3-D ionization structure (in stereoscopic view) of Planetary Nebulae: the case of NGC 1501

Long-slit echellograms of the high excitation planetary nebula NGC1501, reduced according to the methodology developed by Sabbadin et al. (2000a, b), allowed us to obtain the ``true'' distribution of the ionized gas in the eight nebular slices covered by the spectroscopic slit. A 3-D rendering procedure is described and applied, which assembles the tomographic maps and rebuilds the spatial structure. The images of NGC 1501, as seen in 12 directions separated by 15 deg, form a series of stereoscopic pairs giving surprising 3-D views in as many directions. The main nebula consists of an almost oblate ellipsoid of moderate ellipticity (a=44 arcsec, a/b=1.02, a/c=1.11), brighter in the equatorial belt, deformed by several bumps, and embedded in a quite homogeneous, inwards extended cocoon. Some reliability tests are applied to the rebuilt nebula; the radial matter profile, the small scale density fluctuations and the 2-D (morphology) - 3-D (structure) correlation are presented and analysed. The wide applications of the 3-D reconstruction to the morphology, physical conditions, ionization parameters and evolutionary status of expanding nebulae in general (planetary nebulae, nova and supernova remnants, shells around Population I Wolf-Rayet stars, nebulae ejected by symbiotic stars, bubbles surrounding early spectral type main sequence stars etc.) are introduced.