The best ways to display a map of non-Euclidean 3-D space?

[greswd]

You might have seen such a 3-D map of the stars before:

And I was wondering about a 3-D map if space was non-Euclidean, what would be the best ways to display it.

To keep it simple, if you're considering elliptic space, you can consider the entire "global" map. Just like we have world maps of our entire ellipsoidal globe of planet Earth.

And if you're considering hyperbolic space, you can also consider a closed seamless hyperbolic universe in addition to an "open" hyperbolic space.

Another factor to consider is whether the map is static or interactive. Though the region of space which we'll be displaying will be so large that the non-Euclidean geometry will be obvious, it won't be like zooming into a tiny portion of space which appears relatively "flat" and Euclidean.

 

[greswd]

You might have seen such a 3-D map of the stars before:

View attachment 301762


And I was wondering about a 3-D map if space was non-Euclidean, what would be the best ways to display it.

To keep it simple, if you're considering elliptic space, you can consider the entire "global" map. Just like we have world maps of our entire ellipsoidal globe of planet Earth.

And if you're considering hyperbolic space, you can also consider a closed seamless hyperbolic universe in addition to an "open" hyperbolic space.

Another factor to consider is whether the map is static or interactive. Though the region of space which we'll be displaying will be so large that the non-Euclidean geometry will be obvious, it won't be like zooming into a tiny portion of space which appears relatively "flat" and Euclidean.

and maybe the best way to teach non-Euclidean geometries is to use mock maps

 

[robphy]

And I was wondering about a 3-D map if space was non-Euclidean, what would be the best ways to display it.

In my opinion,
the answer for any visualization depends on what information you are trying to convey.
Each representation will have varying degrees of advantages and disadvantages
for various choices of the information to be emphasized.

 

[greswd]

In my opinion,
the answer for any visualization depends on what information you are trying to convey.
Each representation will have varying degrees of advantages and disadvantages
for various choices of the information to be emphasized.

let's say we're trying to convey the locations of all the features in the universe, their locations in 3-D space

kinda like a globe (although its a 2-D surface)

 

[robphy]

let's say we're trying to convey the locations of all the features in the universe, their locations in 3-D space

kinda like a globe (although its a 2-D surface)

I have no specific suggestions.
My comment was to suggest that your question was not specific enough
since the answer depends on what you want to display
(and what you hope your viewer understands from it)
and what distortions you are willing to tolerate
(and hope that your viewer doesn't misinterpret).

https://www.google.com/search?q=vis...ta&oq=visualization+of+three+dimensional+data