A comparative study between RadViz and Star Coordinates

This paper presents a comparison between two visual mappings, RadViz and Star Coordinates.

There is an algebraic idea lurking behind the paper’s method. Specifically, they have two different visual mappings, and they show their “equivalence” by building a pair of maps $v_1, v_0$ that make the following diagrams commute:

In other words, what the authors show is that one way to understand the differences between RadViz and Star Coordinates is to find a method to change the input such that both visual mappings are indistinguishable.