  We define an entanglement witness in a composite quantum system as an
observable having nonnegative expectation value in every separable state. Then
a state is entangled if and only if it has a negative expectation value of some
entanglement witness. Equivalent representations of entanglement witnesses are
as nonnegative biquadratic forms or as positive linear maps of Hermitian
matrices. As reported elsewhere, we have studied extremal entanglement
witnesses in dimension $3\times 3$ by constructing numerical examples of
generic extremal nonnegative forms. These are so complicated that we do not
know how to handle them other than by numerical methods. However, the
corresponding extremal positive maps can be presented graphically, as we
attempt to do in the present paper. We understand that a positive map is
extremal when the image of $\mathcal{D}$, the set of density matrices, fills
out $\mathcal{D}$ maximally, in a certain sense. For the graphical presentation
of a map we transform it to a standard form where it is unital and trace
preserving. We present an iterative algorithm for the transformation, which
converges rapidly in all our numerical examples and presumably works for any
positive map. This standard form of an entanglement witness is unique up to
unitary product transformations.
