Nothing
Polyarea <- function(x) {
x <- rbind(x, x[1, ])
n <- nrow(x)
if (n < 4) return(0)
else abs(sum(x[-n, 1] * x[-1, 2] - x[-1, 1] * x[-n, 2]))/2
}
# ===
Polycenter <- function(x) {
x <- rbind(x, x[1, ])
n <- nrow(x)
if (n < 4) return(colMeans(x[-n, , drop=FALSE]))
xy <- x[-n, 1] * x[-1, 2] - x[-1, 1] * x[-n, 2]
A <- sum(xy)/2
xc <- sum((x[-n, 1] + x[-1, 1]) * xy)/A/6
yc <- sum((x[-n, 2] + x[-1, 2]) * xy)/A/6
structure(c(xc, yc), names=colnames(x))
}
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