nmi: Normalized moment of inertia (NMI)

In spopt: Spatial Optimization for Regionalization, Facility Location, and Market Analysis

Normalized moment of inertia (NMI)

Description

Computes the normalized moment of inertia (NMI), a compactness measure for polygon geometries. The NMI ranges between 0 and 1, where 1 is the most compact shape (a circle) and 0 is an infinitely extending shape (Feng et al. 2022).

Usage

nmi(x)

Arguments

x	An sf object, sfc geometry column, or sfg geometry

Details

The NMI is defined as follows, where A is the area of a geometry, and I is the second moment of inertia (i.e., the second areal moment):

\frac{A^2}{2 \pi I}

See Li et al. (2013, 2014) for additional details.

Value

Numeric vector of normalized moments of inertia.

References

Feng, X., Rey, S., and Wei, R. (2022). "The max-p-compact-regions problem." Transactions in GIS, 26, 717–734. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/tgis.12874")}.

Li, W., Goodchild, M.F., and Church, R.L. 2013. "An Efficient Measure of Compactness for Two-Dimensional Shapes and Its Application in Regionalization Problems." International Journal of Geographical Information Science 27 (6): 1227–50. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/13658816.2012.752093")}.

Li, W., Church, R.L. and Goodchild, M.F. 2014. "The p-Compact-regions Problem." Geogr Anal, 46: 250-273. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/gean.12038")}.

See Also

second_areal_moment()

spopt documentation built on April 22, 2026, 9:07 a.m.