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In a paper I am in the process of writing in LaTeX, I need to draw and incorporate some diagrams of hyperbolic surfaces in my LaTeX document. Is there any software I can use to draw hyperbolic surfaces, either closed, or with boundaries or punctures ? Are there any such freely downloadable softwares that I can use to draw such diagrams ? Please let me know if you know one. I apologize if this is off-topic. Thank you !

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If it is to be published in a journal, consult the web page of the journal about what they want for diagrams. –  Gerald Edgar May 3 '12 at 17:18
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Recently, Dani Calegargi put together a program called wireframe for this purpose. It is documented here and available here. Playing around with it, it seems to work pretty well.

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Try 3D-XplorMath, available for free download at http://3D-XplorMath.org . You can see many surfaces created using the program in The Virtual Math Museum at

http://virtualmathmuseum.org/Surface/gallery_o.html#AlgebraicSurfaces

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POV-Ray can make beautiful 3d plots of surfaces, but it can take a lot of work to get what you want. Here is an ellipsoid that I made using the method described on Friedrich A. Lohmueller's site. Good luck!

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Maybe TikZ and PGF here. Also, there is a package based on TikZ, called PGFPlots, here.

Another option is to use Asymptote: The Vector Graphics Language.

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