Table 1 Calculations for track analysis

dist1

Distance between first point pair (point i and i-1)

P _i  - P_i - 1

Dependent upon original data

dist2

Same as above for i+1 and i

Same as above

Speed

Distance between point pair divided by time difference

$\frac{\left|P_i-P_{i-1}\right|}{t_i-t_{i-1}}$

Distance unit time unit ^-1

Idiothetic turning angle

Angle of 2nd point pair, relative to first point pair

${\theta }_i=\text{acos}\left(\left(\frac{P_{i+1}-P_i}{\left|P_{i+1}-P_i\right|}\right)·\left(\frac{P_i-P_{i-1}}{\left|P_i-P_{i-1}\right|}\right)\right)$

°

Three-dimensional angle

Angle, relative to reference vector

${\theta }_i=\text{acos}\left(\left(\frac{P_i-P_{i-1}}{\left|P_i-P_{i-1}\right|}\right)·w\right)$

w= reference vector

°