M.C. Escher was famous for his wonderful mind-bending images. I loved his drawings as a kid because it created a sense of wonder, playfulness, and unlocked interesting new viewpoints and possibilities simply by violating a single physical or geometric expectation.

We’re used to the world following rules. If we leave a room, we would expect to go back into that same room if we opened the door. But in rendered scenes, none of those rules needs to be followed. We can actually make M.C. Escher like worlds a reality. But how – and more importantly – how could we use them to make an interesting gaming experience?

CodeParade walks us through many interesting effects that can be created using some simple non-Euclidian rendering and movement techniques.

As it turns out – games have been doing this for a little while. One of the first examples of slightly violating the rules of Euclidean space was the use of portals in the mega-hit game Portal (well, Narbacular Drop if you want to get technical). I say slightly because Portal actually does a very good job trying to maintain the physical properties of size, gravity, momentum, and physics of our everyday world when interacting with the portal. But, there are still problems like when you try to pass a portal into itself… or if you start messing with momentum…or if you start sandwiching the portals, etc.

Others started really twisting other rules of Euclidean space and exploring the results. Non-Euclidean spaces seemed ripe to create innovative and interesting puzzle games. I remember seeing early drops of Antichamber and being really fascinated by the simple, yet mind bending puzzles. As Digidigger explains, these tricks are accomplished with a combination of teleportation, creative use of the stencil buffers, and so forth.

Other games quickly followed like Manifold Garden that added the concept of infinite world wrap-around. Hyperbolica uses hyperbolic projection mapping. Then there were forced perspective games like Superliminal. As we quickly see, there is more than one rule to break in Euclidian space.

More recently and to greater effect – non-Euclidean tricks are being used in horror games. The experience of the world shifting around you definitely can create a very unsettling emotional response. Paintings that become doorways, rooms that change when you look away. Whole games have become based on these simple effects. Non-Euclidean techniques are here to stay. The real question is, how will we think of using them next?

Learning more:

Issues Valve ran into when making the game Portal:

How to create portals and solving the most common perspective, distance, scaling, collision detection, and physics issues you’ll encounter:

Hyperbolica devlog (13 video playlist):

Secrets behind how P.T. works. There’s also some pretty awesome exploration and disassembly by Lance McDonald.