My aim is to apply pre-designed pattern on a 3D shape so that it can follow the shape of the 3D elements, including depth. A typical example would be this illustration.
I don't think this is possible with Illustrator (and if it were, I would be very impressed). I think you would need software that is specifically 3D. I'm not sure what people are using these days, but it used to be software like Maya or 3D Studio Max.
Illustrator has some nifty perspective tools, but nothing that allows a pattern to be stretched over a curved surface. AFAIK.