sHexGrid is supposed to define a supra-hexagonal map grid. A
supra-hexagon is a giant hexagon, which seamlessly consists of smaller
hexagons. Due to the symmetric nature, it can be uniquely determined by
specifying the radius away from the grid centroid. This function takes
input the grid radius (or the number of hexagons in the grid, but will
be adjusted to meet the definition of supra-hexagon), and returns a
list (see 'Value' below) containing: the grid radius, the total number
of hexagons in the grid, the 2D coordinates of the grid centroid, the
step for each hexogan away from the grid centroid, and the 2D
coordinates of all hexagons in the grid.
sHexGrid(r = NULL, nHex = NULL)
an object of class "sHex", a list with following components:
r: the grid radius
nHex: the total number of hexagons in the grid. It may
differ from the input value; actually it is always no less than the
input one to ensure a supra-hexagonal grid exactly formed
centroid: the 2D coordinates of the grid centroid
stepCentroid: a vector with the length of nHex. It stores
how many steps a hexagon is awawy from the grid centroid ('1' for the
centroid itself). Starting with the centroid, it orders outward. Also,
for those hexagons of the same step, it orders from the rightmost in an
anti-clock wise
angleCentroid: a vector with the length of nHex. It stores
the angle a hexagon is in terms of the grid centroid ('0' for the
centroid itself). For those hexagons of the same step, it orders from
the rightmost in an anti-clock wise
coord: a matrix of nHex x 2 with each row specifying the
2D coordinates of a hexagon in the grid. The order of rows is the same
as 'centroid' above
call: the call that produced this result
The relationships among return values:
nHex = 1+6*r*(r-1)/2
centroid = coord[1,]
stepCentroid[1] = 1
stepCentroid[2:nHex] = unlist(sapply(2:r, function(x) (c(
(1+6*x*(x-1)/2-6*(x-1)+1) : (1+6*x*(x-1)/2) )>=1)*x ))
# The supra-hexagonal grid is exactly determined by specifying the radius. sHex <- sHexGrid(r=2) # The grid is determined according to the number of input hexagons (after being adjusted). # The return res$nHex is always no less than the input one. # It ensures a supra-hexagonal grid is exactly formed. sHex <- sHexGrid(nHex=12) # Ignore input nHex if r is also given sHex <- sHexGrid(r=3, nHex=100) # By default, r=3 if no parameters are specified sHex <- sHexGrid()Warning message: Ignore the input parameters but use the default radius.