This question starts with this previous question How can I create spherical topology from a 2D image?.
The idea behing all that : this bending makes interesting things, but it is hard to predict how to do them.
An example, before the question. Using the same technics you can obtain a tire shape from a flat surface.
But first the approach gives something that I feel counter intuitive. If we start from the result of the question quoted above, go to edit mode and rotate the shape 90° (so the object own rotations stay 0), we don't obtain a similar result. Testing that I was expecting an ovoid shape but this is not the case.
After that I did a little test, without the empties, just bending the shape. I started with a square 1x1. Playing with the deform angle, we obtain a fan (convergence of the top vertices) at an angle of 114.592°. And, it seems that 360 / 114.592 = 3.14158 (PI). And we can also notice that this value is linearly proportional to the Y dimension of the shape (if the plane is 2m in Y, the angle is 57,28°)
If we continue to 360° (for the deform angle), we found that the shape rotates around a point at Y=0.1591575m. And PI x this number if 5 (very very nearly).
And as the angle can vary from -360 to 360, this last limit point varies 10 / PI around the center.
We can also notice that the diameter of the 'circle' is 1.318311m from (in Y) -0.5 to +0.818311. Which is 1 + (2 x 0.1591575) (the value mentioned above).
The inner circle is nearly (but not so exactly) half of the outer.
Clearly there are some clever rules and calculations behind all that. But what are they ? What is to be understood in order to "predict" how use the modifier well ?
Which "patterns" are interesting to use ? (by pattern, I mean for instance the one of the initial question : using two deforms (180 and 360) and two empties (90,0,0) and (90, 0, 90))