Turn Angle

class ollin.movement_analyzers.turn_angle.Analyzer(movement)

Turn Angle analyzer.

Turn angle refers to the angle formed by two successive steps of an individual motion.

Hence if \(p(t_0) = (x_0, y_0)\), \(p(t_1) = (x_1, y_1)\) and \(p(t_2) = (x_2, y_2)\) are the positions of an individual at times \(t_0, t_0\) and \(t_2\) then the turn angle at time \(t_1\) is defined by:

\[ \begin{align}\begin{aligned}d_1 = (x_1 - x_0, y_1 - y_0)\\d_2 = (x_2 - x_1, y_2 - y_1)\\ta = \arccos\left(\frac{d_1 \cdot d_2}{||d_1|| \cdot ||d_2||}\right)\end{aligned}\end{align} \]

Here \(ta\) is turn angle.

analyze(movement)

Extract turn angles from movement data.

Get the turn angles of all individuals in movement data at every time step. Will result in an array of size [num_individuals, time_steps - 2] so that:

turn_angle = results[i, k]

Means that the i-th individual had a turn angle of turn_angle at the k-th time step.

Parameters:movement (Movement) – Movement data to analyze Returns:results – Array of shape [num_individuals, time_steps - 1] containing the turn angles of all individuals at every time step. Return type:array

plot(ax=None, figsize=(10, 10), num_individual=0, bins=20, width=None, cmap='Reds', alpha=0.8, log=True)

Plot distribution of turning angles.

Parameters:

• ax (matplotlib.axes.Axes, optional) – Axes object in which to plot.
• figsize (tuple or list, optional) – Size of figure to create if no axes are provided.
• num_individual (int or tuple or list or array, optional) – Selection of individuals from which to draw turning angle information. If num_individual=’all’, all information will be plotted.
• bins (int, optional) – Number of bins to use in histogram of turn angle distribution. Defaults to 20.
• width (float, optional) – Width of bars in histogram. If none is given, width will be maximum possible before overlap.
• cmap (str, optional) – Colormap to use to assign colors to histogram bars. Defaults to ‘Reds’.
• alpha (float, optional) – Alpha value of plot. Defaults to 0.8.