I believe this is a Charonia tritonis shell, one of the largest marine snails. I photographed it more than 2 years ago when I was at the Carnegie Museum of Natural History in Pittsburgh.
What especially attracted me to this shell were the numerous varices on it. A varix is a radial ridge that forms on a snail's shell when the snail stops growing temporarily. Here is one of them.
You can see very clearly that regrowth started from under the old shell (shell growth direction was towards the left). Here is another varix, which was in the body whorl (shell growth direction was towards the bottom).
In a couple of posts back in 2006, I discussed the alignment of the old and new shell material along a break in a shell and demonstrated that in land snails new shell always starts out from under old shell. This Charonia shell shows that this is also the case in marine gastropods. It would probably be less practical for a snail to lay new shell material on top of the existing shell, because the mantle that produces the shell is always in contact with the underneath of the existing shell.