XCSPRG

overview | download and install | usage

Overview

The xcsprg is a tool that I was developping while I was writing my diploma thesis. Using Clebsch's representation of the cubic surface in the plane using 6 points, so that the surface is the blowup of the plane in these points, you can discover the space of cubic surfaces containing only real lines.

The screenshot below shows a typical session. In the right window, you can drag the 6 points, in the left, you see the corresponding cubic surface. Here, you see the clebsch surface, which can be represented by the 5 vertecies of a regular fivegon together with its center.

Download and Install

The cubic surface program only runs on unix/linux systems, because the beautiful images of the surfaces are calculated using the software surf which is only available on these systems.

So the first thing to do is to install the surf program.
Then download the file xcsprg-0.81.tar.gz into the directory:
/home/yourname/xcsprg/
Attention! The script that is used to start the cubic surface program only works well if you have used the above directory!
Then change to that directory and unpack the archive, e.g.:
cd /home/yourname/xcsprg
gunzip xcsprg-0.81.tar.gz
tar -xvf xcsprg-0.81.tar

Now you can run the program by typing
xcsprg
on the command line, when you are in the directory /home/yourname/xcsprg.

If you want to be able to start the program from other directories, too, you will need to copy the script xcsprg to a directory that is listed in your PATH.

Usage

When you start the program, you will first want to adjust the size of the image in the cubic surface window, because the start size is very small. This can be done via the properties menu of this window.

The properties menu of the six points window can be used to display lines and other stuff (like the hessian or a tangent plane in a point T or their intersetions with the surface) - just try this out.

In most cases, you will not want to change the mode using the modes menu, but sometimes this might be useful, e.g. to produce movies! Contact me, if you are interested in this feature or if you have got any questions.

xcsprg places all the temporary files in a temporary directory called blowup?????, where the questions marks are replaced by some number. If you want to keep one of the files, change to that directory (e.g. by typing cdSlideshow) and copy the files to another directory. The surf source is the file blowup.pic, the image files are blowup.ras and blowup.jpg.

The xcsprg will not be developped further, because my program spicy can be used to do more or less the same, but has many other features as well - e.g. it is a complete constructive geometry program.

Back to the cubic surface homepage.