trajr (version 1.5.1)

TrajGenerate: Generate a random trajectory

Description

Generates a trajectory. If random is TRUE, the trajectory will be a correllated random walk/idiothetic directed walk (Kareiva & Shigesada, 1983), corresponding to an animal navigating without a compass (Cheung, Zhang, Stricker, & Srinivasan, 2008). If random is FALSE, it will be a directed walk/allothetic directed walk/oriented path, corresponding to an animal navigating with a compass (Cheung, Zhang, Stricker, & Srinivasan, 2007, 2008).

Usage

TrajGenerate(
  n = 1000,
  random = TRUE,
  stepLength = 2,
  angularErrorSd = 0.5,
  angularErrorDist = function(n) stats::rnorm(n, sd = angularErrorSd),
  linearErrorSd = 0.2,
  linearErrorDist = function(n) stats::rnorm(n, sd = linearErrorSd),
  fps = 50,
  ...
)

Value

A new Trajectory with n segments and n + 1 coordinate pairs.

Arguments

n

Number of steps in the trajectory.

random

If TRUE, a random search trajectory is returned, otherwise a directed trajectory (with direction = 0 radians) is returned.

stepLength

Mean length of each step in the trajectory, in arbitrary length units.

angularErrorSd

Standard deviation of angular errors in radians.

angularErrorDist

Function which accepts a single argument - the number of values to return, and generates random deviates according to some distribution. The returned values are added to the previous step angle (when random == TRUE), or to 0 (is random == FALSE) to generate the step angle for each step in the trajectory. If the mean of the returned values is not zero, the walk will be biased.

linearErrorSd

Standard deviation of linear step length errors.

linearErrorDist

Function which accepts a single argument - the number of values to return, and generates random deviates according to some distribution. The returned values are added to stepLength to generate the lengths of each step.

fps

Simulated frames-per-second - used to generate times for each point in the trajectory.

...

Additional arguments are passed to TrajFromCoords.

Details

By default, for both random and directed walks, errors are normally distributed, unbiased, and independent of each other, so are simple directed walks in the terminology of Cheung, Zhang, Stricker, & Srinivasan, (2008). This behaviour may be modified by specifying alternative values for the angularErrorDist and/or linearErrorDist parameters.

The initial angle (for a random walk) or the intended direction (for a directed walk) is 0 radians. To change the initial angle or intended direction, call TrajRotate on the new trajectory. The starting position is (0, 0). To change the starting position, call TrajTranslate on the new trajectory.

References

Kareiva, P. M., & Shigesada, N. (1983). Analyzing insect movement as a correlated random walk. Oecologia, 56(2), 234-238. doi:10.1007/bf00379695

Cheung, A., Zhang, S., Stricker, C., & Srinivasan, M. V. (2007). Animal navigation: the difficulty of moving in a straight line. Biological Cybernetics, 97(1), 47-61. doi:10.1007/s00422-007-0158-0

Cheung, A., Zhang, S., Stricker, C., & Srinivasan, M. V. (2008). Animal navigation: general properties of directed walks. Biological Cybernetics, 99(3), 197-217. doi:10.1007/s00422-008-0251-z

Examples

# Generate a 1000 step correlated random walk
trj <- TrajGenerate()
plot(trj, main = "Correlated walk")

# Generate a 1000 step levy flight - paths lengths follow a cauchy distribution
trj <- TrajGenerate(linearErrorDist = rcauchy)
plot(trj, main = "Levy flight")

# Generate a short directed trajectory
trj <- TrajGenerate(n = 20, random = FALSE)
plot(trj, main = "Directed walk")

# Generate an uncorrelated random walk
trj <- TrajGenerate(500, angularErrorDist = function(n) runif(n, -pi, pi))
plot(trj, main = "Uncorrelated walk")

# Generate a walk directed northwards, starting from (200, 300),
# with a mean step length of 200. The initially generated trajectory
# is directed to angle 0, with starting point (0, 0)
trj <- TrajGenerate(n = 20, stepLength = 200, random = FALSE)
# Rotate 90 degrees about (0, 0) (i.e. from east to north)
trj <- TrajRotate(trj, pi / 2, relative = FALSE)
# Translate to desired starting point
trj <- TrajTranslate(trj, 200, 300)