#==================================================
# for the hexagonal lattice, find the x-y positions  
# for the grid
#==================================================
get.hex.grid <- function(grid.size) {
      # Create a rectangular grid of the required size
      # expand.grid creates an array of grid points
      # corresponding to specifies x and y values.
      # The first col. changes more rapidly than the second.
   hex.pos <- expand.grid(1:grid.size[2],1:grid.size[1])-c(1,1)
      # Swap the cols so the second changes faster.
   hex.pos <- hex.pos[,c(2,1)]
      # Shift every other row by 0.5 to create hexagon
   hex.pos[,1] <- hex.pos[,1]+rep(c(0,.5), (grid.size[2]+1)/2)[1:grid.size[2]]
      # make distances to all neighboring units equal
   hex.pos[,2] <- hex.pos[,2]*sqrt(0.75)   
   return(hex.pos)
}

#################

get.Uhex.grid <- function(grid.size) {
      # Create a grid of the required size (see get.hex.grid)
   hex.pos <- expand.grid(1:grid.size[2],1:grid.size[1])-c(1,1)
     # Swap the rows/cols
   hex.pos <- hex.pos[,c(2,1)]
     # Shift every other row by 0.5 to create hexagon
     # We need multiples of 4 for row shifts of (0,.5,1,.5)
   m.4 <- (grid.size[2]%/%4 + 1)
   hex.pos[,1] <- hex.pos[,1]+rep(c(0,.5,1,.5), m.4)[1:grid.size[2]]
   hex.pos[,2] <- hex.pos[,2]*sqrt(0.75)   # make distances to all neighboring units equal
   return(hex.pos)
}