TrajMeanVectorOfTurningAngles {trajr}

Mean vector of turning angles

Description

Returns the mean vector of the turning angles, as defined by Batschelet, (1981). A unit vector is created for each turning angle in the trajectory, and the centre-of-mass/mean vector is returned.

Usage

TrajMeanVectorOfTurningAngles(trj, compass.direction = NULL)

Arguments

trj

Trajectory object.

compass.direction

If not NULL, step angles are calculated relative to this angle (in radians), otherwise they are calculated relative to the previous step angle.

Details

According to Batschelet (1981), r may serve as a straightness index ranging from 0 to 1, where r is the length of the mean vector of turning angles of a trajectory with constant step length. Values of r near 1 indicating straighter paths. Hence, r = Mod(TrajMeanVectorOfTurningAngles(trj)), assuming that trj has a constant step length (e.g. has been rediscretized).

Value

A complex number r which represents the mean vector, Mod(r) is the length of the mean vector which varies between 0 and 1, Arg(r) is the angle.

References

Batschelet, E. (1981). Circular statistics in biology. ACADEMIC PRESS, 111 FIFTH AVE., NEW YORK, NY 10003, 1981, 388.

See Also

TrajStraightness, TrajAngles, TrajRediscretize for resampling a trajectory to a constant step length, TrajResampleTime for resampling a trajectory to a constant step time.