I'm not very familiar with how to draw geometric figures (say circles, rectangles, surfaces of different genera and cusps etc.). I'd like your opinion on softwares that I can use for this purpose. Are these softwares freely downloadable from internet?
As suggested, I should be more specific. I'm trying to draw:
1) The unit circle and several small circles tangent to it from the inside, and also joining those points of tangencies, I'm looking to draw the part of the circles that intersect the unit circle perpendicularly, so the "hyperbolic geodesics", so to say.
2) Surfaces of genus 1 (torus), and 2, 3, or higher (so double or triple torus or surfaces with "handles"). These surfaces could have "cusps" (imagine putting a hole on the surface and fit an infinitely long tube on that hole whose other end become narrow and narrow and gets close to zero as we walk away to infinity)
I'm not trying to PLOT them, I'm just trying to draw them by hand using may be a pencil in the software.