What asxp does:

It runs under Linux (originally Ubuntu 14.04 LTS, now Ubuntu 18.04 LTS on my machine) and generates perspective views of algebraic surfaces via raycasting:

You define a certain polynomial F(x, y, z, a, b) in the variables x, y, z and parameters a and b in the configuration file of asxp.

Then you can go into a visualizing window for the surface, where the position of the mouse determines the parameters a and b as a0 and b0 and the surface plotted is the (two dimensional projection of the) zero-set

F(x, y, z, a0, b0) = 0

in 3d-space with coordinates x, y, z.

Look at a video:

The current version runs with CUDA support and uses the parallel processing power of the graphic card:

A still drawing from the new asxp:

The new version of asxp can produce cross-hatched drawings of a surface, where the strokes are oriented along the principal directions of curvature.

See the following example:

or that of a developpable algebraic surface of degree 4:

But the best at last

Now I can produce 3D-printable models of algebraic surfaces. I produced a sample at Shapeways, where you can view (and also buy) it:

See it printed:

As I say it on the shop: If you would like to get your special 3D-model of an algebraic surface produced, just contact me via e-mail.

The code

You can find it on GitHub.

A wish to potential users of asxp

If you are interested in using asxp on your computer, I would be happy to receive a mail from you, adressing some questions, whose answers could direct the further development of asxp.

• If you are a Linux user:
  • Do you use Ubuntu? Which version?
  • Do you use another distribution? Which one?
  • When having looked at the Github asxp README do you feel able to build asxp on your machine? (If you did it: Congratulations! Send me a mail, you will be remembered :-))
  • If not, what would help you most, to become able to use asxp on your machine? Do you need an Ubuntu package (seems at the moment a bit too difficult for me, because of the CUDA dependency)? Or would a shell script doing the build be enough? What dependency is the biggest hurdle for you (Qt, CGAL, boost, GTS, CUDA)?
• If you are a Windows or MacOS user:
  • Would you like to have asxp available? (Tell me your operating system).
• General:
  • Do you regard asxp to have unique features which would make it attractive for you to use on your computer (any OS)?
  • If yes, what are these features (in order of importance, if you like)?

A punctured surface