Like the previous post on diagonal lines, curves can also be used to convey movement and direction and can be a good tool for guiding the eye through an image. However, unlike diagonal lines, curves tend to only convey direction one way. The images below are all examples demonstrating the use of curves:
Here the wave provides the curve showing both movement and direction.
This is an example of how a curve can be used to lead the eye up to a point in the image.
The elephants trunk provides the curve and gives a sense of direction.
Finally, the curve here gives a sense of movement. The curve is being exaggerated by using a more acute angle.