Would love to see in addition to current vertical and horizontal perspective changing options a free one, similar to what Snapseed mobile app can do right now.
The Transform tool (Command + T) has a Distort mode which, I believe, is very close to what you're looking for (it only doesn't do the autofill of the transparent areas).
Oh, you are right! I guess I have too old of a version, because my app doesn't have those options yet. Will make sure to update now then! Thanks for the help, that seems to do the job just by looking at the icon.
These options have actually been available for a while now, so I'm guessing you've simply overlooked them. They should be available at the very top of the Tool Options pane when you activate the Transform tool. Let me know if you can find them!