Using methods like this one (and with more details here) can be useful when one tries to draw "free" curves. However, once a free curve is obtained it can be very useful to access arbitrary points on it. Unfortunately, the following naive approach is useless:

  \draw[->] (-2,0) -- (2,0);
  \draw[->] (0,-2) -- (0,2);

  \draw[thick,mark=ball] plot [smooth,tension=1.5] coordinates{(1,1) (1.4,0.5) (0.4,-0.2) (0.6,-0.2) (0.2,-1.4) (-0.5,-1.1) (-1,-1.6) (-1.4,0.4)}
  node[pos=0.5]{A} node[pos=0.9]{B};

since it yields the following:

enter image description here

So what is the right way to specify points on a curve generated as above?

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