I sollicite your kindness to help me draw this picture of Theorem of projection on closed convex , by using the Tikz package.

Thanks in advance for your help.


The line connecting x and P_C(x) has to be normal to C. This can be achieved using the in and out syntax, which is used for almost everything else here.

\begin{tikzpicture}[bullet/.style={circle,fill,inner sep=1.5pt,node contents={}}]
 \draw (0,0) node[bullet,label=left:$P_C(x)$,alias=PC]  -- (15:3) coordinate[midway] (aux)
    node[bullet,label=above right:$x$] -- ++ (-145:4.5) node[midway,below right]{$\|x-z\|$}     node[bullet,label=below left:$z$];
 \draw (PC) to[out=105,in=0] ++ (-0.75,1) to[out=180,in=105] ++ (-1.5,-3)
 node[above right]{$C$} to[out=-75,in=180] ++ (1.25,-1) to[out=0,in=-75] cycle;
 \draw[shorten <=2pt,-latex] (aux) to[out=90,in=-90] ++ (110:0.8) node[above]{$\|x-P_C(x)\|$};

enter image description here

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