Polygon compactness

Polsby-Popper 4 pi A / P^2, Schwartzberg 2 sqrt(pi A) / P, Reock A over the area of the minimum enclosing circle, and A over the convex-hull area; all equal 1 for a disc.

Usage

PolygonCompactness(vertices)

Arguments

vertices

Two-column matrix of polygon vertices (either orientation).

Value

list(area, perimeter, polsby_popper, schwartzberg, reock, convex_hull, enclosing_circle).

References

Polsby, D. D. and Popper, R. D. (1991). The third criterion: compactness as a procedural safeguard against partisan gerrymandering. Yale Law and Policy Review 9, 301-353. Reock, E. C. (1961). A note: measuring compactness as a requirement of legislative apportionment. Midwest Journal of Political Science 5, 70-74. Schwartzberg, J. E. (1966). Reapportionment, gerrymanders, and the notion of compactness. Minnesota Law Review 50, 443-452.

Examples

PolygonCompactness(rbind(c(0, 0), c(1, 0), c(1, 1), c(0, 1)))$polsby_popper
#> [1] 0.7853982