TT-$\pi$ Plot (Parallelity)

The section above used the distance as one spatial aspect. This section introduces a second type of the TT-Plots, called TT-$\pi$ plots, which considers the intra-dataset parallelity aspects in a time plot. One example application for this type of plot is the analysis of foraging movements of an animal which is 'scanning' an area. In figure 5.13 the creation of a TT-$\pi$ plot is illustrated.

Figure 5.13: Creation of a TT-$\pi$ plot. The colors indicate the parallelity relative to P1.

First the point P1 is considered as basis for the calculations. The differences in the direction of the walking path from point P1 to all subsequent points (P2-P4) are then calculated. This results in values from 0-$\pi$ (0-180 degrees). Then the same procedure is applied starting from the next point (P2) as basis. This results in a plot similar to figure 5.8b) with the difference that the length of the arrow now represents the angular deviation from the base point. This matrix is then transformed into the same color scheme used in the previous plots (table 5.6) to maintain a consistent appearance. Blue colors indicate a parallel walking direction, green colors show a walking direction of about 90$^\circ$ and red colors represent an opposite walking direction.

Table 5.6: Color scheme for TT-$\pi$ plots

Color	Parallelity
blue	parallel
green	90$^\circ$
red	anti-parallel (180$^\circ$)