HausdorffDistance {tigers}

Hausdorff Distance

Description

Computes the Hausdorff distance between two polygons. The distances can be directed (i.e., asymmetric) or not.

Usage

  HausdorffDistance(A, B, directed = FALSE)

Arguments

A, B

two two-column matrices giving the coordinates of two polygons.

directed

a logical value. By default, the undirected distance is returned.

Details

If directed = TRUE, the order of the two polygons is important.

Value

a single numeric value.

Author(s)

Emmanuel Paradis

Examples

A <- cbind(c(0, 1, 1, 0), c(0, 0, 1, 1))
B <- A
B[, 1] <- B[, 1] + 2
B[c(1, 4), 1] <- 1.15

plot(rbind(A, B), type = "n", asp = 1)
COLS <- c("blue", "red")
polygon(A, border = COLS[1], lwd = 3)
polygon(B, border = COLS[2], lwd = 3)
text(mean(A[, 1]), mean(A[, 2]), "A", font = 2, col = COLS[1])
text(mean(B[, 1]), mean(B[, 2]), "B", font = 2, col = COLS[2])

(H <- HausdorffDistance(A, B))
(HAB <- HausdorffDistance(A, B, TRUE))
(HBA <- HausdorffDistance(B, A, TRUE))
arrows(0, 0.75, 1.15, 0.75, length = 0.1, code = 3)
text(0.5, 0.85, paste("H(A->B)", "=", HAB))
arrows(1, 0.15, 3, 0.15, length = 0.1, code = 3)
text(2, 0.25, paste("H(B->A)", "=", HBA))
text(1.5, -0.5, paste("H = max(H(A->B), H(B->A))", "=", H))