Function to define the topology of a map grid

Description

sTopology is supposed to define the topology of a 2D map grid. The topological shape can be either a supra-hexagonal grid or a hexagonal/rectangle sheet. It returns an object of "sTopol" class, containing: the total number of hexagons/rectangles in the grid, the grid xy-dimensions, the grid lattice, the grid shape, and the 2D coordinates of all hexagons/rectangles in the grid. The 2D coordinates can be directly used to measure distances between any pair of lattice hexagons/rectangles.

Usage

sTopology(data = NULL, xdim = NULL, ydim = NULL, nHex = NULL, lattice = c("hexa", 
  "rect"), shape = c("suprahex", "sheet", "triangle", "diamond", "hourglass", "trefoil", 
      "ladder", "butterfly", "ring", "bridge"))

Arguments

data
a data frame or matrix of input data
xdim
an integer specifying x-dimension of the grid
ydim
an integer specifying y-dimension of the grid
nHex
the number of hexagons/rectangles in the grid
lattice
the grid lattice, either "hexa" for a hexagon or "rect" for a rectangle
shape
the grid shape, either "suprahex" for a supra-hexagonal grid or "sheet" for a hexagonal/rectangle sheet. Also supported are suprahex's variants (including "triangle" for the triangle-shaped variant, "diamond" for the diamond-shaped variant, "hourglass" for the hourglass-shaped variant, "trefoil" for the trefoil-shaped variant, "ladder" for the ladder-shaped variant, "butterfly" for the butterfly-shaped variant, "ring" for the ring-shaped variant, and "bridge" for the bridge-shaped variant)

Value

an object of class "sTopol", a list with following components:

  • nHex: the total number of hexagons/rectanges in the grid. It is not always the same as the input nHex (if any); see "Note" below for the explaination
  • xdim: x-dimension of the grid
  • ydim: y-dimension of the grid
  • r: the hypothetical radius of the grid
  • lattice: the grid lattice
  • shape: the grid shape
  • coord: a matrix of nHex x 2, with each row corresponding to the coordinates of a hexagon/rectangle in the 2D map grid
  • call: the call that produced this result

Note

The output of nHex depends on the input arguments and grid shape:

  • How the input parameters are used to determine nHex is taken priority in the following order: "xdim & ydim" > "nHex" > "data"
  • If both of xdim and ydim are given, nHex=xdim*ydim for the "sheet" shape, r=(min(xdim,ydim)+1)/2 for the "suprahex" shape
  • If only data is input, nHex=5*sqrt(dlen), where dlen is the number of rows of the input data
  • With nHex in hand, it depends on the grid shape:
    • For "sheet" shape, xy-dimensions of sheet grid is determined according to the square root of the two biggest eigenvalues of the input data
    • For "suprahex" shape, see sHexGrid for calculating the grid radius r. The xdim (and ydim) is related to r via xdim=2*r-1

Examples

# For "suprahex" shape sTopol <- sTopology(xdim=3, ydim=3, lattice="hexa", shape="suprahex") # Error: "The suprahex shape grid only allows for hexagonal lattice" # sTopol <- sTopology(xdim=3, ydim=3, lattice="rect", shape="suprahex") # For "sheet" shape with hexagonal lattice sTopol <- sTopology(xdim=3, ydim=3, lattice="hexa", shape="sheet") # For "sheet" shape with rectangle lattice sTopol <- sTopology(xdim=3, ydim=3, lattice="rect", shape="sheet") # By default, nHex=19 (i.e., r=3; xdim=ydim=5) for "suprahex" shape sTopol <- sTopology(shape="suprahex")
Warning message: Ignore the input parameters but use the default radius.
# By default, xdim=ydim=5 (i.e., nHex=25) for "sheet" shape sTopol <- sTopology(shape="sheet") # Determine the topolopy of a supra-hexagonal grid based on input data # 1) generate an iid normal random matrix of 100x10 data <- matrix(rnorm(100*10,mean=0,sd=1), nrow=100, ncol=10) # 2) from this input matrix, determine nHex=5*sqrt(nrow(data))=50, # but it returns nHex=61, via "sHexGrid(nHex=50)", to make sure a supra-hexagonal grid sTopol <- sTopology(data=data, lattice="hexa", shape="suprahex") # sTopol <- sTopology(data=data, lattice="hexa", shape="trefoil") # do visualisation visHexMapping(sTopol,mappingType="indexes") library(ggplot2)
# another way to do visualisation df_polygon <- sHexPolygon(sTopol) df_coord <- data.frame(sTopol$coord, index=1:nrow(sTopol$coord)) gp <- ggplot(data=df_polygon, aes(x,y,group=index)) + geom_polygon(aes(fill=factor(stepCentroid%%2))) + coord_fixed(ratio=1) + theme_void() + theme(legend.position="none") + geom_text(data=df_coord, aes(x,y,label=index), color="white")

Source code

sTopology.r

Source man

sTopology.Rd sTopology.pdf

See also

sHexGrid, visHexMapping