Calculate polygon area from a matrix of a closed polygon. Closed means that the first coordinate is the same as the last.
polygon_area(x, signed = FALSE)polygon in xy matrix
defaults to FALSE and absolute value of area is returned
numeric vector of area
Only one polygon can be input. We are using the normal definition of polygon which is a plane figure described by straight line segments.
Currently inputs are not checked but are assumed to have the last coordinate as a copy of the first aka 'closed'.
If signed = FALSE the absolute value of area is returned, otherwise the
sign reflects path orientation. Positive means counter-clockwise orientation.
The algorithm used was once on the internet at "w w w .cs.tufts.edu/comp/163/OrientationTests.pdf"
x <- c(2, 10, 8, 11, 7, 2)
y <- c(7, 1, 6, 7, 10, 7)
polygon_area(cbind(x, y), signed = TRUE)
#> [1] 32
xy <-
cbind(x = c(2.3, 1.5, 2.4, 4.5, 4.6, 5.4, 7.6, 8.6, 7.4, 5.1, 2.3),
y = c(-1.4, 7.3, 22.2, 22.5, 14.4, 11.8, 16.4, 5, 0.8, -1.6, -1.4))
polygon_area(xy)
#> [1] 113.535
## xy is clockwise so area is negative
polygon_area(xy, signed = TRUE)
#> [1] -113.535
polygon_area(xy[nrow(xy):1, ], signed = TRUE)
#> [1] 113.535
## Rosetta code example
## https://rosettacode.org/wiki/Shoelace_formula_for_polygonal_area
m <- rbind(c(3,4), c(5,11), c(12,8), c(9,5), c(5,6))
p <- m[c(1:nrow(m), 1), ] ## close it
polygon_area(p)
#> [1] 30