Looking to understand the use of ellipses/polygons in TITAN

I’m a researcher in applied mathematics with very limited background in meteorology. I’m looking to understand more about the internals of TITAN for my current project. In the TITAN paper by Dixon and Wiener (1993), it is stated that ellipses (and later polygons) are used to approximate the projected area of a storm on a horizontal plane. I understand that these shapes are useful for storm-tracking and forecasting but I fail to see how they work exactly. Are they simply for visualization purpose?

I would greatly appreciate any elaboration or pointers to documentation/relevant parts of the code base.

Thank you in advance.