Tensor Product Subspaces

This software lets you investigate subspaces of tensor product spaces defined on two- or three-dimensional domains. Familiarity with the concepts of spline spaces, minimal determining sets, and the Bernstein-Bézier form is assumed. I also assume that you are familiar with the 2D and 3D software, at least to the point that here I can focus on the aspects that are different in the tensor product software.

Invoking the software

You can see what the software does by clicking on the applet at the top of this page. However, this forces you to start from scratch for each new investigation. If you want to be able to save the state of your work, and return to it where you left off, you need to download the software.

Downloading the software

The easiest way to obtain the software is to download this file to a file called message, store it in an empty directory, and then unpack it by giving the Unix Command 
source message

You can also obtain the software by downloading this zip file and unzipping it in an empty directory.

Alternatively, you can download the following individual class files. These are binary files and may not show up properly when your browser tries to display them, but you should be able download them. Make sure you name those files exactly as indicated: LA.class, control.class, hash.class, slice.class, space.class, tp.class.

Running the Software

The most common way to run the software is to give the command 
java tp
This will ordinarily let you continue where you last quit and saved. It is possible to store a state of investigation in a file, say the file discovery. To continue work on the state give the command 
java tp discovery
tp stores the state of an investigation in a file with the extension .tp. When you click on the quit and save button the software saves the current state in the file tpkeepit.tp. When you start it up the next time without specifying a different file name it will read that file and start from there. You specify just the file name, not the extension. If the old state cannot be restored (because the specified file does not exist, or because you have a new version of tp that is inconsistent with older .tp files) the software starts from a default state. If you invoke the software from the applet it always starts in that state.

For complicated problems you may want to cause your system to dedicate additional memory to your job, by giving a command like 

java -ms1024m -mx1024m tp
If you are running java on a PC under Windows it may be necessary to tell java explicitly where to look for the class files, as in 
java -cp . tp

User's Guide

For detailed instructions on how to use this software consult this pdf file (which is also included in the above mentioned message file). Following are gif versions of the Figures in the User's guide.

After starting the software you will see two windows: the control window and a drawing window showing a cubical grid with domain points.

The Control Panel:

The 3D Window:

The 2D Window: