A curve cast is one that creates a curve in the leader by whipping the rod tip to the right or left during the end of the power stroke. Curve casts give you an opportunity to present the fly to the fish before the line becomes visible. It can be used to reach a fish lieing downstream behind a boulder or to put a fly under an overhang with protective cover. Curve casts are also helpful in casting across faster currents so that the fly presents a longer period of a drag-free drift within the slower water on the other side.
Curve casts can be made to go either right or left. If you are right-handed, a left curve is the easier one. The rod is stroked with a side arm cast on a horizontal plane. Check the rod sharply at the completion of the forward stroke. The amount of curve will depend on the extent of the overpower in the forward stroke and how sharply you check the stroke. Some casters will add a reach to the right at the end of the stop to increase the inertia effect on the line and deepen the curve. Another technique, usually used for tighter left curves, is to do an overhand cast with your arm but twist your hand and wrist to the left sharply. The rod tip will make a left curve arc which the line follows.
Pile-Curve: Bring the forward stroke lightly upward. The line will hook and arc upwards, then drop to the water surface in a pile. This technique will only work well on windless days on flat water, particularly for small dries.