Conventional hinges need to connect two surfaces that are running parallel in the same axis in order to work. That can place limitations on your designs. For example, let's say you've designed something with a wildly organic shape, like this Caleb Woodard cabinet, below:
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As you can see, conventional hinges aren't going to cut it here. So Woodard uses knife hinges, also known as pivot hinges. Here's how he installs them:
The hinges Woodard's using are produced by New-Jersey-based Brusso Hardware, who commissioned the video. They've got some more information on knife hinges, like what size to use based on your material thickness and other technical data, here.