T-x, T-y and T-r Plot

In this section I will introduce the T-x, T-y and its generalized version, the T-r plot. The idea is to neglect one of the coordinates defining the point in space and replacing it with a time axis. In the case of the T-x plot, the x axis is retained and the y axis is replaced by a time axis, whereas in the T-y plot, the x axis is replaced by a time axis. Figure 5.4 shows T-x and T-y plots for the object walking along a line. In this artificial example a sinus-like graph is seen in both plots. In figure 5.4a we can follow the (computer-)animal starting from the bottom left of the graph. The horizontal axis represents the x coordinate, whereas the vertical axis indicates time. The animal then starts moving east until it reaches the right edge, turning sharply around and walking in direction west, restarting again at the left edge. In figure 5.4b the graph is rotated by 90 degrees, now representing the y coordinate on the vertical axis and time on the horizontal axis. This is done for illustration purposes. In this example a similar pattern is produced indicating a movement starting north and then periodically going from south to north and reverse.

Figure 5.4: Left: T-x plot Right: T-y plot for the artificial movement pattern walking along a line.

Both T-x and T-y plots are bound to the coordinate system used. Using a different coordinate system could result in different results. This limitation is overcome with the T-r(otation) plot, which allows rotating the coordinate system dynamically. This is roughly illustrated in figure 5.5 in which three rotation angles for the coordinate system are used. The little triangle in the upper right corner indicates the rotation angle. In figure 5.5a the coordinate system is rotated to be more or less parallel to the main movement direction of the (computer-)animal resulting in a narrow horizontal band. In figure 5.5b the coordinate system is not parallel to the main movement direction anymore revealing an oscillating movement, which has its highest amplitude at a rotation angle of about 200 degrees in figure 5.5c.

Figure 5.5: T-r(rotation) plot for the artificial movement pattern walking along a line. The arrow in the top-right corner indicates the angle used as axis for the specific plot (from left to right): 132, 161 and 202 degrees.

a b c