I'm looking for some software that allows one to draw accurate pictures in hyperbolic space. In particular, I want to be able to specify pairs of points and generate the geodesic between them, in various models. I'd like to be able to do this in the upper half-plane model, Poincare disk model, Klein model, and it would be really great if I could also do it in the hyperboloid model. I expect something that does this would have other features, like display multiple geodesics in one picture, and generate tilings and whatnot.

I'm mostly talking about hyperbolic surfaces, but something that addresses 3-manifolds would be awesome too. To be really effective it would have to include a way of zooming in to areas, for instance as distance concatenates near the boundary.

I do have some drawing skills, and I'm able to get by with sketches sometimes, but other times I really want to see what's happening precisely. I must admit I know little about writing code, but am willing to learn. It just seems there is enough interest in hyperbolic geometry these days that somebody must have made some interactive software like this.

  • $\begingroup$ Mathematica is one option, however it is really expensive unless you are a student or have access to it via a university. This will likely require you to do some coding yourself (and it is not hard to learn), but there might be some modules you can just download and use directly (e.g. like this). $\endgroup$ – Winther Sep 26 '15 at 22:39
  • $\begingroup$ @Winther Yeah I had Mathematica on my old computer via student access but couldn't transfer it to my current computer, and didn't want to pay the $$$. $\endgroup$ – j0equ1nn Sep 26 '15 at 23:06
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    $\begingroup$ You could probably use Sage. doc.sagemath.org/html/en/reference/geometry/sage/geometry/… $\endgroup$ – Ben Sheller Sep 27 '15 at 0:09
  • $\begingroup$ @BenS. I came across that page yesterday and posted this doc.sagemath.org/html/en/reference/geometry/sage/geometry/… because it didn't work for me. I'm seeing I got some leads in the comments of that now, so I'm looking into that currently. $\endgroup$ – j0equ1nn Sep 27 '15 at 0:34
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    $\begingroup$ @j0equ1nn It looks like it works on the online version at sagemath.org...I'm not sure about a download for Linux Mint 32. $\endgroup$ – Ben Sheller Sep 27 '15 at 1:14

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