  Asymptotic Giant Branch (AGB) stars generally have spherically symmetric
envelopes, whereas most post-AGB stars and Planetary Nebulae (PNe) show
axisymmetric circumstellar envelopes. While various mechanisms for axisymmetric
circumstellar structures may explain the shapes of PNe, they do not address how
the shape of the circumstellar shell evolves. Here we address the temporal
changes in the axisymmetry of AGB star envelopes, and in particular the
development of the torus required in the Generalized Interacting Stellar Winds
(GISW) model. Assuming (1) an AGB star rotates with sufficient angular speed at
the start of the AGB phase; and (2) that the rotational angular momentum of the
AGB star is conserved, we demonstrate that some very important observational
features of AGB star axisymmetry evolution can be reproduced. We find that,
compared to the star's increasing luminosity and decreasing effective
temperature, the decreasing mass of the star primarily affects the axisymmetry
of the envelope. When a representative mass loss history is adopted, where most
of the mass is lost near the end of the AGB phase, the envelope's axisymmetry
increases over time, with the strongest increase occurring near the end of the
AGB phase. This may naturally explain why most AGB stars have spherically
symmetric envelopes, while axisymmetry seems common-place in the post-AGB/PNe
phase. The degree of axisymmetry at the end of the AGB phase is found to
increase with increasing main sequence mass, and the onset of axisymmetry
occurs only after the onset of the superwind (SW) phase, in good agreement with
the observations.
