  The problem of de-projection of radio line observations of axi-symmetric
expanding circumstellar envelopes is studied with the aim of easing their
analysis in terms of physics models. The arguments developed rest on the remark
that, in principle, when the wind velocity distribution is known, the effective
emissivity can be calculated at any point in space. The paper provides a
detailed study of how much this is true in practice. The wind velocity
distribution assumed to be axi-symmetric and in expansion, is described by four
parameters: the angles defining the orientation of the symmetry axis, an
overall velocity scale and a parameter measuring the elongation (prolateness)
of the distribution. Tools are developed that allow for measuring, or at least
constraining, each of the four parameters. The use of effective emissivity as
relevant quantity, rather than temperature and density being considered
separately, implies important assumptions and simplifications meaning that the
approach being considered here is only a preliminary to, and by no means a
replacement for, a physics analysis accounting for radiative transfer and
hydrodynamics arguments. While most considerations are developed using
simulated observations as examples, two case studies (EP Aqr, observed with
ALMA, and RS Cnc, with NOEMA) are presented that illustrate their usefulness in
practical cases.
