This is possibly not the best place to put this, but I am looking for a software where you can draw on a plane diagram of a torus (unit square with identifications) and it automatically maps the drawing onto a 3D model of a torus. I know it is possible to do such a thing manually (c.f. here) but I would like it to be more interactive. I'm not sure if such a thing exists. If it does not, and anyone would want to work on such a thing, I'd be happy to collaborate.


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    $\begingroup$ I don't know of any such software, but putting something together in HTML/JavaScript looks straightforward. <> Because the question may be considered off-topic for Math.SE, there's a chance it will get moved or closed. If that happens, maybe start a chat thread and ping people who comment here...? $\endgroup$ Sep 22, 2022 at 15:22
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    $\begingroup$ @AndrewD.Hwang It is simple to me conceptually, but I'm not great at graphics programming - I just never know how to start. If you want to work together on it I would be glad to help, or at least do the mathy part on my own. $\endgroup$
    – Andrea B.
    Sep 23, 2022 at 2:05
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    $\begingroup$ There's a version displaying two canvases side-by-side; the left canvas is a $2\times2$ square-tiled piece of plane in which polygon paths in selectable colors can be drawn by mouse-clicking; the right displays (crudely, e.g., without proper spatial layering) the image under a conformal parametrization of a torus. The spatial viewpoint can be rotated using the arrow keys. I'm not yet ready to post a URL (because doing so will cause the page to get indexed by search engines), but am happy to email the URL on request. $\endgroup$ Sep 24, 2022 at 16:10
  • $\begingroup$ Sure, you can email to my throwaway account (lower case L) [email protected] [since I'm unsure of any direct message functionality here] @AndrewD.Hwang $\endgroup$
    – Andrea B.
    Sep 24, 2022 at 20:18
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    $\begingroup$ For posterity (but avoiding a link-only answer), here's a reasonably-permanent URL: mathcs.holycross.edu/~ahwang/teach/software/Torus/index.html $\endgroup$ Oct 5, 2022 at 18:01


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