.024  80.128  138.732  85.048 
138.968  90.006  ] scurve
148.641  90.006 moveto
[ 148.641  90.006  148.370  95.870  147.559 101.695  146.208 107.443 
144.316 113.075  141.884 118.546  138.913 123.812  135.408 128.823 
131.375 133.526  126.826 137.861  121.779 141.767  116.259 145.175 
110.303 148.014  103.962 150.211   97.301 151.691   90.405 152.386 
 83.376 152.234   76.339 151.188   69.438 149.225   62.833 146.350 
 56.689 142.610   51.168 138.096   46.411 132.946   42.519 127.340 
 39.535 121.489   37.428 115.608   36.095 109.889   35.370 104.465 
 35.054  99.384   34.956  94.603   34.940  89.995   34.956  85.387 
 35.054  80.605   35.371  75.523   36.098  70.098   37.432  64.378 
 39.541  58.497   42.527  52.646   46.422  47.042   51.180  41.893 
 56.703  37.380   62.848  33.643   69.454  30.770   76.355  28.809 
 83.392  27.765   90.420  27.615   97.317  28.311  103.977  29.794 
110.317  31.992  116.271  34.832  121.790  38.242  126.837  42.148 
131.385  46.485  135.416  51.188  138.920  56.199  141.890  61.466 
144.321  66.938  146.211  72.569  147.562  78.318  148.371  84.143 
148.641  90.006  ] scurve
156.731  90.007 moveto
[ 156.731  90.007  156.436  96.604  155.551 103.163  154.075 109.647 
152.005 116.016  149.336 122.227  146.066 128.233  142.192 133.981 
137.714 139.414  132.636 144.465  126.967 149.064  120.726 153.128 
113.944 156.572  106.665 159.299   98.956 161.211   90.905 162.210 
 82.630 162.201   74.280 161.104   66.036 158.864   58.111 155.463 
 50.735 150.936   44.149 145.387   38.572 138.995   34.174 132.018 
 31.040 124.775   29.133 117.612   28.286 110.848   28.206 104.711 
 28.532  99.282   28.903  94.463   29.059  89.995   28.903  85.527 
 28.531  80.706   28.206  75.275   28.286  69.137   29.136  62.372 
 31.046  55.208   34.183  47.965   38.584  40.989   44.163  34.600 
 50.751  29.053   58.128  24.529   66.055  21.130   74.299  18.893 
 82.649  17.798   90.923  17.792   98.973  18.793  106.682  20.707 
113.959  23.436  120.741  26.880  126.980  30.946  132.648  35.546 
137.725  40.598  142.201  46.031  146.074  51.780  149.343  57.786 
152.010  63.998  154.079  70.367  155.554  76.852  156.437  83.411 
156.731  90.007  ] scurve
163.777  90.008 moveto
[ 163.777  90.008  163.462  97.223  162.523 104.405  160.952 111.513 
158.745 118.513  155.896 125.360  152.393 132.008  148.229 138.404 
143.397 144.486  137.891 150.184  131.712 155.421  124.869 160.104 
117.383 164.132  109.292 167.391  100.654 169.758   91.560 171.105 
 82.133 171.303   72.540 170.231   62.995 167.795   53.760 163.939 
 45.137 158.675   37.455 152.104   31.033 144.438   26.137 136.011 
 22.923 127.267   21.369 118.718   21.244 110.861   22.102 104.068 
 23.356  98.480   24.409  93.935   24.814  89.996   24.407  86.056 
 23.353  81.509   22.099  75.917   21.242  69.121   21.371  61.262 
 22.929  52.712   26.147  43.969   31.046  35.543   37.472  27.880 
 45.157  21.312   53.781  16.051   63.017  12.199   72.562   9.766 
 82.154   8.697   91.580   8.897  100.674  10.247  109.310  12.616 
117.400  15.877  124.885  19.906  131.726  24.590  137.903  29.828 
143.408  35.528  148.238  41.610  152.401  48.007  155.903  54.654 
158.750  61.502  160.957  68.503  162.525  75.611  163.463  82.793 
163.777  90.008  ] scurve
170.086  90.009 moveto
[ 170.086  90.009  169.975  93.907  169.721  97.749  169.346 101.617 
168.758 105.502  167.996 109.317  167.120 113.120  166.050 116.943 
164.780 120.692  163.389 124.395  161.818 128.105  160.034 131.740 
158.115 135.299  156.020 138.841  153.709 142.297  151.250 145.656 
148.608 148.966  145.754 152.164  142.742 155.246  139.536 158.241 
136.128 161.086  132.556 163.795  128.779 166.363  124.822 168.744 
120.690 170.956  116.365 172.960  111.881 174.745  107.220 176.298 
102.408 177.587   97.449 178.606   92.358 179.321   87.153 179.723 
 81.853 179.782   76.483 179.485   71.071 178.807   65.649 177.735 
 60.253 176.252   54.922 174.348   49.704 172.015   44.646 169.253 
 39.800 166.068   35.221 162.474   30.964 158.493   27.085 154.159 
 23.636 149.518   20.664 144.626   18.208 139.550   16.295 134.370 
 14.939 129.171   14.134 124.047   13.855 119.091   14.057 114.394 
 14.671 110.037   15.608 106.088   16.763 102.590   18.019  99.563 
 19.256  96.994   20.357  94.839   21.223  93.023   21.775  91.447 
 21.965  89.997   21.773  88.547   21.219  86.970   20.352  85.153 
 19.250  82.996   18.012  80.424   16.756  77.395   15.602  73.894 
 14.666  69.943   14.055  65.584   13.856  60.886   14.137  55.929 
 14.945  50.804   16.304  45.606   18.219  40.426   20.678  35.351 
 23.652  30.460   27.103  25.820   30.984  21.489   35.242  17.510 
 39.822  13.917   44.669  10.734   49.728   7.974   54.947   5.644 
 60.277   3.741   65.674   2.260   71.096   1.190   76.508   0.514 
 81.877   0.218   87.176   0.279   92.381   0.682   97.471   1.399 
102.430   2.419  107.241   3.709  111.901   5.263  116.385   7.049 
120.708   9.053  124.840  11.266  128.796  13.648  132.572  16.217 
136.143  18.927  139.551  21.773  142.756  24.768  145.766  27.850 
148.620  31.049  151.261  34.359  153.720  37.718  156.030  41.174 
158.124  44.716  160.042  48.276  161.825  51.912  163.395  55.621 
164.786  59.324  166.055  63.074  167.124  66.897  167.999  70.700 
168.761  74.514  169.348  78.400  169.722  82.268  169.976  86.110 
170.086  90.009  ] scurve
176.126  90.011 moveto
[ 176.126  90.011  175.805  93.077  175.360  95.654  175.192  98.051 
175.277 100.663  175.178 103.748  174.448 106.761  173.651 109.276 
173.153 111.655  172.868 114.292  172.315 117.367  171.161 120.258 
170.037 122.668  169.223 125.021  168.546 127.694  167.460 130.716 
165.882 133.380  164.476 135.648  163.358 137.991  162.208 140.719 
160.494 143.555  158.564 145.881  156.931 148.019  155.458 150.411 
153.642 153.120  151.342 155.503  149.218 157.494  147.337 159.611 
145.265 162.062  142.662 164.345  140.121 166.165  137.839 168.040 
135.394 170.216  132.451 172.221  129.578 173.781  126.926 175.421 
124.023 177.292  120.719 178.846  117.602 180.071  114.567 181.468 
111.138 182.886  107.593 183.849  104.267 184.756  100.727 185.794 
 96.910 186.471   93.293 186.920   89.584 187.477   85.593 187.734 
 81.772 187.712   77.886 187.742   73.789 187.448   69.869 186.919 
 65.844 186.362   61.751 185.427   57.816 184.360   53.751 183.112 
 49.815 181.531   45.917 179.857   42.042 177.847   38.339 175.680 
 34.652 173.258   31.182 170.614   27.787 167.773   24.627 164.695 
 21.609 161.451   18.850 157.996   16.287 154.397   14.016 150.638 
 11.986 146.763   10.273 142.797    8.841 138.755    7.730 134.696 
  6.935 130.626    6.448 126.607    6.281 122.664    6.405 118.835 
  6.811 115.169    7.477 111.692    8.365 108.438    9.443 105.441 
 10.670 102.721   11.997 100.293   13.373  98.167   14.750  96.345 
 16.071  94.814   17.284  93.556   18.339  92.537   19.203  91.715 
 19.849  91.047   20.251  90.492   20.388  89.998   20.250  89.505 
 19.846  88.950   19.198  88.282   18.332  87.458   17.275  86.437 
 16.061  85.178   14.738  83.645   13.362  81.819   11.986  79.691 
 10.659  77.260    9.433  74.537    8.357  71.539    7.471  68.283 
  6.806  64.804    6.403  61.137    6.281  57.307    6.451  53.364 
  6.940  49.345    7.738  45.274    8.851  41.217   10.285  37.175 
 12.001  33.209   14.033  29.335   16.305  25.578   18.869  21.981 
 21.630  18.526   24.649  15.284   27.811  12.207   31.207   9.369 
 34.677   6.725   38.366   4.306   42.068   2.140   45.945   0.131 
 49.842  -1.541   53.779  -3.120   57.844  -4.366   61.778  -5.433 
 65.872  -6.366   69.896  -6.921   73.817  -7.450   77.914  -7.741 
 81.798  -7.711   85.620  -7.732   89.610  -7.472   93.317  -6.916 
 96.935  -6.467  100.752  -5.787  104.289  -4.749  107.615  -3.842 
111.162  -2.878  114.588  -1.457  117.622  -0.062  120.741   1.163 
124.044   2.721  126.943   4.591  129.595   6.229  132.471   7.791 
135.412   9.799  137.854  11.974  140.136  13.848  142.680  15.669 
145.280  17.955  147.350  20.404  149.230  22.520  151.356  24.511 
153.656  26.897  155.468  29.606  156.941  31.996  158.576  34.133 
160.507  36.462  162.216  39.300  163.365  42.026  164.484  44.367 
165.892  46.636  167.469  49.303  168.551  52.325  169.228  54.995 
170.043  57.347  171.169  59.759  172.321  62.654  172.870  65.727 
173.155  68.361  173.656  70.740  174.454  73.257  175.181  76.273 
175.276  79.355  175.192  81.965  175.362  84.362  175.809  86.941 
176.126  90.011  ] scurve
 10.000 -13.000 moveto
  1.000 nbpt mul rm  (Cardioide) show currentpoint
clear
 10.000 -20.000 moveto
  1.000 nbpt mul it  (r ) show currentpoint
  1.000 nbpt mul rm  (= 1 + ) show currentpoint
  1.000 nbpt mul rm  (cos ) show currentpoint  
  1.000 nbpt mul symb  (q) show currentpoint
clear
130.000 -20.000 moveto
  1.000 nbpt mul rm  (Centre  ) show <28> show ( 0.875 , 0 ) show
  <29> show currentpoint
clear
}
\EndFig
\vskip80pt
\centerline{\bf Fig.\ 6}
\vfill\eject



\InsertFig 0.000 178.000  {
%%EPS file  z7.eps
0.72 dup scale
1 mm unit  /nbpt 14 def
  0.000   0.000 translate
  0.452 setlinewidth
 22.825 120.000 moveto
[  22.825 120.000   22.784 117.653   22.663 115.291   22.467 112.902 
 22.202 110.472   21.880 107.989   21.511 105.442   21.111 102.824 
 20.695 100.127   20.278  97.346   19.880  94.478   19.516  91.523 
 19.204  88.480   18.962  85.353   18.805  82.145   18.750  78.864 
 18.810  75.516   18.999  72.109   19.330  68.655   19.812  65.164 
 20.457  61.646   21.271  58.116   22.262  54.586   23.434  51.069 
 24.793  47.580   26.339  44.132   28.076  40.741   30.001  37.419 
 32.115  34.182   34.414  31.043   36.893  28.017   39.549  25.116 
 42.374  22.353   45.362  19.741   48.503  17.292   51.789  15.016 
 55.209  12.924   58.752  11.026   62.407   9.330   66.160   7.844 
 70.000   6.574   73.912   5.528   77.882   4.709   81.897   4.121 
 85.941   3.767   90.000   3.649   94.059   3.767   98.103   4.121 
102.118   4.709  106.088   5.528  110.000   6.574  113.840   7.844 
117.593   9.330  121.248  11.026  124.791  12.924  128.211  15.016 
131.497  17.292  134.638  19.741  137.626  22.353  140.451  25.116 
143.107  28.017  145.586  31.043  147.885  34.182  149.999  37.419 
151.924  40.741  153.661  44.132  155.207  47.580  156.566  51.069 
157.738  54.586  158.729  58.116  159.543  61.646  160.188  65.164 
160.670  68.655  161.001  72.109  161.190  75.516  161.250  78.864 
161.195  82.145  161.038  85.353  160.796  88.480  160.484  91.523 
160.120  94.478  159.722  97.346  159.305 100.127  158.889 102.824 
158.489 105.442  158.120 107.989  157.798 110.472  157.533 112.902 
157.337 115.291  157.216 117.653  157.175 120.000  157.216 122.347 
157.337 124.709  157.533 127.098  157.798 129.528  158.120 132.011 
158.489 134.558  158.889 137.176  159.305 139.873  159.722 142.654 
160.120 145.522  160.484 148.477  160.796 151.520  161.038 154.647 
161.195 157.855  161.250 161.136  161.190 164.484  161.001 167.891 
160.670 171.345  160.188 174.836  159.543 178.354  158.729 181.884 
157.738 185.414  156.566 188.931  155.207 192.420  153.661 195.868 
151.924 199.259  149.999 202.581  147.885 205.818  145.586 208.957 
143.107 211.983  140.451 214.884  137.626 217.647  134.638 220.259 
131.497 222.708  128.211 224.984  124.791 227.076  121.248 228.974 
117.593 230.670  113.840 232.156  110.000 233.426  106.088 234.472 
102.118 235.291   98.103 235.879   94.059 236.233   90.000 236.351 
 85.941 236.233   81.897 235.879   77.882 235.291   73.912 234.472 
 70.000 233.426   66.160 232.156   62.407 230.670   58.752 228.974 
 55.209 227.076   51.789 224.984   48.503 222.708   45.362 220.259 
 42.374 217.647   39.549 214.884   36.893 211.983   34.414 208.957 
 32.115 205.818   30.001 202.581   28.076 199.259   26.339 195.868 
 24.793 192.420   23.434 188.931   22.262 185.414   21.271 181.884 
 20.457 178.354   19.812 174.836   19.330 171.345   18.999 167.891 
 18.810 164.484   18.750 161.136   18.805 157.855   18.962 154.647 
 19.204 151.520   19.516 148.477   19.880 145.522   20.278 142.654 
 20.695 139.873   21.111 137.176   21.511 134.558   21.880 132.011 
 22.202 129.528   22.467 127.098   22.663 124.709   22.784 122.347 
 22.825 120.000  ] scurve
 90.000 120.000 moveto
  0.113 setlinewidth
[  90.000 120.000   85.744 120.000   81.505 120.000   77.300 120.000 
 73.146 120.000   69.057 120.000   65.049 120.000   61.136 120.000 
 57.330 120.000   53.644 120.000   50.086 120.000   46.666 120.000 
 43.390 120.000   40.266 120.000   37.296 120.000   34.484 120.000 
 31.833 120.000   29.340 120.000   26.996 120.000   24.704 120.000 
 22.825 120.000  ] scurve
 90.000 120.000 moveto
[  90.000 120.000   86.000 118.546   82.008 117.106   78.033 115.696 
 74.084 114.330   70.170 113.020   66.299 111.780   62.481 110.620 
 58.724 109.552   55.038 108.584   51.431 107.724   47.913 106.978 
 44.493 106.350   41.178 105.844   37.978 105.459   34.898 105.197 
 31.947 105.055   29.131 105.029   26.455 105.108   23.950 105.206 
 21.470 105.165  ] scurve
 90.000 120.000 moveto
[  90.000 120.000   86.736 117.265   83.464 114.545   80.175 111.854 
 76.861 109.209   73.515 106.623   70.132 104.113   66.704 101.695 
 63.230  99.384   59.706  97.196   56.131  95.148   52.507  93.256 
 48.837  91.536   45.127  90.004   41.385  88.674   37.621  87.560 
 33.847  86.674   30.078  86.027   26.328  85.628   22.551  85.476 
 18.964  85.379  ] scurve
 90.000 120.000 moveto
[  90.000 120.000   87.868 116.312   85.718 112.624   83.535 108.936 
 81.299 105.249   78.994 101.564   76.600  97.884   74.101  94.211 
 71.475  90.551   68.703  86.909   65.766  83.294   62.641  79.718 
 59.308  76.192   55.746  72.736   51.934  69.369   47.851  66.118 
 43.479  63.011   38.801  60.085   33.805  57.379   28.476  54.963 
 22.654  53.345  ] scurve
 90.000 120.000 moveto
[  90.000 120.000   89.259 115.803   88.510 111.592   87.743 107.351 
 86.949 103.064   86.120  98.717   85.243  94.292   84.309  89.773 
 83.303  85.141   82.212  80.378   81.020  75.462   79.706  70.371 
 78.249  65.081   76.624  59.567   74.799  53.799   72.739  47.746 
 70.399  41.375   67.726  34.650   64.657  27.530   61.116  19.970 
 57.348  11.747  ] scurve
 90.000 120.000 moveto
[  90.000 120.000   90.741 115.803   91.491 111.592   92.258 107.351 
 93.051 103.064   93.881  98.717   94.757  94.292   95.692  89.773 
 96.697  85.142   97.788  80.378   98.981  75.462  100.295  70.371 
101.752  65.082  103.377  59.567  105.202  53.799  107.263  47.747 
109.603  41.376  112.276  34.651  115.345  27.531  118.887  19.971 
122.655  11.748  ] scurve
 90.000 120.000 moveto
[  90.000 120.000   92.132 116.312   94.282 112.624   96.465 108.936 
 98.701 105.249  101.007 101.564  103.400  97.884  105.900  94.211 
108.526  90.551  111.297  86.909  114.235  83.295  117.359  79.718 
120.692  76.193  124.254  72.737  128.066  69.370  132.149  66.119 
136.521  63.012  141.199  60.086  146.196  57.381  151.524  54.965 
157.347  53.347  ] scurve
 90.000 120.000 moveto
[  90.000 120.000   93.264 117.265   96.536 114.545   99.825 111.854 
103.139 109.209  106.485 106.623  109.869 104.114  113.296 101.695 
116.770  99.384  120.295  97.196  123.869  95.148  127.493  93.257 
131.163  91.537  134.873  90.005  138.615  88.675  142.379  87.561 
146.153  86.675  149.922  86.028  153.672  85.629  157.448  85.477 
161.036  85.380  ] scurve
 90.000 120.000 moveto
[  90.000 120.000   94.001 118.546   97.992 117.107  101.967 115.697 
105.916 114.330  109.830 113.020  113.701 111.780  117.520 110.620 
121.276 109.552  124.962 108.584  128.569 107.725  132.087 106.978 
135.507 106.351  138.821 105.844  142.022 105.460  145.101 105.197 
148.052 105.055  150.869 105.029  153.544 105.108  156.049 105.206 
158.530 105.166  ] scurve
 90.000 120.000 moveto
[  90.000 120.000   94.256 120.000   98.495 120.000  102.700 120.000 
106.854 120.000  110.943 120.000  114.951 120.000  118.864 120.000 
122.670 120.000  126.357 120.000  129.914 120.000  133.335 120.000 
136.610 120.000  139.735 120.000  142.704 120.000  145.516 120.000 
148.167 120.000  150.660 119.999  153.004 119.999  155.296 119.998 
157.175 119.992  ] scurve
 90.000 120.000 moveto
[  90.000 120.000   94.001 121.454   97.992 122.894  101.967 124.304 
105.916 125.670  109.830 126.980  113.701 128.220  117.520 129.380 
121.276 130.448  124.963 131.416  128.569 132.276  132.087 133.022 
135.507 133.649  138.822 134.156  142.023 134.540  145.102 134.802 
148.053 134.944  150.870 134.970  153.546 134.892  156.051 134.793 
158.530 134.835  ] scurve
 90.000 120.000 moveto
[  90.000 120.000   93.264 122.735   96.536 125.455   99.825 128.146 
103.139 130.791  106.485 133.377  109.868 135.887  113.296 138.305 
116.770 140.617  120.295 142.804  123.870 144.852  127.493 146.744 
131.163 148.464  134.873 149.996  138.616 151.326  142.380 152.440 
146.154 153.326  149.923 153.973  153.674 154.372  157.450 154.524 
161.036 154.621  ] scurve
 90.000 120.000 moveto
[  90.000 120.000   92.132 123.688   94.282 127.376   96.465 131.064 
 98.701 134.751  101.006 138.436  103.400 142.116  105.899 145.789 
108.525 149.449  111.297 153.091  114.234 156.706  117.359 160.283 
120.692 163.808  124.254 167.264  128.066 170.631  132.149 173.883 
136.521 176.990  141.199 179.917  146.196 182.622  151.525 185.039 
157.346 186.656  ] scurve
 90.000 120.000 moveto
[  90.000 120.000   90.741 124.197   91.490 128.408   92.257 132.649 
 93.051 136.936   93.880 141.283   94.757 145.708   95.691 150.227 
 96.697 154.859   97.788 159.622   98.980 164.539  100.294 169.629 
101.750 174.919  103.376 180.434  105.200 186.202  107.261 192.255 
109.601 198.625  112.273 205.351  115.342 212.471  118.883 220.032 
122.650 228.254  ] scurve
 90.000 120.000 moveto
[  90.000 120.000   89.259 124.197   88.509 128.408   87.742 132.649 
 86.949 136.936   86.119 141.283   85.243 145.708   84.308 150.227 
 83.303 154.859   82.211 159.622   81.019 164.538   79.705 169.629 
 78.248 174.919   76.622 180.433   74.797 186.201   72.737 192.253 
 70.396 198.624   67.723 205.349   64.654 212.469   61.112 220.028 
 57.344 228.251  ] scurve
 90.000 120.000 moveto
[  90.000 120.000   87.868 123.688   85.718 127.376   83.535 131.064 
 81.299 134.751   78.993 138.436   76.600 142.116   74.100 145.789 
 71.474 149.449   68.703 153.091   65.765 156.705   62.640 160.282 
 59.308 163.807   55.746 167.263   51.933 170.629   47.850 173.881 
 43.478 176.987   38.801 179.913   33.804 182.618   28.476 185.035 
 22.653 186.653  ] scurve
 90.000 120.000 moveto
[  90.000 120.000   86.736 122.735   83.464 125.455   80.175 128.146 
 76.861 130.791   73.515 133.377   70.131 135.886   66.704 138.305 
 63.230 140.616   59.705 142.804   56.131 144.851   52.507 146.743 
 48.837 148.463   45.127 149.995   41.385 151.325   37.621 152.439 
 33.847 153.324   30.078 153.971   26.328 154.371   22.552 154.523 
 18.964 154.619  ] scurve
 90.000 120.000 moveto
[  90.000 120.000   85.999 121.454   82.008 122.893   78.033 124.303 
 74.084 125.670   70.170 126.980   66.299 128.220   62.480 129.380 
 58.724 130.448   55.038 131.415   51.431 132.275   47.913 133.021 
 44.493 133.649   41.178 134.156   37.978 134.540   34.899 134.802 
 31.948 134.944   29.131 134.970   26.456 134.892   23.951 134.794 
 21.470 134.834  ] scurve
103.378 120.000 moveto
[ 103.378 120.000  103.308 121.380  103.100 122.748  102.755 124.089 
102.275 125.393  101.663 126.644  100.923 127.830  100.061 128.938 
 99.084 129.955   98.002 130.867   96.824 131.663   95.564 132.331 
 94.235 132.861   92.853 133.246   91.436 133.480   90.000 133.558 
 88.564 133.480   87.146 133.246   85.765 132.861   84.436 132.331 
 83.176 131.663   81.998 130.867   80.916 129.955   79.939 128.938 
 79.077 127.830   78.337 126.644   77.725 125.392   77.245 124.089 
 76.900 122.747   76.692 121.380   76.622 120.000   76.692 118.620 
 76.900 117.252   77.245 115.911   77.725 114.607   78.337 113.356 
 79.077 112.170   79.939 111.062   80.916 110.045   81.998 109.133 
 83.176 108.337   84.436 107.669   85.765 107.139   87.147 106.754 
 88.564 106.520   90.000 106.442   91.436 106.520   92.854 106.754 
 94.235 107.139   95.564 107.669   96.824 108.337   98.002 109.133 
 99.084 110.045  100.061 111.062  100.923 112.170  101.663 113.356 
102.275 114.608  102.755 115.911  103.100 117.253  103.308 118.620 
103.378 120.000  ] scurve
121.714 120.000 moveto
[ 121.714 120.000  121.591 123.064  121.221 126.124  120.596 129.173 
119.702 132.203  118.524 135.196  117.045 138.131  115.247 140.977 
113.117 143.691  110.649 146.225  107.845 148.521  104.725 150.517 
101.321 152.152   97.686 153.367   93.886 154.116   90.000 154.370 
 86.114 154.116   82.313 153.367   78.678 152.152   75.275 150.517 
 72.154 148.520   69.351 146.224   66.882 143.690   64.752 140.976 
 62.955 138.131   61.476 135.196   60.298 132.202   59.404 129.173 
 58.779 126.123   58.409 123.064   58.286 120.000   58.409 116.936 
 58.779 113.876   59.404 110.827   60.298 107.797   61.476 104.804 
 62.955 101.869   64.753  99.024   66.883  96.309   69.351  93.775 
 72.155  91.479   75.275  89.483   78.679  87.848   82.314  86.633 
 86.114  85.884   90.000  85.631   93.886  85.884   97.686  86.633 
101.322  87.849  104.725  89.483  107.845  91.479  110.649  93.776 
113.117  96.310  115.247  99.024  117.045 101.869  118.524 104.804 
119.702 107.798  120.596 110.827  121.221 113.877  121.591 116.936 
121.714 120.000  ] scurve
131.601 120.000 moveto
[ 131.601 120.000  131.489 123.762  131.147 127.546  130.555 131.369 
129.683 135.243  128.488 139.171  126.917 143.141  124.912 147.121 
122.413 151.058  119.366 154.873  115.735 158.457  111.510 161.682 
106.722 164.403  101.450 166.476   95.820 167.776   89.999 168.219 
 84.179 167.776   78.549 166.475   73.277 164.402   68.489 161.682 
 64.265 158.456   60.633 154.872   57.587 151.057   55.088 147.120 
 53.083 143.140   51.512 139.171   50.317 135.243   49.445 131.369 
 48.853 127.546   48.511 123.762   48.399 120.000   48.511 116.238 
 48.853 112.454   49.445 108.631   50.317 104.756   51.513 100.829 
 53.083  96.859   55.088  92.879   57.587  88.942   60.634  85.128 
 64.265  81.543   68.490  78.318   73.278  75.597   78.550  73.525 
 84.180  72.224   90.000  71.781   95.821  72.225  101.450  73.525 
106.723  75.598  111.510  78.318  115.735  81.544  119.366  85.128 
122.413  88.943  124.912  92.880  126.917  96.860  128.487 100.829 
129.683 104.757  130.555 108.631  131.147 112.454  131.489 116.238 
131.601 120.000  ] scurve
138.656 120.000 moveto
[ 138.656 120.000  138.575 124.117  138.323 128.283  137.873 132.544 
137.179 136.939  136.174 141.498  134.773 146.232  132.871 151.129 
130.349 156.138  127.088 161.165  122.977 166.061  117.946 170.617 
111.991 174.581  105.202 177.677   97.774 179.655   89.999 180.336 
 82.224 179.655   74.796 177.676   68.008 174.579   62.053 170.616 
 57.023 166.059   52.912 161.164   49.651 156.137   47.130 151.127 
 45.228 146.231   43.827 141.497   42.822 136.939   42.127 132.543 
 41.677 128.283   41.425 124.117   41.344 120.000   41.425 115.883 
 41.677 111.717   42.127 107.456   42.822 103.061   43.827  98.502 
 45.228  93.768   47.130  88.872   49.651  83.862   52.913  78.835 
 57.024  73.940   62.054  69.383   68.009  65.420   74.798  62.323 
 82.225  60.345   90.001  59.664   97.776  60.345  105.203  62.324 
111.992  65.421  117.946  69.384  122.977  73.941  127.088  78.836 
130.349  83.863  132.870  88.872  134.772  93.768  136.173  98.502 
137.178 103.061  137.873 107.456  138.323 111.717  138.575 115.883 
138.656 120.000  ] scurve
144.106 120.000 moveto
[ 144.106 120.000  144.065 124.281  143.932 128.636  143.674 133.139 
143.236 137.857  142.536 142.852  141.460 148.168  139.862 153.824 
137.562 159.796  134.356 165.995  130.038 172.245  124.433 178.265 
117.459 183.671  109.187 188.009   99.881 190.835   89.999 191.818 
 80.116 190.834   70.811 188.008   62.539 183.669   55.566 178.263 
 49.962 172.243   45.644 165.993   42.438 159.794   40.139 153.823 
 38.540 148.167   37.465 142.851   36.764 137.857   36.327 133.139 
 36.069 128.636   35.936 124.281   35.895 120.000   35.935 115.719 
 36.069 111.363   36.327 106.861   36.764 102.143   37.464  97.148 
 38.540  91.832   40.139  86.176   42.439  80.204   45.644  74.006 
 49.963  67.756   55.567  61.735   62.540  56.330   70.813  51.992 
 80.118  49.166   90.001  48.183   99.883  49.166  109.189  51.993 
117.461  56.331  124.433  61.737  130.038  67.757  134.356  74.007 
137.561  80.205  139.861  86.177  141.459  91.833  142.535  97.149 
143.235 102.143  143.673 106.861  143.931 111.363  144.064 115.719 
144.106 120.000  ] scurve
148.486 119.999 moveto
[ 148.486 119.999  148.489 124.323  148.486 128.744  148.444 133.357 
148.303 138.258  147.974 143.543  147.323 149.294  146.171 155.574 
144.282 162.404  141.363 169.725  137.087 177.365  131.134 184.984 
123.285 192.055  113.539 197.897  102.220 201.784   89.998 203.152 
 77.777 201.783   66.458 197.895   56.713 192.053   48.865 184.981 
 42.913 177.362   38.637 169.723   35.719 162.402   33.830 155.573 
 32.678 149.293   32.028 143.542   31.698 138.258   31.557 133.357 
 31.515 128.744   31.512 124.324   31.514 120.000   31.512 115.676 
 31.515 111.255   31.557 106.643   31.697 101.741   32.027  96.457 
 32.678  90.706   33.830  84.426   35.719  77.597   38.637  70.275 
 42.914  62.636   48.866  55.017   56.715  47.946   66.460  42.104 
 77.780  38.216   90.001  36.848  102.222  38.217  113.541  42.105 
123.287  47.947  131.135  55.019  137.087  62.637  141.363  70.277 
144.281  77.598  146.170  84.427  147.321  90.707  147.972  96.458 
148.302 101.741  148.443 106.643  148.485 111.255  148.488 115.676 
148.486 119.999  ] scurve
152.098 119.999 moveto
[ 152.098 119.999  152.101 122.140  152.136 124.280  152.200 126.463 
152.265 128.689  152.353 130.958  152.453 133.314  152.539 135.755 
152.624 138.291  152.683 140.958  152.697 143.752  152.661 146.699 
152.537 149.814  152.308 153.105  151.935 156.591  151.384 160.276 
150.610 164.167  149.562 168.260  148.184 172.545  146.416 177.000 
144.193 181.588  141.451 186.255  138.130 190.930  134.181 195.519 
129.570 199.909  124.290 203.969  118.364 207.560  111.854 210.539 
104.860 212.775   97.519 214.163   89.998 214.634   82.476 214.163 
 75.136 212.774   68.142 210.536   61.632 207.557   55.707 203.966 
 50.427 199.905   45.817 195.515   41.868 190.926   38.548 186.252 
 35.807 181.584   33.585 176.997   31.817 172.542   30.439 168.257 
 29.392 164.165   28.617 160.274   28.066 156.590   27.694 153.103 
 27.465 149.813   27.341 146.698   27.304 143.751   27.318 140.958 
 27.378 138.291   27.462 135.755   27.548 133.315   27.648 130.959 
 27.735 128.689   27.800 126.464   27.865 124.280   27.899 122.141 
 27.902 120.000   27.899 117.859   27.865 115.719   27.800 113.536 
 27.735 111.310   27.648 109.041   27.547 106.685   27.462 104.244 
 27.377 101.709   27.318  99.042   27.304  96.248   27.340  93.301 
 27.464  90.186   27.694  86.896   28.066  83.409   28.617  79.725 
 29.391  75.833   30.439  71.741   31.817  67.456   33.585  63.001 
 35.808  58.414   38.550  53.746   41.870  49.071   45.819  44.482 
 50.429  40.093   55.709  36.032   61.635  32.442   68.145  29.463 
 75.139  27.226   82.480  25.837   90.001  25.367   97.523  25.838 
104.863  27.226  111.857  29.464  118.367  32.443  124.292  36.034 
129.572  40.094  134.182  44.484  138.131  49.073  141.451  53.748 
144.192  58.415  146.415  63.003  148.183  67.457  149.561  71.742 
150.608  75.835  151.383  79.726  151.934  83.410  152.306  86.897 
152.535  90.187  152.659  93.302  152.695  96.249  152.682  99.042 
152.622 101.709  152.537 104.244  152.452 106.685  152.352 109.041 
152.264 111.310  152.199 113.536  152.135 115.719  152.101 117.858 
152.098 119.999  ] scurve
155.234 119.999 moveto
[ 155.234 119.999  155.132 121.508  155.041 122.822  155.134 124.093 
155.357 125.526  155.439 127.130  155.391 128.597  155.478 129.951 
155.746 131.413  155.968 133.118  155.988 134.794  156.083 136.333 
156.364 137.962  156.621 139.861  156.661 141.770  156.766 143.568 
157.034 145.520  157.177 147.737  157.150 149.900  157.247 152.069 
157.347 154.523  157.202 157.067  157.079 159.582  156.954 162.360 
156.565 165.257  156.149 168.170  155.612 171.346  154.811 174.570 
153.933 177.920  152.753 181.436  151.380 184.981  149.715 188.686 
147.752 192.389  145.465 196.182  142.823 199.931  139.801 203.676 
136.399 207.303  132.577 210.804  128.372 214.098  123.761 217.120 
118.783 219.826  113.476 222.133  107.873 223.993  102.046 225.366 
 96.065 226.201   89.997 226.479   83.929 226.201   77.948 225.365 
 72.121 223.991   66.518 222.131   61.212 219.823   56.235 217.117 
 51.624 214.094   47.419 210.800   43.598 207.299   40.197 203.671 
 37.175 199.926   34.534 196.178   32.247 192.384   30.285 188.681 
 28.621 184.976   27.247 181.432   26.068 177.916   25.190 174.567 
 24.390 171.343   23.852 168.167   23.437 165.254   23.048 162.357 
 22.923 159.580   22.800 157.065   22.655 154.522   22.756 152.068 
 22.852 149.899   22.825 147.737   22.968 145.519   23.236 143.568 
 23.341 141.770   23.381 139.861   23.637 137.962   23.919 136.333 
 24.013 134.794   24.033 133.119   24.255 131.413   24.523 129.951 
 24.611 128.597   24.563 127.131   24.643 125.528   24.866 124.094 
 24.959 122.823   24.869 121.509   24.766 120.000   24.869 118.491 
 24.959 117.177   24.866 115.906   24.643 114.472   24.562 112.869 
 24.610 111.403   24.522 110.048   24.255 108.586   24.033 106.881 
 24.013 105.206   23.918 103.667   23.636 102.038   23.380 100.138 
 23.341  98.230   23.235  96.432   22.967  94.480   22.824  92.263 
 22.851  90.101   22.755  87.931   22.654  85.477   22.799  82.934 
 22.922  80.419   23.047  77.641   23.436  74.744   23.852  71.831 
 24.390  68.655   25.190  65.431   26.068  62.081   27.248  58.566 
 28.621  55.021   30.286  51.316   32.248  47.613   34.535  43.819 
 37.177  40.071   40.199  36.326   43.601  32.699   47.422  29.198 
 51.627  25.903   56.238  22.881   61.216  20.175   66.522  17.868 
 72.126  16.008   77.953  14.635   83.934  13.800   90.002  13.521 
 96.069  13.800  102.050  14.636  107.877  16.009  113.480  17.869 
118.787  20.177  123.764  22.883  128.375  25.905  132.580  29.200 
136.401  32.701  139.803  36.328  142.824  40.073  145.466  43.821 
147.752  47.615  149.714  51.318  151.379  55.023  152.752  58.568 
153.932  62.083  154.810  65.433  155.610  68.657  156.148  71.832 
156.563  74.746  156.952  77.643  157.077  80.420  157.200  82.935 
157.345  85.478  157.244  87.932  157.147  90.101  157.175  92.263 
157.032  94.481  156.764  96.432  156.658  98.230  156.619 100.138 
156.363 102.038  156.081 103.667  155.986 105.206  155.966 106.880 
155.745 108.586  155.477 110.048  155.389 111.402  155.437 112.868 
155.357 114.471  155.134 115.905  155.040 117.177  155.131 118.490 
155.234 119.999  ] scurve
  0.000  10.000 moveto
  1.000 nbpt mul rm  (Courbe) show currentpoint
clear
  0.000   0.000 moveto
  1.000 nbpt mul it  (r ) show currentpoint
  1.000 nbpt mul rm  (= ) show currentpoint
  1.350 nbpt mul symb  <d6> show currentpoint
  1.000 nbpt mul rm  (1 - 0.5 cos 2) show currentpoint
  1.000 nbpt mul symb  (q) show currentpoint
clear
  0.342  setlinewidth
 10.500   6.000 moveto
 38.000   6.000 lineto
stroke
140.000   0.000 moveto
  1.000 nbpt mul rm  (Centre ) show <28> show (0,0) show <29> show currentpoint
clear
}
\EndFig
\vskip30pt
\centerline{\bf Fig.\ 7}
\vfill\eject

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%%EPS file  z8.eps
0.72 dup scale
1 mm unit  /nbpt 14 def
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 58.427 115.563   56.417 114.078   54.190 112.388   51.826 110.482 
 49.392 108.356   46.946 106.011   44.535 103.452   42.201 100.688 
 39.977  97.728   37.893  94.585   35.973  91.273   34.239  87.806 
 32.709  84.201   31.399  80.473   30.323  76.642   29.490  72.724 
 28.910  68.739   28.590  64.706   28.536  60.645   28.750  56.574 
 29.235  52.514   29.991  48.484   31.016  44.504   32.307  40.593 
 33.860  36.770   35.670  33.053   37.728  29.461   40.026  26.012 
 42.554  22.721   45.302  19.606   48.256  16.680   51.404  13.958 
 54.731  11.455   58.223   9.180   61.863   7.147   65.633   5.364 
 69.518   3.841   73.498   2.584   77.556   1.600   81.671   0.894 
 85.826   0.469   90.000   0.327   94.174   0.469   98.329   0.894 
102.444   1.600  106.502   2.584  110.482   3.841  114.367   5.364 
118.137   7.147  121.777   9.180  125.269  11.455  128.596  13.958 
131.744  16.680  134.698  19.606  137.446  22.721  139.974  26.012 
142.272  29.461  144.330  33.053  146.140  36.770  147.693  40.593 
148.984  44.504  150.009  48.484  150.765  52.514  151.250  56.574 
151.464  60.645  151.410  64.706  151.090  68.739  150.510  72.724 
149.677  76.642  148.601  80.473  147.291  84.201  145.761  87.806 
144.027  91.273  142.107  94.585  140.023  97.728  137.799 100.688 
135.465 103.452  133.054 106.011  130.608 108.356  128.174 110.482 
125.810 112.388  123.583 114.078  121.573 115.563  119.869 116.861 
118.562 118.003  117.737 119.031  117.455 120.000  117.737 120.969 
118.562 121.997  119.869 123.139  121.573 124.437  123.583 125.922 
125.810 127.612  128.174 129.518  130.608 131.644  133.054 133.989 
135.465 136.548  137.799 139.312  140.023 142.272  142.107 145.415 
144.027 148.727  145.761 152.194  147.291 155.799  148.601 159.527 
149.677 163.358  150.510 167.276  151.090 171.261  151.410 175.294 
151.464 179.355  151.250 183.426  150.765 187.486  150.009 191.516 
148.984 195.496  147.693 199.407  146.140 203.230  144.330 206.947 
142.272 210.539  139.974 213.988  137.446 217.279  134.698 220.394 
131.744 223.320  128.596 226.042  125.269 228.545  121.777 230.820 
118.137 232.853  114.367 234.636  110.482 236.159  106.502 237.416 
102.444 238.400   98.329 239.106   94.174 239.531   90.000 239.673 
 85.826 239.531   81.671 239.106   77.556 238.400   73.498 237.416 
 69.518 236.159   65.633 234.636   61.863 232.853   58.223 230.820 
 54.731 228.545   51.404 226.042   48.256 223.320   45.302 220.394 
 42.554 217.279   40.026 213.988   37.728 210.539   35.670 206.947 
 33.860 203.230   32.307 199.407   31.016 195.496   29.991 191.516 
 29.235 187.486   28.750 183.426   28.536 179.355   28.590 175.294 
 28.910 171.261   29.490 167.276   30.323 163.358   31.399 159.527 
 32.709 155.799   34.239 152.194   35.973 148.727   37.893 145.415 
 39.977 142.272   42.201 139.312   44.535 136.548   46.946 133.989 
 49.392 131.644   51.826 129.518   54.190 127.612   56.417 125.922 
 58.427 124.437   60.131 123.139   61.438 121.997   62.263 120.969 
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[  90.000   0.327   90.000 239.673  ] polygon stroke
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[  90.000 120.000   87.768 120.000   85.558 119.999   83.388 119.999 
 81.277 119.998   79.244 119.998   77.303 119.997   75.467 119.997 
 73.745 119.997   72.144 119.997   70.670 119.997   69.323 119.997 
 68.105 119.997   67.013 119.997   66.041 119.998   65.185 119.998 
 64.432 119.999   63.767 119.999   63.160 120.000   62.530 120.000 
 62.545 120.003  ] scurve
 90.000 120.000 moveto
[  90.000 120.000   87.902 119.238   85.814 118.494   83.747 117.786 
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 74.111 115.265   72.400 115.030   70.785 114.893   69.274 114.852 
 67.874 114.902   66.590 115.037   65.426 115.248   64.383 115.529 
 63.457 115.872   62.641 116.277   61.918 116.765   61.268 117.433 
 61.369 117.935  ] scurve
 90.000 120.000 moveto
[  90.000 120.000   88.286 118.566   86.562 117.150   84.818 115.771 
 83.046 114.447   81.238 113.197   79.391 112.043   77.503 111.002 
 75.578 110.095   73.622 109.342   71.647 108.759   69.666 108.362 
 67.702 108.161   65.775 108.165   63.911 108.374   62.136 108.785 
 60.474 109.388   58.941 110.169   57.523 111.105   56.087 112.144 
 54.682 112.769  ] scurve
 90.000 120.000 moveto
[  90.000 120.000   88.879 118.064   87.738 116.128   86.554 114.193 
 85.305 112.261   83.970 110.335   82.523 108.422   80.940 106.532 
 79.195 104.680   77.262 102.887   75.116 101.181   72.733  99.600 
 70.097  98.189   67.197  97.008   64.036  96.124   60.636  95.614 
 57.040  95.556   53.320  96.028   49.571  97.091   45.865  98.736 
 42.081 100.537  ] scurve
 90.000 120.000 moveto
[  90.000 120.000   89.611 117.796   89.211 115.573   88.789 113.314 
 88.334 110.998   87.831 108.604   87.264 106.110   86.612 103.490 
 85.852 100.716   84.950  97.757   83.867  94.574   82.547  91.128 
 80.919  87.369   78.884  83.247   76.305  78.706   72.994  73.691 
 68.683  68.166   62.994  62.136   55.395  55.709   45.156  49.213 
 31.358  43.378  ] scurve
 90.000 120.000 moveto
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111.402  68.241  117.105  62.240  124.716  55.855  134.959  49.419 
148.735  43.676  ] scurve
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 94.698 112.264   96.035 110.340   97.483 108.429   99.067 106.542 
100.813 104.693  102.747 102.904  104.894 101.203  107.276  99.626 
109.911  98.222  112.809  97.048  115.967  96.171  119.362  95.668 
122.951  95.618  126.663  96.097  130.401  97.165  134.099  98.818 
137.871 100.597  ] scurve
 90.000 120.000 moveto
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104.421 110.108  106.376 109.357  108.350 108.776  110.327 108.381 
112.289 108.183  114.213 108.188  116.073 108.399  117.843 108.811 
119.500 109.415  121.028 110.197  122.440 111.137  123.874 112.193 
125.307 112.777  ] scurve
 90.000 120.000 moveto
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 98.288 117.133  100.279 116.542  102.217 116.030  104.089 115.605 
105.884 115.273  107.594 115.039  109.207 114.903  110.716 114.862 
112.113 114.912  113.395 115.047  114.556 115.258  115.597 115.538 
116.520 115.880  117.334 116.285  118.052 116.773  118.691 117.441 
118.606 117.960  ] scurve
 90.000 120.000 moveto
[  90.000 120.000   92.232 120.000   94.442 120.001   96.612 120.001 
 98.721 120.001  100.753 120.001  102.693 120.001  104.529 120.001 
106.250 120.001  107.849 120.001  109.322 120.000  110.667 120.000 
111.884 120.000  112.976 119.999  113.946 119.998  114.802 119.998 
115.553 119.997  116.218 119.995  116.826 119.991  117.456 119.977 
117.468 119.796  ] scurve
 90.000 120.000 moveto
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 98.287 122.870  100.279 123.461  102.217 123.973  104.089 124.398 
105.886 124.730  107.596 124.963  109.210 125.099  110.719 125.139 
112.118 125.088  113.399 124.953  114.561 124.740  115.602 124.459 
116.525 124.115  117.335 123.708  118.047 123.218  118.664 122.550 
118.590 122.025  ] scurve
 90.000 120.000 moveto
[  90.000 120.000   91.714 121.434   93.438 122.849   95.182 124.228 
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104.422 129.898  106.378 130.650  108.353 131.231  110.333 131.626 
112.297 131.824  114.223 131.818  116.086 131.606  117.860 131.192 
119.520 130.586  121.051 129.801  122.465 128.857  123.900 127.793 
125.317 127.230  ] scurve
 90.000 120.000 moveto
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 94.696 127.738   96.032 129.663   97.480 131.575   99.064 133.464 
100.810 135.315  102.744 137.106  104.892 138.810  107.275 140.389 
109.913 141.797  112.814 142.975  115.976 143.856  119.377 144.363 
122.974 144.418  126.695 143.943  130.445 142.878  134.154 141.230 
137.911 139.452  ] scurve
 90.000 120.000 moveto
[  90.000 120.000   90.389 122.204   90.790 124.427   91.212 126.686 
 91.668 129.002   92.172 131.396   92.741 133.890   93.394 136.510 
 94.156 139.283   95.060 142.243   96.146 145.424   97.469 148.870 
 99.101 152.627  101.141 156.748  103.724 161.286  107.041 166.296 
111.357 171.815  117.049 177.836  124.650 184.250  134.883 190.727 
148.669 196.538  ] scurve
 90.000 120.000 moveto
[  90.000 120.000   89.610 122.204   89.209 124.427   88.786 126.686 
 88.330 129.002   87.826 131.396   87.257 133.890   86.604 136.509 
 85.841 139.283   84.937 142.242   83.850 145.423   82.527 148.869 
 80.894 152.625   78.853 156.744   76.269 161.281   72.950 166.288 
 68.632 171.804   62.937 177.820   55.333 184.227   45.094 190.695 
 31.316 196.489  ] scurve
 90.000 120.000 moveto
[  90.000 120.000   88.879 121.935   87.736 123.871   86.551 125.805 
 85.302 127.737   83.965 129.663   82.517 131.575   80.933 133.463 
 79.187 135.314   77.253 137.105   75.106 138.809   72.723 140.388 
 70.086 141.796   67.186 142.973   64.027 143.854   60.628 144.360 
 57.034 144.414   53.316 143.939   49.571 142.873   45.868 141.223 
 42.099 139.440  ] scurve
 90.000 120.000 moveto
[  90.000 120.000   88.286 121.433   86.561 122.849   84.817 124.227 
 83.043 125.550   81.235 126.799   79.388 127.953   77.500 128.992 
 75.575 129.898   73.619 130.650   71.643 131.231   69.664 131.627 
 67.700 131.827   65.774 131.822   63.912 131.611   62.139 131.199 
 60.480 130.595   58.949 129.813   57.534 128.874   56.099 127.824 
 54.682 127.231  ] scurve
 90.000 120.000 moveto
[  90.000 120.000   87.901 120.761   85.813 121.504   83.746 122.212 
 81.711 122.868   79.718 123.458   77.780 123.971   75.907 124.396 
 74.110 124.728   72.399 124.963   70.784 125.099   69.274 125.140 
 67.875 125.090   66.592 124.955   65.430 124.744   64.387 124.464 
 63.463 124.121   62.649 123.716   61.929 123.228   61.288 122.560 
 61.383 122.051  ] scurve
 96.958 120.001 moveto
[  96.958 120.001   96.925 120.706   96.824 121.407   96.656 122.097 
 96.421 122.772   96.119 123.425   95.750 124.050   95.315 124.640 
 94.817 125.186   94.259 125.683   93.645 126.120   92.981 126.490 
 92.275 126.787   91.535 127.004   90.773 127.136   89.999 127.180 
 89.225 127.136   88.463 127.004   87.724 126.787   87.017 126.490 
 86.353 126.119   85.739 125.682   85.181 125.185   84.683 124.638 
 84.248 124.048   83.880 123.423   83.577 122.770   83.342 122.095 
 83.174 121.405   83.074 120.704   83.041 119.999   83.074 119.293 
 83.175 118.592   83.343 117.902   83.578 117.227   83.881 116.574 
 84.250 115.949   84.685 115.359   85.183 114.813   85.742 114.317 
 86.356 113.879   87.020 113.509   87.727 113.212   88.466 112.996 
 89.228 112.864   90.002 112.820   90.776 112.865   91.538 112.997 
 92.277 113.214   92.983 113.511   93.647 113.882   94.261 114.319 
 94.819 114.816   95.317 115.363   95.751 115.952   96.120 116.577 
 96.422 117.230   96.657 117.905   96.824 118.595   96.925 119.296 
 96.958 120.001  ] scurve
105.824 120.001 moveto
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105.248 125.624  104.872 127.112  104.360 128.642  103.684 130.206 
102.810 131.785  101.708 133.348  100.350 134.849   98.722 136.228 
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 75.639 111.352   76.317 109.788   77.192 108.209   78.296 106.646 
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102.811 108.222  103.684 109.800  104.360 111.363  104.871 112.892 
105.247 114.380  105.514 115.827  105.691 117.239  105.791 118.627 
105.824 120.001  ] scurve
109.995 120.000 moveto
[ 109.995 120.000  109.995 121.485  109.991 123.001  109.973 124.583 
109.919 126.263  109.798 128.072  109.566 130.038  109.162 132.183 
108.504 134.511  107.495 137.004  106.025 139.599  103.986 142.182 
101.307 144.575   97.990 146.549   94.145 147.860   89.998 148.321 
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 73.984 100.391   76.025  97.809   78.705  95.419   82.024  93.449 
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101.316  95.439  103.991  97.833  106.026 100.415  107.494 103.009 
108.501 105.498  109.157 107.825  109.562 109.967  109.794 111.932 
109.915 113.740  109.970 115.418  109.990 117.000  109.994 118.516 
109.995 120.000  ] scurve
112.607 119.999 moveto
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113.100 126.164  113.311 128.066  113.489 130.227  113.559 132.712 
113.414 135.582  112.890 138.879  111.766 142.592  109.769 146.609 
106.620 150.657  102.149 154.260   96.451 156.803   89.996 157.726 
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 68.245  97.393   70.246  93.377   73.398  89.332   77.873  85.734 
 83.573  83.197   90.028  82.281   96.479  83.214  102.169  85.763 
106.631  89.369  109.772  93.416  111.762  97.430  112.882 101.138 
113.404 104.430  113.550 107.296  113.480 109.777  113.304 111.936 
113.094 113.836  112.896 115.540  112.738 117.101  112.640 118.571 
112.607 119.999  ] scurve
114.380 119.998 moveto
[ 114.380 119.998  114.441 121.303  114.629 122.648  114.952 124.093 
115.396 125.711  115.935 127.565  116.548 129.741  117.176 132.355 
117.708 135.538  117.960 139.432  117.619 144.157  116.209 149.729 
113.091 155.895  107.639 161.920   99.675 166.517   89.994 168.263 
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 62.384 144.154   62.044 139.433   62.294 135.542   62.824 132.361 
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 80.360  73.480   90.043  71.746   99.718  73.510  107.667  78.119 
113.102  84.147  116.206  90.309  117.607  95.873  117.943 100.589 
117.691 104.474  117.160 107.651  116.535 110.260  115.925 112.434 
115.389 114.287  114.947 115.904  114.626 117.349  114.439 118.693 
114.380 119.998  ] scurve
115.641 119.996 moveto
[ 115.641 119.996  115.709 121.164  115.953 122.336  116.426 123.602 
117.095 125.081  117.913 126.804  118.934 128.852  120.128 131.423 
121.400 134.686  122.613 138.903  123.432 144.389  123.229 151.440 
120.916 160.089  114.993 169.550  104.349 177.553   89.991 180.795 
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 61.063 128.862   62.081 126.814   62.895 125.090   63.560 123.607 
 64.034 122.337   64.279 121.166   64.345 119.999   64.277 118.831 
 64.030 117.659   63.555 116.387   62.889 114.902   62.075 113.175 
 61.057 111.124   59.868 108.550   58.602 105.285   57.396 101.069 
 56.582  95.585   56.790  88.535   59.110  79.887   65.043  70.428 
 75.700  62.435   90.066  59.214  104.413  62.490  115.029  70.512 
120.923  79.974  123.216  88.611  123.408  95.647  122.586 101.119 
121.374 105.325  120.106 108.580  118.916 111.146  117.901 113.190 
117.088 114.913  116.423 116.393  115.949 117.661  115.705 118.831 
115.641 119.996  ] scurve
116.591 119.993 moveto
[ 116.591 119.993  116.594 120.541  116.617 121.057  116.697 121.540 
116.859 122.009  117.119 122.489  117.485 123.018  117.933 123.646 
118.401 124.378  118.864 125.156  119.376 125.944  119.997 126.767 
120.760 127.699  121.624 128.825  122.511 130.141  123.438 131.599 
124.472 133.248  125.596 135.201  126.734 137.504  127.875 140.190 
128.974 143.370  129.923 147.132  130.588 151.572  130.758 156.778 
130.135 162.791  128.324 169.553  124.854 176.818  119.277 184.060 
111.356 190.432  101.315 194.881   89.986 196.485   78.659 194.873 
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 51.040 143.365   52.139 140.190   53.279 137.508   54.415 135.208 
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 59.236 127.712   59.999 126.778   60.620 125.956   61.129 125.171 
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 63.127 122.007   63.292 121.540   63.373 121.059   63.395 120.546 
 63.395 120.000   63.394 119.453   63.371 118.940   63.288 118.459 
 63.122 117.991   62.857 117.509   62.486 116.972   62.039 116.335 
 61.579 115.597   61.122 114.820   60.612 114.035   59.989 113.212 
 59.224 112.274   58.363 111.142   57.484 109.824   56.562 108.367 
 55.531 106.719   54.410 104.765   53.276 102.463   52.138  99.778 
 51.042  96.600   50.095  92.839   49.431  88.400   49.263  83.194 
 49.889  77.178   51.705  70.413   55.183  63.146   60.772  55.904 
 68.708  49.539   78.765  45.105   90.101  43.522  101.426  45.159 
111.452  49.637  119.348  56.027  124.898  63.278  128.342  70.542 
130.133  77.297  130.740  83.300  130.559  88.494  129.887  92.921 
128.935  96.672  127.834  99.840  126.694 102.518  125.558 104.813 
124.436 106.759  123.406 108.402  122.484 109.856  121.601 111.170 
120.740 112.294  119.979 113.226  119.360 114.046  118.853 114.831 
118.395 115.608  117.934 116.344  117.487 116.977  117.118 117.511 
116.855 117.991  116.690 118.458  116.609 118.937  116.587 119.447 
116.591 119.993  ] scurve
117.438 119.978 moveto
[ 117.438 119.978  117.392 120.420  117.304 120.766  117.255 121.042 
117.256 121.283  117.309 121.504  117.415 121.710  117.581 121.906 
117.822 122.094  118.166 122.294  118.650 122.572  119.194 123.069 
119.566 123.709  119.813 124.275  120.062 124.746  120.369 125.152 
120.767 125.514  121.302 125.856  122.039 126.238  122.993 126.852 
123.858 127.822  124.480 128.812  125.082 129.674  125.826 130.459 
126.829 131.290  128.092 132.433  129.237 133.988  130.198 135.558 
131.312 137.105  132.709 138.943  134.056 141.279  135.272 143.791 
136.641 146.625  137.912 150.028  139.033 153.849  139.973 158.306 
140.534 163.392  140.555 169.201  139.785 175.726  137.908 182.908 
134.573 190.560  129.429 198.320  122.229 205.616  112.960 211.701 
101.966 215.777   89.980 217.213   77.994 215.769   67.002 211.686 
 57.737 205.594   50.542 198.293   45.405 190.529   42.077 182.874 
 40.208 175.691   39.444 169.167   39.472 163.360   40.039 158.278 
 40.983 153.825   42.106 150.008   43.382 146.609   44.750 143.783 
 45.966 141.272   47.315 138.941   48.710 137.110   49.821 135.566 
 50.779 133.998   51.922 132.444   53.185 131.303   54.187 130.474 
 54.930 129.692   55.528 128.837   56.141 127.851   56.992 126.874 
 57.948 126.247   58.692 125.862   59.231 125.522   59.633 125.163 
 59.941 124.763   60.189 124.300   60.427 123.746   60.773 123.107 
 61.304 122.582   61.799 122.288   62.155 122.085   62.402 121.896 
 62.573 121.702   62.682 121.498   62.738 121.279   62.742 121.041 
 62.695 120.770   62.607 120.435   62.548 120.000   62.606 119.566 
 62.694 119.230   62.740 118.960   62.735 118.722   62.678 118.504 
 62.567 118.299   62.395 118.106   62.144 117.917   61.784 117.712 
 61.284 117.411   60.758 116.876   60.421 116.239   60.185 115.689 
 59.937 115.230   59.627 114.831   59.222 114.474   58.677 114.135 
 57.924 113.744   56.966 113.102   56.128 112.117   55.523 111.137 
 54.925 110.287   54.179 109.507   53.171 108.676   51.907 107.525 
 50.773 105.967   49.817 104.403   48.704 102.860   47.307 101.023 
 45.963  98.688   44.748  96.177   43.379  93.345   42.108  89.943 
 40.986  86.121   40.046  81.663   39.485  76.574   39.464  70.761 
 40.238  64.230   42.120  57.040   45.467  49.380   50.627  41.615 
 57.849  34.320   67.142  28.245   78.159  24.190   90.159  22.784 
102.146  24.263  113.127  28.380  122.370  34.497  129.538  41.815 
134.648  49.584  137.953  57.238  139.802  64.415  140.551  70.929 
140.511  76.726  139.938  81.799  138.987  86.241  137.863  90.051 
136.582  93.441  135.217  96.259  134.001  98.769  132.646 101.093 
131.255 102.915  130.150 104.457  129.190 106.029  128.039 107.578 
126.779 108.708  125.785 109.534  125.046 110.317  124.449 111.176 
123.832 112.165  122.973 113.137  122.019 113.753  121.281 114.136 
120.746 114.476  120.347 114.835  120.041 115.237  119.794 115.701 
119.556 116.257  119.208 116.896  118.675 117.418  118.181 117.711 
117.827 117.914  117.579 118.103  117.409 118.297  117.299 118.502 
117.242 118.720  117.235 118.956  117.280 119.224  117.368 119.551 
117.438 119.978  ] scurve
  0.000  10.000 moveto
  1.000 nbpt mul rm  (Courbe) show currentpoint
clear
  0.000   0.000 moveto
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  1.000 nbpt mul rm  (= ) show currentpoint
  1.350 nbpt mul symb  <d6> show currentpoint
  1.000 nbpt mul rm  (1 - 0.9 cos 2) show currentpoint
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  0.342  setlinewidth
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 38.000   6.000 lineto
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140.000   0.000 moveto
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}
\EndFig
\vskip30pt
\centerline{\bf Fig.\ 8}

\end

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1 mm unit  /nbpt 10 def 
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%%% B 11 F 
[   2.000  30.000    5.000  15.000   25.000   5.000   43.000  11.000  
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[  14.000  28.000   14.500  22.500   19.000  18.500   26.000  17.000  
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%%% B 9 F 
[  10.000  20.000   12.000  30.000   24.000  38.000   38.000  34.000  
 54.000  38.000   74.000  20.000   68.000   2.000   48.000  10.000  
 26.000   2.000  ] potatoe 
stroke 
%% / C 
%%% D 
 21.000  12.900 moveto 
%%% B 6 F 
[  21.000  12.900   19.000  18.900   25.000  22.900   33.000  19.900  
 35.000  13.900   28.000   9.900  ] potatoe 
gsave closepath 
%% : 1 
  0.920 setgray  fill 0 setgray  grestore  stroke 
%% / D 
%%% D 
 72.500  24.400 moveto 
%%% Q 
  0.700 disk 
%%% S 
 11.300  28.600 lineto 
stroke 
%%% D 
 11.300  28.600 moveto 
%%% Q 
  0.700 disk 
%%% V 
 10.770 248.199 axis 
%%% D 
  7.300  18.600 moveto 
%%% S 
 15.300  38.600 lineto 
stroke 
%%% D 
 72.500  24.400 moveto 
%%% V 
 10.966 114.228 axis 
%%% D 
 68.000  34.400 moveto 
%%% S 
 77.000  14.900 lineto 
stroke 
%%% D 
 21.000  12.900 moveto 
%%% V 
  0.000 140.000 axis 
%%% D 
 72.400   6.900 moveto 
%%% V 
  0.000  60.000 axis 
%%% D 
 72.500  24.400 moveto 
%%% D 
 67.500  24.800 moveto 
%%% A 
 72.500  24.400   5.016 175.426 114.444 arcn stroke 
%%% D 
 67.500  24.800 moveto 
%%% V 
  0.000 -104.000 axis 
%%% D 
 16.300  28.250 moveto 
%%% A 
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%%% D 
 13.157  33.255 moveto 
%%% V 
  0.000 150.000 axis 
%%% D 
  8.157  28.255 moveto 
%%% K 
%% $ 
  1.000 nbpt mul it  (z) show currentpoint 
clear 
%%% D 
  3.200  14.250 moveto 
%%% K 
%% $ 
  1.000 nbpt mul symb  (t) show currentpoint 
%% $ 
  1.000 nbpt mul rm  (\() show currentpoint 
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  1.000 nbpt mul it  (z) show currentpoint 
%% $ 
  1.000 nbpt mul rm  (\)) show currentpoint 
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%%% D 
 74.200  24.255 moveto 
%%% K 
%% $ 
  1.000 nbpt mul it  (w) show currentpoint 
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%%% D 
 64.657  36.255 moveto 
%%% K 
%% $ 
  1.000 nbpt mul symb  (t) show currentpoint 
%% $ 
  1.000 nbpt mul rm  (\() show currentpoint 
%% $ 
  1.000 nbpt mul it  (w) show currentpoint 
%% $ 
  1.000 nbpt mul rm  (\)) show currentpoint 
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%%% D 
 48.657  16.255 moveto 
%%% K 
%% $ 
  1.000 nbpt mul symb  (W) show currentpoint 
clear 
%%% D 
 74.200   5.255 moveto 
%%% K 
%% $ 
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%% $ 
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showpage 



% Dessin z1.ds1 

%%% < 1 Largeur= 180.000 Hauteur= 240.000 
%%% ~   0.000 180.000   0.000 240.000 
1.2 dup scale 
1 mm unit  /nbpt 10 def 
  0.000   0.000 translate 
%%% +  90.000 120.000  10.000   0.000   0.000  10.000   0.000 254801838.540 
%%% L 
  0.452 setlinewidth 
%%% D 
  0.000   0.000 moveto 
%%% Z 
%%% D 
180.000 120.000 moveto 
%%% Y 181 
[ 180.000 120.000  179.945 124.188  179.781 128.371  179.507 132.543  
179.124 136.701  178.633 140.838  178.033 144.949  177.327 149.031  
176.514 153.076  175.595 157.082  174.572 161.042  173.447 164.953  
172.219 168.808  170.891 172.605  169.465 176.337  167.942 180.000  
166.324 183.590  164.613 187.103  162.812 190.534  160.921 193.879  
158.944 197.135  156.883 200.296  154.741 203.359  152.519 206.321  
150.222 209.177  147.851 211.925  145.410 214.561  142.901 217.082  
140.327 219.485  137.693 221.766  135.000 223.923  132.252 225.954  
129.453 227.855  126.606 229.625  123.715 231.262  120.782 232.763  
117.812 234.127  114.807 235.351  111.773 236.435  108.712 237.378  
105.628 238.177  102.526 238.832   99.408 239.343   96.278 239.708  
 93.141 239.927   90.000 240.000   86.859 239.927   83.722 239.708  
 80.592 239.343   77.474 238.832   74.372 238.177   71.288 237.378  
 68.227 236.435   65.193 235.351   62.188 234.127   59.218 232.763  
 56.285 231.262   53.394 229.625   50.547 227.855   47.748 225.954  
 45.000 223.923   42.307 221.766   39.673 219.485   37.099 217.082  
 34.590 214.561   32.149 211.925   29.778 209.177   27.481 206.321  
 25.259 203.359   23.117 200.296   21.056 197.135   19.079 193.879  
 17.188 190.534   15.387 187.103   13.676 183.590   12.058 180.000  
 10.535 176.337    9.109 172.605    7.781 168.808    6.553 164.953  
  5.428 161.042    4.405 157.082    3.486 153.076    2.673 149.031  
  1.967 144.949    1.367 140.838    0.876 136.701    0.493 132.543  
  0.219 128.371    0.055 124.188    0.000 120.000    0.055 115.812  
  0.219 111.629    0.493 107.457    0.876 103.299    1.367  99.162  
  1.967  95.051    2.673  90.969    3.486  86.924    4.405  82.918  
  5.428  78.958    6.553  75.047    7.781  71.192    9.109  67.395  
 10.535  63.663   12.058  60.000   13.676  56.410   15.387  52.897  
 17.188  49.466   19.079  46.121   21.056  42.866   23.117  39.704  
 25.259  36.641   27.481  33.679   29.778  30.823   32.149  28.075  
 34.590  25.439   37.099  22.918   39.673  20.516   42.307  18.234  
 45.000  16.077   47.748  14.046   50.547  12.145   53.394  10.375  
 56.285   8.738   59.218   7.237   62.188   5.873   65.193   4.649  
 68.227   3.565   71.288   2.622   74.372   1.823   77.474   1.168  
 80.592   0.657   83.722   0.292   86.859   0.073   90.000   0.000  
 93.141   0.073   96.278   0.292   99.408   0.657  102.526   1.168  
105.628   1.823  108.712   2.622  111.773   3.565  114.807   4.649  
117.812   5.873  120.782   7.237  123.715   8.738  126.606  10.375  
129.453  12.145  132.252  14.046  135.000  16.077  137.693  18.234  
140.327  20.515  142.901  22.918  145.410  25.439  147.851  28.075  
150.222  30.823  152.519  33.679  154.741  36.641  156.883  39.704  
158.944  42.865  160.921  46.121  162.812  49.466  164.613  52.897  
166.324  56.410  167.942  60.000  169.465  63.663  170.891  67.395  
172.219  71.192  173.447  75.047  174.572  78.958  175.595  82.918  
176.514  86.923  177.327  90.969  178.033  95.051  178.633  99.162  
179.124 103.299  179.507 107.457  179.781 111.629  179.945 115.812  
180.000 120.000  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% L 
  0.113 setlinewidth 
%%% Y 21  
[  90.000 120.000   84.960 120.000   79.930 120.000   74.920 120.000  
 69.939 120.000   64.999 120.000   60.106 120.000   55.270 120.000  
 50.498 120.000   45.797 120.000   41.173 120.000   36.631 120.000  
 32.177 120.000   27.814 120.000   23.545 120.000   19.373 120.000  
 15.298 120.000   11.322 120.000    7.430 120.000    3.473 120.000  
  0.000 120.002  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% Y 21  
[  90.000 120.000   85.263 118.277   80.531 116.563   75.809 114.866  
 71.103 113.195   66.417 111.558   61.757 109.962   57.128 108.415  
 52.536 106.922   47.986 105.489   43.483 104.120   39.032 102.820  
 34.638 101.591   30.307 100.435   26.043  99.354   21.850  98.348  
 17.732  97.417   13.692  96.559    9.745  95.767    5.998  94.984  
  2.136  94.011  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% Y 21  
[  90.000 120.000   86.137 116.761   82.268 113.530   78.390 110.317  
 74.497 107.131   70.585 103.980   66.651 100.875   62.690  97.823  
 58.701  94.836   54.683  91.922   50.634  89.090   46.556  86.351  
 42.451  83.713   38.320  81.185   34.170  78.775   30.004  76.490  
 25.830  74.337   21.654  72.321   17.482  70.443   13.263  68.638  
  9.454  66.460  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% Y 21  
[  90.000 120.000   87.477 115.633   84.944 111.267   82.391 106.901  
 79.807 102.535   77.181  98.171   74.503  93.809   71.762  89.452  
 68.945  85.102   66.043  80.763   63.041  76.441   59.930  72.142  
 56.695  67.874   53.327  63.649   49.812  59.478   46.142  55.378  
 42.308  51.365   38.303  47.462   34.125  43.691   29.794  40.100  
 25.168  36.768  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% Y 21  
[  90.000 120.000   89.124 115.033   88.242 110.057   87.350 105.064  
 86.443 100.044   85.513  94.987   84.556  89.884   83.565  84.725  
 82.531  79.499   81.446  74.195   80.299  68.800   79.080  63.300  
 77.774  57.682   76.365  51.930   74.832  46.027   73.151  39.954  
 71.291  33.692   69.213  27.220   66.869  20.517   64.193  13.565  
 60.851   6.468  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% Y 21  
[  90.000 120.000   90.876 115.033   91.758 110.057   92.650 105.064  
 93.557 100.044   94.487  94.987   95.444  89.884   96.435  84.725  
 97.469  79.500   98.554  74.195   99.701  68.800  100.920  63.300  
102.226  57.683  103.635  51.930  105.168  46.027  106.849  39.954  
108.709  33.692  110.787  27.220  113.132  20.518  115.808  13.566  
119.150   6.469  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% Y 21  
[  90.000 120.000   92.523 115.633   95.056 111.267   97.609 106.901  
100.193 102.535  102.819  98.171  105.497  93.809  108.238  89.452  
111.055  85.102  113.957  80.763  116.959  76.441  120.070  72.142  
123.305  67.874  126.673  63.649  130.188  59.478  133.858  55.378  
137.692  51.366  141.697  47.463  145.875  43.692  150.205  40.100  
154.833  36.768  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% Y 21  
[  90.000 120.000   93.863 116.761   97.732 113.530  101.610 110.317  
105.503 107.131  109.415 103.980  113.349 100.875  117.310  97.823  
121.299  94.836  125.317  91.922  129.366  89.090  133.444  86.351  
137.549  83.713  141.680  81.185  145.830  78.775  149.996  76.490  
154.170  74.337  158.346  72.321  162.518  70.443  166.737  68.638  
170.546  66.460  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% Y 21  
[  90.000 120.000   94.737 118.277   99.469 116.563  104.191 114.866  
108.897 113.195  113.583 111.558  118.243 109.962  122.872 108.415  
127.464 106.922  132.014 105.489  136.517 104.120  140.968 102.820  
145.361 101.591  149.692 100.435  153.957  99.354  158.150  98.348  
162.268  97.417  166.307  96.559  170.255  95.767  174.002  94.984  
177.864  94.011  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% Y 21  
[  90.000 120.000   95.040 120.000  100.070 120.000  105.080 120.000  
110.061 120.000  115.001 120.000  119.894 120.000  124.730 120.000  
129.502 120.000  134.203 120.000  138.827 120.000  143.368 120.000  
147.823 120.000  152.186 120.000  156.455 120.000  160.627 120.000  
164.702 120.000  168.678 120.000  172.570 120.000  176.527 120.000  
180.000 120.000  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% Y 21  
[  90.000 120.000   94.737 121.723   99.469 123.437  104.191 125.134  
108.897 126.805  113.583 128.442  118.243 130.038  122.872 131.585  
127.464 133.078  132.014 134.511  136.517 135.880  140.968 137.180  
145.361 138.409  149.692 139.565  153.957 140.646  158.150 141.652  
162.268 142.583  166.307 143.441  170.255 144.233  174.002 145.016  
177.864 145.989  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% Y 21  
[  90.000 120.000   93.863 123.239   97.732 126.470  101.610 129.683  
105.503 132.869  109.415 136.020  113.349 139.125  117.310 142.177  
121.299 145.164  125.317 148.078  129.366 150.910  133.444 153.649  
137.549 156.287  141.680 158.815  145.830 161.225  149.996 163.510  
154.170 165.663  158.346 167.679  162.518 169.557  166.737 171.362  
170.546 173.540  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% Y 21  
[  90.000 120.000   92.523 124.367   95.056 128.733   97.609 133.099  
100.193 137.465  102.819 141.829  105.497 146.191  108.238 150.548  
111.055 154.898  113.957 159.237  116.959 163.559  120.070 167.858  
123.305 172.126  126.673 176.351  130.188 180.522  133.858 184.622  
137.692 188.634  141.697 192.537  145.875 196.308  150.206 199.900  
154.833 203.232  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% Y 21  
[  90.000 120.000   90.876 124.967   91.758 129.943   92.650 134.936  
 93.557 139.956   94.487 145.013   95.444 150.116   96.435 155.275  
 97.469 160.500   98.554 165.805   99.701 171.200  100.920 176.699  
102.226 182.317  103.635 188.070  105.168 193.973  106.849 200.046  
108.709 206.308  110.787 212.780  113.131 219.482  115.807 226.434  
119.149 233.532  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% Y 21  
[  90.000 120.000   89.124 124.967   88.242 129.943   87.350 134.936  
 86.443 139.956   85.513 145.013   84.556 150.116   83.565 155.275  
 82.531 160.500   81.446 165.805   80.299 171.200   79.080 176.700  
 77.774 182.317   76.365 188.070   74.832 193.973   73.151 200.046  
 71.291 206.308   69.213 212.780   66.869 219.482   64.193 226.434  
 60.851 233.532  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% Y 21  
[  90.000 120.000   87.477 124.367   84.944 128.733   82.391 133.099  
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 68.945 154.898   66.043 159.237   63.042 163.559   59.930 167.858  
 56.696 172.126   53.327 176.351   49.812 180.522   46.142 184.622  
 42.308 188.634   38.303 192.537   34.125 196.308   29.795 199.900  
 25.168 203.232  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% Y 21  
[  90.000 120.000   86.137 123.239   82.268 126.470   78.390 129.683  
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 58.701 145.164   54.683 148.078   50.634 150.910   46.556 153.649  
 42.451 156.287   38.321 158.815   34.170 161.226   30.004 163.510  
 25.830 165.663   21.655 167.679   17.482 169.557   13.264 171.362  
  9.455 173.541  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% Y 21  
[  90.000 120.000   85.263 121.723   80.531 123.437   75.809 125.134  
 71.103 126.805   66.417 128.442   61.757 130.038   57.128 131.585  
 52.536 133.078   47.986 134.512   43.483 135.880   39.032 137.180  
 34.639 138.409   30.308 139.565   26.043 140.646   21.850 141.652  
 17.732 142.584   13.693 143.441    9.745 144.234    5.998 145.016  
  2.136 145.989  ] scurve 
%%% D 
106.980 120.000 moveto 
%%% Y 61  
[ 106.980 120.000  106.890 121.762  106.620 123.506  106.172 125.215  
105.551 126.871  104.761 128.457  103.810 129.956  102.705 131.352  
101.458 132.628  100.081 133.769   98.588 134.761   96.996 135.591  
 95.321 136.249   93.583 136.726   91.802 137.015   90.000 137.111  
 88.198 137.015   86.417 136.726   84.679 136.249   83.004 135.591  
 81.412 134.761   79.919 133.769   78.542 132.628   77.295 131.352  
 76.190 129.957   75.239 128.457   74.449 126.871   73.828 125.215  
 73.380 123.506   73.110 121.762   73.020 120.000   73.110 118.238  
 73.380 116.494   73.828 114.785   74.449 113.129   75.239 111.543  
 76.190 110.044   77.295 108.648   78.542 107.372   79.919 106.231  
 81.412 105.239   83.004 104.409   84.679 103.751   86.417 103.274  
 88.198 102.985   90.000 102.889   91.802 102.985   93.583 103.274  
 95.321 103.751   96.996 104.409   98.588 105.239  100.081 106.231  
101.458 107.372  102.705 108.648  103.810 110.044  104.761 111.543  
105.551 113.129  106.172 114.785  106.620 116.494  106.890 118.238  
106.980 120.000  ] scurve 
%%% D 
130.830 120.000 moveto 
%%% Y 61  
[ 130.830 120.000  130.643 124.087  130.081 128.150  129.143 132.164  
127.825 136.103  126.122 139.935  124.033 143.627  121.555 147.138  
118.693 150.424  115.455 153.435  111.860 156.118  107.937 158.415  
103.728 160.273   99.288 161.641   94.686 162.480   90.000 162.762  
 85.314 162.480   80.712 161.641   76.272 160.273   72.063 158.415  
 68.140 156.118   64.545 153.435   61.307 150.424   58.445 147.138  
 55.967 143.627   53.878 139.935   52.175 136.103   50.857 132.164  
 49.919 128.150   49.357 124.087   49.170 120.000   49.357 115.913  
 49.919 111.850   50.857 107.836   52.175 103.897   53.878 100.065  
 55.967  96.373   58.445  92.862   61.307  89.576   64.545  86.565  
 68.140  83.882   72.063  81.585   76.272  79.727   80.712  78.358  
 85.314  77.520   90.000  77.238   94.686  77.520   99.288  78.359  
103.728  79.727  107.937  81.585  111.860  83.882  115.455  86.565  
118.693  89.576  121.555  92.862  124.033  96.373  126.122 100.065  
127.825 103.897  129.143 107.836  130.081 111.850  130.643 115.913  
130.830 120.000  ] scurve 
%%% D 
144.321 120.000 moveto 
%%% Y 61  
[ 144.321 120.000  144.106 125.258  143.459 130.502  142.369 135.718  
140.824 140.886  138.802 145.982  136.283 150.971  133.238 155.811  
129.645 160.442  125.483 164.791  120.746 168.767  115.446 172.261  
109.623 175.157  103.357 177.334   96.765 178.689   90.000 179.149  
 83.235 178.689   76.643 177.334   70.377 175.157   64.554 172.261  
 59.254 168.767   54.517 164.791   50.355 160.442   46.762 155.811  
 43.718 150.972   41.198 145.982   39.176 140.886   37.631 135.718  
 36.541 130.502   35.894 125.258   35.679 120.000   35.894 114.742  
 36.541 109.498   37.631 104.282   39.176  99.114   41.197  94.018  
 43.717  89.029   46.762  84.189   50.355  79.558   54.517  75.209  
 59.254  71.233   64.554  67.738   70.377  64.843   76.643  62.666  
 83.235  61.311   90.000  60.851   96.765  61.311  103.357  62.666  
109.623  64.843  115.446  67.739  120.746  71.233  125.483  75.209  
129.645  79.558  133.238  84.189  136.282  89.029  138.802  94.018  
140.824  99.114  142.369 104.282  143.459 109.498  144.106 114.742  
144.321 120.000  ] scurve 
%%% D 
154.428 120.000 moveto 
%%% Y 61  
[ 154.428 120.000  154.207 126.042  153.540 132.085  152.411 138.126  
150.799 144.161  148.668 150.176  145.977 156.148  142.673 162.043  
138.697 167.801  133.988 173.339  128.491 178.538  122.172 183.241  
115.042 187.250  107.178 190.344   98.745 192.309   90.000 192.983  
 81.255 192.309   72.822 190.344   64.958 187.250   57.828 183.241  
 51.510 178.538   46.013 173.339   41.303 167.801   37.327 162.043  
 34.023 156.149   31.332 150.176   29.201 144.161   27.589 138.127  
 26.460 132.085   25.793 126.043   25.572 120.000   25.793 113.958  
 26.460 107.915   27.588 101.874   29.201  95.839   31.331  89.824  
 34.023  83.851   37.327  77.957   41.303  72.199   46.012  66.661  
 51.509  61.462   57.828  56.759   64.958  52.750   72.822  49.656  
 81.255  47.691   90.000  47.016   98.745  47.691  107.178  49.656  
115.042  52.750  122.172  56.760  128.491  61.462  133.988  66.662  
138.697  72.199  142.673  77.957  145.977  83.852  148.668  89.824  
150.799  95.839  152.411 101.873  153.540 107.915  154.207 113.958  
154.428 120.000  ] scurve 
%%% D 
162.644 120.000 moveto 
%%% Y 61  
[ 162.644 120.000  162.427 126.613  161.773 133.240  160.662 139.894  
159.065 146.583  156.938 153.310  154.223 160.071  150.843 166.842  
146.707 173.583  141.706 180.213  135.723 186.608  128.651 192.571  
120.424 197.825  111.076 202.011  100.804 204.740   90.000 205.692  
 79.196 204.740   68.924 202.011   59.576 197.825   51.349 192.571  
 44.277 186.608   38.294 180.214   33.293 173.583   29.157 166.843  
 25.777 160.071   23.062 153.311   20.935 146.583   19.338 139.894  
 18.227 133.241   17.572 126.613   17.356 120.000   17.572 113.387  
 18.227 106.760   19.338 100.106   20.935  93.417   23.062  86.689  
 25.777  79.929   29.157  73.157   33.293  66.417   38.294  59.786  
 44.277  53.392   51.349  47.428   59.576  42.175   68.924  37.988  
 79.196  35.259   90.000  34.308  100.805  35.259  111.076  37.989  
120.424  42.175  128.651  47.429  135.723  53.392  141.706  59.787  
146.707  66.418  150.843  73.158  154.223  79.929  156.938  86.690  
159.065  93.417  160.662 100.106  161.773 106.759  162.427 113.387  
162.644 120.000  ] scurve 
%%% D 
169.610 120.000 moveto 
%%% Y 121 
[ 169.610 120.000  169.553 123.524  169.400 127.043  169.144 130.578  
168.774 134.120  168.302 137.670  167.715 141.245  167.007 144.832  
166.181 148.442  165.221 152.079  164.123 155.737  162.880 159.426  
161.475 163.141  159.903 166.884  158.144 170.653  156.185 174.444  
154.007 178.254  151.590 182.072  148.912 185.889  145.949 189.688  
142.675 193.447  139.064 197.137  135.091 200.722  130.732 204.153  
125.971 207.371  120.803 210.307  115.236 212.880  109.303 215.006  
103.059 216.599   96.590 217.588   90.000 217.923   83.411 217.588  
 76.941 216.599   70.698 215.005   64.764 212.880   59.198 210.307  
 54.029 207.371   49.269 204.153   44.910 200.722   40.936 197.138  
 37.325 193.447   34.051 189.688   31.088 185.890   28.410 182.073  
 25.993 178.254   23.815 174.445   21.856 170.654   20.097 166.884  
 18.525 163.141   17.120 159.427   15.877 155.737   14.779 152.079  
 13.819 148.442   12.993 144.832   12.285 141.245   11.698 137.671  
 11.226 134.120   10.856 130.579   10.600 127.044   10.446 123.524  
 10.390 120.000   10.446 116.476   10.600 112.957   10.855 109.422  
 11.226 105.880   11.698 102.330   12.284  98.755   12.993  95.168  
 13.818  91.558   14.779  87.921   15.876  84.263   17.120  80.574  
 18.524  76.859   20.097  73.116   21.856  69.346   23.815  65.555  
 25.993  61.746   28.410  57.927   31.088  54.110   34.051  50.311  
 37.325  46.552   40.936  42.862   44.909  39.278   49.268  35.847  
 54.029  32.629   59.198  29.693   64.764  27.119   70.698  24.994  
 76.941  23.401   83.411  22.412   90.000  22.077   96.590  22.412  
103.060  23.401  109.303  24.994  115.236  27.120  120.803  29.693  
125.971  32.629  130.732  35.848  135.091  39.278  139.064  42.863  
142.675  46.553  145.949  50.312  148.912  54.111  151.590  57.928  
154.007  61.746  156.185  65.556  158.144  69.347  159.903  73.116  
161.475  76.859  162.880  80.574  164.123  84.263  165.221  87.921  
166.181  91.558  167.007  95.168  167.715  98.755  168.302 102.330  
168.774 105.880  169.144 109.421  169.400 112.957  169.553 116.476  
169.610 120.000  ] scurve 
%%% D 
175.795 120.000 moveto 
%%% Y 181 
[ 175.795 120.000  175.646 122.586  175.457 124.938  175.436 127.263  
175.441 129.809  175.166 132.439  174.779 134.849  174.545 137.189  
174.371 139.728  173.944 142.396  173.368 144.870  172.926 147.265  
172.535 149.852  171.895 152.559  171.125 155.083  170.478 157.573  
169.813 160.268  168.884 162.999  167.913 165.569  167.027 168.217  
165.974 171.033  164.730 173.747  163.535 176.434  162.244 179.285  
160.728 182.100  159.201 184.870  157.559 187.770  155.704 190.632  
153.797 193.485  151.699 196.416  149.431 199.283  147.026 202.188  
144.390 205.061  141.592 207.907  138.550 210.714  135.303 213.451  
131.800 216.103  128.061 218.639  124.059 221.020  119.805 223.218  
115.304 225.181  110.568 226.871  105.626 228.243  100.518 229.256  
 95.290 229.878   90.000 230.087   84.710 229.877   79.482 229.256  
 74.374 228.242   69.433 226.870   64.697 225.181   60.195 223.217  
 55.941 221.020   51.940 218.639   48.200 216.103   44.697 213.451  
 41.451 210.714   38.408 207.907   35.610 205.061   32.974 202.189  
 30.570 199.283   28.301 196.417   26.204 193.486   24.296 190.632  
 22.441 187.770   20.800 184.870   19.272 182.101   17.756 179.285  
 16.465 176.434   15.270 173.747   14.026 171.033   12.974 168.217  
 12.087 165.570   11.116 162.999   10.187 160.268    9.522 157.573  
  8.875 155.083    8.105 152.559    7.465 149.853    7.074 147.266  
  6.632 144.870    6.056 142.397    5.629 139.728    5.455 137.190  
  5.221 134.849    4.834 132.440    4.559 129.809    4.563 127.263  
  4.543 124.938    4.353 122.586    4.205 120.000    4.353 117.414  
  4.543 115.062    4.563 112.737    4.559 110.192    4.834 107.561  
  5.221 105.151    5.455 102.811    5.629 100.272    6.055  97.604  
  6.631  95.130    7.074  92.735    7.464  90.148    8.104  87.441  
  8.875  84.917    9.522  82.427   10.187  79.732   11.115  77.001  
 12.087  74.431   12.973  71.783   14.026  68.967   15.269  66.253  
 16.464  63.566   17.755  60.715   19.272  57.899   20.799  55.130  
 22.441  52.229   24.296  49.368   26.203  46.514   28.301  43.583  
 30.569  40.717   32.974  37.811   35.610  34.939   38.408  32.092  
 41.450  29.285   44.697  26.548   48.200  23.896   51.940  21.361  
 55.941  18.979   60.195  16.782   64.697  14.818   69.433  13.129  
 74.374  11.757   79.483  10.744   84.710  10.122   90.001   9.912  
 95.291  10.122  100.519  10.744  105.627  11.757  110.568  13.130  
115.304  14.819  119.805  16.783  124.059  18.980  128.061  21.362  
131.800  23.897  135.303  26.549  138.550  29.286  141.592  32.093  
144.390  34.939  147.026  37.812  149.431  40.717  151.699  43.584  
153.797  46.515  155.704  49.368  157.559  52.230  159.201  55.130  
160.728  57.900  162.244  60.715  163.535  63.566  164.730  66.253  
165.974  68.967  167.026  71.783  167.913  74.431  168.884  77.001  
169.813  79.732  170.478  82.427  171.125  84.917  171.895  87.441  
172.535  90.148  172.926  92.735  173.368  95.130  173.944  97.603  
174.371 100.272  174.545 102.811  174.779 105.151  175.166 107.560  
175.441 110.191  175.436 112.737  175.457 115.062  175.646 117.414  
175.795 120.000  ] scurve 
%% / / 
%%% D 
 10.000  14.000 moveto 
%%% K 
%% $ 
  1.000 nbpt mul rm  (Ellipse) show currentpoint 
clear 
%%% D 
 10.000   7.000 moveto 
%%% K 
%% $ 
  1.000 nbpt mul it  (x ) show currentpoint 
%% $ 
  1.000 nbpt mul rm  (= 3 cos ) show currentpoint 
%% $ 
  1.000 nbpt mul it  (t) show currentpoint 
clear 
%%% D 
 10.000   2.000 moveto 
%%% K 
%% $ 
  1.000 nbpt mul it  (y ) show currentpoint 
%% $ 
  1.000 nbpt mul rm  (= 4 sin ) show currentpoint 
%% $ 
  1.000 nbpt mul it  (t) show currentpoint 
clear 
%%% D 
144.000   2.000 moveto 
%%% K 
%% $ 
  1.000 nbpt mul rm  (Centre \(0,0\)) show currentpoint 
clear 
%%% > 
showpage 

% Dessin z2.ds1 

%%% < 1 Largeur= 180.000 Hauteur= 240.000 
%%% ~   0.000 180.000   0.000 240.000 
1.2 dup scale 
1 mm unit  /nbpt 10 def 
  0.000   0.000 translate 
%%% +  90.000 120.000  10.000   0.000   0.000  10.000   0.000   0.000 
%%% L
  0.452 setlinewidth 
%%% Z 
%%% D 
180.000 120.000 moveto 
%%% Y 181 
[ 180.000 120.000  179.945 124.188  179.781 128.371  179.507 132.543  
179.124 136.701  178.633 140.838  178.033 144.949  177.327 149.031  
176.514 153.076  175.595 157.082  174.572 161.042  173.447 164.953  
172.219 168.808  170.891 172.605  169.465 176.337  167.942 180.000  
166.324 183.590  164.613 187.103  162.812 190.534  160.921 193.879  
158.944 197.135  156.883 200.296  154.741 203.359  152.519 206.321  
150.222 209.177  147.851 211.925  145.410 214.561  142.901 217.082  
140.327 219.485  137.693 221.766  135.000 223.923  132.252 225.954  
129.453 227.855  126.606 229.625  123.715 231.262  120.782 232.763  
117.812 234.127  114.807 235.351  111.773 236.435  108.712 237.378  
105.628 238.177  102.526 238.832   99.408 239.343   96.278 239.708  
 93.141 239.927   90.000 240.000   86.859 239.927   83.722 239.708  
 80.592 239.343   77.474 238.832   74.372 238.177   71.288 237.378  
 68.227 236.435   65.193 235.351   62.188 234.127   59.218 232.763  
 56.285 231.262   53.394 229.625   50.547 227.855   47.748 225.954  
 45.000 223.923   42.307 221.766   39.673 219.485   37.099 217.082  
 34.590 214.561   32.149 211.925   29.778 209.177   27.481 206.321  
 25.259 203.359   23.117 200.296   21.056 197.135   19.079 193.879  
 17.188 190.534   15.387 187.103   13.676 183.590   12.058 180.000  
 10.535 176.337    9.109 172.605    7.781 168.808    6.553 164.953  
  5.428 161.042    4.405 157.082    3.486 153.076    2.673 149.031  
  1.967 144.949    1.367 140.838    0.876 136.701    0.493 132.543  
  0.219 128.371    0.055 124.188    0.000 120.000    0.055 115.812  
  0.219 111.629    0.493 107.457    0.876 103.299    1.367  99.162  
  1.967  95.051    2.673  90.969    3.486  86.924    4.405  82.918  
  5.428  78.958    6.553  75.047    7.781  71.192    9.109  67.395  
 10.535  63.663   12.058  60.000   13.676  56.410   15.387  52.897  
 17.188  49.466   19.079  46.121   21.056  42.866   23.117  39.704  
 25.259  36.641   27.481  33.679   29.778  30.823   32.149  28.075  
 34.590  25.439   37.099  22.918   39.673  20.516   42.307  18.234  
 45.000  16.077   47.748  14.046   50.547  12.145   53.394  10.375  
 56.285   8.738   59.218   7.237   62.188   5.873   65.193   4.649  
 68.227   3.565   71.288   2.622   74.372   1.823   77.474   1.168  
 80.592   0.657   83.722   0.292   86.859   0.073   90.000   0.000  
 93.141   0.073   96.278   0.292   99.408   0.657  102.526   1.168  
105.628   1.823  108.712   2.622  111.773   3.565  114.807   4.649  
117.812   5.873  120.782   7.237  123.715   8.738  126.606  10.375  
129.453  12.145  132.252  14.046  135.000  16.077  137.693  18.234  
140.327  20.515  142.901  22.918  145.410  25.439  147.851  28.075  
150.222  30.823  152.519  33.679  154.741  36.641  156.883  39.704  
158.944  42.865  160.921  46.121  162.812  49.466  164.613  52.897  
166.324  56.410  167.942  60.000  169.465  63.663  170.891  67.395  
172.219  71.192  173.447  75.047  174.572  78.958  175.595  82.918  
176.514  86.923  177.327  90.969  178.033  95.051  178.633  99.162  
179.124 103.299  179.507 107.457  179.781 111.629  179.945 115.812  
180.000 120.000  ] scurve
%%% L
  0.113 setlinewidth 
%%% D 
120.000 150.000 moveto 
%%% Y 21  
[ 120.000 150.000  115.763 150.040  111.355 150.164  106.773 150.384  
102.020 150.708   97.097 151.146   92.008 151.706   86.759 152.397  
 81.358 153.226   75.815 154.198   70.141 155.316   64.349 156.583  
 58.454 157.996   52.472 159.552   46.417 161.246   40.308 163.069  
 34.160 165.010   27.991 167.057   21.815 169.195   15.645 171.434  
  9.729 174.268  ] scurve 
%%% D 
120.000 150.000 moveto 
%%% Y 21  
[ 120.000 150.000  116.008 148.555  111.827 147.062  107.449 145.525  
102.864 143.950   98.063 142.345   93.037 140.720   87.779 139.086  
 82.283 137.458   76.545 135.855   70.562 134.297   64.338 132.806  
 57.877 131.407   51.192 130.128   44.297 128.994   37.216 128.033  
 29.976 127.270   22.609 126.724   15.153 126.412    7.660 126.333  
  0.122 126.250  ] scurve 
%%% D 
120.000 150.000 moveto 
%%% Y 21  
[ 120.000 150.000  116.767 147.253  113.421 144.346  109.956 141.270  
106.360 138.020  102.622 134.590   98.726 130.972   94.654 127.163  
 90.386 123.157   85.895 118.953   81.152 114.552   76.120 109.957  
 70.758 105.179   65.016 100.236   58.840  95.157   52.170  89.988  
 44.944  84.793   37.106  79.663   28.613  74.715   19.448  70.094  
  9.747  65.684  ] scurve 
%%% D 
120.000 150.000 moveto 
%%% Y 21  
[ 120.000 150.000  117.934 146.311  115.890 142.426  113.870 138.336  
111.877 134.027  109.911 129.484  107.976 124.689  106.073 119.623  
104.203 114.259  102.368 108.569  100.569 102.515   98.807  96.054  
 97.083  89.128   95.398  81.669   93.752  73.584   92.146  64.755  
 90.579  55.018   89.048  44.145   87.549  31.801   86.065  17.459  
 84.534   0.222  ] scurve 
%%% D 
120.000 150.000 moveto 
%%% Y 21  
[ 120.000 150.000  119.348 145.846  118.839 141.561  118.484 137.141  
118.298 132.583  118.293 127.885  118.488 123.043  118.902 118.055  
119.560 112.919  120.488 107.635  121.719 102.205  123.291  96.635  
125.248  90.937  127.639  85.131  130.521  79.246  133.956  73.330  
138.006  67.450  142.728  61.700  148.166  56.202  154.329  51.104  
161.044  46.332  ] scurve 
%%% D 
120.000 150.000 moveto 
%%% Y 21  
[ 120.000 150.000  120.815 145.906  121.822 141.807  123.029 137.710  
124.443 133.626  126.072 129.567  127.924 125.547  130.004 121.581  
132.319 117.689  134.873 113.892  137.668 110.212  140.702 106.676  
143.970 103.311  147.462 100.146  151.163  97.209  155.051  94.527  
159.101  92.126  163.281  90.025  167.557  88.235  171.881  86.672  
176.048  84.831  ] scurve 
%%% D 
120.000 150.000 moveto 
%%% Y 21  
[ 120.000 150.000  122.151 146.461  124.449 143.040  126.890 139.748  
129.469 136.595  132.179 133.592  135.011 130.748  137.955 128.074  
140.999 125.580  144.129 123.272  147.332 121.158  150.590 119.244  
153.888 117.530  157.208 116.019  160.534 114.708  163.847 113.595  
167.133 112.674  170.379 111.940  173.588 111.405  176.860 111.201  
179.796 111.933  ] scurve 
%%% D 
120.000 150.000 moveto 
%%% Y 21  
[ 120.000 150.000  123.201 147.422  126.438 145.026  129.701 142.814  
132.978 140.784  136.258 138.936  139.531 137.268  142.786 135.774  
146.011 134.451  149.198 133.292  152.336 132.291  155.418 131.440  
158.436 130.730  161.384 130.152  164.257 129.698  167.050 129.359  
169.763 129.122  172.400 128.972  174.986 128.861  177.604 128.584  
179.813 127.740  ] scurve 
%%% D 
120.000 150.000 moveto 
%%% Y 21  
[ 120.000 150.000  123.859 148.663  127.631 147.485  131.310 146.460  
134.892 145.578  138.372 144.830  141.748 144.207  145.018 143.700  
148.180 143.298  151.235 142.994  154.183 142.778  157.025 142.642  
159.762 142.578  162.396 142.579  164.931 142.637  167.367 142.748  
169.709 142.910  171.957 143.132  174.110 143.465  176.109 144.077  
178.023 145.017  ] scurve 
%%% D 
120.000 150.000 moveto 
%%% Y 21  
[ 120.000 150.000  124.067 150.036  127.967 150.140  131.705 150.303  
135.285 150.516  138.712 150.774  141.992 151.069  145.130 151.396  
148.133 151.749  151.007 152.124  153.757 152.517  156.390 152.923  
158.910 153.341  161.324 153.766  163.637 154.197  165.851 154.631  
167.968 155.066  169.973 155.500  171.821 155.927  173.392 156.332  
175.633 156.925  ] scurve 
%%% D 
120.000 150.000 moveto 
%%% Y 21  
[ 120.000 150.000  123.813 151.394  127.456 152.735  130.938 154.023  
134.268 155.258  137.452 156.439  140.500 157.569  143.417 158.648  
146.212 159.677  148.891 160.659  151.459 161.595  153.923 162.488  
156.287 163.339  158.558 164.150  160.740 164.922  162.837 165.657  
164.852 166.351  166.786 166.988  168.629 167.520  170.322 167.820  
172.438 168.148  ] scurve 
%%% D 
120.000 150.000 moveto 
%%% Y 21  
[ 120.000 150.000  123.129 152.593  126.160 155.038  129.097 157.343  
131.945 159.514  134.708 161.557  137.389 163.480  139.991 165.287  
142.517 166.986  144.968 168.582  147.347 170.081  149.656 171.488  
151.897 172.808  154.072 174.047  156.182 175.209  158.231 176.298  
160.224 177.318  162.178 178.271  164.149 179.155  166.362 179.912  
168.110 179.612  ] scurve 
%%% D 
120.000 150.000 moveto 
%%% Y 21  
[ 120.000 150.000  122.085 153.504  124.186 156.832  126.301 159.990  
128.426 162.987  130.558 165.828  132.695 168.518  134.832 171.065  
136.966 173.473  139.095 175.747  141.214 177.891  143.321 179.912  
145.413 181.814  147.485 183.600  149.537 185.277  151.564 186.850  
153.563 188.323  155.526 189.708  157.415 191.032  159.084 192.356  
160.901 193.913  ] scurve 
%%% D 
120.000 150.000 moveto 
%%% Y 21  
[ 120.000 150.000  120.786 154.024  121.697 157.920  122.726 161.691  
123.864 165.337  125.106 168.860  126.445 172.259  127.875 175.536  
129.390 178.690  130.984 181.722  132.652 184.630  134.387 187.415  
136.184 190.077  138.037 192.615  139.939 195.029  141.884 197.320  
143.866 199.488  145.881 201.535  147.940 203.480  150.145 205.453  
151.743 207.309  ] scurve 
%%% D 
120.000 150.000 moveto 
%%% Y 21  
[ 120.000 150.000  119.371 154.081  118.921 158.142  118.645 162.177  
118.538 166.183  118.595 170.153  118.813 174.085  119.187 177.972  
119.716 181.812  120.397 185.600  121.228 189.330  122.206 192.998  
123.330 196.598  124.599 200.124  126.010 203.569  127.560 206.926  
129.248 210.188  131.068 213.346  133.011 216.395  134.989 219.335  
136.903 222.417  ] scurve 
%%% D 
120.000 150.000 moveto 
%%% Y 21  
[ 120.000 150.000  118.000 153.648  116.153 157.397  114.461 161.239  
112.924 165.165  111.544 169.172  110.321 173.252  109.256 177.401  
108.351 181.616  107.606 185.894  107.025 190.232  106.610 194.627  
106.366 199.080  106.298 203.587  106.411 208.149  106.715 212.763  
107.220 217.429  107.936 222.142  108.880 226.899  110.089 231.693  
112.016 236.354  ] scurve 
%%% D 
120.000 150.000 moveto 
%%% Y 21  
[ 120.000 150.000  116.844 152.758  113.742 155.695  110.702 158.806  
107.730 162.088  104.832 165.538  102.013 169.152   99.276 172.928  
 96.622 176.862   94.054 180.953   91.572 185.200   89.173 189.604  
 86.858 194.166   84.623 198.889   82.465 203.779   80.378 208.843  
 78.359 214.090   76.398 219.534   74.489 225.192   72.623 231.088  
 71.065 237.314  ] scurve 
%%% D 
120.000 150.000 moveto 
%%% Y 21  
[ 120.000 150.000  116.059 151.505  112.044 153.183  107.962 155.040  
103.820 157.080   99.625 159.305   95.385 161.717   91.106 164.315  
 86.793 167.097   82.451 170.060   78.084 173.199   73.693 176.508  
 69.278 179.981   64.837 183.609   60.367 187.382   55.863 191.290  
 51.318 195.320   46.724 199.458   42.070 203.690   37.336 207.988  
 32.203 211.985  ] scurve 
%%% D 
133.086 150.378 moveto 
%%% Y 61  
[ 133.086 150.378  132.956 151.644  132.714 152.888  132.364 154.103  
131.907 155.280  131.347 156.414  130.686 157.496  129.928 158.518  
129.076 159.473  128.135 160.353  127.109 161.149  126.002 161.854  
124.822 162.459  123.575 162.954  122.271 163.332  120.918 163.585  
119.527 163.704  118.111 163.683  116.684 163.515  115.260 163.196  
113.857 162.723  112.493 162.095  111.185 161.312  109.953 160.379  
108.816 159.300  107.793 158.086  106.903 156.748  106.163 155.302  
105.588 153.763  105.192 152.153  104.984 150.494  104.974 148.811  
105.164 147.127  105.555 145.471  106.143 143.869  106.921 142.347  
107.876 140.929  108.993 139.640  110.252 138.498  111.632 137.521  
113.108 136.722  114.655 136.110  116.246 135.688  117.856 135.457  
119.460 135.414  121.035 135.552  122.561 135.859  124.020 136.325  
125.397 136.936  126.679 137.676  127.856 138.531  128.921 139.486  
129.870 140.526  130.698 141.636  131.404 142.804  131.986 144.017  
132.446 145.264  132.784 146.533  133.003 147.814  133.102 149.099  
133.086 150.378  ] scurve 
%%% D 
148.953 151.852 moveto 
%%% Y 61  
[ 148.953 151.852  148.549 154.344  147.981 156.784  147.254 159.173  
146.367 161.508  145.320 163.786  144.110 166.003  142.735 168.154  
141.190 170.231  139.468 172.225  137.565 174.125  135.473 175.914  
133.187 177.576  130.703 179.088  128.017 180.423  125.131 181.552  
122.049 182.441  118.784 183.051  115.355 183.343  111.789 183.276  
108.125 182.811  104.411 181.913  100.706 180.554   97.074 178.716  
 93.589 176.392   90.324 173.589   87.356 170.326   84.755 166.635  
 82.591 162.560   80.925 158.156   79.815 153.484   79.310 148.620  
 79.451 143.645   80.270 138.655   81.783 133.752   83.993 129.051  
 86.876 124.674   90.383 120.744   94.432 117.377   98.912 114.672  
103.684 112.696  108.598 111.479  113.501 111.008  118.259 111.233  
122.760 112.076  126.927 113.441  130.712 115.231  134.094 117.350  
137.071 119.715  139.655 122.255  141.870 124.913  143.739 127.642  
145.291 130.408  146.551 133.185  147.544 135.953  148.293 138.700  
148.816 141.415  149.132 144.091  149.252 146.724  149.190 149.312  
148.953 151.852  ] scurve 
%%% D 
156.934 153.011 moveto 
%%% Y 61  
[ 156.934 153.011  156.367 155.976  155.643 158.882  154.761 161.733  
153.722 164.534  152.520 167.288  151.149 169.996  149.601 172.657  
147.863 175.270  145.924 177.829  143.766 180.326  141.374 182.747  
138.726 185.075  135.803 187.285  132.584 189.346  129.052 191.217  
125.192 192.846  120.997 194.171  116.473 195.121  111.641 195.615  
106.544 195.568  101.250 194.898   95.848 193.537   90.451 191.431  
 85.186 188.556   80.181 184.915   75.563 180.536   71.449 175.472  
 67.942 169.787   65.133 163.559   63.106 156.870   61.939 149.812  
 61.707 142.484   62.488 135.004   64.354 127.513   67.368 120.188  
 71.564 113.246   76.923 106.947   83.344 101.574   90.621  97.400  
 98.438  94.625  106.416  93.327  114.177  93.438  121.414  94.766  
127.931  97.056  133.640 100.040  138.538 103.486  142.675 107.209  
146.125 111.071  148.969 114.977  151.288 118.863  153.152 122.690  
154.623 126.434  155.755 130.083  156.589 133.633  157.163 137.083  
157.504 140.437  157.636 143.701  157.577 146.880  157.339 149.981  
156.934 153.011  ] scurve 
%%% D 
162.545 153.991 moveto 
%%% Y 61  
[ 162.545 153.991  161.863 157.228  161.036 160.404  160.065 163.527  
158.947 166.607  157.673 169.652  156.237 172.667  154.624 175.658  
152.820 178.625  150.806 181.570  148.560 184.490  146.055 187.376  
143.261 190.216  140.143 192.988  136.663 195.662  132.782 198.195  
128.461 200.528  123.666 202.582  118.374 204.256  112.585 205.430  
106.334 205.964   99.696 205.716   92.797 204.554   85.804 202.381  
 78.914 199.150   72.327 194.868   66.226 189.591   60.764 183.407  
 56.062 176.417   52.218 168.723   49.316 160.421   47.440 151.599  
 46.683 142.347   47.159 132.763   49.006 122.977   52.385 113.174  
 57.459 103.627   64.349  94.736   73.046  87.031   83.299  81.122  
 94.533  77.530  105.933  76.464  116.682  77.714  126.219  80.757  
134.312  84.987  140.982  89.885  146.382  95.078  150.703 100.327  
154.134 105.492  156.837 110.498  158.946 115.309  160.567 119.916  
161.785 124.321  162.666 128.536  163.262 132.574  163.613 136.451  
163.749 140.185  163.695 143.791  163.469 147.285  163.082 150.681  
162.545 153.991  ] scurve 
%%% D 
166.905 154.845 moveto 
%%% Y 61  
[ 166.905 154.845  166.145 158.255  165.242 161.619  164.207 164.913  
163.054 168.184  161.740 171.435  160.279 174.656  158.655 177.886  
156.833 181.111  154.813 184.342  152.551 187.586  150.025 190.834  
147.190 194.088  144.004 197.328  140.411 200.533  136.353 203.663  
131.763 206.660  126.573 209.438  120.724 211.876  114.177 213.814  
106.938 215.052   99.079 215.367   90.760 214.544   82.222 212.415  
 73.758 208.908   65.662 204.049   58.183 197.945   51.504 190.746  
 45.746 182.607   40.987 173.660   37.288 164.010   34.714 153.733  
 33.357 142.887   33.346 131.523   34.872 119.714   38.198 107.586  
 43.664  95.387   51.655  83.580   62.466  72.967   76.000  64.724  
 91.370  60.091  106.906  59.639  120.926  62.794  132.551  68.292  
141.721  74.938  148.783  81.937  154.171  88.853  158.267  95.480  
161.374 101.737  163.718 107.611  165.468 113.118  166.750 118.287  
167.654 123.155  168.253 127.751  168.596 132.117  168.722 136.270  
168.668 140.252  168.436 144.079  168.068 147.766  167.558 151.360  
166.905 154.845  ] scurve 
%%% D 
170.430 155.602 moveto 
%%% Y 121 
[ 170.430 155.602  170.062 157.324  169.697 159.096  169.251 160.910  
168.703 162.684  168.123 164.371  167.578 166.016  167.060 167.694  
166.499 169.439  165.832 171.198  165.091 172.892  164.354 174.530  
163.643 176.184  162.906 177.903  162.071 179.660  161.145 181.380  
160.197 183.054  159.254 184.745  158.264 186.497  157.167 188.278  
155.984 190.027  154.770 191.761  153.513 193.537  152.152 195.352  
150.682 197.157  149.141 198.951  147.518 200.776  145.767 202.619  
143.894 204.449  141.910 206.281  139.781 208.118  137.496 209.936  
135.056 211.734  132.435 213.502  129.625 215.221  126.613 216.877  
123.384 218.445  119.928 219.902  116.237 221.216  112.307 222.351  
108.140 223.270  103.744 223.928   99.137 224.284   94.349 224.294  
 89.418 223.922   84.389 223.136   79.317 221.918   74.259 220.257  
 69.269 218.159   64.400 215.638   59.696 212.716   55.195 209.421  
 50.924 205.784   46.904 201.836   43.151 197.608   39.671 193.124  
 36.472 188.409   33.555 183.481   30.923 178.356   28.578 173.045  
 26.522 167.558   24.760 161.898   23.298 156.070   22.147 150.074  
 21.318 143.909   20.831 137.573   20.708 131.065   20.979 124.381  
 21.681 117.521   22.860 110.488   24.574 103.290   26.892  95.946  
 29.898  88.488   33.690  80.970   38.378  73.481   44.077  66.157  
 50.892  59.200   58.880  52.887   68.002  47.568   78.065  43.622  
 88.689  41.358   99.360  40.905  109.556  42.145  118.884  44.769  
127.142  48.387  134.292  52.634  140.403  57.221  145.589  61.944  
149.980  66.665  153.695  71.300  156.843  75.799  159.513  80.135  
161.782  84.297  163.713  88.282  165.358  92.095  166.756  95.740  
167.951  99.226  168.960 102.570  169.812 105.763  170.543 108.831  
171.144 111.793  171.629 114.625  172.047 117.344  172.391 119.997  
172.626 122.567  172.791 125.017  172.938 127.383  173.045 129.724  
173.057 132.023  172.993 134.216  172.926 136.315  172.873 138.391  
172.769 140.483  172.563 142.536  172.302 144.486  172.062 146.357  
171.851 148.226  171.607 150.138  171.261 152.045  170.840 153.866  
170.430 155.602  ] scurve 
%%% D 
173.141 156.263 moveto 
%%% Y 181 
[ 173.141 156.263  172.955 157.236  172.896 158.298  172.912 159.545  
172.817 161.069  172.327 162.659  171.612 163.935  170.989 164.950  
170.529 165.868  170.221 166.791  170.039 167.791  169.942 168.954  
169.792 170.376  169.304 171.954  168.509 173.282  167.763 174.314  
167.183 175.232  166.760 176.156  166.463 177.168  166.237 178.354  
165.926 179.798  165.261 181.348  164.349 182.619  163.528 183.632  
162.884 184.580  162.388 185.583  161.986 186.737  161.548 188.132  
160.815 189.692  159.788 191.039  158.818 192.118  158.028 193.136  
157.380 194.244  156.772 195.554  155.987 197.091  154.862 198.569  
153.687 199.766  152.679 200.870  151.801 202.081  150.901 203.514  
149.728 205.081  148.331 206.448  147.028 207.644  145.854 208.916  
144.623 210.396  143.109 211.934  141.467 213.263  139.931 214.539  
138.384 215.975  136.589 217.484  134.650 218.821  132.765 220.131  
130.766 221.563  128.530 222.926  126.261 224.173  123.903 225.481  
121.323 226.718  118.675 227.843  115.880 228.964  112.912 229.945  
109.848 230.840  106.601 231.613  103.250 232.230   99.746 232.702  
 96.140 232.977   92.415 233.064   88.615 232.928   84.736 232.566  
 80.823 231.964   76.881 231.113   72.951 230.020   69.047 228.673  
 65.194 227.095   61.421 225.277   57.729 223.247   54.157 221.008  
 50.689 218.577   47.365 215.973   44.160 213.199   41.111 210.287  
 38.186 207.224   35.424 204.052   32.783 200.747   30.309 197.352  
 27.947 193.843   25.758 190.251   23.668 186.568   21.754 182.794  
 19.936 178.956   18.283 175.008   16.741 171.022   15.338 166.912  
 14.076 162.769   12.924 158.504   11.942 154.191   11.056 149.773  
 10.355 145.275    9.758 140.691    9.351 136.000    9.072 131.230  
  8.987 126.334    9.060 121.353    9.344 116.238    9.819 111.022  
 10.536 105.671   11.487 100.200   12.726  94.596   14.262  88.857  
 16.145  82.991   18.416  76.995   21.124  70.884   24.332  64.678  
 28.112  58.410   32.542  52.133   37.708  45.929   43.697  39.915  
 50.581  34.261   58.390  29.188   67.080  24.970   76.490  21.891  
 86.328  20.184   96.204  19.948  105.714  21.108  114.543  23.444  
122.508  26.661  129.554  30.473  135.712  34.638  141.059  38.977  
145.691  43.364  149.706  47.715  153.184  51.974  156.212  56.121  
158.849  60.111  161.157  63.983  163.165  67.666  164.967  71.245  
166.481  74.664  167.892  77.898  169.125  81.116  170.116  84.123  
171.115  86.950  172.028  89.836  172.656  92.590  173.257  95.064  
173.973  97.510  174.549 100.093  174.827 102.509  175.113 104.627  
175.571 106.671  176.067 108.889  176.261 111.193  176.239 113.208  
176.315 114.964  176.583 116.670  176.961 118.544  177.133 120.638  
176.956 122.577  176.753 124.187  176.713 125.628  176.861 127.066  
177.132 128.670  177.274 130.543  177.023 132.391  176.634 133.905  
176.366 135.187  176.275 136.394  176.350 137.643  176.535 139.066  
176.613 140.771  176.293 142.515  175.775 143.934  175.354 145.097  
175.098 146.160  175.001 147.225  175.043 148.384  175.149 149.752  
175.077 151.395  174.594 153.000  173.975 154.263  173.477 155.302  
173.141 156.263  ] scurve 
%% / / 
%%% D 
 10.000  14.000 moveto 
%%% K 
%% $ 
  1.000 nbpt mul rm  (Ellipse) show currentpoint 
clear 
%%% D 
 10.000   7.000 moveto 
%%% K 
%% $ 
  1.000 nbpt mul it  (x ) show currentpoint 
%% $ 
  1.000 nbpt mul rm  (= 3 cos ) show currentpoint 
%% $ 
  1.000 nbpt mul it  (t) show currentpoint 
clear 
%%% D 
 10.000   2.000 moveto 
%%% K 
%% $ 
  1.000 nbpt mul it  (y ) show currentpoint 
%% $ 
  1.000 nbpt mul rm  (= 4 sin ) show currentpoint 
%% $ 
  1.000 nbpt mul it  (t) show currentpoint 
clear 
%%% D 
144.000   2.000 moveto 
%%% K 
%% $ 
  1.000 nbpt mul rm  (Centre \(1,1\)) show currentpoint 
clear 
%%% > 
showpage 

% Dessin z3.ds1 

%%% < 1 Largeur= 180.000 Hauteur= 240.000 
%%% ~   0.000 180.000   0.000 240.000 
1.2 dup scale 
1 mm unit  /nbpt 10 def 
  0.000   0.000 translate
%%% L 
  0.452 setlinewidth 
%%% D 
  0.000 200.000 moveto 
%%% Y 6 
[   0.000 200.000    0.000  30.000  130.000   0.000  180.000  80.000  
110.000 240.000    0.000 200.000  ] polygon 
stroke 
%% / C 
%%% L 
  0.113 setlinewidth 
%%% Z 
%%% D 
 85.000 115.000 moveto 
%%% Y 21  
[  85.000 115.000   80.317 115.012   75.604 115.043   70.872 115.088  
 66.134 115.144   61.400 115.206   56.685 115.271   52.000 115.336  
 47.362 115.399   42.783 115.458   38.280 115.513   33.866 115.561  
 29.555 115.604   25.361 115.641   21.296 115.671   17.369 115.695  
 13.589 115.714    9.962 115.728    6.510 115.745    3.357 115.802  
  0.000 115.944  ] scurve 
%%% D 
 85.000 115.000 moveto 
%%% Y 21  
[  85.000 115.000   80.776 112.970   76.515 110.933   72.224 108.898  
 67.910 106.874   63.577 104.873   59.230 102.904   54.872 100.979  
 50.508  99.110   46.140  97.310   41.771  95.594   37.403  93.978  
 33.041  92.479   28.692  91.114   24.367  89.902   20.079  88.862  
 15.848  88.008   11.700  87.350    7.670  86.892    3.893  86.637  
  0.000  86.611  ] scurve 
%%% D 
 85.000 115.000 moveto 
%%% Y 21  
[  85.000 115.000   82.082 111.332   79.143 107.629   76.174 103.900  
 73.170 100.151   70.122  96.389   67.024  92.620   63.866  88.848  
 60.641  85.077   57.340  81.307   53.953  77.536   50.467  73.761  
 46.867  69.971   43.134  66.152   39.240  62.281   35.144  58.319  
 30.785  54.206   26.057  49.836   20.763  44.992   14.443  39.087  
  7.099  28.362  ] scurve 
%%% D 
 85.000 115.000 moveto 
%%% Y 21  
[  85.000 115.000   83.972 110.431   82.959 105.819   81.952 101.159  
 80.941  96.446   79.919  91.676   78.879  86.845   77.813  81.950  
 76.718  76.987   75.590  71.957   74.425  66.860   73.226  61.700  
 71.993  56.484   70.733  51.226   69.456  45.946   68.172  40.668  
 66.898  35.427   65.649  30.262   64.439  25.216   63.219  20.348  
 61.527  15.801  ] scurve 
%%% D 
 85.000 115.000 moveto 
%%% Y 21  
[  85.000 115.000   86.061 110.447   87.171 105.879   88.330 101.284  
 89.541  96.654   90.805  91.980   92.123  87.252   93.496  82.462  
 94.924  77.601   96.405  72.659   97.938  67.627   99.519  62.492  
101.143  57.236  102.802  51.839  104.487  46.268  106.182  40.478  
107.857  34.395  109.452  27.908  110.822  20.833  111.552  12.942  
110.222   4.564  ] scurve 
%%% D 
 85.000 115.000 moveto 
%%% Y 21  
[  85.000 115.000   87.927 111.369   90.897 107.770   93.921 104.202  
 97.009 100.665  100.171  97.157  103.415  93.677  106.751  90.225  
110.188  86.799  113.737  83.396  117.407  80.018  121.208  76.663  
125.146  73.331  129.228  70.025  133.454  66.750  137.815  63.513  
142.289  60.325  146.838  57.204  151.404  54.170  155.865  51.242  
160.121  48.194  ] scurve 
%%% D 
 85.000 115.000 moveto 
%%% Y 21  
[  85.000 115.000   89.201 113.000   93.400 111.057   97.601 109.181  
101.806 107.380  106.019 105.664  110.245 104.042  114.485 102.522  
118.742 101.115  123.021  99.828  127.324  98.673  131.653  97.658  
136.014  96.797  140.409  96.102  144.845  95.593  149.325  95.294  
153.855  95.241  158.428  95.487  163.011  96.106  167.443  97.163  
171.739  98.882  ] scurve 
%%% D 
 85.000 115.000 moveto 
%%% Y 21  
[  85.000 115.000   89.644 115.013   94.239 115.056   98.777 115.136  
103.248 115.257  107.646 115.427  111.962 115.650  116.190 115.931  
120.322 116.276  124.351 116.689  128.271 117.172  132.074 117.728  
135.754 118.357  139.303 119.060  142.715 119.834  145.983 120.674  
149.101 121.574  152.061 122.525  154.833 123.517  157.276 124.531  
159.950 125.828  ] scurve 
%%% D 
 85.000 115.000 moveto 
%%% Y 21  
[  85.000 115.000   89.180 117.015   93.309 119.006   97.378 120.967  
101.379 122.890  105.303 124.770  109.144 126.600  112.892 128.377  
116.541 130.096  120.084 131.755  123.516 133.351  126.831 134.882  
130.026 136.349  133.098 137.749  136.046 139.085  138.870 140.357  
141.571 141.565  144.151 142.704  146.609 143.741  148.920 144.526  
151.485 145.177  ] scurve 
%%% D 
 85.000 115.000 moveto 
%%% Y 21  
[  85.000 115.000   87.902 118.624   90.796 122.194   93.685 125.701  
 96.576 129.134   99.473 132.483  102.378 135.737  105.293 138.884  
108.220 141.914  111.157 144.815  114.102 147.578  117.049 150.192  
119.993 152.649  122.925 154.943  125.836 157.069  128.713 159.023  
131.546 160.808  134.328 162.426  137.072 163.884  139.948 165.208  
142.515 165.681  ] scurve 
%%% D 
 85.000 115.000 moveto 
%%% Y 21  
[  85.000 115.000   86.053 119.529   87.141 124.023   88.276 128.485  
 89.470 132.919   90.736 137.325   92.087 141.707   93.538 146.064  
 95.104 150.396   96.803 154.700   98.652 158.972  100.674 163.203  
102.889 167.384  105.326 171.496  108.010 175.515  110.970 179.401  
114.230 183.101  117.800 186.537  121.663 189.617  125.812 192.293  
129.783 194.782  ] scurve 
%%% D 
 85.000 115.000 moveto 
%%% Y 21  
[  85.000 115.000   83.985 119.548   83.015 124.102   82.087 128.674  
 81.202 133.279   80.358 137.928   79.555 142.639   78.793 147.426  
 78.072 152.309   77.392 157.306   76.753 162.438   76.155 167.729  
 75.594 173.201   75.060 178.881   74.537 184.794   73.991 190.962  
 73.361 197.399   72.553 204.093   71.432 210.981   69.871 217.902  
 68.129 224.774  ] scurve 
%%% D 
 85.000 115.000 moveto 
%%% Y 21  
[  85.000 115.000   82.106 118.664   79.233 122.362   76.369 126.095  
 73.501 129.862   70.614 133.666   67.693 137.506   64.722 141.383  
 61.682 145.298   58.554 149.250   55.317 153.241   51.950 157.271  
 48.428 161.344   44.723 165.465   40.803 169.646   36.629 173.912  
 32.145 178.309   27.267 182.931   21.848 187.986   15.635 194.055  
  9.539 203.469  ] scurve 
%%% D 
 85.000 115.000 moveto 
%%% Y 21  
[  85.000 115.000   80.794 117.046   76.579 119.127   72.353 121.231  
 68.113 123.346   63.857 125.457   59.583 127.551   55.289 129.612  
 50.976 131.623   46.643 133.568   42.291 135.426   37.923 137.180  
 33.544 138.809   29.162 140.291   24.789 141.606   20.441 142.734  
 16.142 143.659   11.917 144.370    7.806 144.869    3.936 145.198  
  0.000 145.441  ] scurve 
%%% D 
100.487 115.177 moveto 
%%% Y 61  
[ 100.487 115.177  100.368 116.756  100.094 118.310   99.669 119.828  
 99.098 121.296   98.386 122.700   97.538 124.029   96.562 125.271  
 95.464 126.414   94.253 127.445   92.939 128.353   91.533 129.128  
 90.048 129.758   88.498 130.234   86.898 130.549   85.266 130.695  
 83.619 130.668   81.978 130.466   80.362 130.088   78.791 129.538  
 77.284 128.822   75.860 127.946   74.536 126.922   73.328 125.761  
 72.251 124.477   71.316 123.086   70.533 121.603   69.912 120.047  
 69.458 118.434   69.176 116.782   69.069 115.109   69.138 113.433  
 69.382 111.771   69.799 110.143   70.386 108.565   71.138 107.055  
 72.046 105.630   73.103 104.308   74.297 103.104   75.614 102.033  
 77.041 101.108   78.561 100.341   80.156  99.744   81.806  99.322  
 83.492  99.082   85.192  99.027   86.885  99.156   88.550  99.467  
 90.167  99.956   91.716 100.614   93.179 101.432   94.540 102.397  
 95.785 103.495   96.900 104.712   97.875 106.032   98.703 107.438  
 99.377 108.913   99.894 110.441  100.252 112.004  100.449 113.588  
100.487 115.177  ] scurve 
%%% D 
121.464 116.385 moveto 
%%% Y 61  
[ 121.464 116.385  120.978 119.854  120.222 123.229  119.210 126.505  
117.952 129.680  116.449 132.751  114.702 135.711  112.706 138.552  
110.452 141.261  107.929 143.817  105.129 146.192  102.044 148.348  
 98.674 150.239   95.030 151.810   91.138 153.004   87.040 153.761  
 82.800 154.031   78.492 153.780   74.204 152.989   70.022 151.663  
 66.033 149.827   62.311 147.522   58.918 144.803   55.899 141.737  
 53.283 138.389   51.081 134.824   49.292 131.099   47.908 127.263  
 46.916 123.351   46.306 119.395   46.069 115.416   46.201 111.434  
 46.704 107.470   47.583 103.544   48.848  99.683   50.510  95.922  
 52.575  92.303   55.046  88.876   57.914  85.699   61.156  82.830  
 64.738  80.326   68.615  78.235   72.731  76.599   77.027  75.448  
 81.442  74.806   85.910  74.689   90.361  75.103   94.723  76.045  
 98.922  77.498  102.887  79.433  106.554  81.805  109.870  84.559  
112.795  87.632  115.301  90.958  117.377  94.470  119.023  98.104  
120.251 101.801  121.081 105.512  121.541 109.198  121.660 112.829  
121.464 116.385  ] scurve 
%%% D 
132.866 117.855 moveto 
%%% Y 61  
[ 132.866 117.855  132.015 122.134  130.911 126.255  129.573 130.241  
128.008 134.112  126.214 137.885  124.180 141.575  121.884 145.192  
119.298 148.736  116.381 152.201  113.088 155.563  109.363 158.780  
105.153 161.778  100.417 164.452   95.147 166.660   89.392 168.240  
 83.267 169.041   76.942 168.961   70.609 167.961   64.454 166.061  
 58.641 163.318   53.318 159.827   48.601 155.715   44.562 151.138  
 41.219 146.253   38.537 141.198   36.457 136.068   34.909 130.922  
 33.835 125.788   33.189 120.673   32.942 115.571   33.083 110.472  
 33.619 105.366   34.572 100.245   35.982  95.114   37.902  89.998  
 40.393  84.948   43.508  80.050   47.274  75.425   51.671  71.211  
 56.628  67.531   62.043  64.474   67.811  62.089   73.841  60.399  
 80.055  59.427   86.381  59.201   92.728  59.757   98.982  61.125  
105.002  63.304  110.638  66.246  115.764  69.860  120.290  74.028  
124.161  78.626  127.348  83.533  129.842  88.628  131.663  93.792  
132.857  98.917  133.497 103.922  133.662 108.757  133.431 113.401  
132.866 117.855  ] scurve 
%%% D 
141.103 119.456 moveto 
%%% Y 61  
[ 141.103 119.456  139.900 124.165  138.505 128.672  136.933 133.024  
135.186 137.261  133.255 141.419  131.120 145.532  128.752 149.625  
126.107 153.724  123.126 157.843  119.730 161.988  115.814 166.138  
111.245 170.236  105.873 174.150   99.568 177.636   92.320 180.335  
 84.331 181.872   75.985 182.031   67.666 180.815   59.646 178.328  
 52.131 174.670   45.336 169.948   39.496 164.353   34.761 158.198  
 31.103 151.822   28.368 145.464   26.369 139.237   24.948 133.170  
 23.994 127.245   23.432 121.423   23.221 115.657   23.346 109.900  
 23.816 104.101   24.666  98.216   25.963  92.204   27.808  86.049  
 30.346  79.772   33.746  73.480   38.147  67.398   43.554  61.842  
 49.788  57.089   56.585  53.256   63.737  50.319   71.138  48.218  
 78.754  46.928   86.573  46.487   94.551  47.004  102.550  48.624  
110.303  51.442  117.487  55.391  123.866  60.253  129.347  65.783  
133.919  71.796  137.568  78.153  140.264  84.704  142.009  91.251  
142.896  97.593  143.093 103.597  142.776 109.223  142.081 114.493  
141.103 119.456  ] scurve 
%%% D 
147.536 121.109 moveto 
%%% Y 61  
[ 147.536 121.109  146.014 126.034  144.377 130.733  142.632 135.272  
140.769 139.705  138.777 144.083  136.627 148.448  134.290 152.846  
131.714 157.317  128.838 161.906  125.566 166.653  121.763 171.592  
117.228 176.732  111.662 182.003  104.668 187.133   95.937 191.438  
 85.780 193.944   75.192 194.221   64.926 192.611   55.188 189.508  
 46.021 185.015   37.665 179.051   30.682 171.736   25.509 163.738  
 21.958 155.816   19.553 148.305   17.912 141.237   16.797 134.537  
 16.068 128.108   15.647 121.860   15.491 115.705   15.585 109.561  
 15.941 103.347   16.593  96.978   17.614  90.365   19.131  83.416  
 21.365  76.060   24.670  68.323   29.498  60.524   36.025  53.412  
 43.744  47.673   51.951  43.349   60.304  40.140   68.760  37.795  
 77.409  36.201   86.385  35.391   95.802  35.575  105.601  37.159  
115.296  40.571  124.077  45.723  131.513  51.991  137.692  58.863  
142.794  66.151  146.856  73.836  149.720  81.842  151.225  89.819  
151.539  97.305  151.066 104.099  150.133 110.250  148.925 115.881  
147.536 121.109  ] scurve 
%%% D 
152.739 122.758 moveto 
%%% Y 121 
[ 152.739 122.758  151.860 125.285  150.966 127.770  150.036 130.188  
149.110 132.531  148.202 134.852  147.262 137.172  146.279 139.449  
145.300 141.683  144.328 143.929  143.313 146.201  142.244 148.456  
141.166 150.696  140.078 152.976  138.927 155.303  137.713 157.639  
136.468 160.000  135.174 162.433  133.787 164.928  132.317 167.471  
130.768 170.098  129.093 172.827  127.275 175.649  125.297 178.593  
123.105 181.675  120.649 184.902  117.854 188.289  114.610 191.827  
110.770 195.471  106.147 199.082  100.588 202.353   94.170 204.822  
 87.329 206.161   80.559 206.446   74.102 205.961   67.983 204.952  
 62.150 203.563   56.528 201.865   51.052 199.873   45.669 197.563  
 40.350 194.871   35.108 191.692   30.047 187.895   25.411 183.399  
 21.523 178.340   18.536 173.074   16.332 167.927   14.701 163.044  
 13.467 158.451   12.511 154.124   11.754 150.027   11.150 146.126  
 10.658 142.390   10.261 138.786    9.943 135.301    9.679 131.906  
  9.479 128.578    9.329 125.320    9.212 122.100    9.148 118.901  
  9.124 115.732    9.127 112.561    9.178 109.371    9.274 106.172  
  9.401 102.934    9.583  99.637    9.821  96.285   10.111  92.846  
 10.479  89.300   10.934  85.636   11.495  81.817   12.200  77.819  
 13.090  73.609   14.239  69.151   15.755  64.423   17.802  59.442  
 20.590  54.332   24.266  49.403   28.708  45.056   33.557  41.480  
 38.500  38.600   43.385  36.250   48.172  34.286   52.866  32.609  
 57.493  31.152   62.083  29.872   66.669  28.740   71.288  27.742  
 75.973  26.871   80.769  26.133   85.718  25.545   90.872  25.143  
 96.286  24.991  102.005  25.198  108.038  25.943  114.265  27.457  
120.372  29.898  125.975  33.146  130.898  36.879  135.192  40.826  
138.982  44.847  142.381  48.892  145.474  52.958  148.317  57.064  
150.943  61.245  153.357  65.546  155.533  70.020  157.392  74.707  
158.801  79.591  159.632  84.533  159.885  89.318  159.695  93.790  
159.224  97.911  158.585 101.712  157.851 105.237  157.063 108.543  
156.228 111.659  155.377 114.606  154.521 117.432  153.636 120.154  
152.739 122.758  ] scurve 
%%% D 
156.882 124.351 moveto 
%%% Y 181 
[ 156.882 124.351  156.318 125.877  155.870 127.563  155.277 129.449  
154.394 131.214  153.532 132.679  152.876 134.037  152.403 135.472  
151.976 137.122  151.318 138.943  150.400 140.567  149.562 141.925  
148.931 143.225  148.465 144.634  148.019 146.278  147.314 148.084  
146.366 149.680  145.516 151.036  144.869 152.365  144.370 153.838  
143.842 155.567  143.016 157.403  142.020 158.999  141.166 160.424  
140.504 161.903  139.920 163.605  139.145 165.542  138.092 167.377  
137.087 169.006  136.267 170.665  135.514 172.563  134.544 174.680  
133.348 176.686  132.241 178.589  131.248 180.666  130.108 183.015  
128.714 185.364  127.339 187.687  125.956 190.258  124.304 193.040  
122.482 195.875  120.513 198.974  118.163 202.332  115.404 205.931  
111.966 209.838  107.475 213.865  101.530 217.364   94.650 219.253  
 88.082 219.575   82.224 219.076   76.960 218.216   72.141 217.157  
 67.624 216.021   63.344 214.782   59.228 213.533   55.202 212.188  
 51.286 210.824   47.349 209.380   43.463 207.843   39.498 206.232  
 35.483 204.439   31.349 202.486   27.061 200.210   22.605 197.496  
 18.069 194.024   13.929 189.510   10.931 184.319    9.067 179.262  
  7.897 174.671    7.058 170.498    6.493 166.660    6.013 163.165  
  5.603 159.793    5.378 156.650    5.103 153.759    4.799 150.859  
  4.698 148.041    4.614 145.498    4.372 143.016    4.178 140.406  
  4.210 137.912    4.200 135.669    4.006 133.446    3.819 131.043  
  3.885 128.664    3.977 126.540    3.880 124.499    3.673 122.294  
  3.661 119.938    3.830 117.770    3.879 115.785    3.736 113.739  
  3.607 111.457    3.743 109.151    3.920 107.069    3.911 105.050  
  3.776 102.844    3.811 100.435    4.038  98.153    4.154  96.009  
  4.096  93.743    4.114  91.219    4.356  88.711    4.543  86.323  
  4.577  83.798    4.706  81.009    5.017  78.220    5.247  75.420  
  5.452  72.349    5.856  69.090    6.301  65.732    6.820  62.041  
  7.600  58.049    8.649  53.680   10.285  48.838   12.948  43.707  
 16.923  39.046   21.556  35.550   26.109  33.037   30.406  31.112  
 34.403  29.555   38.220  28.188   41.852  27.047   45.308  25.948  
 48.752  24.960   52.032  24.099   55.251  23.182   58.528  22.374  
 61.670  21.652   64.814  20.841   68.065  20.127   71.224  19.488  
 74.428  18.750   77.780  18.103   81.097  17.514   84.532  16.845  
 88.144  16.280   91.818  15.737   95.744  15.196   99.895  14.783  
104.358  14.441  109.257  14.342  114.678  14.665  120.592  15.887  
126.374  18.423  131.236  21.861  135.168  25.504  138.458  29.042  
141.348  32.467  143.913  35.730  146.328  38.893  148.521  42.000  
150.629  44.969  152.674  47.980  154.557  50.931  156.469  53.836  
158.318  56.863  160.066  59.862  161.879  62.943  163.603  66.217  
165.283  69.605  166.908  73.343  168.178  77.464  168.870  81.832  
168.857  86.092  168.396  89.958  167.665  93.471  166.803  96.535  
166.060  99.332  165.280 102.084  164.348 104.585  163.542 106.799  
162.912 109.006  162.195 111.313  161.271 113.428  160.446 115.255  
159.841 117.037  159.318 118.976  158.583 121.017  157.663 122.807  
156.882 124.351  ] scurve 
%% / / 
%%% D 
  0.000 230.000 moveto 
%%% K 
%% $ 
  1.000 nbpt mul rm  (Domaine polygonal convexe) show currentpoint 
clear 
%%% > 
showpage 

% Dessin z4.ds1 

%%% < 1 Largeur= 180.000 Hauteur= 240.000 
%%% ~   0.000 180.000   0.000 240.000 
1.2 dup scale 
1 mm unit  /nbpt 10 def 
  0.000   0.000 translate 
%%% D 
  0.000 190.000 moveto 
%%% L 
  0.452 setlinewidth 
%%% Y 6 
[   0.000 190.000    0.000  40.000  180.000   0.000  130.000 100.000  
180.000 240.000    0.000 190.000  ] polygon 
stroke 
%% / C 
%%% L 
  0.113 setlinewidth 
%%% D 
  0.000 190.000 moveto 
%%% Z 
%%% D 
 70.000 115.000 moveto 
%%% Y 21  
[  70.000 115.000   65.870 114.985   61.744 114.962   57.636 114.930  
 53.557 114.893   49.518 114.852   45.529 114.807   41.602 114.761  
 37.747 114.715   33.974 114.670   30.292 114.627   26.710 114.587  
 23.236 114.550   19.878 114.518   16.639 114.490   13.525 114.468  
 10.538 114.453    7.679 114.456    4.948 114.527    2.379 114.855  
  0.000 115.552  ] scurve 
%%% D 
 70.000 115.000 moveto 
%%% Y 21  
[  70.000 115.000   66.286 113.196   62.578 111.392   58.876 109.600  
 55.182 107.832   51.498 106.099   47.824 104.412   44.163 102.782  
 40.516 101.219   36.885  99.736   33.271  98.343   29.680  97.052  
 26.115  95.875   22.584  94.823   19.096  93.906   15.664  93.133  
 12.302  92.511    9.027  92.046    5.843  91.771    2.727  91.867  
  0.000  92.697  ] scurve 
%%% D 
 70.000 115.000 moveto 
%%% Y 21  
[  70.000 115.000   67.437 111.764   64.875 108.528   62.301 105.296  
 59.704 102.072   57.075  98.861   54.404  95.667   51.680  92.494  
 48.895  89.345   46.037  86.222   43.096  83.124   40.057  80.053  
 36.904  77.004   33.614  73.974   30.156  70.957   26.483  67.946  
 22.524  64.934   18.159  61.926   13.170  58.967    7.114  56.321  
  0.000  54.983  ] scurve 
%%% D 
 70.000 115.000 moveto 
%%% Y 21  
[  70.000 115.000   69.095 110.974   68.195 106.944   67.291 102.899  
 66.377  98.829   65.444  94.727   64.486  90.584   63.494  86.394  
 62.462  82.151   61.387  77.853   60.265  73.499   59.098  69.089  
 57.893  64.627   56.660  60.119   55.416  55.574   54.185  51.005  
 52.993  46.425   51.863  41.849   50.798  37.284   49.644  32.698  
 47.899  29.356  ] scurve 
%%% D 
 70.000 115.000 moveto 
%%% Y 21  
[  70.000 115.000   70.931 110.982   71.872 106.967   72.834 102.946  
 73.823  98.908   74.848  94.842   75.913  90.736   77.024  86.576  
 78.182  82.350   79.387  78.042   80.632  73.633   81.906  69.107  
 83.190  64.443   84.450  59.622   85.639  54.624   86.691  49.443  
 87.518  44.087   88.018  38.595   88.093  33.057   87.721  27.650  
 86.654  20.744  ] scurve 
%%% D 
 70.000 115.000 moveto 
%%% Y 21  
[  70.000 115.000   72.579 111.784   75.161 108.585   77.757 105.408  
 80.380 102.262   83.045  99.150   85.765  96.080   88.558  93.056  
 91.444  90.084   94.444  87.169   97.585  84.317  100.900  81.539  
104.431  78.846  108.230  76.258  112.365  73.807  116.921  71.547  
122.001  69.570  127.714  68.027  134.113  67.134  141.042  67.118  
145.900  68.201  ] scurve 
%%% D 
 70.000 115.000 moveto 
%%% Y 21  
[  70.000 115.000   73.717 113.219   77.416 111.449   81.094 109.705  
 84.745 108.000   88.366 106.350   91.952 104.769   95.499 103.276  
 98.999 101.887  102.445 100.619  105.827  99.492  109.131  98.521  
112.342  97.721  115.438  97.105  118.395  96.677  121.184  96.436  
123.773  96.362  126.121  96.417  128.170  96.527  129.819  96.583  
131.526  96.948  ] scurve 
%%% D 
 70.000 115.000 moveto 
%%% Y 21  
[  70.000 115.000   74.123 115.004   78.225 114.995   82.292 114.973  
 86.310 114.934   90.262 114.877   94.133 114.800   97.907 114.701  
101.567 114.578  105.099 114.429  108.488 114.250  111.722 114.040  
114.790 113.795  117.685 113.512  120.400 113.186  122.934 112.809  
125.289 112.368  127.477 111.834  129.526 111.133  131.445 110.032  
132.994 108.384  ] scurve 
%%% D 
 70.000 115.000 moveto 
%%% Y 21  
[  70.000 115.000   73.717 116.792   77.437 118.557   81.159 120.283  
 84.882 121.954   88.606 123.554   92.329 125.068   96.051 126.477  
 99.770 127.765  103.482 128.913  107.181 129.904  110.859 130.720  
114.504 131.348  118.102 131.773  121.634 131.990  125.078 131.996  
128.411 131.794  131.605 131.391  134.615 130.776  137.309 129.838  
140.112 128.313  ] scurve 
%%% D 
 70.000 115.000 moveto 
%%% Y 21  
[  70.000 115.000   72.575 118.231   75.175 121.453   77.813 124.663  
 80.503 127.858   83.261 131.035   86.102 134.192   89.045 137.327  
 92.109 140.439   95.318 143.526   98.698 146.583  102.283 149.607  
106.115 152.588  110.246 155.507  114.742 158.335  119.687 161.011  
125.184 163.430  131.331 165.398  138.166 166.590  145.536 166.550  
153.291 165.215  ] scurve 
%%% D 
 70.000 115.000 moveto 
%%% Y 21  
[  70.000 115.000   70.916 119.032   71.850 123.083   72.808 127.163  
 73.794 131.286   74.814 135.464   75.870 139.711   76.964 144.041  
 78.095 148.471   79.259 153.017   80.448 157.696   81.647 162.530  
 82.832 167.539   83.968 172.742   85.005 178.158   85.872 183.794  
 86.479 189.637   86.722 195.641   86.498 201.708   85.682 207.703  
 83.627 213.230  ] scurve 
%%% D 
 70.000 115.000 moveto 
%%% Y 21  
[  70.000 115.000   69.071 119.031   68.135 123.084   67.181 127.166  
 66.200 131.286   65.181 135.449   64.114 139.661   62.991 143.926  
 61.801 148.248   60.540 152.627   59.202 157.062   57.787 161.551  
 56.299 166.090   54.750 170.669   53.156 175.280   51.543 179.907  
 49.944 184.531   48.393 189.124   46.931 193.659   45.649 198.197  
 45.329 202.591  ] scurve 
%%% D 
 70.000 115.000 moveto 
%%% Y 21  
[  70.000 115.000   67.412 118.226   64.805 121.454   62.168 124.677  
 59.493 127.887   56.770 131.078   53.991 134.242   51.149 137.373  
 48.235 140.465   45.240 143.514   42.156 146.515   38.970 149.466  
 35.667 152.365   32.227 155.209   28.621 157.996   24.808 160.719  
 20.725 163.362   16.279 165.880   11.331 168.159    5.737 169.950  
  0.000 171.191  ] scurve 
%%% D 
 70.000 115.000 moveto 
%%% Y 21  
[  70.000 115.000   66.270 116.780   62.532 118.548   58.790 120.291  
 55.048 122.000   51.312 123.663   47.586 125.271   43.873 126.814  
 40.178 128.282   36.505 129.664   32.860 130.952   29.248 132.135  
 25.676 133.204   22.153 134.151   18.688 134.967   15.294 135.649  
 11.984 136.196    8.772 136.615    5.675 136.950    2.764 137.387  
  0.000 138.086  ] scurve 
%%% D 
 83.828 114.960 moveto 
%%% Y 61  
[  83.828 114.960   83.770 116.384   83.569 117.799   83.225 119.192  
 82.740 120.548   82.117 121.853   81.358 123.093   80.469 124.254  
 79.459 125.320   78.335 126.277   77.110 127.113   75.797 127.814  
 74.412 128.371   72.971 128.775   71.492 129.020   69.995 129.102  
 68.498 129.020   67.020 128.777   65.580 128.376   64.194 127.822  
 62.880 127.125   61.652 126.294   60.522 125.341   59.503 124.279  
 58.605 123.119   57.834 121.877   57.198 120.565   56.701 119.200  
 56.348 117.793   56.141 116.361   56.080 114.917   56.166 113.474  
 56.399 112.048   56.777 110.652   57.295 109.300   57.951 108.006  
 58.739 106.784   59.651 105.648   60.680 104.611   61.814 103.685  
 63.042 102.882   64.351 102.213   65.726 101.686   67.151 101.309  
 68.609 101.086   70.082 101.021   71.552 101.114   73.002 101.363  
 74.415 101.766   75.772 102.315   77.060 103.003   78.264 103.820  
 79.372 104.755   80.373 105.795   81.258 106.929   82.021 108.142  
 82.654 109.423   83.155 110.758   83.519 112.134   83.744 113.539  
 83.828 114.960  ] scurve 
%%% D 
102.572 114.539 moveto 
%%% Y 61  
[ 102.572 114.539  102.583 117.646  102.356 120.790  101.868 123.972  
101.092 127.182   99.995 130.401   98.542 133.595   96.704 136.714  
 94.460 139.696   91.808 142.463   88.768 144.934   85.384 147.031  
 81.721 148.692   77.858 149.873   73.878 150.553   69.860 150.728  
 65.878 150.411   61.997 149.621   58.277 148.388   54.770 146.746  
 51.521 144.737   48.570 142.409   45.942 139.813   43.652 137.004  
 41.705 134.031   40.094 130.940   38.809 127.765   37.837 124.536  
 37.164 121.273   36.780 117.991   36.679 114.702   36.859 111.417  
 37.323 108.145   38.078 104.900   39.136 101.698   40.507  98.564  
 42.204  95.528   44.236  92.629   46.601  89.915   49.292  87.435  
 52.284  85.241   55.546  83.382   59.033  81.898   62.697  80.822  
 66.483  80.181   70.335  79.992   74.190  80.266   77.983  81.006  
 81.643  82.202   85.099  83.828   88.286  85.840   91.152  88.176  
 93.666  90.765   95.818  93.536   97.620  96.425   99.098  99.382  
100.283 102.376  101.203 105.389  101.883 108.418  102.338 111.466  
102.572 114.539  ] scurve 
%%% D 
112.387 113.991 moveto 
%%% Y 61  
[ 112.387 113.991  112.582 117.697  112.591 121.523  112.368 125.500  
111.849 129.650  110.954 133.982  109.583 138.478  107.621 143.082  
104.952 147.682  101.493 152.102   97.238 156.112   92.286 159.485  
 86.823 162.059   81.068 163.769   75.212 164.633   69.396 164.710  
 63.715 164.065   58.239 162.750   53.033 160.809   48.170 158.278  
 43.732 155.215   39.797 151.702   36.417 147.851   33.600 143.783  
 31.316 139.602   29.512 135.383   28.132 131.170   27.121 126.984  
 26.440 122.828   26.059 118.697   25.963 114.579   26.148 110.460  
 26.622 106.327   27.405 102.172   28.530  97.991   30.042  93.794  
 31.996  89.612   34.446  85.500   37.438  81.547   40.985  77.868  
 45.054  74.584   49.573  71.797   54.450  69.575   59.594  67.952  
 64.927  66.949   70.386  66.587   75.906  66.896   81.402  67.922  
 86.753  69.705   91.789  72.248   96.321  75.480  100.194  79.240  
103.336  83.311  105.782  87.481  107.638  91.598  109.035  95.582  
110.096  99.418  110.915 103.129  111.551 106.759  112.039 110.362  
112.387 113.991  ] scurve 
%%% D 
119.126 113.347 moveto 
%%% Y 61  
[ 119.126 113.347  119.560 117.269  119.899 121.397  120.080 125.789  
120.028 130.500  119.639 135.588  118.763 141.099  117.181 147.047  
114.597 153.342  110.691 159.706  105.288 165.609   98.584 170.430  
 91.114 173.802   83.431 175.741   75.873 176.474   68.579 176.235  
 61.575 175.182   54.857 173.391   48.441 170.866   42.401 167.581  
 36.899 163.533   32.140 158.831   28.258 153.713   25.240 148.448  
 22.958 143.226   21.261 138.136   20.020 133.199   19.143 128.399  
 18.565 123.708   18.248 119.089   18.170 114.503   18.327 109.912  
 18.730 105.277   19.406 100.562   20.402  95.732   21.793  90.762  
 23.684  85.649   26.215  80.438   29.537  75.257   33.743  70.340  
 38.782  65.968   44.464  62.346   50.567  59.535   56.931  57.504  
 63.477  56.206   70.180  55.617   77.049  55.775   84.072  56.804  
 91.135  58.908   97.928  62.282  103.951  66.920  108.729  72.457  
112.110  78.298  114.298  83.936  115.657  89.109  116.533  93.780  
117.168  98.041  117.693 102.018  118.175 105.824  118.651 109.564  
119.126 113.347  ] scurve 
%%% D 
124.115 112.601 moveto 
%%% Y 61  
[ 124.115 112.601  124.834 116.560  125.526 120.799  126.150 125.386  
126.631 130.399  126.894 135.941  126.790 142.162  126.052 149.226  
124.189 157.258  120.383 166.083  113.774 174.692  104.632 181.322  
 94.577 185.157   84.862 186.771   75.834 186.951   67.424 186.183  
 59.472 184.696   51.826 182.547   44.391 179.665   37.184 175.858  
 30.472 170.901   24.816 164.837   20.622 158.239   17.731 151.738  
 15.751 145.600   14.377 139.844   13.414 134.410   12.755 129.223  
 12.326 124.213   12.096 119.308   12.040 114.459   12.156 109.594  
 12.456 104.668   12.961  99.608   13.726  94.355   14.825  88.832  
 16.404  82.968   18.689  76.723   22.036  70.188   26.811  63.776  
 32.973  58.199   39.956  53.878   47.249  50.716   54.654  48.483  
 62.127  47.020   69.713  46.204   77.570  46.017   85.896  46.649  
 94.774  48.557  103.875  52.470  112.015  58.880  117.737  66.969  
120.827  75.111  122.080  82.298  122.400  88.283  122.434  93.255  
122.524  97.567  122.723 101.536  123.007 105.277  123.463 108.893  
124.115 112.601  ] scurve 
%%% D 
127.976 111.687 moveto 
%%% Y 121 
[ 127.976 111.687  128.538 113.646  129.033 115.705  129.500 117.789  
130.011 119.918  130.571 122.171  131.110 124.583  131.589 127.106  
132.058 129.713  132.554 132.472  133.029 135.443  133.442 138.623  
133.809 142.030  134.108 145.740  134.275 149.810  134.250 154.302  
133.917 159.310  133.075 164.915  131.399 171.144  128.413 177.819  
123.688 184.324  117.365 189.694  110.293 193.365  103.302 195.519  
 96.763 196.621   90.735 197.051   85.166 197.047   79.977 196.756  
 75.092 196.258   70.451 195.607   65.993 194.827   61.681 193.934  
 57.467 192.937   53.319 191.822   49.209 190.587   45.098 189.203  
 40.968 187.637   36.793 185.839   32.568 183.724   28.327 181.186  
 24.184 178.088   20.392 174.367   17.247 170.172   14.855 165.834  
 13.097 161.617   11.788 157.630   10.794 153.879   10.024 150.358  
  9.395 147.029    8.891 143.843    8.500 140.810    8.161 137.914  
  7.857 135.091    7.632 132.323    7.478 129.656    7.328 127.074  
  7.176 124.504    7.082 121.927    7.063 119.398    7.053 116.933  
  7.018 114.463    7.010 111.938    7.083 109.395    7.197 106.882  
  7.295 104.358    7.401 101.752    7.582  99.067    7.832  96.355  
  8.098  93.592    8.399  90.708    8.796  87.696    9.293  84.578  
  9.880  81.312   10.615  77.847   11.563  74.176   12.791  70.275  
 14.432  66.133   16.663  61.831   19.641  57.587   23.341  53.746  
 27.494  50.541   31.803  47.963   36.103  45.881   40.340  44.162  
 44.522  42.721   48.660  41.508   52.783  40.493   56.892  39.683  
 60.958  39.050   64.994  38.536   69.039  38.099   73.164  37.721  
 77.439  37.425   81.916  37.247   86.663  37.238   91.747  37.485  
 97.242  38.122  103.194  39.383  109.534  41.627  115.885  45.283  
121.442  50.464  125.483  56.569  127.978  62.750  129.307  68.544  
129.800  73.807  129.683  78.453  129.218  82.436  128.632  85.850  
128.013  88.815  127.422  91.375  126.963  93.597  126.696  95.611  
126.605  97.542  126.616  99.480  126.625 101.424  126.595 103.291  
126.596 105.024  126.712 106.652  126.987 108.248  127.424 109.898  
127.976 111.687  ] scurve 
%%% D 
131.120 110.279 moveto 
%%% Y 181 
[ 131.120 110.279  131.953 111.729  132.437 113.468  132.593 115.045  
132.734 116.382  133.007 117.589  133.469 118.774  134.147 120.072  
134.952 121.682  135.527 123.633  135.759 125.509  135.967 127.147  
136.349 128.679  136.973 130.281  137.772 132.180  138.405 134.445  
138.745 136.688  139.126 138.774  139.744 140.914  140.523 143.399  
141.115 146.226  141.570 149.065  142.189 152.028  142.879 155.436  
143.391 159.213  143.889 163.332  144.285 168.100  144.366 173.603  
143.875 180.116  142.067 187.814  137.666 196.149  130.206 202.903  
121.797 206.535  114.226 207.999  107.702 208.419  102.032 208.348  
 96.956 208.013   92.416 207.528   88.184 207.017   84.248 206.350  
 80.640 205.731   77.084 205.141   73.697 204.372   70.588 203.666  
 67.463 203.085   64.303 202.331   61.398 201.488   58.588 200.822  
 55.610 200.174   52.650 199.283   49.910 198.402   47.121 197.688  
 44.113 196.878   41.169 195.834   38.328 194.857   35.281 193.933  
 32.053 192.756   28.867 191.427   25.486 190.049   21.832 188.309  
 18.052 186.109   14.157 183.171   10.772 179.234    8.489 174.868  
  7.090 170.779    6.142 167.012    5.600 163.597    5.149 160.616  
  4.634 157.750    4.336 154.876    4.281 152.321    4.128 150.086  
  3.776 147.892    3.435 145.509    3.429 143.129    3.565 141.095  
  3.546 139.307    3.306 137.545    2.944 135.593    2.791 133.404  
  2.988 131.375    3.196 129.679    3.221 128.152    3.032 126.618  
  2.694 124.899    2.475 122.879    2.648 120.867    2.947 119.181  
  3.105 117.710    3.057 116.287    2.816 114.760    2.506 112.956  
  2.471 110.895    2.777 109.008    3.070 107.415    3.179 105.948  
  3.079 104.444    2.822 102.731    2.658 100.683    2.878  98.580  
  3.233  96.756    3.437  95.102    3.422  93.419    3.249  91.504  
  3.195  89.243    3.499  86.955    3.861  84.897    4.032  82.886  
  4.023  80.659    4.108  78.059    4.515  75.373    4.949  72.781  
  5.247  70.001    5.662  66.797    6.416  63.362    7.361  59.680  
  8.800  55.499   11.235  51.136   14.719  47.264   18.711  44.335  
 22.674  42.262   26.317  40.667   29.828  39.281   33.192  38.226  
 36.263  37.264   39.316  36.233   42.458  35.403   45.392  34.761  
 48.200  34.002   51.205  33.186   54.361  32.675   57.324  32.421  
 60.075  32.155   62.847  31.796   65.636  31.571   68.238  31.323  
 70.872  30.839   73.792  30.324   76.779  30.003   79.713  29.611  
 82.890  29.090   86.325  28.715   89.836  28.376   93.666  27.980  
 97.866  27.739  102.456  27.591  107.675  27.684  113.679  28.253  
120.713  29.872  128.430  33.739  134.782  40.519  138.104  48.205  
139.379  54.972  139.794  60.674  139.840  65.703  139.609  70.234  
139.183  74.535  138.150  78.623  136.613  81.863  135.279  84.277  
134.343  86.372  133.595  88.481  132.662  90.567  131.564  92.228  
130.666  93.469  130.059  94.511  129.705  95.480  129.565  96.442  
129.617  97.452  129.832  98.595  130.097  99.995  130.100 101.626  
129.758 103.082  129.392 104.216  129.158 105.155  129.077 105.995  
129.146 106.788  129.367 107.564  129.756 108.356  130.336 109.220  
131.120 110.279  ] scurve 
%% / / 
%%% D 
  0.000 230.000 moveto 
%%% K 
%% $ 
  1.000 nbpt mul rm  (Domaine polygonal non convexe) show currentpoint 
clear 
%%% > 
showpage 

% Dessin z5.ds1 

%%% < 1 Largeur= 180.000 Hauteur= 180.000 
%%% ~   0.000 180.000   0.000 180.000 
1.2 dup scale 
1 mm unit  /nbpt 10 def 
  0.000   0.000 translate 
%%% +  90.000  90.000  70.000   0.000   0.000  70.000   0.000   0.000 
%%% L 
  0.452 setlinewidth 
%%% Z 
%%% D 
 39.600  90.000 moveto 
%%% Y 181 
[  39.600  90.000   39.333  88.231   38.544  86.402   37.265  84.457  
 35.550  82.347   33.471  80.032   31.116  77.484   28.584  74.687  
 25.983  71.644   23.426  68.369   21.023  64.895   18.882  61.266  
 17.099  57.542   15.761  53.791   14.937  50.088   14.678  46.513  
 15.017  43.146   15.965  40.063   17.512  37.334   19.629  35.020  
 22.268  33.166   25.366  31.803   28.846  30.944   32.622  30.584  
 36.603  30.697   40.696  31.242   44.808  32.157   48.855  33.369  
 52.760  34.789   56.458  36.322   59.900  37.865   63.052  39.318  
 65.896  40.579   68.432  41.558   70.677  42.174   72.660  42.360  
 74.426  42.067   76.026  41.266   77.521  39.950   78.975  38.133  
 80.452  35.850   82.011  33.157   83.707  30.130   85.585  26.858  
 87.676  23.444   90.000  20.000   92.562  16.641   95.351  13.483  
 98.341  10.637  101.496   8.205  104.763   6.277  108.083   4.926  
111.390   4.208  114.615   4.157  117.688   4.785  120.543   6.083  
123.122   8.020  125.376  10.545  127.268  13.589  128.778  17.070  
129.900  20.891  130.647  24.952  131.047  29.146  131.145  33.369  
131.001  37.521  130.686  41.512  130.282  45.263  129.874  48.709  
129.553  51.804  129.406  54.519  129.514  56.844  129.950  58.787  
130.774  60.376  132.030  61.650  133.744  62.666  135.922  63.487  
138.549  64.186  141.592  64.837  144.995  65.514  148.687  66.289  
152.580  67.223  156.574  68.369  160.560  69.767  164.425  71.444  
168.056  73.409  171.344  75.657  174.187  78.168  176.498  80.909  
178.203  83.832  179.248  86.883  179.600  90.000  179.248  93.117  
178.203  96.168  176.498  99.091  174.187 101.832  171.344 104.343  
168.056 106.591  164.425 108.556  160.560 110.233  156.574 111.631  
152.580 112.777  148.687 113.711  144.995 114.486  141.592 115.163  
138.549 115.814  135.922 116.513  133.744 117.334  132.030 118.350  
130.774 119.624  129.950 121.213  129.514 123.156  129.406 125.481  
129.553 128.196  129.874 131.291  130.282 134.737  130.686 138.488  
131.001 142.479  131.145 146.631  131.047 150.854  130.647 155.048  
129.900 159.109  128.778 162.930  127.268 166.411  125.376 169.455  
123.122 171.980  120.543 173.917  117.688 175.215  114.615 175.843  
111.390 175.792  108.083 175.074  104.763 173.723  101.496 171.795  
 98.341 169.363   95.351 166.517   92.562 163.359   90.000 160.000  
 87.676 156.556   85.585 153.142   83.707 149.870   82.011 146.843  
 80.452 144.150   78.975 141.867   77.521 140.050   76.026 138.734  
 74.426 137.933   72.660 137.640   70.677 137.826   68.432 138.442  
 65.896 139.421   63.052 140.682   59.900 142.135   56.458 143.678  
 52.760 145.211   48.855 146.631   44.808 147.843   40.696 148.758  
 36.603 149.303   32.622 149.416   28.846 149.056   25.366 148.197  
 22.268 146.834   19.629 144.980   17.512 142.666   15.965 139.937  
 15.017 136.854   14.678 133.487   14.937 129.912   15.761 126.209  
 17.099 122.458   18.882 118.734   21.023 115.105   23.426 111.631  
 25.983 108.356   28.584 105.313   31.116 102.516   33.471  99.968  
 35.550  97.653   37.265  95.543   38.544  93.598   39.333  91.769  
 39.600  90.000  ] scurve 
%%% D 
 90.000  90.000 moveto 
%%% L 
  0.113 setlinewidth 
%%% Y 21  
[  90.000  90.000   87.069  89.999   84.139  89.999   81.209  90.000  
 78.281  90.001   75.355  90.002   72.432  90.003   69.518  90.005  
 66.618  90.008   63.740  90.010   60.899  90.013   58.110  90.016  
 55.395  90.018   52.780  90.020   50.294  90.022   47.968  90.023  
 45.828  90.024   43.897  90.023   42.170  90.023   40.547  90.026  
 39.600  90.070  ] scurve 
%%% D 
 90.000  90.000 moveto 
%%% Y 21  
[  90.000  90.000   87.360  88.728   84.719  87.457   82.078  86.186  
 79.437  84.916   76.795  83.648   74.149  82.382   71.497  81.121  
 68.833  79.866   66.149  78.623   63.432  77.398   60.665  76.201  
 57.825  75.049   54.881  73.965   51.796  72.988   48.522  72.177  
 45.016  71.631   41.250  71.501   37.275  72.001   33.361  73.349  
 29.804  76.050  ] scurve 
%%% D 
 90.000  90.000 moveto 
%%% Y 21  
[  90.000  90.000   88.173  87.708   86.345  85.417   84.517  83.126  
 82.688  80.834   80.860  78.543   79.033  76.248   77.210  73.949  
 75.394  71.640   73.592  69.313   71.813  66.960   70.070  64.564  
 68.382  62.110   66.778  59.574   65.297  56.934   63.998  54.167  
 62.958  51.265   62.279  48.245   62.081  45.166   62.551  42.098  
 64.029  39.762  ] scurve 
%%% D 
 90.000  90.000 moveto 
%%% Y 21  
[  90.000  90.000   89.348  87.142   88.696  84.284   88.043  81.426  
 87.389  78.568   86.734  75.711   86.077  72.857   85.418  70.010  
 84.756  67.176   84.088  64.363   83.411  61.583   82.724  58.855  
 82.022  56.200   81.302  53.644   80.563  51.218   79.805  48.955  
 79.033  46.888   78.261  45.050   77.518  43.475   76.885  42.223  
 76.237  41.115  ] scurve 
%%% D 
 90.000  90.000 moveto 
%%% Y 21  
[  90.000  90.000   90.653  87.142   91.305  84.284   91.958  81.425  
 92.610  78.565   93.262  75.702   93.912  72.835   94.561  69.961  
 95.207  67.072   95.848  64.161   96.480  61.211   97.098  58.205  
 97.693  55.112   98.252  51.894   98.750  48.492   99.146  44.827  
 99.359  40.782   99.228  36.191   98.397  30.849   96.092  24.679  
 90.706  19.029  ] scurve 
%%% D 
 90.000  90.000 moveto 
%%% Y 21  
[  90.000  90.000   91.828  87.709   93.657  85.417   95.486  83.124  
 97.316  80.832   99.147  78.540  100.981  76.250  102.819  73.966  
104.667  71.692  106.528  69.436  108.412  67.208  110.327  65.025  
112.287  62.908  114.303  60.887  116.388  58.998  118.547  57.290  
120.775  55.817  123.048  54.636  125.306  53.784  127.406  53.217  
129.471  52.902  ] scurve 
%%% D 
 90.000  90.000 moveto 
%%% Y 21  
[  90.000  90.000   92.641  88.729   95.284  87.458   97.926  86.187  
100.569  84.915  103.211  83.643  105.851  82.369  108.484  81.092  
111.106  79.810  113.708  78.517  116.279  77.210  118.800  75.882  
121.251  74.524  123.604  73.130  125.825  71.694  127.875  70.216  
129.713  68.700  131.298  67.160  132.592  65.602  133.528  63.955  
133.605  62.600  ] scurve 
%%% D 
 90.000  90.000 moveto 
%%% Y 21  
[  90.000  90.000   92.931  90.001   95.863  90.003   98.795  90.004  
101.729  90.007  104.664  90.010  107.603  90.013  110.550  90.017  
113.510  90.021  116.495  90.026  119.517  90.031  122.599  90.038  
125.769  90.046  129.073  90.056  132.573  90.069  136.368  90.086  
140.612  90.111  145.580  90.150  151.817  90.217  160.723  90.364  
179.522  91.468  ] scurve 
%%% D 
 90.000  90.000 moveto 
%%% Y 21  
[  90.000  90.000   92.640  91.273   95.281  92.546   97.921  93.820  
100.561  95.095  103.199  96.371  105.834  97.650  108.462  98.931  
111.079 100.219  113.674 101.517  116.237 102.829  118.751 104.163  
121.193 105.524  123.537 106.920  125.748 108.356  127.788 109.831  
129.616 111.340  131.194 112.870  132.482 114.415  133.409 116.043  
133.522 117.440  ] scurve 
%%% D 
 90.000  90.000 moveto 
%%% Y 21  
[  90.000  90.000   91.827  92.292   93.653  94.585   95.478  96.878  
 97.304  99.171   99.129 101.463  100.957 103.753  102.789 106.037  
104.629 108.311  106.482 110.568  108.357 112.797  110.264 114.982  
112.215 117.101  114.224 119.127  116.303 121.021  118.458 122.736  
120.685 124.218  122.960 125.409  125.225 126.270  127.334 126.841  
129.474 127.145  ] scurve 
%%% D 
 90.000  90.000 moveto 
%%% Y 21  
[  90.000  90.000   90.651  92.858   91.302  95.715   91.951  98.572  
 92.600 101.430   93.249 104.289   93.895 107.152   94.539 110.021  
 95.180 112.904   95.814 115.809   96.439 118.751   97.047 121.748  
 97.631 124.830   98.176 128.037   98.657 131.423   99.029 135.068  
 99.211 139.084   99.036 143.630   98.143 148.895   95.770 154.911  
 90.381 160.528  ] scurve 
%%% D 
 90.000  90.000 moveto 
%%% Y 21  
[  90.000  90.000   89.347  92.857   88.693  95.713   88.040  98.569  
 87.386 101.424   86.731 104.276   86.075 107.125   85.417 109.966  
 84.756 112.793   84.090 115.598   83.417 118.368   82.733 121.085  
 82.035 123.729   81.321 126.273   80.589 128.688   79.839 130.939  
 79.078 132.996   78.317 134.827   77.587 136.397   76.966 137.645  
 76.229 138.879  ] scurve 
%%% D 
 90.000  90.000 moveto 
%%% Y 21  
[  90.000  90.000   88.172  92.291   86.344  94.581   84.517  96.871  
 82.691  99.160   80.865 101.450   79.042 103.742   77.224 106.039  
 75.415 108.346   73.620 110.670   71.849 113.021   70.116 115.413  
 68.440 117.864   66.848 120.395   65.382 123.029   64.098 125.786  
 63.073 128.674   62.405 131.675   62.214 134.727   62.685 137.755  
 64.209 140.157  ] scurve 
%%% D 
 90.000  90.000 moveto 
%%% Y 21  
[  90.000  90.000   87.359  91.271   84.719  92.542   82.080  93.812  
 79.440  95.083   76.800  96.352   74.158  97.620   71.510  98.884  
 68.850 100.142   66.170 101.389   63.458 102.620   60.696 103.823  
 57.861 104.984   54.921 106.078   51.838 107.068   48.564 107.894  
 45.052 108.460   41.272 108.612   37.268 108.131   33.314 106.781  
 29.729 104.034  ] scurve 
%%% D 
 99.271  90.005 moveto 
%%% Y 61  
[  99.271  90.005   99.220  90.974   99.067  91.933   98.815  92.870  
 98.466  93.776   98.025  94.640   97.496  95.453   96.884  96.206  
 96.198  96.892   95.443  97.502   94.629  98.029   93.764  98.469  
 92.859  98.816   91.921  99.066   90.963  99.217   89.995  99.267  
 89.026  99.215   88.069  99.062   87.133  98.811   86.228  98.463  
 85.364  98.022   84.551  97.494   83.798  96.884   83.113  96.198  
 82.503  95.444   81.975  94.631   81.535  93.767   81.188  92.862  
 80.937  91.925   80.785  90.968   80.734  90.000   80.785  89.032  
 80.936  88.074   81.186  87.137   81.534  86.231   81.973  85.367  
 82.501  84.553   83.112  83.799   83.797  83.112   84.551  82.502  
 85.365  81.973   86.229  81.532   87.135  81.184   88.072  80.932  
 89.031  80.780   90.000  80.729   90.969  80.779   91.928  80.931  
 92.866  81.182   93.773  81.530   94.638  81.971   95.452  82.500  
 96.206  83.111   96.892  83.798   97.503  84.553   98.031  85.367  
 98.472  86.232   98.819  87.139   99.070  88.076   99.221  89.035  
 99.271  90.005  ] scurve 
%%% D 
112.756  90.020 moveto 
%%% Y 61  
[ 112.756  90.020  112.621  92.418  112.225  94.781  111.581  97.077  
110.706  99.281  109.616 101.375  108.325 103.344  106.845 105.174  
105.186 106.852  103.356 108.358  101.368 109.672   99.242 110.770  
 97.002 111.631   94.683 112.241   92.317 112.594   89.939 112.691  
 87.576 112.540   85.252 112.151   82.985 111.534   80.791 110.695  
 78.685 109.639   76.689 108.368   74.827 106.888   73.126 105.210  
 71.614 103.352   70.315 101.339   69.246  99.202   68.415  96.973  
 67.824  94.682   67.471  92.353   67.353  90.007   67.467  87.661  
 67.816  85.331   68.403  83.038   69.231  80.806   70.297  78.666  
 71.595  76.648   73.106  74.785   74.808  73.101   76.672  71.616  
 78.671  70.341   80.780  69.281   82.980  68.439   85.253  67.820  
 87.583  67.430   89.952  67.280   92.337  67.379   94.708  67.736  
 97.032  68.351   99.275  69.218  101.403  70.322  103.392  71.642  
105.221  73.155  106.880  74.839  108.357  76.675  109.644  78.649  
110.731  80.748  111.601  82.956  112.239  85.255  112.628  87.620  
112.756  90.020  ] scurve 
%%% D 
121.012  90.034 moveto 
%%% Y 61  
[ 121.012  90.034  120.787  93.398  120.149  96.666  119.158  99.769  
117.881 102.680  116.372 105.405  114.661 107.964  112.747 110.376  
110.613 112.645  108.230 114.749  105.577 116.638  102.662 118.238  
 99.531 119.475   96.268 120.296   92.970 120.697   89.720 120.713  
 86.563 120.398   83.512 119.807   80.557 118.972   77.679 117.901  
 74.868 116.578   72.136 114.969   69.523 113.039   67.101 110.771  
 64.956 108.186   63.162 105.346   61.755 102.341   60.729  99.260  
 60.045  96.164   59.657  93.082   59.530  90.014   59.651  86.946  
 60.032  83.863   60.710  80.766   61.729  77.680   63.128  74.670  
 64.917  71.821   67.059  69.226   69.481  66.947   72.096  65.006  
 74.834  63.387   77.653  62.056   80.540  60.978   83.507  60.139  
 86.570  59.545   89.740  59.231   93.003  59.251   96.312  59.660  
 99.584  60.492  102.720  61.741  105.637  63.353  108.289  65.253  
110.670  67.366  112.802  69.644  114.712  72.064  116.421  74.631  
117.924  77.364  119.194  80.285  120.176  83.396  120.801  86.668  
121.012  90.034  ] scurve 
%%% D 
127.895  90.052 moveto 
%%% Y 61  
[ 127.895  90.052  127.511  94.407  126.477  98.502  124.994 102.208  
123.253 105.534  121.375 108.568  119.397 111.417  117.289 114.174  
114.973 116.892  112.333 119.566  109.250 122.108  105.660 124.334  
101.631 126.014   97.380 126.989   93.176 127.268   89.203 127.002  
 85.511 126.375   82.053 125.528   78.741 124.529   75.478 123.379  
 72.188 122.022   68.840 120.346   65.479 118.214   62.257 115.507  
 59.410 112.213   57.160 108.487   55.582 104.585   54.595 100.729  
 54.039  97.027   53.767  93.478   53.685  90.020   53.761  86.562  
 54.026  83.014   54.573  79.312   55.548  75.455   57.111  71.546  
 59.349  67.807   62.188  64.495   65.410  61.768   68.777  59.618  
 72.135  57.928   75.436  56.559   78.711  55.400   82.039  54.392  
 85.514  53.539   89.227  52.911   93.223  52.650   97.448  52.943  
101.713  53.939  105.747  55.641  109.334  57.886  112.411  60.441  
115.046  63.125  117.358  65.851  119.464  68.615  121.440  71.474  
123.316  74.519  125.051  77.860  126.523  81.583  127.537  85.692  
127.895  90.052  ] scurve 
%%% D 
134.393  90.077 moveto 
%%% Y 61  
[ 134.393  90.077  133.691  95.681  131.944 100.624  129.720 104.731  
127.418 108.176  125.204 111.223  123.090 114.107  120.994 117.007  
118.768 120.055  116.182 123.308  112.933 126.682  108.738 129.843  
103.605 132.189   98.071 133.244   92.846 133.107   88.266 132.263  
 84.287 131.141   80.713 129.979   77.326 128.860   73.931 127.763  
 70.360 126.590   66.487 125.143   62.294 123.116   58.003 120.134  
 54.178 116.013   51.443 111.100   49.935 106.097   49.305 101.482  
 49.129  97.350   49.119  93.590   49.129  90.023   49.116  86.457  
 49.120  82.701   49.286  78.576   49.899  73.966   51.381  68.960  
 54.088  64.028   57.899  59.873   62.195  56.857   66.402  54.806  
 70.290  53.344   73.874  52.159   77.283  51.051   80.685  49.919  
 84.281  48.744   88.289  47.614   92.907  46.772   98.171  46.657  
103.726  47.750  108.859  50.136  113.041  53.323  116.274  56.712  
118.850  59.970  121.071  63.021  123.165  65.926  125.283  68.817  
127.501  71.878  129.805  75.345  132.020  79.483  133.739  84.458  
134.393  90.077  ] scurve 
%%% D 
141.184  90.115 moveto 
%%% Y 61  
[ 141.184  90.115  139.787  97.536  136.754 103.303  133.495 107.477  
130.580 110.706  128.096 113.494  125.970 116.201  124.051 119.064  
122.156 122.297  119.964 126.079  116.956 130.477  112.335 135.120  
105.651 138.647   98.184 139.594   91.787 138.492   86.826 136.691  
 82.862 134.923   79.448 133.425   76.222 132.237   72.917 131.291  
 69.276 130.484   65.031 129.568   59.960 128.086   54.148 125.180  
 48.712 119.982   45.453 113.205   44.486 106.780   44.645 101.497  
 45.088  97.175   45.449  93.460   45.576  90.024   45.450  86.589  
 45.087  82.882   44.638  78.573   44.461  73.309   45.384  66.898  
 48.582  60.095   53.993  54.828   59.826  51.868   64.927  50.361  
 69.194  49.433   72.850  48.618   76.166  47.660   79.404  46.456  
 82.838  44.936   86.837  43.145   91.857  41.332   98.327  40.259  
105.834  41.283  112.499  44.880  117.082  49.553  120.062  53.958  
122.239  57.738  124.127  60.967  126.049  63.828  128.184  66.538  
130.682  69.338  133.613  72.594  136.879  76.818  139.879  82.655  
141.184  90.115  ] scurve 
%%% D 
149.157  90.185 moveto 
%%% Y 121 
[ 149.157  90.185  148.226  95.845  146.042 100.543  143.403 104.094  
140.803 106.752  138.414 108.801  136.304 110.435  134.479 111.843  
132.859 113.125  131.421 114.293  130.197 115.411  129.149 116.575  
128.197 117.817  127.313 119.109  126.531 120.471  125.846 121.989  
125.175 123.727  124.450 125.676  123.666 127.863  122.744 130.396  
121.501 133.322  119.727 136.635  117.086 140.244  113.190 143.728  
108.018 146.242  102.361 147.076   97.248 146.436   93.083 145.027  
 89.771 143.387   87.094 141.761   84.892 140.269   82.991 138.975  
 81.271 137.836   79.714 136.832   78.272 136.012   76.843 135.374  
 75.369 134.850   73.869 134.403   72.337 134.074   70.690 133.883  
 68.842 133.776   66.779 133.681   64.478 133.603   61.816 133.506  
 58.688 133.237   55.033 132.598   50.827 131.255   46.321 128.709  
 42.287 124.645   39.675 119.552   38.651 114.482   38.674 110.070  
 39.194 106.398   39.904 103.338   40.635 100.776   41.272  98.562  
 41.820  96.569   42.291  94.774   42.622  93.147   42.786  91.588  
 42.827  90.023   42.787  88.458   42.627  86.900   42.299  85.277  
 41.830  83.489   41.282  81.504   40.645  79.299   39.913  76.752  
 39.196  73.713   38.660  70.068   38.601  65.685   39.559  60.632  
 42.087  55.508   46.073  51.360   50.590  48.733   54.833  47.340  
 58.524  46.678   61.682  46.399   64.366  46.300   66.681  46.222  
 68.754  46.126   70.612  46.017   72.265  45.826   73.799  45.495  
 75.300  45.042   76.776  44.508   78.210  43.858   79.658  43.024  
 81.222  42.005   82.952  40.845   84.872  39.524   87.108  38.007  
 89.833  36.361   93.209  34.714   97.453  33.329  102.634  32.759  
108.308  33.692  113.447  36.283  117.294  39.807  119.893  43.431  
121.635  46.746  122.853  49.669  123.759  52.194  124.533  54.374  
125.251  56.317  125.918  58.049  126.602  59.561  127.385  60.918  
128.273  62.206  129.231  63.445  130.288  64.607  131.524  65.727  
132.974  66.901  134.609  68.191  136.455  69.611  138.588  71.273  
140.995  73.363  143.604  76.078  146.225  79.709  148.343  84.488  
149.157  90.185  ] scurve 
%%% D 
160.427  90.358 moveto 
%%% Y 181 
[ 160.427  90.358  158.855  97.251  155.605 102.341  152.142 105.735  
148.917 108.106  146.082 109.662  143.795 110.905  141.672 112.076  
139.624 112.872  138.010 113.388  136.762 113.967  135.651 114.707  
134.452 115.503  133.229 116.060  132.275 116.457  131.572 116.905  
131.032 117.480  130.563 118.228  130.006 119.126  129.329 119.936  
128.765 120.617  128.389 121.314  128.184 122.128  128.103 123.170  
127.944 124.517  127.554 125.905  127.199 127.197  127.042 128.581  
127.048 130.310  126.896 132.536  126.421 134.930  125.937 137.530  
125.283 140.773  123.942 144.622  121.648 149.021  117.571 153.665  
111.252 157.048  104.208 157.581   98.435 156.009   94.201 153.773  
 90.986 151.453   88.659 149.267   86.776 147.503   85.005 145.860  
 83.616 144.168   82.626 142.803   81.688 141.802   80.640 140.980  
 79.508 140.093   78.593 139.103   77.917 138.315   77.273 137.782  
 76.559 137.443   75.705 137.226   74.680 136.975   73.695 136.579  
 72.871 136.246   72.092 136.092   71.260 136.136   70.257 136.369  
 68.944 136.637   67.499 136.697   66.157 136.740   64.805 136.987  
 63.206 137.499   61.094 138.059   58.678 138.353   56.098 138.664  
 52.912 139.055   48.910 139.031   44.109 138.304   38.458 136.059  
 33.138 131.277   30.257 124.737   29.881 118.680   30.673 113.902  
 31.882 110.093   33.238 107.185   34.329 104.832   35.347 102.626  
 36.528 100.781   37.515  99.413   38.172  98.206   38.628  96.948  
 39.122  95.593   39.780  94.414   40.319  93.525   40.625  92.746  
 40.727  91.960   40.669  91.079   40.591  90.025   40.663  88.965  
 40.726  88.077   40.633  87.289   40.336  86.512   39.807  85.633  
 39.147  84.471   38.642  83.117   38.189  81.856   37.542  80.651  
 36.569  79.298   35.388  77.477   34.366  75.284   33.285  72.950  
 31.935  70.088   30.709  66.336   29.877  61.641   30.125  55.676  
 32.773  49.111   37.954  44.108   43.659  41.665   48.561  40.856  
 52.637  40.793   55.897  41.181   58.511  41.512   60.939  41.804  
 63.084  42.356   64.709  42.884   66.068  43.149   67.406  43.200  
 68.847  43.252   70.176  43.512   71.191  43.751   72.027  43.803  
 72.803  43.657   73.619  43.327   74.590  42.922   75.617  42.653  
 76.478  42.428   77.193  42.083   77.837  41.540   78.515  40.739  
 79.438  39.740   80.565  38.846   81.602  38.002   82.536  36.958  
 83.557  35.533   85.011  33.826   86.793  32.183   88.700  30.352  
 91.146  28.113   94.471  25.817   98.848  23.618  104.753  22.208  
111.779  22.971  117.959  26.464  121.936  31.123  124.170  35.521  
125.461  39.366  126.079  42.590  126.546  45.179  127.000  47.573  
127.126  49.782  127.113  51.490  127.271  52.863  127.626  54.151  
128.011  55.538  128.163  56.876  128.243  57.910  128.449  58.717  
128.827  59.408  129.392  60.084  130.073  60.888  130.636  61.781  
131.111  62.525  131.659  63.096  132.374  63.539  133.346  63.937  
134.580  64.508  135.776  65.306  136.899  66.033  138.178  66.601  
139.845  67.131  141.921  67.982  144.043  69.173  146.380  70.429  
149.276  72.073  152.508  74.548  155.968  78.084  159.111  83.360  
160.427  90.358  ] scurve 
%% / / 
%%% D 
 20.000   7.000 moveto 
%%% K 
%% $ 
  1.000 nbpt mul rm  (Courbe d'‚quation polaire) show currentpoint 
clear 
%%% D 
 20.000   0.000 moveto 
%%% K 
%% $ 
  1.000 nbpt mul it  (r ) show currentpoint 
%% $ 
  1.000 nbpt mul rm  (= 1 + 0.28 cos 5) show currentpoint   
%% $ 
  1.000 nbpt mul symb  (q) show currentpoint 
clear
%%% D 
140.000   0.000 moveto 
%%% K 
%% $ 
  1.000 nbpt mul rm  (Centre \(0,0\)) show currentpoint 
clear 
%%% > 
showpage 

% Dessin z6.ds1 

%%% < 1 Largeur= 180.000 Hauteur= 180.000 
%%% ~   0.000 180.000 -30.000 210.000 
1.2 dup scale 
1 mm unit  /nbpt 10 def 
  0.000   0.000 translate 
%%% +  20.000  90.000  80.000   0.000   0.000  80.000
%%% L 
  0.452 setlinewidth 
%%% Z 
%%% D 
 20.000  90.000 moveto 
%%% Y 181 
[  20.000  90.000   19.951  89.998   19.806  89.986   19.564  89.954  
 19.229  89.892   18.803  89.789   18.290  89.637   17.694  89.425  
 17.021  89.146   16.276  88.790   15.466  88.350   14.599  87.818  
 13.682  87.187   12.723  86.451   11.732  85.604   10.718  84.641  
  9.691  83.558    8.661  82.352    7.639  81.019    6.636  79.559  
  5.662  77.969    4.730  76.250    3.849  74.403    3.031  72.428  
  2.288  70.329    1.631  68.109    1.070  65.771    0.617  63.321  
  0.280  60.764    0.072  58.108    0.000  55.359    0.075  52.526  
  0.304  49.617    0.696  46.642    1.258  43.612    1.997  40.536  
  2.918  37.427    4.027  34.296    5.328  31.155    6.825  28.018  
  8.520  24.896   10.416  21.804   12.512  18.755   14.809  15.762  
 17.305  12.839   20.000  10.000   22.889   7.258   25.970   4.628  
 29.236   2.122   32.683  -0.247   36.304  -2.465   40.091  -4.521  
 44.036  -6.403   48.129  -8.098   52.361  -9.596   56.720 -10.887  
 61.195 -11.961   65.774 -12.809   70.443 -13.424   75.190 -13.797  
 80.000 -13.923   84.859 -13.796   89.751 -13.410   94.662 -12.764  
 99.576 -11.853  104.477 -10.676  109.349  -9.232  114.177  -7.523  
118.943  -5.548  123.633  -3.311  128.229  -0.815  132.718   1.935  
137.082   4.935  141.307   8.177  145.379  11.655  149.282  15.359  
153.004  19.281  156.530  23.410  159.849  27.735  162.948  32.245  
165.817  36.927  168.445  41.767  170.823  46.752  172.942  51.867  
174.794  57.098  176.372  62.427  177.672  67.841  178.688  73.321  
179.416  78.853  179.854  84.418  180.000  90.000  179.854  95.582  
179.416 101.147  178.688 106.679  177.672 112.159  176.372 117.573  
174.794 122.902  172.942 128.133  170.823 133.248  168.445 138.233  
165.817 143.073  162.948 147.755  159.849 152.265  156.530 156.590  
153.004 160.719  149.282 164.641  145.379 168.345  141.307 171.823  
137.082 175.065  132.718 178.065  128.229 180.815  123.633 183.311  
118.943 185.548  114.177 187.523  109.349 189.232  104.477 190.676  
 99.576 191.853   94.662 192.764   89.751 193.410   84.859 193.796  
 80.000 193.923   75.190 193.797   70.443 193.424   65.774 192.809  
 61.195 191.961   56.720 190.887   52.361 189.596   48.129 188.098  
 44.036 186.403   40.091 184.521   36.304 182.465   32.683 180.247  
 29.236 177.878   25.970 175.372   22.889 172.742   20.000 170.000  
 17.305 167.161   14.809 164.238   12.512 161.245   10.416 158.196  
  8.520 155.104    6.825 151.982    5.328 148.845    4.027 145.704  
  2.918 142.573    1.997 139.464    1.258 136.388    0.696 133.358  
  0.304 130.383    0.075 127.474    0.000 124.641    0.072 121.892  
  0.280 119.236    0.617 116.679    1.070 114.229    1.631 111.891  
  2.288 109.671    3.031 107.572    3.849 105.597    4.730 103.750  
  5.662 102.031    6.636 100.441    7.639  98.981    8.661  97.648  
  9.691  96.442   10.718  95.359   11.732  94.396   12.723  93.549  
 13.682  92.813   14.599  92.182   15.466  91.650   16.276  91.210  
 17.021  90.854   17.694  90.575   18.290  90.363   18.803  90.211  
 19.229  90.108   19.564  90.046   19.806  90.014   19.951  90.002  
 20.000  90.000  ] scurve 
%%% D 
 90.000  90.000 moveto 
%%% L 
  0.113 setlinewidth 
%%% Y 21  
[  90.000  90.000   85.265  89.999   80.547  89.999   75.855  89.998  
 71.200  89.998   66.595  89.997   62.054  89.997   57.594  89.996  
 53.233  89.996   48.991  89.996   44.892  89.995   40.964  89.995  
 37.236  89.995   33.744  89.995   30.526  89.995   27.628  89.995  
 25.100  89.996   23.002  89.996   21.398  89.997   20.369  89.998  
 20.000  90.000  ] scurve 
%%% D 
 90.000  90.000 moveto 
%%% Y 21  
[  90.000  90.000   85.550  88.382   81.110  86.777   76.684  85.192  
 72.276  83.639   67.892  82.129   63.535  80.674   59.211  79.290  
 54.922  77.994   50.674  76.805   46.469  75.745   42.310  74.837  
 38.200  74.112   34.138  73.599   30.124  73.335   26.155  73.358  
 22.225  73.715   18.325  74.454   14.442  75.632   10.557  77.311  
  6.603  79.507  ] scurve 
%%% D 
 90.000  90.000 moveto 
%%% Y 21  
[  90.000  90.000   86.370  86.958   82.736  83.930   79.093  80.925  
 75.434  77.949   71.751  75.012   68.034  72.119   64.272  69.281  
 60.452  66.503   56.558  63.794   52.574  61.160   48.480  58.605  
 44.255  56.136   39.875  53.755   35.313  51.461   30.541  49.255  
 25.527  47.132   20.239  45.084   14.640  43.099    8.689  41.167  
  2.251  39.615  ] scurve 
%%% D 
 90.000  90.000 moveto 
%%% Y 21  
[  90.000  90.000   87.627  85.898   85.243  81.802   82.837  77.711  
 80.401  73.622   77.926  69.530   75.401  65.432   72.818  61.320  
 70.167  57.187   67.438  53.024   64.625  48.819   61.718  44.560  
 58.711  40.233   55.598  35.822   52.376  31.312   49.041  26.682  
 45.594  21.916   42.035  16.991   38.368  11.888   34.574   6.583  
 30.217   1.421  ] scurve 
%%% D 
 90.000  90.000 moveto 
%%% Y 21  
[  90.000  90.000   89.173  85.332   88.336  80.660   87.485  75.975  
 86.620  71.268   85.738  66.532   84.840  61.756   83.928  56.933  
 83.005  52.052   82.073  47.105   81.138  42.084   80.206  36.979  
 79.283  31.784   78.378  26.491   77.499  21.094   76.657  15.589  
 75.861   9.970   75.122   4.234   74.451  -1.620   73.796  -7.611  
 72.465 -13.614  ] scurve 
%%% D 
 90.000  90.000 moveto 
%%% Y 21  
[  90.000  90.000   90.821  85.330   91.639  80.651   92.460  75.957  
 93.289  71.242   94.133  66.502   94.997  61.735   95.890  56.937  
 96.818  52.106   97.787  47.242   98.805  42.344   99.879  37.414  
101.015  32.452  102.219  27.462  103.499  22.447  104.858  17.408  
106.302  12.352  107.836   7.281  109.466   2.195  111.210  -3.022  
112.521  -8.141  ] scurve 
%%% D 
 90.000  90.000 moveto 
%%% Y 21  
[  90.000  90.000   92.370  85.892   94.744  81.779   97.129  77.661  
 99.532  73.539  101.960  69.418  104.417  65.298  106.908  61.185  
109.438  57.081  112.010  52.991  114.626  48.917  117.290  44.866  
120.003  40.839  122.765  36.843  125.579  32.880  128.444  28.955  
131.359  25.071  134.324  21.232  137.323  17.444  140.206  13.753  
143.146   9.703  ] scurve 
%%% D 
 90.000  90.000 moveto 
%%% Y 21  
[  90.000  90.000   93.632  86.951   97.270  83.902  100.915  80.859  
104.569  77.828  108.234  74.814  111.911  71.823  115.601  68.860  
119.302  65.929  123.014  63.034  126.737  60.178  130.470  57.365  
134.211  54.598  137.959  51.878  141.713  49.209  145.471  46.591  
149.232  44.026  152.994  41.513  156.766  39.032  160.610  36.383  
163.520  33.135  ] scurve 
%%% D 
 90.000  90.000 moveto 
%%% Y 21  
[  90.000  90.000   94.456  88.378   98.914  86.758  103.370  85.145  
107.820  83.545  112.262  81.961  116.691  80.396  121.106  78.855  
125.502  77.339  129.878  75.851  134.232  74.392  138.561  72.963  
142.864  71.566  147.138  70.202  151.382  68.871  155.594  67.573  
159.775  66.309  163.925  65.078  168.073  63.872  172.446  62.618  
176.113  61.475  ] scurve 
%%% D 
 90.000  90.000 moveto 
%%% Y 21  
[  90.000  90.000   94.742  90.001   99.484  90.001  104.219  90.002  
108.942  90.002  113.646  90.003  118.328  90.003  122.983  90.004  
127.609  90.004  132.201  90.005  136.758  90.005  141.277  90.006  
145.756  90.006  150.193  90.007  154.587  90.007  158.938  90.007  
163.244  90.008  167.508  90.008  171.764  90.009  176.255  90.011  
180.000  90.025  ] scurve 
%%% D 
 90.000  90.000 moveto 
%%% Y 21  
[  90.000  90.000   94.456  91.623   98.913  93.244  103.369  94.858  
107.819  96.459  112.260  98.045  116.689  99.610  121.103 101.152  
125.499 102.669  129.875 104.158  134.229 105.618  138.558 107.048  
142.860 108.446  147.134 109.811  151.377 111.143  155.590 112.441  
159.770 113.706  163.920 114.938  168.068 116.146  172.440 117.403  
176.099 118.573  ] scurve 
%%% D 
 90.000  90.000 moveto 
%%% Y 21  
[  90.000  90.000   93.632  93.050   97.268  96.100  100.912  99.144  
104.566 102.176  108.231 105.190  111.907 108.182  115.596 111.146  
119.296 114.078  123.008 116.974  126.731 119.830  130.463 122.644  
134.204 125.413  137.951 128.133  141.705 130.804  145.463 133.422  
149.223 135.988  152.985 138.501  156.756 140.983  160.597 143.634  
163.506 146.886  ] scurve 
%%% D 
 90.000  90.000 moveto 
%%% Y 21  
[  90.000  90.000   92.369  94.108   94.742  98.222   97.126 102.341  
 99.528 106.463  101.955 110.585  104.411 114.705  106.901 118.819  
109.430 122.924  112.001 127.015  114.617 131.089  117.280 135.141  
119.991 139.168  122.753 143.166  125.566 147.130  128.430 151.056  
131.345 154.940  134.309 158.780  137.308 162.568  140.191 166.259  
143.135 170.307  ] scurve 
%%% D 
 90.000  90.000 moveto 
%%% Y 21  
[  90.000  90.000   90.820  94.670   91.637  99.350   92.457 104.044  
 93.285 108.759   94.127 113.499   94.991 118.266   95.882 123.065  
 96.808 127.896   97.777 132.761   98.793 137.659   99.866 142.589  
101.001 147.551  102.204 152.542  103.482 157.558  104.840 162.597  
106.283 167.654  107.816 172.726  109.445 177.813  111.186 183.031  
112.477 188.157  ] scurve 
%%% D 
 90.000  90.000 moveto 
%%% Y 21  
[  90.000  90.000   89.172  94.667   88.334  99.340   87.482 104.025  
 86.615 108.731   85.732 113.467   84.833 118.243   83.920 123.066  
 82.995 127.946   82.062 132.893   81.126 137.914   80.192 143.019  
 79.268 148.214   78.361 153.507   77.481 158.903   76.637 164.409  
 75.839 170.028   75.099 175.764   74.426 181.618   73.769 187.608  
 72.439 193.611  ] scurve 
%%% D 
 90.000  90.000 moveto 
%%% Y 21  
[  90.000  90.000   87.626  94.101   85.241  98.196   82.834 102.287  
 80.397 106.376   77.921 110.467   75.395 114.564   72.811 118.675  
 70.159 122.807   67.429 126.970   64.614 131.175   61.706 135.433  
 58.698 139.759   55.584 144.168   52.360 148.678   49.024 153.306  
 45.575 158.071   42.014 162.995   38.344 168.097   34.549 173.401  
 30.188 178.559  ] scurve 
%%% D 
 90.000  90.000 moveto 
%%% Y 21  
[  90.000  90.000   86.369  93.041   82.734  96.068   79.091  99.073  
 75.431 102.047   71.748 104.984   68.030 107.875   64.267 110.713  
 60.446 113.489   56.552 116.198   52.568 118.831   48.473 121.384  
 44.248 123.851   39.867 126.231   35.305 128.523   30.533 130.727  
 25.519 132.848   20.230 134.894   14.630 136.876    8.679 138.804  
  2.242 140.354  ] scurve 
%%% D 
 90.000  90.000 moveto 
%%% Y 21  
[  90.000  90.000   85.550  91.617   81.109  93.221   76.683  94.805  
 72.275  96.357   67.890  97.866   63.533  99.319   59.208 100.702  
 54.920 101.998   50.671 103.186   46.467 104.245   42.308 105.152  
 38.198 105.876   34.137 106.388   30.124 106.652   26.156 106.627  
 22.228 106.270   18.330 105.530   14.449 104.350   10.568 102.670  
  6.614 100.475  ] scurve 
%%% D 
104.987  90.002 moveto 
%%% Y 61  
[ 104.987  90.002  104.905  91.565  104.662  93.111  104.260  94.624  
103.703  96.089  102.996  97.489  102.146  98.808  101.162 100.034  
100.054 101.151   98.834 102.147   97.514 103.010   96.110 103.730  
 94.635 104.298   93.108 104.708   91.545 104.953   89.965 105.031  
 88.386 104.940   86.826 104.683   85.303 104.261   83.836 103.681  
 82.441 102.951   81.133 102.079   79.927 101.076   78.835  99.955  
 77.868  98.729   77.035  97.413   76.345  96.021   75.802  94.569  
 75.411  93.071   75.175  91.542   75.097  89.998   75.176  88.455  
 75.412  86.926   75.803  85.428   76.346  83.975   77.037  82.584  
 77.870  81.268   78.837  80.042   79.929  78.922   81.136  77.919  
 82.444  77.047   83.839  76.317   85.307  75.738   86.829  75.317  
 88.389  75.059   89.969  74.969   91.549  75.048   93.112  75.293  
 94.639  75.703   96.113  76.271   97.517  76.992   98.837  77.855  
100.057  78.852  101.165  79.969  102.148  81.194  102.998  82.514  
103.704  83.914  104.261  85.379  104.663  86.893  104.906  88.439  
104.987  90.002  ] scurve 
%%% D 
126.437  90.004 moveto 
%%% Y 61  
[ 126.437  90.004  126.251  93.744  125.695  97.452  124.773 101.093  
123.488 104.635  121.848 108.044  119.864 111.285  117.547 114.325  
114.914 117.128  111.985 119.658  108.784 121.882  105.341 123.766  
101.690 125.278   97.872 126.389   93.931 127.074   89.920 127.316  
 85.894 127.100   81.913 126.424   78.036 125.295   74.326 123.729  
 70.839 121.755   67.628 119.412   64.735 116.748   62.190 113.817  
 60.013 110.676   58.209 107.381   56.769 103.981   55.680 100.519  
 54.922  97.023   54.477  93.512   54.330  89.996   54.477  86.480  
 54.924  82.969   55.682  79.473   56.772  76.011   58.212  72.612  
 60.018  69.317   62.196  66.176   64.741  63.246   67.635  60.582  
 70.847  58.240   74.334  56.267   78.045  54.702   81.922  53.574  
 85.904  52.899   89.930  52.685   93.940  52.927   97.880  53.613  
101.698  54.725  105.349  56.238  108.791  58.123  111.991  60.347  
114.920  62.879  117.552  65.682  119.868  68.722  121.852  71.964  
123.491  75.373  124.775  78.915  125.697  82.557  126.252  86.264  
126.437  90.004  ] scurve 
%%% D 
138.968  90.006 moveto 
%%% Y 61  
[ 138.968  90.006  138.731  94.963  138.022  99.883  136.842 104.728  
135.194 109.460  133.083 114.037  130.514 118.419  127.496 122.560  
124.044 126.416  120.174 129.936  115.910 133.070  111.283 135.766  
106.331 137.972  101.103 139.636   95.660 140.709   90.072 141.150  
 84.423 140.925   78.807 140.014   73.328 138.415   68.092 136.144  
 63.207 133.245   58.772 129.786   54.869 125.858   51.553 121.574  
 48.850 117.054   46.746 112.419   45.195 107.773   44.121 103.191  
 43.439  98.710   43.068  94.324   42.952  89.995   43.069  85.666  
 43.440  81.280   44.123  76.798   45.198  72.216   46.751  67.570  
 48.856  62.936   51.560  58.416   54.877  54.132   58.782  50.206  
 63.218  46.748   68.104  43.850   73.340  41.581   78.820  39.983  
 84.436  39.074   90.085  38.850   95.672  39.293  101.115  40.368  
106.342  42.033  111.294  44.240  115.920  46.937  120.183  50.072  
124.052  53.593  127.504  57.449  130.520  61.591  133.088  65.973  
135.198  70.551  136.845  75.282  138.024  80.128  138.732  85.048  
138.968  90.006  ] scurve 
%%% D 
148.641  90.006 moveto 
%%% Y 61  
[ 148.641  90.006  148.370  95.870  147.559 101.695  146.208 107.443  
144.316 113.075  141.884 118.546  138.913 123.812  135.408 128.823  
131.375 133.526  126.826 137.861  121.779 141.767  116.259 145.175  
110.303 148.014  103.962 150.211   97.301 151.691   90.405 152.386  
 83.376 152.234   76.339 151.188   69.438 149.225   62.833 146.350  
 56.689 142.610   51.168 138.096   46.411 132.946   42.519 127.340  
 39.535 121.489   37.428 115.608   36.095 109.889   35.370 104.465  
 35.054  99.384   34.956  94.603   34.940  89.995   34.956  85.387  
 35.054  80.605   35.371  75.523   36.098  70.098   37.432  64.378  
 39.541  58.497   42.527  52.646   46.422  47.042   51.180  41.893  
 56.703  37.380   62.848  33.643   69.454  30.770   76.355  28.809  
 83.392  27.765   90.420  27.615   97.317  28.311  103.977  29.794  
110.317  31.992  116.271  34.832  121.790  38.242  126.837  42.148  
131.385  46.485  135.416  51.188  138.920  56.199  141.890  61.466  
144.321  66.938  146.211  72.569  147.562  78.318  148.371  84.143  
148.641  90.006  ] scurve 
%%% D 
156.731  90.007 moveto 
%%% Y 61  
[ 156.731  90.007  156.436  96.604  155.551 103.163  154.075 109.647  
152.005 116.016  149.336 122.227  146.066 128.233  142.192 133.981  
137.714 139.414  132.636 144.465  126.967 149.064  120.726 153.128  
113.944 156.572  106.665 159.299   98.956 161.211   90.905 162.210  
 82.630 162.201   74.280 161.104   66.036 158.864   58.111 155.463  
 50.735 150.936   44.149 145.387   38.572 138.995   34.174 132.018  
 31.040 124.775   29.133 117.612   28.286 110.848   28.206 104.711  
 28.532  99.282   28.903  94.463   29.059  89.995   28.903  85.527  
 28.531  80.706   28.206  75.275   28.286  69.137   29.136  62.372  
 31.046  55.208   34.183  47.965   38.584  40.989   44.163  34.600  
 50.751  29.053   58.128  24.529   66.055  21.130   74.299  18.893  
 82.649  17.798   90.923  17.792   98.973  18.793  106.682  20.707  
113.959  23.436  120.741  26.880  126.980  30.946  132.648  35.546  
137.725  40.598  142.201  46.031  146.074  51.780  149.343  57.786  
152.010  63.998  154.079  70.367  155.554  76.852  156.437  83.411  
156.731  90.007  ] scurve 
%%% D 
163.777  90.008 moveto 
%%% Y 61  
[ 163.777  90.008  163.462  97.223  162.523 104.405  160.952 111.513  
158.745 118.513  155.896 125.360  152.393 132.008  148.229 138.404  
143.397 144.486  137.891 150.184  131.712 155.421  124.869 160.104  
117.383 164.132  109.292 167.391  100.654 169.758   91.560 171.105  
 82.133 171.303   72.540 170.231   62.995 167.795   53.760 163.939  
 45.137 158.675   37.455 152.104   31.033 144.438   26.137 136.011  
 22.923 127.267   21.369 118.718   21.244 110.861   22.102 104.068  
 23.356  98.480   24.409  93.935   24.814  89.996   24.407  86.056  
 23.353  81.509   22.099  75.917   21.242  69.121   21.371  61.262  
 22.929  52.712   26.147  43.969   31.046  35.543   37.472  27.880  
 45.157  21.312   53.781  16.051   63.017  12.199   72.562   9.766  
 82.154   8.697   91.580   8.897  100.674  10.247  109.310  12.616  
117.400  15.877  124.885  19.906  131.726  24.590  137.903  29.828  
143.408  35.528  148.238  41.610  152.401  48.007  155.903  54.654  
158.750  61.502  160.957  68.503  162.525  75.611  163.463  82.793  
163.777  90.008  ] scurve 
%%% D 
170.086  90.009 moveto 
%%% Y 121 
[ 170.086  90.009  169.975  93.907  169.721  97.749  169.346 101.617  
168.758 105.502  167.996 109.317  167.120 113.120  166.050 116.943  
164.780 120.692  163.389 124.395  161.818 128.105  160.034 131.740  
158.115 135.299  156.020 138.841  153.709 142.297  151.250 145.656  
148.608 148.966  145.754 152.164  142.742 155.246  139.536 158.241  
136.128 161.086  132.556 163.795  128.779 166.363  124.822 168.744  
120.690 170.956  116.365 172.960  111.881 174.745  107.220 176.298  
102.408 177.587   97.449 178.606   92.358 179.321   87.153 179.723  
 81.853 179.782   76.483 179.485   71.071 178.807   65.649 177.735  
 60.253 176.252   54.922 174.348   49.704 172.015   44.646 169.253  
 39.800 166.068   35.221 162.474   30.964 158.493   27.085 154.159  
 23.636 149.518   20.664 144.626   18.208 139.550   16.295 134.370  
 14.939 129.171   14.134 124.047   13.855 119.091   14.057 114.394  
 14.671 110.037   15.608 106.088   16.763 102.590   18.019  99.563  
 19.256  96.994   20.357  94.839   21.223  93.023   21.775  91.447  
 21.965  89.997   21.773  88.547   21.219  86.970   20.352  85.153  
 19.250  82.996   18.012  80.424   16.756  77.395   15.602  73.894  
 14.666  69.943   14.055  65.584   13.856  60.886   14.137  55.929  
 14.945  50.804   16.304  45.606   18.219  40.426   20.678  35.351  
 23.652  30.460   27.103  25.820   30.984  21.489   35.242  17.510  
 39.822  13.917   44.669  10.734   49.728   7.974   54.947   5.644  
 60.277   3.741   65.674   2.260   71.096   1.190   76.508   0.514  
 81.877   0.218   87.176   0.279   92.381   0.682   97.471   1.399  
102.430   2.419  107.241   3.709  111.901   5.263  116.385   7.049  
120.708   9.053  124.840  11.266  128.796  13.648  132.572  16.217  
136.143  18.927  139.551  21.773  142.756  24.768  145.766  27.850  
148.620  31.049  151.261  34.359  153.720  37.718  156.030  41.174  
158.124  44.716  160.042  48.276  161.825  51.912  163.395  55.621  
164.786  59.324  166.055  63.074  167.124  66.897  167.999  70.700  
168.761  74.514  169.348  78.400  169.722  82.268  169.976  86.110  
170.086  90.009  ] scurve 
%%% D 
176.126  90.011 moveto 
%%% Y 181 
[ 176.126  90.011  175.805  93.077  175.360  95.654  175.192  98.051  
175.277 100.663  175.178 103.748  174.448 106.761  173.651 109.276  
173.153 111.655  172.868 114.292  172.315 117.367  171.161 120.258  
170.037 122.668  169.223 125.021  168.546 127.694  167.460 130.716  
165.882 133.380  164.476 135.648  163.358 137.991  162.208 140.719  
160.494 143.555  158.564 145.881  156.931 148.019  155.458 150.411  
153.642 153.120  151.342 155.503  149.218 157.494  147.337 159.611  
145.265 162.062  142.662 164.345  140.121 166.165  137.839 168.040  
135.394 170.216  132.451 172.221  129.578 173.781  126.926 175.421  
124.023 177.292  120.719 178.846  117.602 180.071  114.567 181.468  
111.138 182.886  107.593 183.849  104.267 184.756  100.727 185.794  
 96.910 186.471   93.293 186.920   89.584 187.477   85.593 187.734  
 81.772 187.712   77.886 187.742   73.789 187.448   69.869 186.919  
 65.844 186.362   61.751 185.427   57.816 184.360   53.751 183.112  
 49.815 181.531   45.917 179.857   42.042 177.847   38.339 175.680  
 34.652 173.258   31.182 170.614   27.787 167.773   24.627 164.695  
 21.609 161.451   18.850 157.996   16.287 154.397   14.016 150.638  
 11.986 146.763   10.273 142.797    8.841 138.755    7.730 134.696  
  6.935 130.626    6.448 126.607    6.281 122.664    6.405 118.835  
  6.811 115.169    7.477 111.692    8.365 108.438    9.443 105.441  
 10.670 102.721   11.997 100.293   13.373  98.167   14.750  96.345  
 16.071  94.814   17.284  93.556   18.339  92.537   19.203  91.715  
 19.849  91.047   20.251  90.492   20.388  89.998   20.250  89.505  
 19.846  88.950   19.198  88.282   18.332  87.458   17.275  86.437  
 16.061  85.178   14.738  83.645   13.362  81.819   11.986  79.691  
 10.659  77.260    9.433  74.537    8.357  71.539    7.471  68.283  
  6.806  64.804    6.403  61.137    6.281  57.307    6.451  53.364  
  6.940  49.345    7.738  45.274    8.851  41.217   10.285  37.175  
 12.001  33.209   14.033  29.335   16.305  25.578   18.869  21.981  
 21.630  18.526   24.649  15.284   27.811  12.207   31.207   9.369  
 34.677   6.725   38.366   4.306   42.068   2.140   45.945   0.131  
 49.842  -1.541   53.779  -3.120   57.844  -4.366   61.778  -5.433  
 65.872  -6.366   69.896  -6.921   73.817  -7.450   77.914  -7.741  
 81.798  -7.711   85.620  -7.732   89.610  -7.472   93.317  -6.916  
 96.935  -6.467  100.752  -5.787  104.289  -4.749  107.615  -3.842  
111.162  -2.878  114.588  -1.457  117.622  -0.062  120.741   1.163  
124.044   2.721  126.943   4.591  129.595   6.229  132.471   7.791  
135.412   9.799  137.854  11.974  140.136  13.848  142.680  15.669  
145.280  17.955  147.350  20.404  149.230  22.520  151.356  24.511  
153.656  26.897  155.468  29.606  156.941  31.996  158.576  34.133  
160.507  36.462  162.216  39.300  163.365  42.026  164.484  44.367  
165.892  46.636  167.469  49.303  168.551  52.325  169.228  54.995  
170.043  57.347  171.169  59.759  172.321  62.654  172.870  65.727  
173.155  68.361  173.656  70.740  174.454  73.257  175.181  76.273  
175.276  79.355  175.192  81.965  175.362  84.362  175.809  86.941  
176.126  90.011  ] scurve 
%% / / 
%%% D 
 10.000 -13.000 moveto 
%%% K 
%% $ 
  1.000 nbpt mul rm  (Cardioide) show currentpoint 
clear 
%%% D 
 10.000 -20.000 moveto 
%%% K 
%% $ 
  1.000 nbpt mul it  (r ) show currentpoint 
%% $ 
  1.000 nbpt mul rm  (= 1 + ) show currentpoint
%% $ 
  1.000 nbpt mul rm  (cos ) show currentpoint   
%% $ 
  1.000 nbpt mul symb  (q) show currentpoint 
clear
%%% D 
130.000 -20.000 moveto 
%%% K 
%% $ 
  1.000 nbpt mul rm  (Centre  \( 0.875 , 0 \)) show currentpoint 
clear 
%%% > 
showpage 

% Dessin z7.ds1 

%%% < 1 Largeur= 180.000 Hauteur= 240.000 
%%% ~   0.000 180.000   0.000 240.000 
1.2 dup scale 
1 mm unit  /nbpt 10 def 
  0.000   0.000 translate 
%%% +  90.000  120.000  95.000   0.000   0.000  95.000 
%%% L 
  0.452 setlinewidth
%%% Z 
%%% D 
 22.825 120.000 moveto 
%%% Y 181 
[  22.825 120.000   22.784 117.653   22.663 115.291   22.467 112.902  
 22.202 110.472   21.880 107.989   21.511 105.442   21.111 102.824  
 20.695 100.127   20.278  97.346   19.880  94.478   19.516  91.523  
 19.204  88.480   18.962  85.353   18.805  82.145   18.750  78.864  
 18.810  75.516   18.999  72.109   19.330  68.655   19.812  65.164  
 20.457  61.646   21.271  58.116   22.262  54.586   23.434  51.069  
 24.793  47.580   26.339  44.132   28.076  40.741   30.001  37.419  
 32.115  34.182   34.414  31.043   36.893  28.017   39.549  25.116  
 42.374  22.353   45.362  19.741   48.503  17.292   51.789  15.016  
 55.209  12.924   58.752  11.026   62.407   9.330   66.160   7.844  
 70.000   6.574   73.912   5.528   77.882   4.709   81.897   4.121  
 85.941   3.767   90.000   3.649   94.059   3.767   98.103   4.121  
102.118   4.709  106.088   5.528  110.000   6.574  113.840   7.844  
117.593   9.330  121.248  11.026  124.791  12.924  128.211  15.016  
131.497  17.292  134.638  19.741  137.626  22.353  140.451  25.116  
143.107  28.017  145.586  31.043  147.885  34.182  149.999  37.419  
151.924  40.741  153.661  44.132  155.207  47.580  156.566  51.069  
157.738  54.586  158.729  58.116  159.543  61.646  160.188  65.164  
160.670  68.655  161.001  72.109  161.190  75.516  161.250  78.864  
161.195  82.145  161.038  85.353  160.796  88.480  160.484  91.523  
160.120  94.478  159.722  97.346  159.305 100.127  158.889 102.824  
158.489 105.442  158.120 107.989  157.798 110.472  157.533 112.902  
157.337 115.291  157.216 117.653  157.175 120.000  157.216 122.347  
157.337 124.709  157.533 127.098  157.798 129.528  158.120 132.011  
158.489 134.558  158.889 137.176  159.305 139.873  159.722 142.654  
160.120 145.522  160.484 148.477  160.796 151.520  161.038 154.647  
161.195 157.855  161.250 161.136  161.190 164.484  161.001 167.891  
160.670 171.345  160.188 174.836  159.543 178.354  158.729 181.884  
157.738 185.414  156.566 188.931  155.207 192.420  153.661 195.868  
151.924 199.259  149.999 202.581  147.885 205.818  145.586 208.957  
143.107 211.983  140.451 214.884  137.626 217.647  134.638 220.259  
131.497 222.708  128.211 224.984  124.791 227.076  121.248 228.974  
117.593 230.670  113.840 232.156  110.000 233.426  106.088 234.472  
102.118 235.291   98.103 235.879   94.059 236.233   90.000 236.351  
 85.941 236.233   81.897 235.879   77.882 235.291   73.912 234.472  
 70.000 233.426   66.160 232.156   62.407 230.670   58.752 228.974  
 55.209 227.076   51.789 224.984   48.503 222.708   45.362 220.259  
 42.374 217.647   39.549 214.884   36.893 211.983   34.414 208.957  
 32.115 205.818   30.001 202.581   28.076 199.259   26.339 195.868  
 24.793 192.420   23.434 188.931   22.262 185.414   21.271 181.884  
 20.457 178.354   19.812 174.836   19.330 171.345   18.999 167.891  
 18.810 164.484   18.750 161.136   18.805 157.855   18.962 154.647  
 19.204 151.520   19.516 148.477   19.880 145.522   20.278 142.654  
 20.695 139.873   21.111 137.176   21.511 134.558   21.880 132.011  
 22.202 129.528   22.467 127.098   22.663 124.709   22.784 122.347  
 22.825 120.000  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% L 
  0.113 setlinewidth 
%%% Y 21  
[  90.000 120.000   85.744 120.000   81.505 120.000   77.300 120.000  
 73.146 120.000   69.057 120.000   65.049 120.000   61.136 120.000  
 57.330 120.000   53.644 120.000   50.086 120.000   46.666 120.000  
 43.390 120.000   40.266 120.000   37.296 120.000   34.484 120.000  
 31.833 120.000   29.340 120.000   26.996 120.000   24.704 120.000  
 22.825 120.000  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% Y 21  
[  90.000 120.000   86.000 118.546   82.008 117.106   78.033 115.696  
 74.084 114.330   70.170 113.020   66.299 111.780   62.481 110.620  
 58.724 109.552   55.038 108.584   51.431 107.724   47.913 106.978  
 44.493 106.350   41.178 105.844   37.978 105.459   34.898 105.197  
 31.947 105.055   29.131 105.029   26.455 105.108   23.950 105.206  
 21.470 105.165  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% Y 21  
[  90.000 120.000   86.736 117.265   83.464 114.545   80.175 111.854  
 76.861 109.209   73.515 106.623   70.132 104.113   66.704 101.695  
 63.230  99.384   59.706  97.196   56.131  95.148   52.507  93.256  
 48.837  91.536   45.127  90.004   41.385  88.674   37.621  87.560  
 33.847  86.674   30.078  86.027   26.328  85.628   22.551  85.476  
 18.964  85.379  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% Y 21  
[  90.000 120.000   87.868 116.312   85.718 112.624   83.535 108.936  
 81.299 105.249   78.994 101.564   76.600  97.884   74.101  94.211  
 71.475  90.551   68.703  86.909   65.766  83.294   62.641  79.718  
 59.308  76.192   55.746  72.736   51.934  69.369   47.851  66.118  
 43.479  63.011   38.801  60.085   33.805  57.379   28.476  54.963  
 22.654  53.345  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% Y 21  
[  90.000 120.000   89.259 115.803   88.510 111.592   87.743 107.351  
 86.949 103.064   86.120  98.717   85.243  94.292   84.309  89.773  
 83.303  85.141   82.212  80.378   81.020  75.462   79.706  70.371  
 78.249  65.081   76.624  59.567   74.799  53.799   72.739  47.746  
 70.399  41.375   67.726  34.650   64.657  27.530   61.116  19.970  
 57.348  11.747  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% Y 21  
[  90.000 120.000   90.741 115.803   91.491 111.592   92.258 107.351  
 93.051 103.064   93.881  98.717   94.757  94.292   95.692  89.773  
 96.697  85.142   97.788  80.378   98.981  75.462  100.295  70.371  
101.752  65.082  103.377  59.567  105.202  53.799  107.263  47.747  
109.603  41.376  112.276  34.651  115.345  27.531  118.887  19.971  
122.655  11.748  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% Y 21  
[  90.000 120.000   92.132 116.312   94.282 112.624   96.465 108.936  
 98.701 105.249  101.007 101.564  103.400  97.884  105.900  94.211  
108.526  90.551  111.297  86.909  114.235  83.295  117.359  79.718  
120.692  76.193  124.254  72.737  128.066  69.370  132.149  66.119  
136.521  63.012  141.199  60.086  146.196  57.381  151.524  54.965  
157.347  53.347  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% Y 21  
[  90.000 120.000   93.264 117.265   96.536 114.545   99.825 111.854  
103.139 109.209  106.485 106.623  109.869 104.114  113.296 101.695  
116.770  99.384  120.295  97.196  123.869  95.148  127.493  93.257  
131.163  91.537  134.873  90.005  138.615  88.675  142.379  87.561  
146.153  86.675  149.922  86.028  153.672  85.629  157.448  85.477  
161.036  85.380  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% Y 21  
[  90.000 120.000   94.001 118.546   97.992 117.107  101.967 115.697  
105.916 114.330  109.830 113.020  113.701 111.780  117.520 110.620  
121.276 109.552  124.962 108.584  128.569 107.725  132.087 106.978  
135.507 106.351  138.821 105.844  142.022 105.460  145.101 105.197  
148.052 105.055  150.869 105.029  153.544 105.108  156.049 105.206  
158.530 105.166  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% Y 21  
[  90.000 120.000   94.256 120.000   98.495 120.000  102.700 120.000  
106.854 120.000  110.943 120.000  114.951 120.000  118.864 120.000  
122.670 120.000  126.357 120.000  129.914 120.000  133.335 120.000  
136.610 120.000  139.735 120.000  142.704 120.000  145.516 120.000  
148.167 120.000  150.660 119.999  153.004 119.999  155.296 119.998  
157.175 119.992  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% Y 21  
[  90.000 120.000   94.001 121.454   97.992 122.894  101.967 124.304  
105.916 125.670  109.830 126.980  113.701 128.220  117.520 129.380  
121.276 130.448  124.963 131.416  128.569 132.276  132.087 133.022  
135.507 133.649  138.822 134.156  142.023 134.540  145.102 134.802  
148.053 134.944  150.870 134.970  153.546 134.892  156.051 134.793  
158.530 134.835  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% Y 21  
[  90.000 120.000   93.264 122.735   96.536 125.455   99.825 128.146  
103.139 130.791  106.485 133.377  109.868 135.887  113.296 138.305  
116.770 140.617  120.295 142.804  123.870 144.852  127.493 146.744  
131.163 148.464  134.873 149.996  138.616 151.326  142.380 152.440  
146.154 153.326  149.923 153.973  153.674 154.372  157.450 154.524  
161.036 154.621  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% Y 21  
[  90.000 120.000   92.132 123.688   94.282 127.376   96.465 131.064  
 98.701 134.751  101.006 138.436  103.400 142.116  105.899 145.789  
108.525 149.449  111.297 153.091  114.234 156.706  117.359 160.283  
120.692 163.808  124.254 167.264  128.066 170.631  132.149 173.883  
136.521 176.990  141.199 179.917  146.196 182.622  151.525 185.039  
157.346 186.656  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% Y 21  
[  90.000 120.000   90.741 124.197   91.490 128.408   92.257 132.649  
 93.051 136.936   93.880 141.283   94.757 145.708   95.691 150.227  
 96.697 154.859   97.788 159.622   98.980 164.539  100.294 169.629  
101.750 174.919  103.376 180.434  105.200 186.202  107.261 192.255  
109.601 198.625  112.273 205.351  115.342 212.471  118.883 220.032  
122.650 228.254  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% Y 21  
[  90.000 120.000   89.259 124.197   88.509 128.408   87.742 132.649  
 86.949 136.936   86.119 141.283   85.243 145.708   84.308 150.227  
 83.303 154.859   82.211 159.622   81.019 164.538   79.705 169.629  
 78.248 174.919   76.622 180.433   74.797 186.201   72.737 192.253  
 70.396 198.624   67.723 205.349   64.654 212.469   61.112 220.028  
 57.344 228.251  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% Y 21  
[  90.000 120.000   87.868 123.688   85.718 127.376   83.535 131.064  
 81.299 134.751   78.993 138.436   76.600 142.116   74.100 145.789  
 71.474 149.449   68.703 153.091   65.765 156.705   62.640 160.282  
 59.308 163.807   55.746 167.263   51.933 170.629   47.850 173.881  
 43.478 176.987   38.801 179.913   33.804 182.618   28.476 185.035  
 22.653 186.653  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% Y 21  
[  90.000 120.000   86.736 122.735   83.464 125.455   80.175 128.146  
 76.861 130.791   73.515 133.377   70.131 135.886   66.704 138.305  
 63.230 140.616   59.705 142.804   56.131 144.851   52.507 146.743  
 48.837 148.463   45.127 149.995   41.385 151.325   37.621 152.439  
 33.847 153.324   30.078 153.971   26.328 154.371   22.552 154.523  
 18.964 154.619  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% Y 21  
[  90.000 120.000   85.999 121.454   82.008 122.893   78.033 124.303  
 74.084 125.670   70.170 126.980   66.299 128.220   62.480 129.380  
 58.724 130.448   55.038 131.415   51.431 132.275   47.913 133.021  
 44.493 133.649   41.178 134.156   37.978 134.540   34.899 134.802  
 31.948 134.944   29.131 134.970   26.456 134.892   23.951 134.794  
 21.470 134.834  ] scurve 
%%% D 
103.378 120.000 moveto 
%%% Y 61  
[ 103.378 120.000  103.308 121.380  103.100 122.748  102.755 124.089  
102.275 125.393  101.663 126.644  100.923 127.830  100.061 128.938  
 99.084 129.955   98.002 130.867   96.824 131.663   95.564 132.331  
 94.235 132.861   92.853 133.246   91.436 133.480   90.000 133.558  
 88.564 133.480   87.146 133.246   85.765 132.861   84.436 132.331  
 83.176 131.663   81.998 130.867   80.916 129.955   79.939 128.938  
 79.077 127.830   78.337 126.644   77.725 125.392   77.245 124.089  
 76.900 122.747   76.692 121.380   76.622 120.000   76.692 118.620  
 76.900 117.252   77.245 115.911   77.725 114.607   78.337 113.356  
 79.077 112.170   79.939 111.062   80.916 110.045   81.998 109.133  
 83.176 108.337   84.436 107.669   85.765 107.139   87.147 106.754  
 88.564 106.520   90.000 106.442   91.436 106.520   92.854 106.754  
 94.235 107.139   95.564 107.669   96.824 108.337   98.002 109.133  
 99.084 110.045  100.061 111.062  100.923 112.170  101.663 113.356  
102.275 114.608  102.755 115.911  103.100 117.253  103.308 118.620  
103.378 120.000  ] scurve 
%%% D 
121.714 120.000 moveto 
%%% Y 61  
[ 121.714 120.000  121.591 123.064  121.221 126.124  120.596 129.173  
119.702 132.203  118.524 135.196  117.045 138.131  115.247 140.977  
113.117 143.691  110.649 146.225  107.845 148.521  104.725 150.517  
101.321 152.152   97.686 153.367   93.886 154.116   90.000 154.370  
 86.114 154.116   82.313 153.367   78.678 152.152   75.275 150.517  
 72.154 148.520   69.351 146.224   66.882 143.690   64.752 140.976  
 62.955 138.131   61.476 135.196   60.298 132.202   59.404 129.173  
 58.779 126.123   58.409 123.064   58.286 120.000   58.409 116.936  
 58.779 113.876   59.404 110.827   60.298 107.797   61.476 104.804  
 62.955 101.869   64.753  99.024   66.883  96.309   69.351  93.775  
 72.155  91.479   75.275  89.483   78.679  87.848   82.314  86.633  
 86.114  85.884   90.000  85.631   93.886  85.884   97.686  86.633  
101.322  87.849  104.725  89.483  107.845  91.479  110.649  93.776  
113.117  96.310  115.247  99.024  117.045 101.869  118.524 104.804  
119.702 107.798  120.596 110.827  121.221 113.877  121.591 116.936  
121.714 120.000  ] scurve 
%%% D 
131.601 120.000 moveto 
%%% Y 61  
[ 131.601 120.000  131.489 123.762  131.147 127.546  130.555 131.369  
129.683 135.243  128.488 139.171  126.917 143.141  124.912 147.121  
122.413 151.058  119.366 154.873  115.735 158.457  111.510 161.682  
106.722 164.403  101.450 166.476   95.820 167.776   89.999 168.219  
 84.179 167.776   78.549 166.475   73.277 164.402   68.489 161.682  
 64.265 158.456   60.633 154.872   57.587 151.057   55.088 147.120  
 53.083 143.140   51.512 139.171   50.317 135.243   49.445 131.369  
 48.853 127.546   48.511 123.762   48.399 120.000   48.511 116.238  
 48.853 112.454   49.445 108.631   50.317 104.756   51.513 100.829  
 53.083  96.859   55.088  92.879   57.587  88.942   60.634  85.128  
 64.265  81.543   68.490  78.318   73.278  75.597   78.550  73.525  
 84.180  72.224   90.000  71.781   95.821  72.225  101.450  73.525  
106.723  75.598  111.510  78.318  115.735  81.544  119.366  85.128  
122.413  88.943  124.912  92.880  126.917  96.860  128.487 100.829  
129.683 104.757  130.555 108.631  131.147 112.454  131.489 116.238  
131.601 120.000  ] scurve 
%%% D 
138.656 120.000 moveto 
%%% Y 61  
[ 138.656 120.000  138.575 124.117  138.323 128.283  137.873 132.544  
137.179 136.939  136.174 141.498  134.773 146.232  132.871 151.129  
130.349 156.138  127.088 161.165  122.977 166.061  117.946 170.617  
111.991 174.581  105.202 177.677   97.774 179.655   89.999 180.336  
 82.224 179.655   74.796 177.676   68.008 174.579   62.053 170.616  
 57.023 166.059   52.912 161.164   49.651 156.137   47.130 151.127  
 45.228 146.231   43.827 141.497   42.822 136.939   42.127 132.543  
 41.677 128.283   41.425 124.117   41.344 120.000   41.425 115.883  
 41.677 111.717   42.127 107.456   42.822 103.061   43.827  98.502  
 45.228  93.768   47.130  88.872   49.651  83.862   52.913  78.835  
 57.024  73.940   62.054  69.383   68.009  65.420   74.798  62.323  
 82.225  60.345   90.001  59.664   97.776  60.345  105.203  62.324  
111.992  65.421  117.946  69.384  122.977  73.941  127.088  78.836  
130.349  83.863  132.870  88.872  134.772  93.768  136.173  98.502  
137.178 103.061  137.873 107.456  138.323 111.717  138.575 115.883  
138.656 120.000  ] scurve 
%%% D 
144.106 120.000 moveto 
%%% Y 61  
[ 144.106 120.000  144.065 124.281  143.932 128.636  143.674 133.139  
143.236 137.857  142.536 142.852  141.460 148.168  139.862 153.824  
137.562 159.796  134.356 165.995  130.038 172.245  124.433 178.265  
117.459 183.671  109.187 188.009   99.881 190.835   89.999 191.818  
 80.116 190.834   70.811 188.008   62.539 183.669   55.566 178.263  
 49.962 172.243   45.644 165.993   42.438 159.794   40.139 153.823  
 38.540 148.167   37.465 142.851   36.764 137.857   36.327 133.139  
 36.069 128.636   35.936 124.281   35.895 120.000   35.935 115.719  
 36.069 111.363   36.327 106.861   36.764 102.143   37.464  97.148  
 38.540  91.832   40.139  86.176   42.439  80.204   45.644  74.006  
 49.963  67.756   55.567  61.735   62.540  56.330   70.813  51.992  
 80.118  49.166   90.001  48.183   99.883  49.166  109.189  51.993  
117.461  56.331  124.433  61.737  130.038  67.757  134.356  74.007  
137.561  80.205  139.861  86.177  141.459  91.833  142.535  97.149  
143.235 102.143  143.673 106.861  143.931 111.363  144.064 115.719  
144.106 120.000  ] scurve 
%%% D 
148.486 119.999 moveto 
%%% Y 61  
[ 148.486 119.999  148.489 124.323  148.486 128.744  148.444 133.357  
148.303 138.258  147.974 143.543  147.323 149.294  146.171 155.574  
144.282 162.404  141.363 169.725  137.087 177.365  131.134 184.984  
123.285 192.055  113.539 197.897  102.220 201.784   89.998 203.152  
 77.777 201.783   66.458 197.895   56.713 192.053   48.865 184.981  
 42.913 177.362   38.637 169.723   35.719 162.402   33.830 155.573  
 32.678 149.293   32.028 143.542   31.698 138.258   31.557 133.357  
 31.515 128.744   31.512 124.324   31.514 120.000   31.512 115.676  
 31.515 111.255   31.557 106.643   31.697 101.741   32.027  96.457  
 32.678  90.706   33.830  84.426   35.719  77.597   38.637  70.275  
 42.914  62.636   48.866  55.017   56.715  47.946   66.460  42.104  
 77.780  38.216   90.001  36.848  102.222  38.217  113.541  42.105  
123.287  47.947  131.135  55.019  137.087  62.637  141.363  70.277  
144.281  77.598  146.170  84.427  147.321  90.707  147.972  96.458  
148.302 101.741  148.443 106.643  148.485 111.255  148.488 115.676  
148.486 119.999  ] scurve 
%%% D 
152.098 119.999 moveto 
%%% Y 121 
[ 152.098 119.999  152.101 122.140  152.136 124.280  152.200 126.463  
152.265 128.689  152.353 130.958  152.453 133.314  152.539 135.755  
152.624 138.291  152.683 140.958  152.697 143.752  152.661 146.699  
152.537 149.814  152.308 153.105  151.935 156.591  151.384 160.276  
150.610 164.167  149.562 168.260  148.184 172.545  146.416 177.000  
144.193 181.588  141.451 186.255  138.130 190.930  134.181 195.519  
129.570 199.909  124.290 203.969  118.364 207.560  111.854 210.539  
104.860 212.775   97.519 214.163   89.998 214.634   82.476 214.163  
 75.136 212.774   68.142 210.536   61.632 207.557   55.707 203.966  
 50.427 199.905   45.817 195.515   41.868 190.926   38.548 186.252  
 35.807 181.584   33.585 176.997   31.817 172.542   30.439 168.257  
 29.392 164.165   28.617 160.274   28.066 156.590   27.694 153.103  
 27.465 149.813   27.341 146.698   27.304 143.751   27.318 140.958  
 27.378 138.291   27.462 135.755   27.548 133.315   27.648 130.959  
 27.735 128.689   27.800 126.464   27.865 124.280   27.899 122.141  
 27.902 120.000   27.899 117.859   27.865 115.719   27.800 113.536  
 27.735 111.310   27.648 109.041   27.547 106.685   27.462 104.244  
 27.377 101.709   27.318  99.042   27.304  96.248   27.340  93.301  
 27.464  90.186   27.694  86.896   28.066  83.409   28.617  79.725  
 29.391  75.833   30.439  71.741   31.817  67.456   33.585  63.001  
 35.808  58.414   38.550  53.746   41.870  49.071   45.819  44.482  
 50.429  40.093   55.709  36.032   61.635  32.442   68.145  29.463  
 75.139  27.226   82.480  25.837   90.001  25.367   97.523  25.838  
104.863  27.226  111.857  29.464  118.367  32.443  124.292  36.034  
129.572  40.094  134.182  44.484  138.131  49.073  141.451  53.748  
144.192  58.415  146.415  63.003  148.183  67.457  149.561  71.742  
150.608  75.835  151.383  79.726  151.934  83.410  152.306  86.897  
152.535  90.187  152.659  93.302  152.695  96.249  152.682  99.042  
152.622 101.709  152.537 104.244  152.452 106.685  152.352 109.041  
152.264 111.310  152.199 113.536  152.135 115.719  152.101 117.858  
152.098 119.999  ] scurve 
%%% D 
155.234 119.999 moveto 
%%% Y 181 
[ 155.234 119.999  155.132 121.508  155.041 122.822  155.134 124.093  
155.357 125.526  155.439 127.130  155.391 128.597  155.478 129.951  
155.746 131.413  155.968 133.118  155.988 134.794  156.083 136.333  
156.364 137.962  156.621 139.861  156.661 141.770  156.766 143.568  
157.034 145.520  157.177 147.737  157.150 149.900  157.247 152.069  
157.347 154.523  157.202 157.067  157.079 159.582  156.954 162.360  
156.565 165.257  156.149 168.170  155.612 171.346  154.811 174.570  
153.933 177.920  152.753 181.436  151.380 184.981  149.715 188.686  
147.752 192.389  145.465 196.182  142.823 199.931  139.801 203.676  
136.399 207.303  132.577 210.804  128.372 214.098  123.761 217.120  
118.783 219.826  113.476 222.133  107.873 223.993  102.046 225.366  
 96.065 226.201   89.997 226.479   83.929 226.201   77.948 225.365  
 72.121 223.991   66.518 222.131   61.212 219.823   56.235 217.117  
 51.624 214.094   47.419 210.800   43.598 207.299   40.197 203.671  
 37.175 199.926   34.534 196.178   32.247 192.384   30.285 188.681  
 28.621 184.976   27.247 181.432   26.068 177.916   25.190 174.567  
 24.390 171.343   23.852 168.167   23.437 165.254   23.048 162.357  
 22.923 159.580   22.800 157.065   22.655 154.522   22.756 152.068  
 22.852 149.899   22.825 147.737   22.968 145.519   23.236 143.568  
 23.341 141.770   23.381 139.861   23.637 137.962   23.919 136.333  
 24.013 134.794   24.033 133.119   24.255 131.413   24.523 129.951  
 24.611 128.597   24.563 127.131   24.643 125.528   24.866 124.094  
 24.959 122.823   24.869 121.509   24.766 120.000   24.869 118.491  
 24.959 117.177   24.866 115.906   24.643 114.472   24.562 112.869  
 24.610 111.403   24.522 110.048   24.255 108.586   24.033 106.881  
 24.013 105.206   23.918 103.667   23.636 102.038   23.380 100.138  
 23.341  98.230   23.235  96.432   22.967  94.480   22.824  92.263  
 22.851  90.101   22.755  87.931   22.654  85.477   22.799  82.934  
 22.922  80.419   23.047  77.641   23.436  74.744   23.852  71.831  
 24.390  68.655   25.190  65.431   26.068  62.081   27.248  58.566  
 28.621  55.021   30.286  51.316   32.248  47.613   34.535  43.819  
 37.177  40.071   40.199  36.326   43.601  32.699   47.422  29.198  
 51.627  25.903   56.238  22.881   61.216  20.175   66.522  17.868  
 72.126  16.008   77.953  14.635   83.934  13.800   90.002  13.521  
 96.069  13.800  102.050  14.636  107.877  16.009  113.480  17.869  
118.787  20.177  123.764  22.883  128.375  25.905  132.580  29.200  
136.401  32.701  139.803  36.328  142.824  40.073  145.466  43.821  
147.752  47.615  149.714  51.318  151.379  55.023  152.752  58.568  
153.932  62.083  154.810  65.433  155.610  68.657  156.148  71.832  
156.563  74.746  156.952  77.643  157.077  80.420  157.200  82.935  
157.345  85.478  157.244  87.932  157.147  90.101  157.175  92.263  
157.032  94.481  156.764  96.432  156.658  98.230  156.619 100.138  
156.363 102.038  156.081 103.667  155.986 105.206  155.966 106.880  
155.745 108.586  155.477 110.048  155.389 111.402  155.437 112.868  
155.357 114.471  155.134 115.905  155.040 117.177  155.131 118.490  
155.234 119.999  ] scurve 
%% / / 
%%% D 
  0.000  10.000 moveto 
%%% K 
%% $ 
  1.000 nbpt mul rm  (Courbe) show currentpoint 
clear 
%%% D 
  0.000   3.000 moveto 
%%% K 
%% $ 
  1.000 nbpt mul it  (r ) show currentpoint 
%% $ 
  1.000 nbpt mul rm  (= ) show currentpoint 
%% $ 
  1.000 nbpt mul symb  (\326) show currentpoint 
%% $ 
  1.000 nbpt mul rm  (1 - 0.5 cos 2) show currentpoint 
%% $ 
  1.000 nbpt mul symb  (q) show currentpoint
clear 
%%% D 
  8.300   7.000 moveto 
%%% S 
 31.700   7.000 lineto 
stroke 
%%% D 
140.000   3.000 moveto 
%%% K 
%% $ 
  1.000 nbpt mul rm  (Centre \(0,0\)) show currentpoint 
clear 
%%% > 
showpage 

% Dessin z8.ds1 

%%% < 1 Largeur= 180.000 Hauteur= 240.000 
%%% ~   0.000 180.000   0.000 240.000 
1.2 dup scale 
1 mm unit  /nbpt 10 def 
  0.000   0.000 translate 
%%% +  90.000  120.000 114.000   0.000   0.000 114.000 
%%% L 
  0.452 setlinewidth
%%% Z 
%%% D 
 62.545 120.000 moveto 
%%% Y 181 
[  62.545 120.000   62.263 119.031   61.438 118.003   60.131 116.861  
 58.427 115.563   56.417 114.078   54.190 112.388   51.826 110.482  
 49.392 108.356   46.946 106.011   44.535 103.452   42.201 100.688  
 39.977  97.728   37.893  94.585   35.973  91.273   34.239  87.806  
 32.709  84.201   31.399  80.473   30.323  76.642   29.490  72.724  
 28.910  68.739   28.590  64.706   28.536  60.645   28.750  56.574  
 29.235  52.514   29.991  48.484   31.016  44.504   32.307  40.593  
 33.860  36.770   35.670  33.053   37.728  29.461   40.026  26.012  
 42.554  22.721   45.302  19.606   48.256  16.680   51.404  13.958  
 54.731  11.455   58.223   9.180   61.863   7.147   65.633   5.364  
 69.518   3.841   73.498   2.584   77.556   1.600   81.671   0.894  
 85.826   0.469   90.000   0.327   94.174   0.469   98.329   0.894  
102.444   1.600  106.502   2.584  110.482   3.841  114.367   5.364  
118.137   7.147  121.777   9.180  125.269  11.455  128.596  13.958  
131.744  16.680  134.698  19.606  137.446  22.721  139.974  26.012  
142.272  29.461  144.330  33.053  146.140  36.770  147.693  40.593  
148.984  44.504  150.009  48.484  150.765  52.514  151.250  56.574  
151.464  60.645  151.410  64.706  151.090  68.739  150.510  72.724  
149.677  76.642  148.601  80.473  147.291  84.201  145.761  87.806  
144.027  91.273  142.107  94.585  140.023  97.728  137.799 100.688  
135.465 103.452  133.054 106.011  130.608 108.356  128.174 110.482  
125.810 112.388  123.583 114.078  121.573 115.563  119.869 116.861  
118.562 118.003  117.737 119.031  117.455 120.000  117.737 120.969  
118.562 121.997  119.869 123.139  121.573 124.437  123.583 125.922  
125.810 127.612  128.174 129.518  130.608 131.644  133.054 133.989  
135.465 136.548  137.799 139.312  140.023 142.272  142.107 145.415  
144.027 148.727  145.761 152.194  147.291 155.799  148.601 159.527  
149.677 163.358  150.510 167.276  151.090 171.261  151.410 175.294  
151.464 179.355  151.250 183.426  150.765 187.486  150.009 191.516  
148.984 195.496  147.693 199.407  146.140 203.230  144.330 206.947  
142.272 210.539  139.974 213.988  137.446 217.279  134.698 220.394  
131.744 223.320  128.596 226.042  125.269 228.545  121.777 230.820  
118.137 232.853  114.367 234.636  110.482 236.159  106.502 237.416  
102.444 238.400   98.329 239.106   94.174 239.531   90.000 239.673  
 85.826 239.531   81.671 239.106   77.556 238.400   73.498 237.416  
 69.518 236.159   65.633 234.636   61.863 232.853   58.223 230.820  
 54.731 228.545   51.404 226.042   48.256 223.320   45.302 220.394  
 42.554 217.279   40.026 213.988   37.728 210.539   35.670 206.947  
 33.860 203.230   32.307 199.407   31.016 195.496   29.991 191.516  
 29.235 187.486   28.750 183.426   28.536 179.355   28.590 175.294  
 28.910 171.261   29.490 167.276   30.323 163.358   31.399 159.527  
 32.709 155.799   34.239 152.194   35.973 148.727   37.893 145.415  
 39.977 142.272   42.201 139.312   44.535 136.548   46.946 133.989  
 49.392 131.644   51.826 129.518   54.190 127.612   56.417 125.922  
 58.427 124.437   60.131 123.139   61.438 121.997   62.263 120.969  
 62.545 120.000  ] scurve 
%%% L 
  0.113 setlinewidth
%%% D
 90.000   0.327 moveto
%%% Y 2 
[  90.000   0.327   90.000 239.673  ] polygon stroke 
%%% D 
 90.000 120.000 moveto 
%%% Y 21  
[  90.000 120.000   87.768 120.000   85.558 119.999   83.388 119.999  
 81.277 119.998   79.244 119.998   77.303 119.997   75.467 119.997  
 73.745 119.997   72.144 119.997   70.670 119.997   69.323 119.997  
 68.105 119.997   67.013 119.997   66.041 119.998   65.185 119.998  
 64.432 119.999   63.767 119.999   63.160 120.000   62.530 120.000  
 62.545 120.003  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% Y 21  
[  90.000 120.000   87.902 119.238   85.814 118.494   83.747 117.786  
 81.712 117.129   79.720 116.537   77.781 116.024   75.908 115.598  
 74.111 115.265   72.400 115.030   70.785 114.893   69.274 114.852  
 67.874 114.902   66.590 115.037   65.426 115.248   64.383 115.529  
 63.457 115.872   62.641 116.277   61.918 116.765   61.268 117.433  
 61.369 117.935  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% Y 21  
[  90.000 120.000   88.286 118.566   86.562 117.150   84.818 115.771  
 83.046 114.447   81.238 113.197   79.391 112.043   77.503 111.002  
 75.578 110.095   73.622 109.342   71.647 108.759   69.666 108.362  
 67.702 108.161   65.775 108.165   63.911 108.374   62.136 108.785  
 60.474 109.388   58.941 110.169   57.523 111.105   56.087 112.144  
 54.682 112.769  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% Y 21  
[  90.000 120.000   88.879 118.064   87.738 116.128   86.554 114.193  
 85.305 112.261   83.970 110.335   82.523 108.422   80.940 106.532  
 79.195 104.680   77.262 102.887   75.116 101.181   72.733  99.600  
 70.097  98.189   67.197  97.008   64.036  96.124   60.636  95.614  
 57.040  95.556   53.320  96.028   49.571  97.091   45.865  98.736  
 42.081 100.537  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% Y 21  
[  90.000 120.000   89.611 117.796   89.211 115.573   88.789 113.314  
 88.334 110.998   87.831 108.604   87.264 106.110   86.612 103.490  
 85.852 100.716   84.950  97.757   83.867  94.574   82.547  91.128  
 80.919  87.369   78.884  83.247   76.305  78.706   72.994  73.691  
 68.683  68.166   62.994  62.136   55.395  55.709   45.156  49.213  
 31.358  43.378  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% Y 21  
[  90.000 120.000   90.390 117.796   90.791 115.574   91.214 113.315  
 91.671 110.999   92.177 108.606   92.746 106.113   93.401 103.494  
 94.165 100.723   95.071  97.765   96.159  94.586   97.485  91.143  
 99.121  87.391  101.165  83.276  103.754  78.745  107.078  73.745  
111.402  68.241  117.105  62.240  124.716  55.855  134.959  49.419  
148.735  43.676  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% Y 21  
[  90.000 120.000   91.121 118.065   92.264 116.130   93.449 114.196  
 94.698 112.264   96.035 110.340   97.483 108.429   99.067 106.542  
100.813 104.693  102.747 102.904  104.894 101.203  107.276  99.626  
109.911  98.222  112.809  97.048  115.967  96.171  119.362  95.668  
122.951  95.618  126.663  96.097  130.401  97.165  134.099  98.818  
137.871 100.597  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% Y 21  
[  90.000 120.000   91.714 118.567   93.439 117.152   95.183 115.774  
 96.956 114.451   98.764 113.204  100.610 112.051  102.497 111.012  
104.421 110.108  106.376 109.357  108.350 108.776  110.327 108.381  
112.289 108.183  114.213 108.188  116.073 108.399  117.843 108.811  
119.500 109.415  121.028 110.197  122.440 111.137  123.874 112.193  
125.307 112.777  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% Y 21  
[  90.000 120.000   92.099 119.239   94.187 118.496   96.253 117.789  
 98.288 117.133  100.279 116.542  102.217 116.030  104.089 115.605  
105.884 115.273  107.594 115.039  109.207 114.903  110.716 114.862  
112.113 114.912  113.395 115.047  114.556 115.258  115.597 115.538  
116.520 115.880  117.334 116.285  118.052 116.773  118.691 117.441  
118.606 117.960  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% Y 21  
[  90.000 120.000   92.232 120.000   94.442 120.001   96.612 120.001  
 98.721 120.001  100.753 120.001  102.693 120.001  104.529 120.001  
106.250 120.001  107.849 120.001  109.322 120.000  110.667 120.000  
111.884 120.000  112.976 119.999  113.946 119.998  114.802 119.998  
115.553 119.997  116.218 119.995  116.826 119.991  117.456 119.977  
117.468 119.796  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% Y 21  
[  90.000 120.000   92.098 120.762   94.186 121.505   96.253 122.214  
 98.287 122.870  100.279 123.461  102.217 123.973  104.089 124.398  
105.886 124.730  107.596 124.963  109.210 125.099  110.719 125.139  
112.118 125.088  113.399 124.953  114.561 124.740  115.602 124.459  
116.525 124.115  117.335 123.708  118.047 123.218  118.664 122.550  
118.590 122.025  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% Y 21  
[  90.000 120.000   91.714 121.434   93.438 122.849   95.182 124.228  
 96.954 125.552   98.762 126.800  100.610 127.954  102.497 128.993  
104.422 129.898  106.378 130.650  108.353 131.231  110.333 131.626  
112.297 131.824  114.223 131.818  116.086 131.606  117.860 131.192  
119.520 130.586  121.051 129.801  122.465 128.857  123.900 127.793  
125.317 127.230  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% Y 21  
[  90.000 120.000   91.121 121.936   92.263 123.871   93.447 125.806  
 94.696 127.738   96.032 129.663   97.480 131.575   99.064 133.464  
100.810 135.315  102.744 137.106  104.892 138.810  107.275 140.389  
109.913 141.797  112.814 142.975  115.976 143.856  119.377 144.363  
122.974 144.418  126.695 143.943  130.445 142.878  134.154 141.230  
137.911 139.452  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% Y 21  
[  90.000 120.000   90.389 122.204   90.790 124.427   91.212 126.686  
 91.668 129.002   92.172 131.396   92.741 133.890   93.394 136.510  
 94.156 139.283   95.060 142.243   96.146 145.424   97.469 148.870  
 99.101 152.627  101.141 156.748  103.724 161.286  107.041 166.296  
111.357 171.815  117.049 177.836  124.650 184.250  134.883 190.727  
148.669 196.538  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% Y 21  
[  90.000 120.000   89.610 122.204   89.209 124.427   88.786 126.686  
 88.330 129.002   87.826 131.396   87.257 133.890   86.604 136.509  
 85.841 139.283   84.937 142.242   83.850 145.423   82.527 148.869  
 80.894 152.625   78.853 156.744   76.269 161.281   72.950 166.288  
 68.632 171.804   62.937 177.820   55.333 184.227   45.094 190.695  
 31.316 196.489  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% Y 21  
[  90.000 120.000   88.879 121.935   87.736 123.871   86.551 125.805  
 85.302 127.737   83.965 129.663   82.517 131.575   80.933 133.463  
 79.187 135.314   77.253 137.105   75.106 138.809   72.723 140.388  
 70.086 141.796   67.186 142.973   64.027 143.854   60.628 144.360  
 57.034 144.414   53.316 143.939   49.571 142.873   45.868 141.223  
 42.099 139.440  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% Y 21  
[  90.000 120.000   88.286 121.433   86.561 122.849   84.817 124.227  
 83.043 125.550   81.235 126.799   79.388 127.953   77.500 128.992  
 75.575 129.898   73.619 130.650   71.643 131.231   69.664 131.627  
 67.700 131.827   65.774 131.822   63.912 131.611   62.139 131.199  
 60.480 130.595   58.949 129.813   57.534 128.874   56.099 127.824  
 54.682 127.231  ] scurve 
%%% D 
 90.000 120.000 moveto 
%%% Y 21  
[  90.000 120.000   87.901 120.761   85.813 121.504   83.746 122.212  
 81.711 122.868   79.718 123.458   77.780 123.971   75.907 124.396  
 74.110 124.728   72.399 124.963   70.784 125.099   69.274 125.140  
 67.875 125.090   66.592 124.955   65.430 124.744   64.387 124.464  
 63.463 124.121   62.649 123.716   61.929 123.228   61.288 122.560  
 61.383 122.051  ] scurve 
%%% D 
 96.958 120.001 moveto 
%%% Y 61  
[  96.958 120.001   96.925 120.706   96.824 121.407   96.656 122.097  
 96.421 122.772   96.119 123.425   95.750 124.050   95.315 124.640  
 94.817 125.186   94.259 125.683   93.645 126.120   92.981 126.490  
 92.275 126.787   91.535 127.004   90.773 127.136   89.999 127.180  
 89.225 127.136   88.463 127.004   87.724 126.787   87.017 126.490  
 86.353 126.119   85.739 125.682   85.181 125.185   84.683 124.638  
 84.248 124.048   83.880 123.423   83.577 122.770   83.342 122.095  
 83.174 121.405   83.074 120.704   83.041 119.999   83.074 119.293  
 83.175 118.592   83.343 117.902   83.578 117.227   83.881 116.574  
 84.250 115.949   84.685 115.359   85.183 114.813   85.742 114.317  
 86.356 113.879   87.020 113.509   87.727 113.212   88.466 112.996  
 89.228 112.864   90.002 112.820   90.776 112.865   91.538 112.997  
 92.277 113.214   92.983 113.511   93.647 113.882   94.261 114.319  
 94.819 114.816   95.317 115.363   95.751 115.952   96.120 116.577  
 96.422 117.230   96.657 117.905   96.824 118.595   96.925 119.296  
 96.958 120.001  ] scurve 
%%% D 
105.824 120.001 moveto 
%%% Y 61  
[ 105.824 120.001  105.791 121.376  105.691 122.763  105.515 124.176  
105.248 125.624  104.872 127.112  104.360 128.642  103.684 130.206  
102.810 131.785  101.708 133.348  100.350 134.849   98.722 136.228  
 96.830 137.412   94.702 138.329   92.398 138.910   89.998 139.109  
 87.599 138.909   85.295 138.328   83.167 137.412   81.275 136.227  
 79.647 134.849   78.289 133.348   77.187 131.784   76.313 130.205  
 75.636 128.642   75.124 127.112   74.747 125.623   74.480 124.175  
 74.304 122.761   74.203 121.373   74.171 119.997   74.204 118.621  
 74.304 117.233   74.481 115.819   74.749 114.371   75.126 112.882  
 75.639 111.352   76.317 109.788   77.192 108.209   78.296 106.646  
 79.655 105.146   81.284 103.768   83.177 102.585   85.305 101.670  
 87.609 101.091   90.008 100.894   92.407 101.095   94.710 101.677  
 96.836 102.594   98.727 103.780  100.353 105.158  101.710 106.659  
102.811 108.222  103.684 109.800  104.360 111.363  104.871 112.892  
105.247 114.380  105.514 115.827  105.691 117.239  105.791 118.627  
105.824 120.001  ] scurve 
%%% D 
109.995 120.000 moveto 
%%% Y 61  
[ 109.995 120.000  109.995 121.485  109.991 123.001  109.973 124.583  
109.919 126.263  109.798 128.072  109.566 130.038  109.162 132.183  
108.504 134.511  107.495 137.004  106.025 139.599  103.986 142.182  
101.307 144.575   97.990 146.549   94.145 147.860   89.998 148.321  
 85.851 147.859   82.006 146.547   78.690 144.574   76.012 142.181  
 73.974 139.598   72.503 137.003   71.494 134.512   70.836 132.184  
 70.430 130.040   70.197 128.073   70.076 126.264   70.021 124.583  
 70.001 123.000   69.997 121.482   69.996 119.997   69.997 118.511  
 70.001 116.993   70.021 115.409   70.076 113.728   70.198 111.918  
 70.432 109.951   70.839 107.805   71.499 105.477   72.510 102.985  
 73.984 100.391   76.025  97.809   78.705  95.419   82.024  93.449  
 85.870  92.141   90.017  91.684   94.162  92.149   98.004  93.464  
101.316  95.439  103.991  97.833  106.026 100.415  107.494 103.009  
108.501 105.498  109.157 107.825  109.562 109.967  109.794 111.932  
109.915 113.740  109.970 115.418  109.990 117.000  109.994 118.516  
109.995 120.000  ] scurve 
%%% D 
112.607 119.999 moveto 
%%% Y 61  
[ 112.607 119.999  112.641 121.427  112.741 122.898  112.900 124.460  
113.100 126.164  113.311 128.066  113.489 130.227  113.559 132.712  
113.414 135.582  112.890 138.879  111.766 142.592  109.769 146.609  
106.620 150.657  102.149 154.260   96.451 156.803   89.996 157.726  
 83.542 156.800   77.846 154.257   73.377 150.653   70.230 146.606  
 68.234 142.590   67.111 138.879   66.586 135.584   66.439 132.715  
 66.508 130.231   66.683 128.070   66.893 126.167   67.092 124.462  
 67.249 122.899   67.349 121.427   67.382 119.997   67.348 118.568  
 67.248 117.095   67.090 115.531   66.892 113.824   66.682 111.920  
 66.508 109.757   66.440 107.271   66.590 104.401   67.117 101.104  
 68.245  97.393   70.246  93.377   73.398  89.332   77.873  85.734  
 83.573  83.197   90.028  82.281   96.479  83.214  102.169  85.763  
106.631  89.369  109.772  93.416  111.762  97.430  112.882 101.138  
113.404 104.430  113.550 107.296  113.480 109.777  113.304 111.936  
113.094 113.836  112.896 115.540  112.738 117.101  112.640 118.571  
112.607 119.999  ] scurve 
%%% D 
114.380 119.998 moveto 
%%% Y 61  
[ 114.380 119.998  114.441 121.303  114.629 122.648  114.952 124.093  
115.396 125.711  115.935 127.565  116.548 129.741  117.176 132.355  
117.708 135.538  117.960 139.432  117.619 144.157  116.209 149.729  
113.091 155.895  107.639 161.920   99.675 166.517   89.994 168.263  
 80.315 166.512   72.354 161.913   66.907 155.887   63.793 149.723  
 62.384 144.154   62.044 139.433   62.294 135.542   62.824 132.361  
 63.449 129.748   64.059 127.572   64.596 125.716   65.038 124.097  
 65.360 122.650   65.547 121.304   65.607 119.998   65.546 118.691  
 65.357 117.345   65.034 115.896   64.592 114.275   64.055 112.418  
 63.446 110.239   62.822 107.623   62.295 104.439   62.048 100.546  
 62.393  95.822   63.809  90.252   66.932  84.089   72.390  78.067  
 80.360  73.480   90.043  71.746   99.718  73.510  107.667  78.119  
113.102  84.147  116.206  90.309  117.607  95.873  117.943 100.589  
117.691 104.474  117.160 107.651  116.535 110.260  115.925 112.434  
115.389 114.287  114.947 115.904  114.626 117.349  114.439 118.693  
114.380 119.998  ] scurve 
%%% D 
115.641 119.996 moveto 
%%% Y 61  
[ 115.641 119.996  115.709 121.164  115.953 122.336  116.426 123.602  
117.095 125.081  117.913 126.804  118.934 128.852  120.128 131.423  
121.400 134.686  122.613 138.903  123.432 144.389  123.229 151.440  
120.916 160.089  114.993 169.550  104.349 177.553   89.991 180.795  
 75.635 177.545   64.999 169.537   59.083 160.076   56.776 151.430  
 56.576 144.385   57.395 138.905   58.605 134.693   59.873 131.432  
 61.063 128.862   62.081 126.814   62.895 125.090   63.560 123.607  
 64.034 122.337   64.279 121.166   64.345 119.999   64.277 118.831  
 64.030 117.659   63.555 116.387   62.889 114.902   62.075 113.175  
 61.057 111.124   59.868 108.550   58.602 105.285   57.396 101.069  
 56.582  95.585   56.790  88.535   59.110  79.887   65.043  70.428  
 75.700  62.435   90.066  59.214  104.413  62.490  115.029  70.512  
120.923  79.974  123.216  88.611  123.408  95.647  122.586 101.119  
121.374 105.325  120.106 108.580  118.916 111.146  117.901 113.190  
117.088 114.913  116.423 116.393  115.949 117.661  115.705 118.831  
115.641 119.996  ] scurve 
%%% D 
116.591 119.993 moveto 
%%% Y 121 
[ 116.591 119.993  116.594 120.541  116.617 121.057  116.697 121.540  
116.859 122.009  117.119 122.489  117.485 123.018  117.933 123.646  
118.401 124.378  118.864 125.156  119.376 125.944  119.997 126.767  
120.760 127.699  121.624 128.825  122.511 130.141  123.438 131.599  
124.472 133.248  125.596 135.201  126.734 137.504  127.875 140.190  
128.974 143.370  129.923 147.132  130.588 151.572  130.758 156.778  
130.135 162.791  128.324 169.553  124.854 176.818  119.277 184.060  
111.356 190.432  101.315 194.881   89.986 196.485   78.659 194.873  
 68.621 190.418   60.705 184.042   55.134 176.797   51.672 169.531  
 49.866 162.770   49.249 156.759   49.423 151.557   50.090 147.122  
 51.040 143.365   52.139 140.190   53.279 137.508   54.415 135.208  
 55.537 133.258   56.569 131.611   57.491 130.155   58.374 128.839  
 59.236 127.712   59.999 126.778   60.620 125.956   61.129 125.171  
 61.587 124.394   62.048 123.658   62.495 123.023   62.864 122.489  
 63.127 122.007   63.292 121.540   63.373 121.059   63.395 120.546  
 63.395 120.000   63.394 119.453   63.371 118.940   63.288 118.459  
 63.122 117.991   62.857 117.509   62.486 116.972   62.039 116.335  
 61.579 115.597   61.122 114.820   60.612 114.035   59.989 113.212  
 59.224 112.274   58.363 111.142   57.484 109.824   56.562 108.367  
 55.531 106.719   54.410 104.765   53.276 102.463   52.138  99.778  
 51.042  96.600   50.095  92.839   49.431  88.400   49.263  83.194  
 49.889  77.178   51.705  70.413   55.183  63.146   60.772  55.904  
 68.708  49.539   78.765  45.105   90.101  43.522  101.426  45.159  
111.452  49.637  119.348  56.027  124.898  63.278  128.342  70.542  
130.133  77.297  130.740  83.300  130.559  88.494  129.887  92.921  
128.935  96.672  127.834  99.840  126.694 102.518  125.558 104.813  
124.436 106.759  123.406 108.402  122.484 109.856  121.601 111.170  
120.740 112.294  119.979 113.226  119.360 114.046  118.853 114.831  
118.395 115.608  117.934 116.344  117.487 116.977  117.118 117.511  
116.855 117.991  116.690 118.458  116.609 118.937  116.587 119.447  
116.591 119.993  ] scurve 
%%% D 
117.438 119.978 moveto 
%%% Y 181 
[ 117.438 119.978  117.392 120.420  117.304 120.766  117.255 121.042  
117.256 121.283  117.309 121.504  117.415 121.710  117.581 121.906  
117.822 122.094  118.166 122.294  118.650 122.572  119.194 123.069  
119.566 123.709  119.813 124.275  120.062 124.746  120.369 125.152  
120.767 125.514  121.302 125.856  122.039 126.238  122.993 126.852  
123.858 127.822  124.480 128.812  125.082 129.674  125.826 130.459  
126.829 131.290  128.092 132.433  129.237 133.988  130.198 135.558  
131.312 137.105  132.709 138.943  134.056 141.279  135.272 143.791  
136.641 146.625  137.912 150.028  139.033 153.849  139.973 158.306  
140.534 163.392  140.555 169.201  139.785 175.726  137.908 182.908  
134.573 190.560  129.429 198.320  122.229 205.616  112.960 211.701  
101.966 215.777   89.980 217.213   77.994 215.769   67.002 211.686  
 57.737 205.594   50.542 198.293   45.405 190.529   42.077 182.874  
 40.208 175.691   39.444 169.167   39.472 163.360   40.039 158.278  
 40.983 153.825   42.106 150.008   43.382 146.609   44.750 143.783  
 45.966 141.272   47.315 138.941   48.710 137.110   49.821 135.566  
 50.779 133.998   51.922 132.444   53.185 131.303   54.187 130.474  
 54.930 129.692   55.528 128.837   56.141 127.851   56.992 126.874  
 57.948 126.247   58.692 125.862   59.231 125.522   59.633 125.163  
 59.941 124.763   60.189 124.300   60.427 123.746   60.773 123.107  
 61.304 122.582   61.799 122.288   62.155 122.085   62.402 121.896  
 62.573 121.702   62.682 121.498   62.738 121.279   62.742 121.041  
 62.695 120.770   62.607 120.435   62.548 120.000   62.606 119.566  
 62.694 119.230   62.740 118.960   62.735 118.722   62.678 118.504  
 62.567 118.299   62.395 118.106   62.144 117.917   61.784 117.712  
 61.284 117.411   60.758 116.876   60.421 116.239   60.185 115.689  
 59.937 115.230   59.627 114.831   59.222 114.474   58.677 114.135  
 57.924 113.744   56.966 113.102   56.128 112.117   55.523 111.137  
 54.925 110.287   54.179 109.507   53.171 108.676   51.907 107.525  
 50.773 105.967   49.817 104.403   48.704 102.860   47.307 101.023  
 45.963  98.688   44.748  96.177   43.379  93.345   42.108  89.943  
 40.986  86.121   40.046  81.663   39.485  76.574   39.464  70.761  
 40.238  64.230   42.120  57.040   45.467  49.380   50.627  41.615  
 57.849  34.320   67.142  28.245   78.159  24.190   90.159  22.784  
102.146  24.263  113.127  28.380  122.370  34.497  129.538  41.815  
134.648  49.584  137.953  57.238  139.802  64.415  140.551  70.929  
140.511  76.726  139.938  81.799  138.987  86.241  137.863  90.051  
136.582  93.441  135.217  96.259  134.001  98.769  132.646 101.093  
131.255 102.915  130.150 104.457  129.190 106.029  128.039 107.578  
126.779 108.708  125.785 109.534  125.046 110.317  124.449 111.176  
123.832 112.165  122.973 113.137  122.019 113.753  121.281 114.136  
120.746 114.476  120.347 114.835  120.041 115.237  119.794 115.701  
119.556 116.257  119.208 116.896  118.675 117.418  118.181 117.711  
117.827 117.914  117.579 118.103  117.409 118.297  117.299 118.502  
117.242 118.720  117.235 118.956  117.280 119.224  117.368 119.551  
117.438 119.978  ] scurve 
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