Awesome, will try on desktop later. Reporting that mobile doesnt work so hot (I can scroll up and down but not side to side)
@marc.eichberger1 Wow. Simply, wow.
If I remember well, there is a championship of this kind of go every year in Finland
Interesting side effect of the cube-to-sphere mapping - most of the intersections on the sphere have 4 liberties, except for the 6 corner spots, which all have 3 liberties
As such, if a stone is chased into a corner by an opponent, and wants to nobi - they have no choice but to make an empty triangle i.e. nobi to the left or right, but not up, as that will be a hanging connection…
I wonder if there is another mapping transformation will will allow all intersections on the sphere to have 4 liberties?
TOPOLOGY NERDS… ASSEMBLE!
8
forehead slap - of course! yes 8
Also - it’s always good to see Cunningham’s Law in action - even though my cube-corner mis-count was genuine
: P
its possible to show torus as square
its also possible to show only center part of that square and hide other
and is possible to draw that smaller center square as circle
so its possible to create illusion of sphere, which is actually torus
I really like that idea. I don’t know enough about coding, but I’m guessing it would be fairly easy to suspend the viewer’s camera over a sphere - then project the image of that torus grid onto that sphere so that it wraps at the edges
However, the player’s focus of stitched together image would always display towards the camera regardless of how it was oriented, so you’d never see whatever distortion effects might happen on the “other side” of the sphere, away from the camera view
That way you wouldn’t have to perfectly map the grid to a sphere - because you’d always be seeing one side of it - sort of if Pac-Man could exit the game on top and re-appear on the bottom, but it would just be a grid of Pac-Man displays in all x/y directions - your fish-eye lens display would only show you one small part of that larger / virtual whole
I hope that makes sense…
Oh the menu Thing is a bit annyoing, didnt notice that, the Stones should be larger, true. Same for larger sphere, stones should be smaller, but i wont tweak anymore but functionality ;p
Sadly the camera is wierdly positioned on mobile. But i wont change that. I am happy with the pc version:p
This sounds interisting but i dont really understand. I only know thats its impossible to have a grid on a sphere with 4 liberties everywhere. Oh wait, i get what you mean, but i can imagine thats not too easy to code
full 3d shere do not exist in this idea
only half of sphere
part of surface of torus is projected on that half of sphere
That would be sick
I keep poking around - I’m not sure if this article describes a way of doing what I mentioned above, but it may be on the right track?
So the Go game and the player interactions at the intersections would live on a 2D board that looked flat, but was in effect a torus because the left / right sides would be stitched together, and the up / down sides would be stitched together. As I understand it - this is fairly easy in Unity - you just tell the board to “wrap” on top and bottom, so that when a player moves off the right side of the board, they re-appear on the left with no break in continuity
So then you map that 2D board image on top of the sphere so that the grid appears as if through a fish-eye lens, and half of the board disappears over the horizon so that the camera can only see half - well, probably less than half depending on the fish-eye effect - of the board. The 2D board is never actually attached to the sphere, it’s just warped by it so that you can only see part of the grid at any one time. Or, if the 3D effects of the stones raised above the board / casting shadows etc, get too intensive, you could limit the camera so that one can only ever see part of a larger sphere, but not the edge.
You nailed it!
It works perfekt, after work ill publish this Version too, exciting!
An octahedron has degree 4 for each vertex, and fits on a sphere. It only has eight vertices though. If you take the dual of a rhombic dodecahedron then you have twelve vertices.
You can expand any of these graphs to an arbitrary number of vertices with the following transformation:
It’s not guaranteed to produce something nice - it certainly won’t locally be squares.
Actually you can just paste a square grid onto each side of a cube (then inflate to a sphere). If you don’t have a vertex on the corners, all vertices have four liberties. This is the dual of the graph from the OP.
It turns out this has been talked about before on the forums.
Or this one.
like this? 
https://holz231.github.io/go-4-ever/ (deleted)
