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PostPosted: Mon Oct 16, 2017 4:46 am 
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How can you possibly have a checkered patterned sphere?


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PostPosted: Mon Oct 16, 2017 7:05 am 
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well, it's a torus for one thing

but yeah, this totally ruins the realism of sonic 3 :/


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PostPosted: Mon Oct 16, 2017 7:50 am 
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I had never thought about this, but... you're right!


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PostPosted: Mon Oct 16, 2017 8:05 am 
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The playfield in Tetrisphere is also a torus.


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PostPosted: Mon Oct 16, 2017 10:01 am 
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adam_smasher wrote:
well, it's a torus for one thing
It would make sense, but is this canon?

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PostPosted: Mon Oct 16, 2017 11:42 am 
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Literally unplayable!


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PostPosted: Mon Oct 16, 2017 4:33 pm 
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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.

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PostPosted: Tue Oct 17, 2017 11:02 am 
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I wonder how the back facing side of a "torus sphere" would look like.


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PostPosted: Tue Oct 17, 2017 11:49 am 
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Well, the image viewed from the back is just reversed, but it has the same wrapping topology either way.


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PostPosted: Tue Oct 17, 2017 3:32 pm 
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Don't look at videos of the cancelled Sonic X-Treme, whatever you do.


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PostPosted: Tue Oct 17, 2017 5:59 pm 
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strat wrote:
Don't look at videos of the cancelled Sonic X-Treme, whatever you do.

Whaump Whaump

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PostPosted: Tue Oct 17, 2017 6:46 pm 
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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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PostPosted: Wed Oct 18, 2017 7:14 am 
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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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PostPosted: Wed Oct 18, 2017 7:37 am 
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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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PostPosted: Wed Oct 18, 2017 8:35 am 
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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:
 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:
                  b         
  +-------------------------------+
  |                               |
  |                               |
  |                               |
a |                               | a'
  |                               |
  |                               |
  |                               |
  +-------------------------------+
                  b'


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