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Topological Quantum Field Theory diagrams with pstricks or tikz

I am trying to draw surfaces with complete hyperbolic structures and surfaces which are topologically tori. The hyperbolic surfaces I need to draw are torus with one or two holes on it, or torus with punctures on it, or torus with a cusp attached to it . They could also be torus torus with one or more than one handles attached to it.

For example, see the diagrams on : http://www.maths.bris.ac.uk/~mazag/hyperbolic/index.html

Or see the diagrams on : http://lamington.wordpress.com/2010/04/18/hyperbolic-geometry-notes-4-fenchel-nielsen-coordinates/

to get ideas about what surfaces I am talking about. They are not given by any easy equations.

Is there a software I can use to draw them ? People who study Riemann Surfaces or Hyperbolic Geometry or Teichmmuller Theory would definitely know exactly what surfaces I am talking about.Please let me know if you use such a software. Thanks a lot in advance !!

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    Welcome to TeX.sx! This site is about TeX, LaTeX and friends. While they have great support for math, this isn't a math site. In your current form your question is not on-topic IMHO. If your rephrase it and ask how to draw such diagrams using (La)TeX than it would be on-topic. If you just look for any software to draw them ask either on our math related sister site http://math.stackexchange.com or one of the software related ones like http://www.superusers.com. – Martin Scharrer May 10 '12 at 22:54
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    In general there are two larger (La)TeX packages for drawing diagrams: pstricks and tikz/pgf. They are very powerful and should allows to draw any form of diagram, at least in theory. – Martin Scharrer May 10 '12 at 22:56
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    Also have a look at this question that led to a package by Andrew Stacey. – percusse May 10 '12 at 23:27
  • The blog post ones can definitely be done by the TQFT package. The one on the webpage could mostly be done by that, but the end would need a little extra (not hard to do by hand, I deem). – Andrew Stacey May 11 '12 at 07:16

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