Context : Various morphologies such as multi-concentric shells and spiral-like patterns have been observed around Proto-Planetary Nebulae and AGB stars .
It is widely argued that the regular density patterns are produced by binary systems .

Aims : The goal is to build up a simple dynamical model for the out-flowing circumstellar envelope around AGB stars in a wide binary system to explore the parameter dependence of the geometrical characteristics of column density patterns .

Methods : For an AGB star in a wide binary system , the orbital motion of the star can be approximated as a series of pistons that simultaneously push out dust and gas along radial directions , but work in different oscillation phases .
The piston model can fast produce column density patterns with high enough spatial resolutions for parameter dependence exploration .

Results : The formation of 3-D quasi-spherical density structure is induced by orbital motion of the AGB star .
The column density pattern only depends on two parameters : eccentricity of the orbit e and the terminal outflow velocity to mean orbital velocity ratio \gamma .
When viewed perpendicular to the orbital plane , spiral , broken spiral , and incomplete concentric shell patterns can be seen , while when viewed along the orbital plane , alternative concentric half-shell , egg-shell , and half-shell half-gap patterns will develop .
Non-zero eccentricity causes asymmetry , while larger \gamma makes a weaker pattern and helps bring out asymmetry .
A spiral pattern may becomes broken when e > 0.4 .
The spiral center is always less than 12 \% of spiral pitch away from the orbit center .
One should have more chances ( \sim 80 \% ) seeing spiral-like patterns than seeing concentric shells ( \sim 20 \% ) in the circumstellar envelope of wide binary AGB stars .

Conclusions :