The Frechet (geodesic \(L^2\)) mean of a set of lines or rays

An iterative algorithm for computing the Frechet mean — the line or ray that minimizes the Frechet variance. The iterations continue until error squared of epsilon is achieved or steps iterations have been used. Try multiple seeds, to improve your chances of finding the global optimum.

Usage

geodesic_mean_line(x, ...)

geodesic_mean_ray(x, ...)

geodesic_var_line(x, ...)

geodesic_var_ray(x, ...)

geodesic_meanvariance_line(x, seeds = 5L, steps = 100L)

geodesic_meanvariance_ray(x, seeds = 5L, steps = 100L)

Source

lineMeanVariance from geologyGeometry (J.R. Davis)

Arguments

x

object of class "Vec3", "Line", "Ray" or "Plane"

...

parameters passed to geodesic_meanvariance_line() or geodesic_meanvariance_ray()

seeds

positive integer. How many x to try as seeds

steps

positive integer. Bound on how many iterations to use.

Value

geodesic_meanvariance_* (* either line or ray) returns a list consisting of $variance (numeric), $mean (a line), $error (an integer) and $min.eigenvalue (numeric). geodesic_mean_* and geodesic_var_* are convenience wrapper and only return the mean and the variance, respectively.

Details

Error should be 0 and min.eigenvalue should be positive. Otherwise there was some problem in the optimization. If error is non-zero, then try increasing steps.

References

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

See also

sph_mean() for arithmetic mean and geodesic_mean_pair() for geodesic mean of pairs.

Examples

geodesic_meanvariance_line(example_lines)
#> $variance
#> [1] 0.06118261
#> 
#> $mean
#> Line object (n = 1):
#>  azimuth   plunge 
#> 69.64016 14.87899 
#> 
#> $error
#> [1] 0
#> 
#> $min.eigenvalue
#> [1] 0
#> 
geodesic_mean_line(example_lines)
#> Line object (n = 1):
#>  azimuth   plunge 
#> 69.63944 14.87954 
geodesic_var_line(example_lines)
#> [1] 0.06118261