Toroidal (R)

toroidal.R

toroidal <- function(points, values) {
  d <- ncol(points)

  shifts <- sapply(
    1:d,
    function(x) { max(points[, x]) - min(points[, x]) }
  )
  directions <- c(0, 1, -1)
  all_shifts <- expand.grid(
    lapply(
      as.list(shifts),
      function(shift) {
        shift * directions
      })
  )
  
  toroidal_points <- c()
  for (i in 1:nrow(all_shifts)) {
    shift <- unlist(all_shifts[i, ])
    toroidal_points <- rbind(toroidal_points, sweep(points, d, shift))
  }
  
  toroidal_values <- rep(values, nrow(all_shifts))
  
  list(points = toroidal_points, values = toroidal_values)
}

d <- 2

points <- c(
  c(0, 0),
  c(0, 2),
  c(2, 0),
  c(0.5, 0.5)
)
dim(points) = c(d, length(points) / d)
points <- t(points)

values <- c(
  1, 1, 1, 4  
)

tor <- toroidal(points, values)