  Tomographic and 3-D analyses for extended, emission-line objects are applied
to long-slit ESO NTT + EMMI high-resolution spectra of the intriguing planetary
nebula NGC 7009, covered at twelve position angles. We derive the gas expansion
law, the diagnostics and ionic radial profiles, the distance and the central
star parameters, the nebular photo-ionization model and the spatial recovery of
the plasma structure and evolution. The Saturn Nebula (distance~1.4 kpc,
age~6000 yr, ionized mass~0.18 Mo) consists of several interconnected
components, characterized by different morphology, physical conditions,
excitation and kinematics. The internal shell, the main shell, the streams and
the ansae expand at V(exp)~4.0xR" km/s, the outer shell, the caps and the
equatorial pseudo-ring at V(exp)~3.15xR" km/s, and the halo at V(exp)~10 km/s.
We compare the radial distribution of the physical conditions and the line
fluxes observed in the eight sub-systems with the theoretical profiles coming
from the photo-ionization code CLOUDY, inferring that all the spectral
characteristics of NGC 7009 are explainable in terms of photo-ionization by the
central star, a hot (logT*~4.95) and luminous (log L*/Lo~3.70) 0.60--0.61 Mo
post--AGB star in the hydrogen-shell nuclear burning phase. The 3--D shaping of
the Saturn Nebula is discussed within an evolutionary scenario dominated by
photo-ionization and supported by the fast stellar wind: it begins with the
superwind ejection, passes through the neutral, transition phase (lasting ~
3000 yr), the ionization start (occurred ~2000 yr ago), and the full ionization
of the main shell (~1000 yr ago), at last reaching the present days: the whole
nebula is optically thin to the UV stellar flux, except the caps and the ansae.
