what is
tess?
Tess is a computer program that graphically renders tessellations in
Euclidean and non-Euclidean geometries. A tessellation or tiling,
in its most general form, is simply a repeated geometrical pattern.
We are all familiar with Euclidean tessellations; they surround us on
carpets, wallpaper, and ceiling tiles. But tessellations exist in
non-Euclidean spaces as well. Euclidean and non-Euclidean spaces
have different geometries, and tessellations are rendered differently in
each. Thus in addition to being intrinsically interesting
mathematical constructions, tessellations illustrate the essential
differences between Euclidean and non-Euclidean geometries.
Tess is currently in an early
stage of development. The software has been fully tested only on
the Sun Solaris operating system, although it will probably function on
most other UNIX/Linux systems. Documentation is forthcoming but
not available at this point. Volunteers are welcome!
how does tess
work?
Tess uses the theory of projective geometry to reduce the calculation of
tessellations to iterated matrix multiplication. It renders the
tessellations either in the Euclidean plane, or in one of several
non-Euclidean models. Currently, Tess can render hyperbolic
tessellations in the Poincaré unit disc model, the Poincaré upper
half-plane model, or the Klein model.
sample tess output
Check out the following tessellations of the ideal triangle (0-0-0
angled) in the Poincaré unit disc model, the
Poincaré upper half-plane model, and the
Klein model. You will need
Ghostview to view these
files.
how do i run tess?
To run Tess, download the tarball below. Unpack it by running
tar xvf tess0.xx.tar
The next step is to compile the software:
cd tess0.xx
./configure
make
To finally run the program,
execute
tess
This will present you with an interactive menu which will explain the
available options and guide you through rendering a tessellation.
In order to view the PostScript output created by Tess, you will need
Ghostview.
download tess
tess 0.42
Tess was developed at the
Experimental Geometry Lab
at the University of Maryland.
For more information about Tess, email the co-director of the
Experimental Geometry Lab, Bill
Goldman. |