most recent 30 from http://mathoverflow.net 2013-05-20T00:27:08Z http://mathoverflow.net/feeds/question/96622 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/96622/what-is-are-the-softwares-to-use-to-draw-surfaces-of-the-form-of-a-two-or-three Analysis Now 2012-05-10T22:39:36Z 2012-05-11T12:38:08Z

<p>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.</p> <p>For example, see the diagrams on : <a href="http://www.maths.bris.ac.uk/~mazag/hyperbolic/index.html" rel="nofollow">http://www.maths.bris.ac.uk/~mazag/hyperbolic/index.html</a></p> <p>Or see the diagrams on : <a href="http://lamington.wordpress.com/2010/04/18/hyperbolic-geometry-notes-4-fenchel-nielsen-coordinates/" rel="nofollow">http://lamington.wordpress.com/2010/04/18/hyperbolic-geometry-notes-4-fenchel-nielsen-coordinates/</a></p> <p>to get ideas about what surfaces I am talking about. They are not given by any easy equations.</p> <p>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 !!</p>

http://mathoverflow.net/questions/96622/what-is-are-the-softwares-to-use-to-draw-surfaces-of-the-form-of-a-two-or-three/96654#96654 Neil Strickland 2012-05-11T09:32:39Z 2012-05-11T09:32:39Z

<p>The solutions that people have mentioned are good if you are happy with a two-dimensional line drawing. It would be better to have three-dimensional equations that could be plotted using Maple, or something like that, but that seems to be surprisingly hard. The equation $$ 3x_3^2x_4-2(x_1^2+x_2^2)x_4-2x_4^3+2(x_1^2-x_2^2)x_3 = 0 $$ defines a highly symmetric surface of genus 2 embedded in $S^3$, and one can project stereographically into $\mathbb{R}^3$ to get a nice picture like this: <img src="http://neil-strickland.staff.shef.ac.uk/misc/XX.jpg" alt="alt text"></p> <p>(There's a lot to be said about this example; I will have an undergraduate working on it over the summer.) However, I do not know similarly nice equations for surfaces of higher genus, or with the two tori in the same plane rather than at right angles, or with cusps.</p>

http://mathoverflow.net/questions/96622/what-is-are-the-softwares-to-use-to-draw-surfaces-of-the-form-of-a-two-or-three/96664#96664 Dick Palais 2012-05-11T12:38:08Z 2012-05-11T12:38:08Z

<p>If you go to the Algebraic Surface page of The Virtual Math Museum at</p> <p><a href="http://virtualmathmuseum.org/Surface/gallery_o.html#AlgebraicSurfaces" rel="nofollow">http://virtualmathmuseum.org/Surface/gallery_o.html#AlgebraicSurfaces</a></p> <p>you will see many nice examples. These were created using the program 3D-XplorMath which you can download at <a href="http://3D-XplorMath.org" rel="nofollow">http://3D-XplorMath.org</a> . If you install that and go to the Implicit Surface category you will see many examples with documentation.</p>