I've been experimenting with making 3D models of illegible gravestones using photogrammetry, and it's working surprisingly well, so I thought it would be helpful to post instructions for others to follow. This is somewhat like taking a stone rubbing, except without actually contacting or damaging the stone.
[This was previously posted in the Find A Grave forum, but that forum is only visible to members, and posts are not editable, so this is the version I will keep up-to-date]
(There are other photogrammetry software solutions if this doesn't fit your computer’s operating system or hardware, but I don't know how to use them, so I can’t write instructions for them.)
I got better models when I took close-up photos while "scanning" across the stone, rather than photos of the entire stone. It's probably good to take at least two photos of the entire stone, so the software can figure out where the close-ups fit into the whole, though.
There's a trade-off in the number of photos you take. If you take too few, it might not produce a legible model, but if you take too many, it will take too long to process. Usually I got good results with 16-33 close-up photos, while 11 wide-angle photos didn't work great.
(On the other hand, I once used only 4 wide-angle photos and got good results. It depends on the stone texture, the depth of the engraving, etc.)
I used the Open Camera Android app, since it allows me to turn off my phone’s built-in image sharpening (which degrades the 3D modeling) and I can put it in "Repeat" mode, so it automatically focuses and takes a photo once per second, and I don't need to push the button each time, reducing blurriness.