So I got sort of a unique problem that I’ve pondered on and off over the past few years, never able to come to a conclusion.
It involves wrapping a voxel world (think Minecraft) around a sphere.
So lets say you have a world, like in a video game, that is flat and composed of blocks, each block being a perfect cube. Lets say it is 255 layers tall (just like a Minecraft world, but we don’t know the length and width of it).
Now generally, if you were to wrap this voxel world around a sphere, you’d get one of two things. The first option is that, closer to the center of the sphere, the blocks would collide with each other as they’re mushed together. On the farthest reaches of the sphere, the blocks would be spread apart from each other, no longer touching one another. Option two is that the blocks would be distorted.
We’ll be using option two for my question. So, if we used a block world that was flat, it’d look something like this when wrapped around a circle: (image found on Google)
Think of the “cells” as blocks, or at least supposed to be perfect squares. Note the distortion.
Take notice of layers 4 and 5 (starting at the center). They appear to have the least distortion out of all the other layers. By this, I mean they are the most “cube/square” like.
So this means that, on a sphere that has distorted cubes wrapped around it, there is a zone in the middle, or close to the middle, that has the least amount of distortion.
The larger the sphere is, the greater the “layer or layers” or least distorted blocks there are.
So lets say you could make your sphere as big as you want.
We know that at a very large scale, there is a single layer of blocks that has a distortion level that is too small to see with the naked eye. Of course we don’t know the value of this scale.
So now lets go back to the idea of a world that is 255 layers.
How big would the sphere have to be in order to have a “playing zone” where all distortion through layers 1 – 255 is too small to see with the naked eye? Basically layer 1 has distortion too small to see with the naked eye, but layer 255 also does (and thus ‘securing’ all the layers between). The idea is that there is still distortion; it’s just not on any noticeable level.
So how big would the sphere have to be? Note that I have no idea how to solve this but this question spikes my curiosity a lot so I’m seeking answers for it.
*The eye can see down to about 1 arcminute of an angle. Although I don’t really know what that is lol.
*I think it will help to first find the answer for the flat version (see the image above) first, using 255 layers. It may also help, for both flat and 3d, to fine one layer that has no visible distortion and then maybe use it as some sort of multiplier.
*The blocks being used in this problem will be 1 cubic meter blocks.
*The “playing zone” is where, if this were a video game like Minecraft, the player would play in and be able to build and destroy blocks throughout all 255 layers without any noticeable distortion.
*There can be layers below layer 1 and above layer 255, but they wouldn’t be part of the “playing zone.”
*The poles will be heavily distorted, so there there will be a radius around the North and South poles that is also not part of the “playing zone.” This means that the “playing zone” will be more like a super thick ring around the sphere.
The big questions:
*What is the minimum size required for the sphere? I’m not sure the units of the size, but maybe something like number of blocks (including distorted blocks and blocks below layer 1 and above layer 255) for the diameter and/or radius.
*What is the minimum width (up and down, with up being North and down being South), in number of blocks, that the “playing zone” can be without any noticeable distortion? The idea here is that even tough the poles are off limits, there should still be a very large amount of area north and south of the equator to play in.
Also, I apologize if this is the wrong place to ask this type of question. I was recommended this place by someone who tried to answer the question but was unable to.
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