This is not a Curve cast as this cast is for a totally different application altogether. The Hook cast is designed to literally kick the fly around the corner at the extremity of the cast, the result being a sharp elbow shape in the end section of your fly line, giving you the ability to put your fly into a blind spot behind a rock for instance, or around a protrusion on the bank etc. in both instances it allows you, the angler, to target those difficult to reach fish, and in many cases affording you the added bonus of allowing you to stay out of sight whilst doing so.
This cast can be produced with an overpowered side cast (a Tuck cast on it's side) assisted by quite a short sharp stop at the end of the forward cast, or alternatively if you do not have the room available to create a side cast, then an Overhead cast with a sharp inward tuck of the wrist or forefinger (depending on grip) at the end of the forward cast will also work. If you have no room available behind, then this is yet another cast that can be made off the back of a Spey Cast.