Draws a BAS sample from a SpatialLines* object.
bas.line(x, n, balance = "1D", init.n.factor = 10)A SpatialLines or SpatialLinesDataFrame object. This object must
contain at least 1 line. If it contains more than 1 line, the BAS sample is
drawn from the union of all lines.
Sample size. Number of locations to draw from the set of all lines
contained in x.
Option specifying how spatial balance is maintained. The options are "1D" or "2D".
Under "1D" all lines in x are stretched straight
and laid end-to-end in the order they appear in x and a 1-dimensional
BAS sample is taken from the amalgamated line. 1D sample locations on the
amalgamated line are
mapped back to two dimensional space for output and
appear on the original lines. This
method maintains 1D spatial balance, but not necessarily 2D balance. Spatially
balanced samples in 1D may not look spatially balanced when plotted
in 2 dimensions.
Under "2D" a systematic sample of points along the union of all lines
in x is drawn first, and a 2-dimensional BAS sample of the points
is drawn (see init.n.factor below and bas.point).
This maintains 2D spatial balance of sample locations on the lines. Depending
on init.n.factor, the "2D" balance option can take significantly
longer to run than the "1D" option.
If balance == "2D", this is a
scalar controlling the number of points to
place on the lines before drawing the 2D BAS sample.
Number of points created on the line is
n*init.n.factor, so this number can grow quickly. On average, this
is the number of un-selected points between each selected point. See
Details.
If one desires an underlying grid spaced w meters apart, set
init.n.factor to L/(w*n), where L is total length
of all lines in x and n is sample size.
A SpatialPointsDataFrame containing locations in the BAS sample,
in BAS order.
Attributes of the sample points are:
sampleID: A unique identifier for every sample point. This
encodes the BAS order. If BAS order is lost, return[ order(
return$sampleID ),] will resort the
returned object (i.e., return) into BAS order.
geometryID: The ID of the line in x on which each
sample point falls. The
ID of lines in x are row.names(x).
Any attributes of the original lines (in x).
Additional attributes of the output object, beyond those which
make it a SpatialPointsDataFrame, are:
frame: Name of the input sampling frame.
frame.type: Type of resource in sampling frame. (i.e., "line").
sample.type: Type of sample drawn. (i.e., "BAS").
balance: The type of balance ("1d" or "2d").
random.start: The random seed for the random-start
1D or 2D Halton sequence
that produced the sample.
If balance=="1D", this is a single uniform random
integer between 0 and maxU. If balance=="2D", this is
a vector of two uniform random
integers between 0 and maxU.
bas.bbox: If balance=="2D", this is the
bounding box surrounding x
used to scale Halton points. The scaled Halton sequence is
bas.bbox[,"min"]+ t(halton(n,2,random.start))*
rep(max( diff(t(bas.bbox))), 2).
If balance=="1D", this is a vector containing the 1D
bounding box. Lower limit of the 1D bounding box is 0. Upper
limit of the 1D box is the total
length of lines in x. In this case, Halton points
are scaled as bas.bbox[,"min"]+ halton(n,1,random.start)*
diff(bas.bbox) which is equivalent to halton(n,1, random.start)*
bas.bbox[2] because bas.bbox[1] is zero.
If a "1D" sample is requested, spatial balance is maintained on the lines when laid end-to-end in the order they appear. Points far apart in 1 dimension may be close together in 2 dimensions, and vice versa. Thus the sample may not look spatially balanced on a 2D map. This is a true infinite sample in that any of an infinite number of points along the lines could be selected.
If a "2D" BAS sample is requested, spatial balance is maintained
in 2 dimensions. Points are well balance on a 2D map. This is
done by discretization of lines with a dense systematic
sample of points (with
random start) where density of the systematic points is controlled
by init.n.factor. After
discretization of the line, points are selected
using bas.point. The BAS method for points places
a small square (pixel) around each and samples the set of squares
using the BAS method for polygons (see bas.polygon). The BAS
method of polygons computes Halton points until n fall
inside the squares surrounding discretization points. When a
Halton
point falls in a square, the square is selected and the
sample location is the center of the square (which falls somewhere on the
original lines).
# NOT RUN {
# Draw sample of Hawaii coastline
# This takes approximately 60 seconds to run
samp <- bas.line( HI.coast, 50 )
plot(HI.coast)
points( samp, pch=16, col="red" )
# }
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