The Fréchet (geodesic \(L^2\)) mean

An iterative algorithm for computing the Fréchet mean, i.e. the vector that minimizes the Fréchet variance.

Usage

geodesic_mean(x, ...)

# S3 method for class 'Vec3'
geodesic_mean(x, ...)

# S3 method for class 'Line'
geodesic_mean(x, ...)

# S3 method for class 'Ray'
geodesic_mean(x, ...)

# S3 method for class 'Plane'
geodesic_mean(x, ...)

# S3 method for class 'Pair'
geodesic_mean(x, ...)

Source

geologyGeometry (J.R. Davis): http://www.joshuadavis.us/software/

geologyGeometry (J.R. Davis): http://www.joshuadavis.us/software/

Arguments

x

object of class "Vec3", "Line", "Ray", "Plane", "Pair", or "Fault", where the rows are the observations and the columns are the coordinates.

...

parameters passed to geodesic_meanvariance_ray() (if x is a Ray), geodesic_meanvariance_line() (if x is a Vec3, Line or Plane) or geodesic_mean_pair() (if x is a Pair or a Fault).

Value

the Fréchet mean vector as an object of class x.

References

Davis, J. R., & Titus, S. J. (2017). Modern methods of analysis for three-dimensional orientational data. Journal of Structural Geology, 96, 65–89. doi:10.1016/j.jsg.2017.01.002

See also

geodesic_var() for Fréchet variance, sph_mean() for the arithmetic mean, projected_mean() for projected mean

Examples

set.seed(20250411)
geodesic_mean(example_planes)
#> Plane object (n = 1):
#> dip_direction           dip 
#>     345.92363      75.35166