We're big fans of laser cutters here at oomlout, and in particular how they can create new and exciting uses for everyday materials. Aaron Porterfield is a fellow enthusiast, and recently published the results of his experiments with creating lattice hinges - laser-cut patterns that make wood flexible like paper - and curved surfaces, building on the work of Patrick Fenner at Deferred Procrastination.
I'm no engineer, so all of what I've found is through trial and error. I tried a lot of different patterns to try to achieve different results, most of which were failed attempts at making a doubly curved surface. Some turned out to be more flexible than I expected. Some were much less than expected. [Wave lattice] is one that turned out to be more flexible than expected. It was an attempt to bend in two directions, which it does not. It does however bend in one direction pretty well for such short spring members. [Cross lattice] is what I've found to be the most flexible pattern so far. In thinner materials, it's even able to bend on a diagonal. I have come up with two ways to create curved bends. The first is manually warping a pattern with Illustrator and Photoshop. The second is parametrically generating the pattern on a surface. Warping will take some practice. It helps to have a good understanding of how to work with bezier curves when using Illustrator and Photoshop.Aaron's experiments with creating lattice hinges capable of bending a sheet of wood along a curve are particularly interesting. These can be found towards the end of his 10-step Instructables post.