You can warp images without meshes at all. Put some control points onto an image to be distorted and move them. No problem at all. The only thing, what should be kept in mind, is that if one control point is moved, the whole image will be distorced.
This fact could be treated as a defect, in comparison with mesh-based methods, or as an advantage. On the other hand, if you want to restrict distortion of some area of an image, put there some anchor points and do not move them.
Or select a rectangular part of the whole image and warp it, leaving the rest untouched. Fix result of warping inside this rectangular area, select another area, warp it and so on.
You may repeat it as much times as you need. One can put a lot of control points, more than two hundreds in fact. Load photo of your beloved boss and go ahead.