Summarise geometric elongation of clusters

Computes shape descriptors for each cluster in a ctdf, based on the convex hull of its locations and the minimum rotated rectangle enclosing that hull.

Usage

ctdf_elongation(ctdf)

Arguments

ctdf

A ctdf object.

Value

A data.table with one row per cluster.

Details

For each cluster, the function computes:

convex_hull_area

Area of the cluster convex hull.

log_axis_length

Log of the maximum edge length of the minimum rotated rectangle.

log_shape_ratio

Log ratio axis_length^2 / convex_hull_area.

elongation

Product of the standardised values of axis_length and log_shape_ratio. Clusters below average on either component receive a score of 0 so only above-average values on both components increase the score.

Larger values indicate clusters that are both relatively large in one principal dimension and relatively elongated for their area.

References

Chorley, R. J., Malm, D. E. G., & Pogorzelski, H. A. (1957). A new standard for estimating drainage basin shape. American Journal of Science, 255, 138–141.

See also

summary.ctdf(), cluster_track(), sf::st_minimum_rotated_rectangle()

Examples

data(mini_ruff)
x = as_ctdf(mini_ruff)
cluster_track(x)
#> → Find putative cluster regions.
#> ! Repairing[1]...
#> → Local clustering.
#> ! Repairing[2]...
#> ! Compute lof scores...
o = ctdf_elongation(x)
head(o)
#>    cluster axis_length convex_hull_area log_axis_length         log_shape_ratio
#>      <int>       <num>          <units>           <num>                 <units>
#> 1:       1    17706.40   54669211 [m^2]        9.781682 1.746552 [ln(re 1 m-2)]
#> 2:       2    20378.79   98142821 [m^2]        9.922250 1.442566 [ln(re 1 m-2)]
#> 3:       3    23526.12  155042745 [m^2]       10.065867 1.272522 [ln(re 1 m-2)]
#> 4:       4    23615.77  146762134 [m^2]       10.069670 1.335016 [ln(re 1 m-2)]
#>    elongation
#>         <num>
#> 1:          0
#> 2:          0
#> 3:          0
#> 4:          0