Standard deviation of related circumscribing circle (Shape metric)

## Arguments

- landscape
A categorical raster object: SpatRaster; Raster* Layer, Stack, Brick; stars or a list of SpatRasters.

- directions
The number of directions in which patches should be connected: 4 (rook's case) or 8 (queen's case).

## Details

$$CIRCLE_{SD} = sd(CIRCLE[patch_{ij}])$$ where \(CIRCLE[patch_{ij}]\) is the related circumscribing circle of each patch.

CIRCLE_SD is a 'Shape metric' and summarises the landscape as the standard deviation of the related circumscribing circle of all patches in the landscape. CIRCLE describes the ratio between the patch area and the smallest circumscribing circle of the patch and characterises the compactness of the patch. The metric describes the differences among all patches of the landscape.

Because the metric is based on distances or areas please make sure your data
is valid using `check_landscape`

.

## References

McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org

Baker, W. L., and Y. Cai. 1992. The r.le programs for multiscale analysis of landscape structure using the GRASS geographical information system. Landscape Ecology 7: 291-302.

Based on C++ code from Project Nayuki (https://www.nayuki.io/page/smallest-enclosing-circle).