To be fair, the wall touching puzzles are like less than 1% of Antichamber. The game has a lot of mind-bending puzzles. If you liked getting a whole new way of thinking in Portal 1 then you'll love Antichamber.
TotalBiscuit did a run-through of the beginning of the game together with the creator of the game ("WTF is Antichamber"). It is a pretty darn good sell if you're still not sold on the game, without spoiling much of the puzzles.
Fun fact, non-euclidean geometry is very very new. The first discovery of non-euclidean geometries date back to the early 19th century, while euclidean geometry dates back to 300 BCE.
@@Sammysapphira have you ever heard of the word new being used in a relative context? 300 BCE was 2300 years ago, while 19th century was ~200 years ago...
@@gracefool Some similar mathematics is used in non-euclidean geometry as is used for navigation, but they're not the same thing. If you told a mathematician at any point during that history that navigation breaks the laws of Euclidean geometry they'd've just said something like "The shortest path between two points on Earth is still a straight line, we just obviously can't travel straight through the Earth and therefore have to take a longer path." The Earth does not exist in spherical geometry, it is a sphere within a Euclidean space. The difference being that in an actual spherical space, a geodesic is not merely the shortest available path, as is true on Earth, but rather the shortest *possible* path.
12:50 also just in anti-chamber's defense there's puzzle mechanics involving the gun where you slowly build sort of "upgrades" that augment it's behavior for it that help solve other puzzles in the game. It's got some pretty engaging stuff in my opinion.
Currently working on a non-euclidean horror game as my first C++ project for when Source 2 drops towards the end of this month (hopefully). Played Anti-Chamber back in like 2014 and love these kinds of concept implementations. A more recent example that I love was a recent Doom mod called "MyHouse" you all should check out if you like this sort of thing. The person who made it was made all within the Doom engine.
I don't know anything about game development, so I humour myself, why wait for Source 2? I thought non-euclidean math would not fit into traditional rendering engines. Do you plan to project the world into 3D euclidean space before rendering? Or are you just using a game engine for the physics?
@@harrytsang1501 I'm familiar with the map making tool, Hammer, from the original source engine. I'm not looking to necessarily get into the game dev job market if I don't have to. Also, I liked the way HL:Alyx turned out and want to know if it's feasible to get non-euclidean rendering into a VR set. VR systems engineering is something I would like to get into when I finish up college. I am planning on first implementing the kind of psuedo-non-euclidean concepts that antichamber and superliminal has, then attempt to go into projecting the world into a non-euclidean format before it renders as it nears towards the "finale" of the game. If not, perhaps diverging the way the ray marching occurs within the engine might be possible? Also I kept hearing rumors the S2 engine will have ray tracing capability, but we'll see when it drops. I have about a year to play around with some prototyping. Definitely some hurdles involved but I feel if I can tackle the concept I can tackle anything.
I downloaded MyHouse per your suggestion as I used to love wads such as The Void by Cyb. I noticed there was a journal file and started reading it. This whole project became a lot more interesting to me.
1:45 it's funny you say that, because existing along the surface of a sphere is an example of non-euclidean geometry. The shortest path between two places on earth would be through the ground, but because we are limited to traveling along the surface and have gravity pulling us down, it can be modeled as non-euclidean space.
The Angular Diameter thing is quite interesting. I created a space exploration simulator (not a game yet), and a super giant star can look like a normal star from a certain distance. In space the only way to *really* get a sense of scale, you need to move - FTL speed. Only then you can see that a giant star is passing by slowly while regular stars are passing by quickly.
at 11:34 prime's microphone stand thing makes a blurred line and that's exactly where the player teleports. it looks like his stand is making a portal there lol
The original Unreal tournament you could make these types of rooms and such easily because of the portal systems they had. They later changed it because it caused a lot of performance issues. People made some seriously crazy maps with it. Myself included.
The answer to "Why is the answer always arctan?" (16:16) is that if you used arcsin or arccos, you'd need the hypotenuse value, and that would require an extra square root calculation.
I do not consider the portal games as good applications of non euclidean geometry since in these games the world is almost perfectly euclidean with only tiny discontinuities. Much better examples would be racing games when the vehicules are driving on curved surfaces : think driving inside or outside pipes in F-Zero or Redout since these are cases where you have a continuous non-euclidean behaviour.
6:00 The area of the triangle multiplied by the curvature of the surface is exactly how far away the angle sum is from 180°. Although it's in radians. Also if the curvature isn't constant you have to integrate. So the angle sum can be a lot larger than 270°. In particular, given a triangle on a closed surface like a sphere, there is nothing distinguishing which side is inside and which is outside. So the 270° triangle they show could just as well be a triangle where *each angle* is 270°, by swapping outside and inside. The area is 7 times larger, and the 180° discrepancy is also 7 times larger.
Triangle can go above 360. I think the theoretical upper limit is 900. The smallest internal angle triangle you can form has 180 degrees, but those same lines form a complementary triangle on with the external angles which would be at most 360*3 - 180 = 900.
5:34 - Sum of angles in triangles in different geometries: 0 < Hyperbolic Angle < 180 Euclidean angle == 180 180 < Spherical Angle < 540 In Hyperbolic geometry, each angle can approach a minimum total angle of 0°. 3 × 0 = 0. In Euclidean geometry, the sum of all angles is always 180°. In Spherical geometry, each angle can approach a maximum total angle of 180°. 3 × 180 = 540.
It's so weird to realise that for someone Portal was this mind exploding experience. I played it when I was less than 8 years old so it actually feels like a common sense and before that I think I saw my mother play it. It's like portal physics are just as common sense to me as real physics now. Which is why I could never understand why Portal 1 tutorial chambers are so long and why people couldn't understand seemingly simple stuff like speedy thing goes in, speedy thing goes out
From what I've seen most people don't really have a grasp on ORDINARY physics, let alone anything unusual. All they probably know is heavy thing goes down harder and light thing can float.
Plus if you'd played Prey (2006) first then Portal (2007) was slightly less groundbreaking, Prey had a lot of portal and gravity tricks in it (e.g.: ua-cam.com/video/zpQRePtEpRw/v-deo.html)
6:06 To answer your question it depends on the Gaussian curvature of the surface you draw the triangle onto. If it is 0 throughout the surface of the triangle (so the surface isn't curved) then the sum is π (or 180), if the curvature is positive throughout it then it is greater than π and if it's negative throughout it it is less than π. This is an example on the manifolds and geodesic curves concepts of differential geometry if you're interested for more.
For positive curvature, triangles can be any angle above 180° depending on the location and size of the triangle and the surface, so for a sphere triangles can be anywhere between 180° (non inclusive) and 270° (inclusive). You were correct. For a mind trippy case, you can think up a space where a triangle is 360° or more. You can even use angles above 180° depending on the space so you’re angle is kind of only bounded by 180° and 360°.
For even more fun, there's negative curvature too. Triangles have an internal angle sum of anywhere from 180 degrees (when they're infinitesimally small) to 0 degrees (When they're infinitely large, made up of parallel lines). You also have the regular apeirogon, which is a regular polyhedron with internal angles of 180 degrees... and external angles greater than 180 degrees.
On a sphere a triangle can have a sum of inner angles between 180 and *900* degrees, actually. To reach the two extremes you draw a single tiny triangle (tiny compared to the radius of the sphere) and declare one or the other side to be the inside. On a flat plane you can not declare the "outside" to be the area enclosed by the triangle, but on a sphere you can!
Its always arctan or tan because it ( tangent ) is the only function that can be calculated with just two sides of a triangle and the angle between them without knowing the hypotenuse ( ina right triangle if not you make two right triangls from a normal one ). Just CLASSIC tangent 😅
And to answer the most important question everyone has, yes it all can be done in javascript. Had a project that leveraged similar techniques to simulate nuclear-to-galactic scales.
5:50 Yes, good observation apart from getting the upper bound wrong... fortunately chat corrected you, except they were also wrong, it's not 360 either. The maximum sum of angles of a triangle on a sphere is actually 540 degrees, 720 degrees, or unbounded, depending on the precise definition of a triangle and how to measure the angle at each corner. The corresponding triangles cover half the sphere, the entire sphere, or more than the entire sphere (self-overlapping) in the three cases respectively.
A triangle on a sphere can actually have an angle sum up to 3 * 360 - 180 = 900 degrees (depending on what you consider a triangle). Think of a very small triangle on a sphere. The "outside" of that triangle can be considered the inside of another triangles with the same sides, which would then have angles that summed to 3*360 degrees minus the sum of the angles of the small triangle. Anyway, the angle sum will always be 180 + 720 * A_triangle / A_sphere, where A_thething is the area of thething.
There's a pretty sick Super Mario World romhack that goes by the name Cthulhu Mario, that tries to implement non-euclidian feeling and does some pretty cool wonky stuff. One really cool thing was seeing how someone ported Portal on N64.
2:20 In Euclidean space, the shortest path between two points on a sphere is still a straight line, the line just goes through the sphere. 4:20 The line drawn onto the sphere here is not the shortest distance between the points (even assuming we must remain on the surface of the sphere) but simply a line of latitude. If we have to remain on the surface, the shortest path would be an arc swept on the surface by a line drawn from the centre of the sphere to its surface. None of the lines of latitude (except the equator) are such arcs. 5:55 Man just made a gigabrain obseravation and chat just starts memeing "streamer dumb lol." That is exactly correct. Though with the small caveat that the angles can increase further up to 900 degrees if you allow the triangle to take up most of the sphere. But if you limit the triangle to being maximum one octant of the surface (an easy mistake to make), it will vary between 180 and 270.
We all live in Non Euclidean space. We live on a sphere. It's just very large. Euclidian space is what isn't real. It's an over simplification that would only apply if the world was 2d.
A triangle on a sphere actually has between 180 and 540 degrees of angle. Those are called irregular cases where either the triangle has 3 180 degree angles (and is thus equal to a great circle), or 1 180 degree and 2 0 degree angles, and then it's equal to a line.
Portal 1 was lightning in a bottle. Portal 2 was wires and lightbulbs. Because camera distance to a point IS Arctan. Unit circle from trig, it's the inverse tangent line.
11:00 I encountered something similar in N64 games. The infinite stairs of Mario 64. You go up for a few minutes and then you turn around and you're still at the start. Or in Quest 64 in the last area, you sometimes enter a door which leads to a room with not much in it. But when you leave the room again using the same door, you suddenly ended up in a different place than you came from after a short load time. As a maybe 6yo child, I was mindblown by this.
Imagine taking the triangle with the three 90 degree corners on the sphere. Drag the two points on the equator outwards until they're on opposite sides of the sphere: now the angle on the north pole is 180 degrees. Now you can rotate the side of the triangle that's on the equator so that it passes by the south pole (that is, the triangle is now a great circle). Now all three angles are 180 degrees and add up to 540 degrees. But you could carry on further and drag the south side past the south pole so the two angles on the equator are greater than 180 degrees. That's still a totally valid triangle in spherical geometry. You could drag them all the way to the north pole so two of the angles are now 360 degrees and the remaining one 180, adding up to 900 degrees. I don't know what the maximum possible is.
@6:12, technically you are wrong. On a sphere the lower limit for the angle sum is 180 degrees. This is when it uses a tiny portion of the sphere. The upper limit is 900 degrees. This is where you use all bar a tiny portion of the sphere. Basically consider that tiny triangle from above, but the area outside that triangle is the area inside this one. So the exterior angle of 300 degrees for the above triangle is now the interior angle for our massive triangle. If instead you want to restrict the triangle to less than half the the sphere, the limit is 540 degrees, where the 3 angles approach 180 degrees. Mathematically, this relates to gaussian curvature, where the angle sum of the triangle, in radians, is pi plus the area enclosed multiplied by the curvature. For hyperbolic geometry, they range from 0 to 180 degres.
Interesting that we built all these game engines to mimic physics of the world that we live in. We didn't think of making them more flexible. Thus making non euclidean game basically means either hacking the heck out of game engine or building new game engine entirely from scratch. I think the biggest issue with non-Euclidean worlds is that because they don't follow our experience - it's literally immeasurable number of ways to build them, so there is no way how to agree on what we would want from game engine to support, on other had, real world is simply reference that can be used to agree upon and focus resources on building a common game engine/framework.
5:55 "how big it is" on the Earth, yes. A triangle with flat straight lines, sum=180°. Maximum Euclidean curvature, circle, sum=360°. More than 360° the lines won't connect into any 2D shape. Less than 180° is concave. A Y shape has 0° at the end points.
I love portal. I did speedrunning on it for a few years, though I wasn't the best at it. My pb in inbounds (you can use glitches but not exit the map) is a little under 19 minutes.
Actually, a straight line always is the shortest distance between two points. Great circles exist as the shortest distance between two points ON THE SURFACE OF A SPHERE. Great circles are conditional. The straight line through the interior of the sphere is still shorter than a great circle.
"As the mole digs" would be better than, "as the crow flies" for a statement. Unless you're flat earth, in which case it would be, as the turtle changes its boyancy relative to the angular chemtrail when it's driving, not traveling.
@@maxave7448 A friend of mine used to call that kind of debugging for the "snitch method" (sounds better in my language), as the print statements would basically be snitches for where the error occurred. With that said, there is many ways of debugging, and if you're trying to find an error that's especially hard to find, then the "snitch method" tends not to be the best. If how ever it's a pretty simple problem, then it tend to be faster to just write in "snitches" to find the problem in my experience.
The real non or pseudo Euclidean "games" are centered around the special theory of relativity. No tricks, no subterfuge, just the mind-bending physics.
Dev: "Can you render 2D?" PC: "Sure" Dev: "Can you render 3D?" PC: "Sure" Dev: "Can you render 4D?" PC: "Sure" Dev: "But our universe is just in 3D" PC: "What the hell is a "universe"?" ua-cam.com/video/vZp0ETdD37E/v-deo.html
I always found this way of explaining non euclidean geometry weird... because in my head, if the angles of a "triangle" drawn over a sphere don't add up to 180, it's because it's not a frikkin triangle! It's a curved triangle! Things don't add up simply because you think you are doing a triangle but you aren't! Maybe then someone could come and say "Actually, it's a triangle because the definition of lines also changes", and I'll tell them to f@ck off.
Yes, it's an analogy. In true non-euclidean geometry, it wouldn't be on the surface of a sphere, where you can look at the sphere from flat 3D space. Rather, space itself would be spherical, so there is no other reference point.
Portal, Braid, Antichamber, the Swapper.... what other games change your brain? I've only replayed the first 2, Antichamber is curious but is not exactly fun, i couldn't finish.
It's funny how the video actually spends some time trying to explain what "non-euclidean" means, but then only very briefly showcases one non-euclidean tech demo and _one_ non-euclidean game, Hyperbolica, (while forgetting the other significant non-euclidean game, HyperRogue) without explaining anything about how they work (as the video title promised). Instead, the rest of the video talks about Antichamber and Superliminal, neither of which is actually non-euclidean, their space has zero curvature. They're just sometimes called "non-euclidean" by people who don't know the actual meaning of the term, but the video author can't claim that excuse.
The parallel lines round a sphere demonstration was false. He assumed the lines have to pass through the poles of the sphere but parallel lines can be drawn round a sphere and have them stay the same distance apart all the way round. The difference is that unless they are equal distance from the diameter line of the sphere where the sphere can be cut in half to form two equal domes, the lines will be different lengths. Consider it like cutting the sphere into perfectly flat chips, or rather discs. Each disc is created from two parallel lines bisecting the sphere. EDIT: In fact he follows that illustration with one of 3 "rubber bands" circling a sphere. Each of those rubber bands is a pair of parallel lines circling the sphere!
To be fair, the wall touching puzzles are like less than 1% of Antichamber. The game has a lot of mind-bending puzzles. If you liked getting a whole new way of thinking in Portal 1 then you'll love Antichamber.
TotalBiscuit did a run-through of the beginning of the game together with the creator of the game ("WTF is Antichamber"). It is a pretty darn good sell if you're still not sold on the game, without spoiling much of the puzzles.
This. I wondered why the video kept showing the same entry level puzzles. It gets nuts after a while.
It's almost like showing portal with the turrets and cubes, but not showing the portal gun.
@@MasterHigure rip TB
Fun fact, non-euclidean geometry is very very new. The first discovery of non-euclidean geometries date back to the early 19th century, while euclidean geometry dates back to 300 BCE.
200 years ago isn't what anyone would consider as new
@@Sammysapphira have you ever heard of the word new being used in a relative context? 300 BCE was 2300 years ago, while 19th century was ~200 years ago...
@@Sammysapphira for mathematicians isaac newton is the new cool kid in school that everyone hangs with
Non-euclidean geometry has been used for thousands of years in navigation... Or are y'all flat earthers?
@@gracefool Some similar mathematics is used in non-euclidean geometry as is used for navigation, but they're not the same thing. If you told a mathematician at any point during that history that navigation breaks the laws of Euclidean geometry they'd've just said something like "The shortest path between two points on Earth is still a straight line, we just obviously can't travel straight through the Earth and therefore have to take a longer path."
The Earth does not exist in spherical geometry, it is a sphere within a Euclidean space. The difference being that in an actual spherical space, a geodesic is not merely the shortest available path, as is true on Earth, but rather the shortest *possible* path.
NO VIEW CREW
Video live 6 minutes ago, comment 7 minutes ago. Nice
Let's go
12:50 also just in anti-chamber's defense there's puzzle mechanics involving the gun where you slowly build sort of "upgrades" that augment it's behavior for it that help solve other puzzles in the game. It's got some pretty engaging stuff in my opinion.
Currently working on a non-euclidean horror game as my first C++ project for when Source 2 drops towards the end of this month (hopefully). Played Anti-Chamber back in like 2014 and love these kinds of concept implementations. A more recent example that I love was a recent Doom mod called "MyHouse" you all should check out if you like this sort of thing. The person who made it was made all within the Doom engine.
I don't know anything about game development, so I humour myself, why wait for Source 2?
I thought non-euclidean math would not fit into traditional rendering engines. Do you plan to project the world into 3D euclidean space before rendering? Or are you just using a game engine for the physics?
@@harrytsang1501 I'm familiar with the map making tool, Hammer, from the original source engine. I'm not looking to necessarily get into the game dev job market if I don't have to. Also, I liked the way HL:Alyx turned out and want to know if it's feasible to get non-euclidean rendering into a VR set. VR systems engineering is something I would like to get into when I finish up college. I am planning on first implementing the kind of psuedo-non-euclidean concepts that antichamber and superliminal has, then attempt to go into projecting the world into a non-euclidean format before it renders as it nears towards the "finale" of the game. If not, perhaps diverging the way the ray marching occurs within the engine might be possible? Also I kept hearing rumors the S2 engine will have ray tracing capability, but we'll see when it drops. I have about a year to play around with some prototyping.
Definitely some hurdles involved but I feel if I can tackle the concept I can tackle anything.
@@ogpurpledaddy for non-euclidian stuff in VR check out the channel "Henry Segerman", e.g. their video "Non-euclidean virtual reality"
I downloaded MyHouse per your suggestion as I used to love wads such as The Void by Cyb. I noticed there was a journal file and started reading it. This whole project became a lot more interesting to me.
Yup MyHouse is insane, there is a youtuber name Power Pack covered the whole subject, it's 1h42 and damn, I recommend
1:45 it's funny you say that, because existing along the surface of a sphere is an example of non-euclidean geometry. The shortest path between two places on earth would be through the ground, but because we are limited to traveling along the surface and have gravity pulling us down, it can be modeled as non-euclidean space.
The Angular Diameter thing is quite interesting. I created a space exploration simulator (not a game yet), and a super giant star can look like a normal star from a certain distance. In space the only way to *really* get a sense of scale, you need to move - FTL speed. Only then you can see that a giant star is passing by slowly while regular stars are passing by quickly.
Viewfinder (the game) maxed out non-euclidean... this whole game from beginning to the end is mindfuck
at 11:34 prime's microphone stand thing makes a blurred line and that's exactly where the player teleports. it looks like his stand is making a portal there lol
This must be the work of an enemy stand!
The original Unreal tournament you could make these types of rooms and such easily because of the portal systems they had. They later changed it because it caused a lot of performance issues. People made some seriously crazy maps with it. Myself included.
The answer to "Why is the answer always arctan?" (16:16) is that if you used arcsin or arccos, you'd need the hypotenuse value, and that would require an extra square root calculation.
I do not consider the portal games as good applications of non euclidean geometry since in these games the world is almost perfectly euclidean with only tiny discontinuities.
Much better examples would be racing games when the vehicules are driving on curved surfaces : think driving inside or outside pipes in F-Zero or Redout since these are cases where you have a continuous non-euclidean behaviour.
6:00 The area of the triangle multiplied by the curvature of the surface is exactly how far away the angle sum is from 180°. Although it's in radians. Also if the curvature isn't constant you have to integrate.
So the angle sum can be a lot larger than 270°. In particular, given a triangle on a closed surface like a sphere, there is nothing distinguishing which side is inside and which is outside. So the 270° triangle they show could just as well be a triangle where *each angle* is 270°, by swapping outside and inside. The area is 7 times larger, and the 180° discrepancy is also 7 times larger.
I know it was rhetorical, but it's always arctan because it takes an x and y coordinate and gives you back an angle, which is really useful.
Triangle can go above 360. I think the theoretical upper limit is 900. The smallest internal angle triangle you can form has 180 degrees, but those same lines form a complementary triangle on with the external angles which would be at most 360*3 - 180 = 900.
5:34 - Sum of angles in triangles in different geometries:
0 < Hyperbolic Angle < 180
Euclidean angle == 180
180 < Spherical Angle < 540
In Hyperbolic geometry, each angle can approach a minimum total angle of 0°. 3 × 0 = 0.
In Euclidean geometry, the sum of all angles is always 180°.
In Spherical geometry, each angle can approach a maximum total angle of 180°. 3 × 180 = 540.
It's so weird to realise that for someone Portal was this mind exploding experience. I played it when I was less than 8 years old so it actually feels like a common sense and before that I think I saw my mother play it.
It's like portal physics are just as common sense to me as real physics now. Which is why I could never understand why Portal 1 tutorial chambers are so long and why people couldn't understand seemingly simple stuff like speedy thing goes in, speedy thing goes out
From what I've seen most people don't really have a grasp on ORDINARY physics, let alone anything unusual. All they probably know is heavy thing goes down harder and light thing can float.
Plus if you'd played Prey (2006) first then Portal (2007) was slightly less groundbreaking, Prey had a lot of portal and gravity tricks in it (e.g.: ua-cam.com/video/zpQRePtEpRw/v-deo.html)
6:06 To answer your question it depends on the Gaussian curvature of the surface you draw the triangle onto. If it is 0 throughout the surface of the triangle (so the surface isn't curved) then the sum is π (or 180), if the curvature is positive throughout it then it is greater than π and if it's negative throughout it it is less than π. This is an example on the manifolds and geodesic curves concepts of differential geometry if you're interested for more.
For positive curvature, triangles can be any angle above 180° depending on the location and size of the triangle and the surface, so for a sphere triangles can be anywhere between 180° (non inclusive) and 270° (inclusive). You were correct. For a mind trippy case, you can think up a space where a triangle is 360° or more. You can even use angles above 180° depending on the space so you’re angle is kind of only bounded by 180° and 360°.
For even more fun, there's negative curvature too. Triangles have an internal angle sum of anywhere from 180 degrees (when they're infinitesimally small) to 0 degrees (When they're infinitely large, made up of parallel lines). You also have the regular apeirogon, which is a regular polyhedron with internal angles of 180 degrees... and external angles greater than 180 degrees.
On a sphere a triangle can have a sum of inner angles between 180 and *900* degrees, actually. To reach the two extremes you draw a single tiny triangle (tiny compared to the radius of the sphere) and declare one or the other side to be the inside. On a flat plane you can not declare the "outside" to be the area enclosed by the triangle, but on a sphere you can!
Its always arctan or tan because it ( tangent ) is the only function that can be calculated with just two sides of a triangle and the angle between them without knowing the hypotenuse ( ina right triangle if not you make two right triangls from a normal one ). Just CLASSIC tangent 😅
You forgot about cotangent.
@@razvanfodor5653 no I didn't cotangent is not a real thing it is just the reciprocal of tangent
I would 1000% watch a Primeagen playthrough of Superliminal!!!
And to answer the most important question everyone has, yes it all can be done in javascript. Had a project that leveraged similar techniques to simulate nuclear-to-galactic scales.
5:50 Yes, good observation apart from getting the upper bound wrong... fortunately chat corrected you, except they were also wrong, it's not 360 either. The maximum sum of angles of a triangle on a sphere is actually 540 degrees, 720 degrees, or unbounded, depending on the precise definition of a triangle and how to measure the angle at each corner. The corresponding triangles cover half the sphere, the entire sphere, or more than the entire sphere (self-overlapping) in the three cases respectively.
A triangle on a sphere can actually have an angle sum up to 3 * 360 - 180 = 900 degrees (depending on what you consider a triangle). Think of a very small triangle on a sphere. The "outside" of that triangle can be considered the inside of another triangles with the same sides, which would then have angles that summed to 3*360 degrees minus the sum of the angles of the small triangle. Anyway, the angle sum will always be 180 + 720 * A_triangle / A_sphere, where A_thething is the area of thething.
To be fair, Antichamber is less about touching walls and a lot more about how you use your mega-puzzle-solving-gun. Just try it.
Duke Nukem 3D has non-euclidean engine (the old game) and had actually some very few non-euclid levels if you pay attention ;-)
There's a pretty sick Super Mario World romhack that goes by the name Cthulhu Mario, that tries to implement non-euclidian feeling and does some pretty cool wonky stuff.
One really cool thing was seeing how someone ported Portal on N64.
Horizontally and vertically centering in a div is harder than non-euclidian geometry. There, I said it.
2:20
In Euclidean space, the shortest path between two points on a sphere is still a straight line, the line just goes through the sphere.
4:20
The line drawn onto the sphere here is not the shortest distance between the points (even assuming we must remain on the surface of the sphere) but simply a line of latitude. If we have to remain on the surface, the shortest path would be an arc swept on the surface by a line drawn from the centre of the sphere to its surface. None of the lines of latitude (except the equator) are such arcs.
5:55
Man just made a gigabrain obseravation and chat just starts memeing "streamer dumb lol."
That is exactly correct. Though with the small caveat that the angles can increase further up to 900 degrees if you allow the triangle to take up most of the sphere. But if you limit the triangle to being maximum one octant of the surface (an easy mistake to make), it will vary between 180 and 270.
We all live in Non Euclidean space. We live on a sphere. It's just very large. Euclidian space is what isn't real. It's an over simplification that would only apply if the world was 2d.
No, we live in 3D Euclidean space. We're just on a sphere. A straight line is still the shortest, it would just go trough the earth.
1:15 The genie was already out of the bottle at Narbacular Drop, which Valve just bought and slapped grafisk onto.
Someone in chat suggested to play Stanley's Parable, +1 to that message! The game is awesome.
Antichamber is just great... Mind bending
(so are Portal, Portal2)
A triangle on a sphere actually has between 180 and 540 degrees of angle. Those are called irregular cases where either the triangle has 3 180 degree angles (and is thus equal to a great circle), or 1 180 degree and 2 0 degree angles, and then it's equal to a line.
Portal 1 was lightning in a bottle. Portal 2 was wires and lightbulbs.
Because camera distance to a point IS Arctan. Unit circle from trig, it's the inverse tangent line.
Even in a spherical earth, the shortest distance between to points is a straight line, but you would have to dig through the earth
Antichamber is also one of the greatest games I've ever played, highly recommend!
11:00 I encountered something similar in N64 games.
The infinite stairs of Mario 64. You go up for a few minutes and then you turn around and you're still at the start.
Or in Quest 64 in the last area, you sometimes enter a door which leads to a room with not much in it. But when you leave the room again using the same door, you suddenly ended up in a different place than you came from after a short load time.
As a maybe 6yo child, I was mindblown by this.
Lost Woods too
Antichamber is great. And the touching wall mechanics are very sparse.
Yo, i was just thinking about making a non euclidean game! This is feels to me like a major coincidence!
if you havent played antichamber you should give it a shot its one of my favorite games
Imagine taking the triangle with the three 90 degree corners on the sphere. Drag the two points on the equator outwards until they're on opposite sides of the sphere: now the angle on the north pole is 180 degrees. Now you can rotate the side of the triangle that's on the equator so that it passes by the south pole (that is, the triangle is now a great circle). Now all three angles are 180 degrees and add up to 540 degrees. But you could carry on further and drag the south side past the south pole so the two angles on the equator are greater than 180 degrees. That's still a totally valid triangle in spherical geometry. You could drag them all the way to the north pole so two of the angles are now 360 degrees and the remaining one 180, adding up to 900 degrees.
I don't know what the maximum possible is.
PS antichamber is an incredible game. There's lots of variety in its puzzles, it's not just touching walls.
This remember me in college, in calculos one Solids of revolution, in my entire software engineer career never needed it!
There is someone writing non Euclidean Minecraft in rust, really cool project
@6:12, technically you are wrong.
On a sphere the lower limit for the angle sum is 180 degrees. This is when it uses a tiny portion of the sphere.
The upper limit is 900 degrees. This is where you use all bar a tiny portion of the sphere. Basically consider that tiny triangle from above, but the area outside that triangle is the area inside this one. So the exterior angle of 300 degrees for the above triangle is now the interior angle for our massive triangle.
If instead you want to restrict the triangle to less than half the the sphere, the limit is 540 degrees, where the 3 angles approach 180 degrees.
Mathematically, this relates to gaussian curvature, where the angle sum of the triangle, in radians, is pi plus the area enclosed multiplied by the curvature.
For hyperbolic geometry, they range from 0 to 180 degres.
Interesting that we built all these game engines to mimic physics of the world that we live in. We didn't think of making them more flexible. Thus making non euclidean game basically means either hacking the heck out of game engine or building new game engine entirely from scratch. I think the biggest issue with non-Euclidean worlds is that because they don't follow our experience - it's literally immeasurable number of ways to build them, so there is no way how to agree on what we would want from game engine to support, on other had, real world is simply reference that can be used to agree upon and focus resources on building a common game engine/framework.
5:55 "how big it is" on the Earth, yes. A triangle with flat straight lines, sum=180°. Maximum Euclidean curvature, circle, sum=360°. More than 360° the lines won't connect into any 2D shape. Less than 180° is concave. A Y shape has 0° at the end points.
I love portal. I did speedrunning on it for a few years, though I wasn't the best at it.
My pb in inbounds (you can use glitches but not exit the map) is a little under 19 minutes.
I got a sphere space type of effect watching snow fall reflected on a lake
As a user of Netflix I want those divs nicely centred and non of my time and space bent, thanks
fun fact red = 1,0,0 green = 0,1,0 blue = 0,0,1 => projected on a sphere = xbox logo
2:56 Actually, to be rigorous, there are around 20 rules (according to Hilbert).
6:00 I think it's between 0 and 360.
i would gladly watch him play superliminal
RIP to Bram Moolenaar, creator of Vim
yep, tomorrow i'll get a tribute to him going
Great, I enjoyed this so much. Thanks divtouchegen!
Actually, a straight line always is the shortest distance between two points. Great circles exist as the shortest distance between two points ON THE SURFACE OF A SPHERE. Great circles are conditional. The straight line through the interior of the sphere is still shorter than a great circle.
"As the mole digs" would be better than, "as the crow flies" for a statement.
Unless you're flat earth, in which case it would be, as the turtle changes its boyancy relative to the angular chemtrail when it's driving, not traveling.
If you play and vod superliminal im 100% gonna watch it. Its a great game with a great message ✌️🤙
0:22 this is a great game! Surreal!
In order for plane to go the shortest distance it would have to dig underground in a straight line
Not on a flat globe, or a turtle's postulate
@@Jabberwockybird how can globe be flat
@@panjak323 that's the joke
I suppose the testers have huge salaries. Also, how do you write tests (automated) for these? What to expect? "Let me calculate" 😅
it's formulas, pretty easy to test if you know quick maths
@@cheebadigga4092😂 CLASSIC quick math
You guys got automated tests? I just use print statements
@@maxave7448 i got print statements in my automated tests, fite me
@@maxave7448
A friend of mine used to call that kind of debugging for the "snitch method" (sounds better in my language), as the print statements would basically be snitches for where the error occurred. With that said, there is many ways of debugging, and if you're trying to find an error that's especially hard to find, then the "snitch method" tends not to be the best. If how ever it's a pretty simple problem, then it tend to be faster to just write in "snitches" to find the problem in my experience.
If you like Portal or the witness, you'll like anti-chamber
I like how he has the exact reaction the scientific community had when non-euclidean geometry was invented.
ok, the joke about flat earth was disarmingly good and sooo right 😅
atan and atan2 is the ancient magic of 3d programming.
Ah, non euclidean spaces. A space were it requires whisky to explain it. Lol.
You can play Hyperbolica in VR and it's wild
You should really play subliminal, it is a lot of fun! It was not too hard once you get the idea and has some Portal-inspired humour in it.
thanks for the video, i'll watch this later.
OPTICAL ILLUSIONS
People are so creative! it's so cool
Oh there's a vr version of hyperbolica
The real non or pseudo Euclidean "games" are centered around the special theory of relativity. No tricks, no subterfuge, just the mind-bending physics.
Give me more of that delicious screen tearing!
Dev: "Can you render 2D?"
PC: "Sure"
Dev: "Can you render 3D?"
PC: "Sure"
Dev: "Can you render 4D?"
PC: "Sure"
Dev: "But our universe is just in 3D"
PC: "What the hell is a "universe"?" ua-cam.com/video/vZp0ETdD37E/v-deo.html
For me, a game developer, it's Tuesday 😅
16:14 waiting for Angular joke...
Are you going to React to the Angular joke?
I can't change your mind, I can lock it
I always found this way of explaining non euclidean geometry weird... because in my head, if the angles of a "triangle" drawn over a sphere don't add up to 180, it's because it's not a frikkin triangle! It's a curved triangle! Things don't add up simply because you think you are doing a triangle but you aren't! Maybe then someone could come and say "Actually, it's a triangle because the definition of lines also changes", and I'll tell them to f@ck off.
It's a non-euclidean triangle.
Yes, it's an analogy. In true non-euclidean geometry, it wouldn't be on the surface of a sphere, where you can look at the sphere from flat 3D space. Rather, space itself would be spherical, so there is no other reference point.
Does this guys hate vsync?
Love that prime still has not moved to Sway haha
antichamber is *amazing*, please *please* play it, it's not very long
i feel like superliminal came about because the dev fucked up the code and decided that it would be a fun game mechanic.
portal was just the demo for portal 2
lol "O shoot, I'm too stupid for this"
Antichamber is sick
That's some extreme frame tearing.
PrimeTimeGaming let's go! (Warframe's gonna sue us)
portal was *THE* game. 😞need to find more games like that.
Portal 2? jk, you know it, I guess ;) But have you played the Portal mod Rexaura? Easily ups the difficulty by one two to orders of magnitude.
Wonder why was a portal 2? Valve hss a talk about that. Maybe something to look at during your game dev arc
I wish my gold worked like that Cheese ramp did. Kekw
i just center divs, im an expert at centering divs you know. i know you know cause u r a knower you know
Portal, Braid, Antichamber, the Swapper.... what other games change your brain?
I've only replayed the first 2, Antichamber is curious but is not exactly fun, i couldn't finish.
haskell cult-friendly content
Hey. Sometimes the answer isn't arctan but arctan2
this is facts
4d golf - codeparade
It's funny how the video actually spends some time trying to explain what "non-euclidean" means, but then only very briefly showcases one non-euclidean tech demo and _one_ non-euclidean game, Hyperbolica, (while forgetting the other significant non-euclidean game, HyperRogue) without explaining anything about how they work (as the video title promised). Instead, the rest of the video talks about Antichamber and Superliminal, neither of which is actually non-euclidean, their space has zero curvature. They're just sometimes called "non-euclidean" by people who don't know the actual meaning of the term, but the video author can't claim that excuse.
is "Let's play" coming?
The parallel lines round a sphere demonstration was false. He assumed the lines have to pass through the poles of the sphere but parallel lines can be drawn round a sphere and have them stay the same distance apart all the way round. The difference is that unless they are equal distance from the diameter line of the sphere where the sphere can be cut in half to form two equal domes, the lines will be different lengths. Consider it like cutting the sphere into perfectly flat chips, or rather discs. Each disc is created from two parallel lines bisecting the sphere.
EDIT: In fact he follows that illustration with one of 3 "rubber bands" circling a sphere. Each of those rubber bands is a pair of parallel lines circling the sphere!
do you use nvidia gpu? so screen tearing
The Euclideagen