Sonic 3 special stages are impossible
Moderator: Moderators
-
- Posts: 3140
- Joined: Wed May 19, 2010 6:12 pm
Sonic 3 special stages are impossible
How can you possibly have a checkered patterned sphere?
-
- Posts: 271
- Joined: Sun Mar 27, 2011 10:49 am
- Location: Victoria, BC
Re: Sonic 3 special stages are impossible
well, it's a torus for one thing
but yeah, this totally ruins the realism of sonic 3 :/
but yeah, this totally ruins the realism of sonic 3 :/
Re: Sonic 3 special stages are impossible
I had never thought about this, but... you're right!
Re: Sonic 3 special stages are impossible
The playfield in Tetrisphere is also a torus.
Re: Sonic 3 special stages are impossible
It would make sense, but is this canon?adam_smasher wrote:well, it's a torus for one thing
Re: Sonic 3 special stages are impossible
Literally unplayable!
- rainwarrior
- Posts: 8732
- Joined: Sun Jan 22, 2012 12:03 pm
- Location: Canada
- Contact:
Re: Sonic 3 special stages are impossible
It's true, but this also applies to like every JRPGpsycopathicteen wrote:How can you possibly have a checkered patterned sphere?
Edit: here's a funny visualization of the concept: https://imgur.com/a/fUD7n
Edit: I was remembering FF7 incorrectly.
Last edited by rainwarrior on Wed Oct 18, 2017 12:48 pm, edited 1 time in total.
-
- Posts: 3140
- Joined: Wed May 19, 2010 6:12 pm
Re: Sonic 3 special stages are impossible
I wonder how the back facing side of a "torus sphere" would look like.
- rainwarrior
- Posts: 8732
- Joined: Sun Jan 22, 2012 12:03 pm
- Location: Canada
- Contact:
Re: Sonic 3 special stages are impossible
Well, the image viewed from the back is just reversed, but it has the same wrapping topology either way.
Re: Sonic 3 special stages are impossible
Don't look at videos of the cancelled Sonic X-Treme, whatever you do.
Re: Sonic 3 special stages are impossible
Whaump Whaumpstrat wrote:Don't look at videos of the cancelled Sonic X-Treme, whatever you do.
Here come the fortune cookies! Here come the fortune cookies! They're wearing paper hats!
-
- Posts: 3140
- Joined: Wed May 19, 2010 6:12 pm
Re: Sonic 3 special stages are impossible
If you continue the checkerboard pattern all the way around, wouldn't it have to warp into a fractal pattern in the back.rainwarrior wrote:Well, the image viewed from the back is just reversed, but it has the same wrapping topology either way.
Re: Sonic 3 special stages are impossible
Final Fantasy VII and others 3D JRPGs have the exact same problem. The fact the graphics are physically 3D doesn't change the fact you can warp around N/S axis, and as thus, the world is not spherical.rainwarrior wrote: It's true, but this also applies to like every JRPG before Final Fantasy VII too, probably any game with a 2D wrapping world map, really.
Also, it not being spherical does not necessary mean it's a torus. Because the inner diameter would be much smaller than the outer diameter, mapping a world onto a torus is quite problematic as well.
rainwarrior wrote:Edit: here's a funny visualization of the concept: https://imgur.com/a/fUD7n
It would be very cool to have an universe based on a coffee cup shaped planet :phttps://imgur.com/a/fUD7n wrote: a coffee mug with a handle can also have this map projected onto it.
- rainwarrior
- Posts: 8732
- Joined: Sun Jan 22, 2012 12:03 pm
- Location: Canada
- Contact:
Re: Sonic 3 special stages are impossible
It wasn't that it was 3D, I was just mis-remembering it. I thought Final Fantasy VII was an actual globe with a north pole / south pole, but my memory was mistaken, it's just like most game maps. I think I was remembering the northern crater as being a pole, but it's not.Bregalad wrote:Final Fantasy VII and others 3D JRPGs have the exact same problem. The fact the graphics are physically 3D doesn't change the fact you can warp around N/S axis, and as thus, the world is not spherical.rainwarrior wrote: It's true, but this also applies to like every JRPG before Final Fantasy VII too, probably any game with a 2D wrapping world map, really.
Well, they're not a 3D doughnut shaped torus, just a toroidal topology. You can't build a solid 3D torus from a square map without distorting/stretching part of it, but as a 2D topology it's fine. You could probably build it without stretching in 4D though? (At least that's my intuition... would have to think about it.)Bregalad wrote:Also, it not being spherical does not necessary mean it's a torus. Because the inner diameter would be much smaller than the outer diameter, mapping a world onto a torus is quite problematic as well.
Re: Sonic 3 special stages are impossible
An octahedron is isotopic to a sphere. By ripping four edges adjacent to one vertex, it becomes isotopic to a square interior. You go off (say) edge b, and you come out at edge b', from which it was ripped.
So if you rip it at the edges near the south pole, you get the north pole at the center, the south pole at all four corners, the equator in the diagonal of each quadrant, and the prime meridian down from N to the d rip, along the d rip to the south pole, up the b rip, and up to the north pole.
Compare this to a torus sliced twice, which does wrap like a stereotypical video game map.
So if you rip it at the edges near the south pole, you get the north pole at the center, the south pole at all four corners, the equator in the diagonal of each quadrant, and the prime meridian down from N to the d rip, along the d rip to the south pole, up the b rip, and up to the north pole.
Code: Select all
S b b' S
+------P-M------+------W-d------+
| - : - |
| T : A |
| - P - |
a'| - M - | c
| - : - |
| O : U |
| - : - |
+ - - - - - - - N - - - - - - - +
| - : - |
| R : Q |
| - : - |
a | - P - | c'
| - M - |
| - : E |
| - : - |
+------W-d------+------P-M------+
S d' d S
Code: Select all
b
+-------------------------------+
| |
| |
| |
a | | a'
| |
| |
| |
+-------------------------------+
b'