halton.lattice.polygon: Halton lattice inside a `SpatialPolygon*` object.

Description

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.

Usage

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

Arguments

A SpatialPolygons or SpatialPolygonsDataFrame object.

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.

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.

Value

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)).

Details

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

Examples

Run this code

# NOT RUN {
# 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, 
# }