Axial data • ggcircular

Directional versus axial

Directional observations have a head and tail. Axial observations represent an orientation where angles separated by pi are equivalent.

Examples

Fiber orientations, fault orientations and undirected line segments are common examples of axial data.

Doubling angles

The usual computational approach doubles angles, applies directional circular statistics, then halves the resulting mean direction.

library(ggplot2)
library(ggcircular)

circular_summary(axial_orientations, orientation, axial = TRUE)
#> # A tibble: 1 × 7
#>       n  mean     R  Rbar variance    sd kappa
#>   <int> <dbl> <dbl> <dbl>    <dbl> <dbl> <dbl>
#> 1   300 0.865  206. 0.688    0.312 0.864  1.94

Axial rose diagram

ggplot(axial_orientations, aes(x = orientation, fill = group)) +
  geom_rose(bins = 18, axial = TRUE, alpha = 0.7) +
  scale_x_circular_degrees(limits = c(0, pi)) +
  coord_circular() +
  theme_circular()

Axial mean

ggplot(axial_orientations, aes(x = orientation, fill = group)) +
  geom_rose(bins = 18, axial = TRUE, alpha = 0.5) +
  geom_mean_direction(axial = TRUE) +
  scale_x_circular_degrees(limits = c(0, pi)) +
  coord_circular() +
  theme_circular()

Axial density

ggplot(axial_orientations, aes(x = orientation, colour = group)) +
  geom_circular_density(axial = TRUE, linewidth = 1) +
  scale_x_circular_degrees(limits = c(0, pi)) +
  coord_circular() +
  theme_circular()

Communication

Reports should state clearly whether angles are directional or axial, because the interpretation of the same numeric angle can change.