I found SketchChair while looking for CNC related projects on Kickstarter. It is an open source application that you can use to draw chairs and output the design files for cutting on a CNC or laser cutter.
They have an design library of chairs that other people have made using the application. I downloaded a few of them, resized the chairs to work with paper as a test. The modified design files can be found in laser-furniture repo on my github account.