There are some differing concepts regarding this cast and how it should be performed. For me the Curve cast is a useful cast when you need to create a uniformed curve of the fly line between the rod tip and the fly, not a sharp elbow at the far end which is a hook cast (hence the name) (see Hook cast) this is for an entirely different application altogether. Curve Cast examples:
If you are faced with a situation such as a large section of reeds on a Stillwater for instance which are growing around a natural bend along the bank, (quite common on a stillwater) it would be a great advantage to be able to cast your fly line in a progressive curve around these reeds to target fish that may be feeding along this potentially rich area, thus allowing you to retrieve your fly along the natural curve of the reeds as it will inevitably follow the path of your fly line on it's return. Or:
If you are casting across an almost uniformed current on a river, but the middle section is just slightly faster than the rest, but not fast enough to warrant a reach mend, (see Reach mend cast) then an upstream Curve cast will come in handy. Shooting line into the Curve cast will not only add extra distance to your cast, but will also help prevent the fly line form straightening out again before touching down. You may also want to place your curve on the downstrean side to speed your fly up, or to gently swing your fly around protruding obstacles where fish may be in residence.
Curves can be introduced in several ways and can also be used in many different scenarios, but always bear in mind that a good Curve cast is created via a deviation in your tracking e.g. deviating from a straight line path, usually during the forward stroke. I say usually, as it can also be inadvertantly created in the back cast, or purposely if required. So get practicing and give them a go.