angleToPlane {celltrackR}

Angle with a Reference Plane

Description

Compute the angle between a track's overall displacement and a reference plane. Useful to detect directed movement and/or tracking artefacts.

Usage

angleToPlane(
  x,
  p1 = c(0, 0, 0),
  p2 = c(0, 1, 0),
  p3 = c(1, 0, 0),
  from = 1,
  degrees = TRUE
)

Arguments

x

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

p1, p2, p3

numeric vectors of coordinates of three points specifying a reference plane to compute distances 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 plane should be roughly 32.7 degrees. Lower angles to the border planes of an imaging volume can be indicative of tracking artefacts, and systematic deviations from 32.7 can indicate a directional bias (Beltman et al, 2009).

Value

A single angle.

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

distanceToPlane to compute the distance to the reference plane, and AngleAnalysis for other methods to compute angles and distances.

Examples

## Plotting the angle versus the distance to a reference plane can be informative to
## detect tracking artefacts near the border of the imaging volume.
## We should be suspicious especially when small angles are more frequent at low distances
## to the border planes.
load( system.file("extdata", "TCellsRaw.rda", package="celltrackR" ) )
steps <- subtracks( TCellsRaw, 1 )
minz <- boundingBox( TCellsRaw )["min","z"]
## Compute angles and distances to the lower plane in z-dimension
angles <- sapply( steps, angleToPlane, p1 = c(0,0,minz), p2 = c(1,0,minz), p3 = c(0,1,minz) )
distances <- sapply( steps, distanceToPlane, p1 = c(0,0,minz), p2 = c(1,0,minz), p3 = c(0,1,minz) )
scatter.smooth( distances, angles )
abline( h = 32.7, col = "red" )