celltrackR (version 1.2.1)

angleToDir: Angle with a Reference Direction

Description

Compute the angle between a track's overall displacement and a reference direction. Useful to detect biased movement when the directional bias is known (see examples).

Usage

angleToDir(x, dvec = c(1, 1, 1), from = 1, degrees = TRUE)

Value

A single angle.

Arguments

x

a single input track; a matrix whose first column is time and whose remaining columns are a spatial coordinate.

dvec

numeric vector specifying a reference direction to compute angles to.

from

index, or vector of indices, of the first row of the track. If from is a vector, angles are returned for all steps starting at the indices in from.

degrees

logical; should angles be returned in degrees rather than radians? (default = TRUE).

Details

The average angle of steps to a reference direction should be 90 degrees if there is no bias towards movement in the direction of the reference point. If there is such a bias, there should be an enrichment of smaller angles. The expected distribution without bias is a uniform distribution in 2D or a sine distribution in 3D (Beltman et al, 2009).

References

Joost B. Beltman, Athanasius F.M. Maree and Rob. J. de Boer (2009), Analysing immune cell migration. Nature Reviews Immunology 9, 789--798. doi:10.1038/nri2638

See Also

AngleAnalysis for other methods to compute angles and distances.

Examples

## Get a distribution of Neutrophil step angles with the reference direction in positive
## y direction. The histogram is enriched for low angles, suggesting directed movement:
steps <- subtracks( Neutrophils, 1 )
hist( sapply( steps, angleToDir, dvec=c(1,-1) ) )