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Concepts and guides in photography are building blocks to creating and capturing wonderful images. While the rule of thirds is among the most common building block in composition, the S-curve is also one to be on the look out for.
The S-curve can lead into or out of a scene, start at the bottom or side, but fundamentally it will roughly shape the letter S and either define the photograph or split the composition into two sections.
In the photo below, you'll notice that it doesn't follow the rule of thirds for the horizon placement but that's OK. The S-curve is placed into the right third most of the frame, so vertically speaking it does separate the composition in a pleasing manner. Utilizing an S-curve is all about balance.
S-curves also don't need to be used as separators or dividers, they can also be utilized as the focal point of the photo, as seen below in this winter photo at the mountain.
While these three examples show mostly landscapes, S-curves are visible in most all types of photography, including shooting people and groups. The key is to look for and exploit the oppertunities you have to utilize these soft, flowing lines to either help create compositional separation in the frame or utilize the curve itself as the focal point and featured portion of the image.