Add this to the list of things we never knew existed but now desperately need: The Evolution Door, a "flip-panel" invention by Austrian designer Klemens Torggler.
This is not Torggler's only alternative-door solution; his website actually lists several models. They're all based on rotating squares, but some systems incorporate rods, while others make use of a wheel, and a track arranged in an epitrochoid curve. The Evolution Door works by virtue of four strategically attached triangles that separate, fold and rotate with a gentle flick of the wrist. It's a wonderful play on geometry that makes it possible to move the screen from side to side without the use of a track, a topological trick that Torggler says "opens up new applications for the door." Personally, I'm having a hard time deciding whether Torggler's systems are actually practical or just eye-catching, but to be honest I'm not sure I care; these things are just an utter joy to witness in action:
I will say that some of Torggler's rod-based systems (above) look to fall into that category of contraption that's fun to use right up until it lops off a few unfortunately placed fingers, at which point the novelty wears off rather quickly. To his credit, Torggler has addressed this concern in the triangular-paneled system of the Evolution Door:
It looks like it might still be a tad uncomfortable, but it'll still save you a ziploc full of ice and a trip to the ER.