Here's a strange invention intended to let you cut freehand curves in paper, easier than you could with an X-Acto: This HARAC Handy Paper Cutter, manufactured by Japan-based Hasegawa Cutlery.
"The Handy Paper Cutter cuts out designs as if you were photoshopping with your mouse," reads the product description. "A sharp, rust-proof ceramic blade allows you to trace drawing lines and cut out the most intricate shapes with minimal force."
Here it is in action:
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As far as how it works, the ceramic blade is described as not being exposed; the photos below aren't the greatest, but it seems that when you press the button just the very tip extends out of the clear plastic housing, and I'm guessing the blade housing rotates in the manner of a drag knife.