Sonic 3 special stages are impossible

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psycopathicteen
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Sonic 3 special stages are impossible

Post by psycopathicteen »

How can you possibly have a checkered patterned sphere?
adam_smasher
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Re: Sonic 3 special stages are impossible

Post by adam_smasher »

well, it's a torus for one thing

but yeah, this totally ruins the realism of sonic 3 :/
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tokumaru
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Re: Sonic 3 special stages are impossible

Post by tokumaru »

I had never thought about this, but... you're right!
tepples
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Re: Sonic 3 special stages are impossible

Post by tepples »

The playfield in Tetrisphere is also a torus.
nitro2k01
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Re: Sonic 3 special stages are impossible

Post by nitro2k01 »

adam_smasher wrote:well, it's a torus for one thing
It would make sense, but is this canon?
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Nioreh
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Re: Sonic 3 special stages are impossible

Post by Nioreh »

Literally unplayable!
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rainwarrior
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Re: Sonic 3 special stages are impossible

Post by rainwarrior »

psycopathicteen wrote:How can you possibly have a checkered patterned sphere?
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.

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.
psycopathicteen
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Re: Sonic 3 special stages are impossible

Post by psycopathicteen »

I wonder how the back facing side of a "torus sphere" would look like.
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rainwarrior
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Re: Sonic 3 special stages are impossible

Post by rainwarrior »

Well, the image viewed from the back is just reversed, but it has the same wrapping topology either way.
strat
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Re: Sonic 3 special stages are impossible

Post by strat »

Don't look at videos of the cancelled Sonic X-Treme, whatever you do.
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Dwedit
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Re: Sonic 3 special stages are impossible

Post by Dwedit »

strat wrote:Don't look at videos of the cancelled Sonic X-Treme, whatever you do.
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psycopathicteen
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Re: Sonic 3 special stages are impossible

Post by psycopathicteen »

rainwarrior wrote:Well, the image viewed from the back is just reversed, but it has the same wrapping topology either way.
If you continue the checkerboard pattern all the way around, wouldn't it have to warp into a fractal pattern in the back.
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Bregalad
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Re: Sonic 3 special stages are impossible

Post by Bregalad »

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.
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.

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
https://imgur.com/a/fUD7n wrote: a coffee mug with a handle can also have this map projected onto it.
It would be very cool to have an universe based on a coffee cup shaped planet :p
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rainwarrior
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Re: Sonic 3 special stages are impossible

Post by rainwarrior »

Bregalad wrote:
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.
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.
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: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.
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.)
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Re: Sonic 3 special stages are impossible

Post by tepples »

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.

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
Compare this to a torus sliced twice, which does wrap like a stereotypical video game map.

Code: Select all

                  b         
  +-------------------------------+
  |                               |
  |                               |
  |                               |
a |                               | a'
  |                               |
  |                               |
  |                               |
  +-------------------------------+
                  b'
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