  The unprecedented quality of the observations available from the Atacama
Large Millimetre/sub-millimetre Array (ALMA) calls for analysis methods making
the best of them. Reconstructing in space the morphology and kinematics of
radio sources is an underdetermined problem that requires imposing additional
constraints for its solution. The hypothesis of rotational invariance about a
well-defined star axis, which is a good approximation to the description of the
gas envelopes of many evolved stars and protostars, is particularly efficient
in this role. In the first part of the article, a systematic use of simulated
observations allows for identifying the main problems and for constructing
quantities aimed at solving them. In particular the evaluation of the
orientation of the star axis in space and the differentiation between expansion
along the star axis and rotation about it are given special attention. The use
of polar rather than Cartesian sky coordinates is shown to better match the
morphology and kinematics of actual stars. The radial dependence of the gas
density and temperature and the possible presence of velocity gradients are
briefly considered. In the second part, the results obtained in the first part
are applied to a few stars taken as examples with the aim of evaluating their
usefulness when applied to concrete cases. A third part takes stock of what
precedes and formulates some guidelines for modelling the radio emission of
axisymmetric radio sources, limited however to the mathematics and geometry of
the problem, physics considerations being ignored.
