  We consider the polar curves $\PSO$ arising from generic projections of a
germ $(S,0)$ of complex surface singularity onto $\C^2$. Taking $(S,0)$ to be a
minimal singularity of normal surface (i.e. a rational singularity with reduced
tangent cone), we give the $\delta$-invariant of these polar curves, as well as
the equisingularity-type of their generic plane projections, which are also the
discriminants of generic projections of $(S,0)$. These two
(equisingularity)-data for $\PSO$ are described in term, on the one side of the
geometry of the tangent cone of $(S,0)$ and on the other side of the
limit-trees introduced by T. de Jong and D. van Straten for the deformation
theory of these minimal singularities. These trees give a combinatorial device
for the description of the polar curve which makes it much clearer than in our
previous Note on the subject. This previous work mainly relied on a result of
M. Spivakovsky. Here we give a geometrical proof via deformations (on the
tangent cone, and what we call Scott deformations) and blow-ups, although we
need Spivakovsky's result at some point, extracting some other consequences of
it along the way.
