Rendering of Twisted Loop Examples for Psychometric Tests

Ongoing research on the psychometrics of mental rotation at the University of Graz is based on images of twisted loops like the ones shown in Figure 1. The subject is given images of two different views of the same twisted loop and has to decide, along which principal axis the loop has to be rotated to get from one view to the other. A multitude of geometric parameters, e.g., number of turns, depth complexity, can be used as a measure of difficulty, thus opening up the possibility of adaptive testing.

(a)

(b)

Figure 1: Two different views of the same loop: (a) front, (b) left.

We were approached by the researchers at University of Graz asking for help in developing a rendering system to produce the images of such twisted loops needed in adaptive mental rotation tests. The goals of this work are:

• Find a suitable shape representation for twisted loops
• Develop an algorithm for automatic generation of twisted loops considering of the set of psychometrically relevant geometric parameters
• Develop a rendering system for twisted loops
• Create a database that allows querying for images of twisted loops of a given difficulty level