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Non-Euclidean rendering

Non-Euclidean rendering

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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.

Fun with spheres

Fun with spheres

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Three interesting and mind bending mathematical experiments on spheres.

The Banach–Tarski paradox is a theorem in set-theoretic geometry which states: Given a solid ball in three-dimensional space, there exists a decomposition of the ball into a finite number of disjoint subsets, which can then be put back together in a different way to yield two identical copies of the original ball. Indeed, the reassembly process involves only moving the pieces around and rotating them without changing their shape. However, the pieces themselves are not “solids” in the usual sense, but infinite scatterings of points. The reconstruction can work with as few as five pieces. How it works is as fascinating as the paradox itself

The paradox of creating 2 identical spheres from 1 was also used as the key plot element in Futurama.

Turning a sphere inside out without tearing it

In differential topology, sphere eversion is the process of turning a sphere inside out in a three-dimensional space (the word eversion means “turning inside out”). Remarkably, it is possible to smoothly and continuously turn a sphere inside out in this way (allowing self-intersections of the sphere’s surface) without cutting or tearing it or creating any crease. This is surprising, both to non-mathematicians and to those who understand regular homotopy, and can be regarded as a veridical paradox; that is something that, while being true, on first glance seems false

Visualizing being inside a spherical mirror.

You’ve definitely seen infinity mirrors where one mirror is placed in front and one behind you to create the illusion of a long hallway of repeating images. But what if you were inside a round room that was coated like a mirror?

Retro Japanese vending machines

Retro Japanese vending machines

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The Sagamihara Used Tire Mart and Vending Machine Corner in Kanagawa, Japan has an amazing collection of very old vending machines. The staff maintains them and even cooks the meals for them. See old mechanical hot and cold serve coffee/tea machines, hamburgers, potstickers, squeezed orange juice, candied apples, Kodak film vending machine, ice cream machines, an ultra rare hot curry machine that worked before microwave technology, popcorn machines, machines with old nixie tube displays, and some old pachinko and video game machines.

Here we go – AI reimagines Aliens as a Wes Anderson movie

Here we go – AI reimagines Aliens as a Wes Anderson movie

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AI Fungi used generative AI technology to simulate what a Wes Anderson’s version of the classic sci-fi/horror flick Aliens might look like. He injects Tilda Swinton in the role of Ripley as well as some other recognizable regulars on Anderson’s movies and the Nostromo getting a colorful upgrade.

Yes, AI can do this today. Imagine in a few years from now…

Now live properly

Now live properly

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“Think of yourself as dead. You have lived your life. Now, take what’s left and live it properly. What doesn’t transmit light creates its own darkness.”

Marcus Aurelius, Meditations

Or, what about this:

For we know that our old self was crucified with him so that the body ruled by sin might be done away with, that we should no longer be slaves to sin.  Now if we died with Christ, we believe that we will also live with him.

Romans 6:6

Aurelius is not at all far from Christian thought when you translate the wording. What Aurelius would call living ‘improperly’ would be what Christians called ‘sin’. What would ‘living properly’ look like to Aurelius? He would likely have been pretty close to the Greek philosophy of living virtuously. Something that required a well developed understanding and the self control to pursue the good while rejecting bad.

For the Christian, living ‘properly’ would be living as Christ taught – a life of love, service to others before self, and radical conversion of heart and mind. In the case of the Christian though, you do not need to do this alone. By forming a relationship with Christ over time, He takes upon himself the pain of your sins, paying for them with his own sacrifice, and then leads you to live a new life in grace and conversion via his teaching – with forgiveness when you fail. For the Christian, living a new life is not something you do alone. You have a companion always there to pick you up, find forgiveness, and start anew on the path to conversion which leads to true happiness for all eternity; as well as other travelers along the same path leading to the same truth.

AI Jesus

AI Jesus

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We started with the AI based show about nothing, then AI Spongebob. Now we have a live streaming AI Jesus. The video, audio, and what he says is all generated by AI. What’s surprising is that it accepts a lot of different questions – and often answers them with a higher degree of accuracy than I would have thought (though I would certainly NOT take any of your religious formation from the AI version).

I think it’s more revealing the kinds of questions people ask. While some are clearly humor others are quite serious and reveal the depth of things people are struggling with.

I guess it’s only slightly better than when some Lutherans let chatGPT run an entire service with a sermon.

No Mavericks, no martyrs

No Mavericks, no martyrs

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This is one of the best talks on leading and setting expectations on a creative, collaborative production group that I have ever run across. It was given during GDC 2022 by a director at Obsidian Entertainment who clearly came with years of likely painful learning. I loved this quote:

We must bust the myths that equate ‘passion’ with overwork and aggressive ownership, and we must normalize collaborative, sustainable habits.

As she described the work situations and the martyr and maverick worker types, I found myself finally hearing in words many things I experienced but didn’t know how to express. I have personally seen the destruction of many extremely talented teams by just a few divisive elements. They could even be rockstars, but they end up cratering the whole production and driving people away from those teams. Carrie Patel does an amazing job describing how even well intentioned mavericks/martyrs damage the team. This is true to the point that hiring less technically good people that are good teamworkers produces consistently better results than extremely talented people that can’t work with others.

Are mavericks and martyrs inherently bad? No, but they absolutely can be if they are not managed properly. That requires being aware of how their behaviors affect the long-term success of the team.

As it turns out, this is not new learning. Other organizations have learned these lessons long ago.

Special forces teams as well as Mark Cuban point out these same learnings for business and sports teams. People who work more collaboratively and think of the entire team’s impact when making individual choices produce far more productive teams than rockstars/martyrs do. Special forces teams often do not look for the absolute best person – they look for who works in the team. This doesn’t mean you can’t have rockstars or martyr types, but what you want to find and reward is behaviors and an environment that encourages sustainable and truly collaborative teamwork.