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What asxp does:

It runs under Linux (Ubuntu 14.04 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:

My Shapeways shop

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.

Download an earlier version ("Algebraic surface explorer")

An algebraic raytracer: Download asxp-cuda.tgz for Linux - date 2014 05 20

The program makes pictures of an algebraic surface in real affine 3-space with two free parameters a,b which are set by x and y of mouse position. It uses CUDA for rendering speed.


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