The Fréchet (geodesic \(L^2\)) mean of a set of lines or rays
Source:R/geodesic_mean.R
geodesic-line.RdAn iterative algorithm for computing the Fréchet mean — the line or ray that
minimizes the Fréchet 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)Arguments
- x
object of class
"Vec3","Line","Ray", or"Plane", where the rows are the observations and the columns are the coordinates.- ...
parameters passed to
geodesic_meanvariance_line()orgeodesic_meanvariance_ray()- seeds
positive integer. How many
xto 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
#> 69.64251 14.87961
#>
#> $error
#> [1] 0
#>
#> $min.eigenvalue
#> [1] 0
#>
geodesic_mean_line(example_lines)
#> Line object (n = 1):
#> azimuth plunge
#> 69.64075 14.87885
geodesic_var_line(example_lines)
#> [1] 0.06118261