Non-analytical Method
The non-analytical method digitizes the profile and path you specify for the the revolution or extrusion and uses these points to create the revolution or extrusion. For a revolution, it also moves the profile making it perpendicular to the path along which you are revolving the profile, and then performs the revolution. The resulting solid geometry for both a revolution and extrusion are sharp edges where the points of the profile were. The geometry is not smoothed.
When you modify an extrusion or revolution created using the non-analytical method, you move the original profile points to change the solid.
Comparision of revolutions created with analytical and non-analytical methods
Comparision of extrusions created with analytical and non-analytical methods