For the extremely basic case of static stability - no perturbing forces like wind or things bumping into it - it's pretty straightforward. Just use Rhino to find the center of gravity of the structure and project it vertically to the ground. You will need to have some additional structure of some sort which is attached to your structure and extends to cover the point on the ground directly beneath the center of gravity. Kind of like keeping your feet under your hips if you don't want to fall over.
If you can assume your structure is extremely stiff, you can also make some assumptions about how far you would like the structure to be allowed to rotate and still return to it's initial position. Then you must make the added "foot" large enough to cover the area on the ground which contains the projections of all possible allowed locations of the CG. The supporting "foot's" bottom surface must be of such a shape that as the structure rotates, it's center of gravity will rise. This will make the structure want to return to it's rest position. This is called positive static stability.
It starts to get more involved if it's a flexible structure subject to various types of loading.
Does this help?