halton.lattice.polygon: Halton lattice inside a 'SpatialPolygon*' object.
In SDraw: Spatially Balanced Samples of Spatial Objects

Description Usage Arguments Details Value Author(s) See Also Examples

Constructs a lattice of Halton boxes (a Halton lattice) inside a SpatialPolygons or SpatialPolygons DataFrame object. This is a wrapper for halton.lattice, which does all the hard work.

halton.lattice.polygon(
  x,
  N = 10000,
  J = NULL,
  eta = c(1, 1),
  triangular = FALSE,
  bases = c(2, 3)
)

`x`	A `SpatialPolygons` or `SpatialPolygonsDataFrame` object.
`N`	Approximate number of points to place in the lattice. If `J` is specified, it takes precedence. If `J` is NULL, the algorithm attempts to place `N` points in the bounding box using Halton boxes that are as close to square as possible. This `N` is not exact, but is a target.
`J`	A 2X1 vector of base powers which determines the size and shape of the Halton boxes. See additional description in help for `hip.polygon` function.
`eta`	A 2X1 vector of the number of points to add inside each Halton box. e.g., if `eta` = `c(3,2)`, a small grid of 3 by 2 points is added inside each Halton box. `eta[1]` is for the horizontal dimension, `eta[2]` is for the vertical dimension.
`triangular`	boolean, if TRUE, construct a triangular grid. If FALSE, construct rectangular grid. See help for `hip.polygon`.
`bases`	A 2X1 vector of Halton bases. These must be co-prime.

This routine is called internally by hip.polygon, and is not normally called by the user.

A SpatialPointsDataFrame containing locations in the Halton lattice

Attributes of the points are:

latticeID: A unique identifier for every point. ID's are integers numbering points in row-major order from the south.
geometryID: The ID of the polygon in x containing each point. The ID of polygons in x are row.names(geometry(x)).
Any attributes of the original polygons (in x).

Additional attributes of the output object, beyond those which make it a SpatialPointsDataFrame, are:

J: the J vector used to construct the lattice. This is either the input J or the computed J when only N is specified.
eta: the eta vector used in the lattice.
bases: the bases of the van der Corput sequences used in the lattice, one per dimension.
triangular: Whether the lattice is triangular or square.
hl.bbox: the bounding box surrounding the input x object. This is saved because bounding box of the return object is not the same as the bounding box of x (i.e., bbox(return) != bbox(x)).

Trent McDonald

hip.polygon, halton.lattice

# Take and plot Halton lattice to illustrate
WA.hgrid <- halton.lattice.polygon( WA, J=c(3,2), eta=c(3,2), triangular=TRUE )
plot(WA)
points(WA.hgrid, pch=16, cex=.5, col="red" )

# Plot the Halton boxes
tmp.J <- attr(WA.hgrid,"J")
tmp.b <- attr(WA.hgrid,"bases")
tmp.bb <- attr(WA.hgrid,"hl.bbox")

for(d in 1:2){
  tmp2 <- tmp.bb[d,1] + (0:(tmp.b[d]^tmp.J[d]))*(diff(tmp.bb[d,]))/(tmp.b[d]^tmp.J[d])
  if( d == 1){
      abline(v=tmp2, col="blue")
  } else{
      abline(h=tmp2, col="blue")
  }
}

# To explore, re-run the above changing J, eta, and triangular,