You don't need to make it a full circle. Fan menus are also good. https://cuppalabs.github.io/angular-fan-menu/

This assumes the phone knows what angle your finger is coming in from. Even if you assume it is coming in from the bottom half that introduces problems when the hit point is near the top of the screen.

You can ask which hand is being used. It doesn't have to span the whole screen either. It's used in games and works just fine in practice.