Solids of Rotation? (2.77)

I was working on a roughly cylindrical object, when I realized, that the outline of the object along the Z-X plane would create the full object by rotating the whole thing by 2 pi, leaving vertices along the path. However, the only way I found to make this happen was to take the basic line, extrude by 0, then rotate only the new vertices around the Z axis (taking the most central point as the one to pivot around) for 5°, then rinse and repeat with the just created line as new start. To make the whole 360° and using mirroring twice, it took 18 repetitions - which is a PITA in itself, as each repetition is a series of about 6 commands, plus setting up the mirrors. The result is usually pretty good, but changing some parts if you realize a vertex of the original line was off or adding some detail to the original path, this is the real PITA.

So I was wondering, if there is a faster way to create the body of rotation of a line with just one series of commands instead of repeating the steps outlined above. I hope this might make the modifying of the result by just changing the first line and running the command again much easier to test out different angles or such.

For those that speak math, one simple example would be:
There be a graph with f(x)=x²/3+1 for x={-1,1}
Wanted is the body, that is created by the rotation of f(x) by 2*pi around the X-axis.

EDIT:
Random experimenting brought up the SCREW modifier for Bezir Curves, which apparently is what I searched… Solved up to the point that that modifier does not work on Bezier Curves :confused:

see the spin tool in wiki !

happy bl

Sadly Spin does not work on a Bezier curve. So… how to make a Curve into a Mesh first?

[edit] ok, ALT+C first, THEN Screw tool is the way…

Look into User Preferences, Addons. Check Add Mesh, AddMesh: Extra Objects.
Add Mesh (Shift-A) will have Math Function, Z Math Surface, which is where you put your formula in…