Exposed pool walls, spas, or water features are typically 12" thick. So the coping has to be cut from a wider pieces - usually 16" wide (usually natural stone - examples: travertine, marble, shellstone, firerock)
You also have to factor in veneer thickness for exposed pool beams. Stucco doesn’t add significant thickness. You need to account for the extra thickness if you use something like a 1 1/2” thick split stone veneer.
Long, linear manmade products don’t work well for curved pools unless they are specifically designed as coping for a curved pool. This is because you can not cut the factory edge of a manmade product such as Shellock pavers. In that case you would have to use the Shellock pool coping with the bullnose edge. Natural stones such as travertine or marble can have the edges cut. So they can be used on curved pools.
We are running in to issues with artisitic coping used on spas with ledger stone.. by the time you add ledger the spa beam is almost too wide for artisitic
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Coping