Spherical Geometry Is Stranger Than Hyperbolic - Hyperbolica Devlog #2

I was going to talk about rendering but actually this is something I forgot to mention in the last video You'd think that hyperbolic geometry is harder to understand than spherical because it's harder to visualize And that's true, but when it comes to what you actually see, it's quite the opposite In general hyperbolic geometry looks like a more exaggerated euclidean geometry You know because it's "hyperbolic". Things appear to get smaller faster more space fits into the same perceived space But things seem overall familiar But let's take a trip to spherical flatland We'll just say that everything below the equator is underground and everything above is open space So we can jump up and down and walk around In fact, if we keep walking in either direction, we'll eventually come back to where we started But what would you actually see? Let's cast some rays from our perspective to see where they end up Objects close by aren't really affected much and look like you'd expect But an object on the other side Well, look how many of our light rays hit this rock this tiny object literally on the other side of the world would look enormouIn the sky and appear upside down Sort of like a giant magnifying lens The result is a reverse perspective farther away objects can appear larger than closer ones Also notice that all rays eventually hit the ground There's no sky per se at least not when you can see without using fog or a draw distance Alright, are you ready to go up one dimension higher? We're going to switch to first person now, but all the same things. I just talked about in 2d apply to 3d Should be pretty obvious now why I chose the title of this video The reverse perspective is obvious far away things appear huge and flipped upside down Take a look at this house. It's pretty normal up close But now, let's go to the opposite side of the level It's a pretty crazy effect it's kind of like the house is inside out The roof is above us and the walls are around us but not in the way you'd expect Also, if you walk in a straight line to the left or right it looks like the world is rotating even though you're actually going straight Here I added a fence to divide the level in half It's a really neat effect, are you fenced in or fenced out? Anyway, there's a lot of really cool things to explore in spherical geometry and I still want to leave some things for you to discover When the game comes out So be sure to add Hyperbolica to your steam wishlist or subscribe to get the latest updates and i'll see you all next time

Channel: CodeParade

Views: 1,616,841

Keywords: Non-Euclidean Geometry, Game Development, Math, Hypersphere, 4D

Id: yY9GAyJtuJ0

Length: 4min 0sec (240 seconds)

Published: Tue Jul 28 2020