Function to define the topology of a map grid

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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

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sTopology(data = NULL, xdim = NULL, ydim = NULL, nHex = NULL,
lattice = c("hexa", "rect"), shape = c("suprahex", "sheet"))

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

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

  • 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

See Also

sHexGrid, visHexMapping

Examples

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# 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")

# 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")

# visualise a supre-hexagonal grid
visHexMapping(sTopol,mappingType="indexes")

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