According tp page 46 of Practical Homicidal Investigation: Tactics, Procedures, and Forensic Techniques by Vernon J. Gerberth (published in 1983), drawing a chalk outline of a victim’s body is “good procedure” if said victim is not dead and is going to be rushed to a hospital.
I’m not really sure how this could be more time efficient than a quick picture, but that’s what it says. Old book, I know, but it does show that this method has been used at some point in time
Well, you’d take lots of pictures from lots of angles, hopefully with a photographer who knows his trade and his (hopefully also good) equipment. Using the right lens for the right picture would also make a difference. Longeer lenses, IIRC, tend to distort images less than shorter/wider lenses, but they may be more limiting in where you can take the picture from (since you’d have to be able to stand farther back to use the longer lens).
+52XP
You found a fish fin! 
My suggestion for carpet would be cat barf. It will be there until you replace the carpet.
As a volunteer EMT, I can confirm that this does happen quite often. With mice, that is.
And I can also confirm that a) it is very funny, and b) it does point out the need for pest control.
I so need one of those beach towels. I’d tan funny, though, because I would absolutely have to lie in the position dictated by the outline. All the time.