# Detect Patterns in Vector Fields Detect patterns in vector fields represented on a grid by looking in the rook's neighbourhood of each grid cell. Four patterns are detected: convergences occur when the vectors in the four adjacent cells in the rook's neighbourhood point towards the focal cell; divergences occur when the vectors in the four adjacent cells point away from the focal cell; Partial convergences occur when three of the four vectors point towards the focal cell and the final vector points neither towards nor away from the focal cell; Partial divergences occur when three of the four vectors point away the focal grid cell and the final vector points neither towards nor away from the focal grid. For all of the patterns above a sub-pattern is specified if all arrows point clockwise or counter-clockwise. ```r PatternDetect(vfdf) ``` ## Arguments - `vfdf`: A data frame as returned by `DispField`, `DispFieldST`, or `DispFieldSTall` with at least five rows (more is better) ## Returns A data frame as returned by `DispField`, `DispFieldST`, or `DispFieldSTall`, with three additional columns. The first additional column is called Pattern in which the patterns around each focal cell are categorized as convergence, divergence, partial convergence, partial divergence, or NA. The second additional column, called SubPattern, indicates whether all arrows point clockwise or counter-clockwise. The third additional column is called PatternCt, which contains a one if all four neighbourhood grid cells contain displacement estimates, and a NA otherwise. ## Examples ```r # creating convergence/divergence patterns Mat1 <- matrix(rep(0,9*9), nrow = 9) Mat1[3, c(4, 6)] <- 1 Mat1[7, c(4, 6)] <- 1 Mat1[c(4, 6), 3] <- 1 Mat1[c(4, 6), 7] <- 1 Mat1 Mat2 <- matrix(rep(0,9*9), nrow = 9) Mat2[2, c(4, 6)] <- 1 Mat2[8, c(4, 6)] <- 1 Mat2[c(4, 6), 2] <- 1 Mat2[c(4, 6), 8] <- 1 Mat2 # rasterizing rast1 <- terra::rast(Mat1) terra::plot(rast1) rast2 <- terra::rast(Mat2) terra::plot(rast2) # Detecting a divergence (VFdf1 <- DispField(rast1, rast2, factv1 = 3, facth1 = 3, restricted = TRUE)) (patdf1 <- PatternDetect(VFdf1)) # Detecting a convergence (VFdf2 <- DispField(rast2, rast1, factv1 = 3, facth1 = 3, restricted = TRUE)) (patdf2 <- PatternDetect(VFdf2)) ```

PatternDetect function