Least-square fit of small and great circles to spherically projected data

Fits a great circle arc to a set of lines, based on an independent scalar variable.

Usage

regression_greatcircle(
  x,
  val = seq_len(nrow(x)),
  iterations = 1000L,
  n_points = 100L
)

regression_smallcircle(
  x,
  val = seq_len(nrow(x)),
  num_seeds = 5L,
  iterations = 1000L,
  n_points = 100L
)

Arguments

x: object of class "Vec3", "Line", "Ray", or "Plane", where the rows are the observations and the columns are the coordinates.
val: A vector of real numbers. Values of independent scalar variables. Same length as x.
iterations: A real number (positive integer). A bound on the number of numerical optimization iterations allowed.
n_points: A real number (positive integer). The number of points along the regression curve requested.
num_seeds: A real number (positive integer)

Value

list.

vec: axis of best-fit great- or small-circle. Class as x
cone: half-apical angle of the best-fit small-circle (in radians if x is of class "Vec3", degrees otherwise)
convergence: An integer code. 0 indicates successful completion.
min_eigenvalue: Positive if successful completion
r_squared: \(R^2\) value of the regression
points: A set of Vec3 points for the regression line
range: Range of the regression line (in radians if x is of class "Vec3", degrees otherwise)

References

Davis, J.R. and 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

Examples

set.seed(20250411)
data("gray_example")
bestgc_clea <- regression_greatcircle(gray_example[1:8, ])
bestgc_bedd <- regression_greatcircle(gray_example[9:16, ])
bestgc_all <- regression_greatcircle(gray_example)

bestsc_clea <- regression_smallcircle(gray_example[1:8, ])
bestsc_bedd <- regression_smallcircle(gray_example[9:16, ])
bestsc_all <- regression_smallcircle(gray_example)

stereoplot()
points(gray_example[1:8, ], col = "blue")
points(gray_example[9:16, ], col = "red", pch = "x")

# best for cleavage
lines(bestsc_clea$vec, bestsc_clea$cone, col = "lightblue")
points(bestsc_clea$vec, col = "lightblue", pch = 16)
lines(bestgc_clea$vec, lty = 2, col = "blue")
points(bestgc_clea$vec, col = "blue", pch = 17)

# best for bedding
lines(bestsc_bedd$vec, bestsc_bedd$cone, col = "sienna")
points(bestsc_bedd$vec, col = "sienna", pch = 16)
lines(bestgc_bedd$vec, lty = 2, col = "red")
points(bestgc_bedd$vec, col = "red", pch = 17)

# best for all
lines(bestsc_all$vec, bestsc_all$cone, col = "gray80")
points(bestsc_all$vec, col = "gray80", pch = 16)
lines(bestgc_all$vec, lty = 2, col = "gray50")
points(bestgc_all$vec, col = "gray50", pch = 17)