<div class="aide"><a name="para">
On note ici les deux paramtres \( u ) et \( v ) : de manire compacte,
<p> <center>
\(\vec{OM}=\vec{OA}+ uV_1+vV_2   \quad  (u,v)\in D)
</center></p>
avec 
<p> <center>
\( D=\lbrace (u,v )| 0\leq u\leq  1, 0\leq v \leq 1 \rbrace)
</center></p>
ou 
<p> <center>
\( \left \lbrace \begin{matrix} x&=&a+ua_1+va_1\\y&=&b+ub_1+vb_2\\z&=&c+uc_1+vc_2  \end{matrix} \quad  (u,v)\in D
 )
</center></p>

si \(A) est le point de coordonnes \((a , b , c)) et \(V_1) et \(V_2) les vecteurs 
\((a_1 , b_1 , c_1)) et \((a_2 , b_2 , c_2)). </div>

\def{text L=randint(1..4),randint(1..4),randint(1..4),-randint(1..4),randint(1..4),random(+,-)randint(1..4)}
\def{text data=\L[1]*u+\L[4]*v,\L[2]*u+\L[5]*v,\L[3]*u+\L[6]*v,0,1,0,1}
\def{integer a1=\L[1]}
\def{integer a2=\L[2]}
\def{integer a3=\L[3]}
\def{integer a4=\L[4]}
\def{integer a5=\L[5]}
\def{integer a6=\L[6]}
\def{text data1=\data[1]}
\def{text data2=\data[2]}
\def{text data3=\data[3]}
\def{text data4=\data[4]}
\def{text data5=\data[5]}
\def{text data6=\data[6]}
\def{text data7=\data[7]}
\def{text data8=\data[8]}
\def{text data9=\data[9]}
\def{text data10=\data[10]}
\def{text data11=\data[11]}
\def{text data12=\data[12]}
\def{text data13=\data[13]}

<div class="exercice"> \reload{<img src="gifs/doc/etoile.gif" alt="rechargez" width="20" height="20">}{para} Le 
\tool{module=tool/geometry/animtrace.fr&+cmd=new&+type=parametric3DS&+special_parm=noshow&+quality=4&+x1=\data1&+y1=\data2&+z1=\data3&+uleft=\data4&+uright=\data5&+vleft=\data6&vright=\data7&
+xleft=\data8&+xright=\data9&+yleft=\data10&+yright=\data11&+zleft=\data12&+zright=\data13}{
Trac} pour \(v_1 = (\a1,\a2,\a3)) et \(v_2 = (\a4,\a5,\a6)).
</div>