Mean of related circumscribing circle (Shape metric)
lsm_l_circle_mn(landscape, directions = 8)tibble
Raster* Layer, Stack, Brick, SpatRaster (terra), stars, or a list of rasterLayers.
The number of directions in which patches should be connected: 4 (rook's case) or 8 (queen's case).
$$CIRCLE_{MN} = mean(CIRCLE[patch_{ij}])$$ where \(CIRCLE[patch_{ij}]\) is the related circumscribing circle of each patch.
CIRCLE_MN is a 'Shape metric' and summarises the landscape as the mean 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.
None
CIRCLE_MN > 0
Approaches CIRCLE_MN = 0 if the related circumscribing circle of all patches is small. Increases, without limit, as the related circumscribing circles increase.
McGarigal, K., SA Cushman, and E Ene. 2012. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical and Continuous Maps. Computer software program produced by the authors at the University of Massachusetts, Amherst. Available at the following web site: https://www.umass.edu/landeco/
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).
lsm_p_circle,
mean,
lsm_c_circle_mn,
lsm_c_circle_sd,
lsm_c_circle_cv,
lsm_l_circle_sd,
lsm_l_circle_cv