sss.polygon: Draws a Simple Systematic Sample (SSS) from an area resource...
In SDraw: Spatially Balanced Samples of Spatial Objects

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

Draws a systematic, or grid, sample from a SpatialPolygons or SpatialPolygonsDataFrame object. Optional parameters control control the relative spacing in horizontal and vertical directions, whether a square or triangular grid is produced, and whether the grid baseline has random orientation.

1	sss.polygon(x, n, spacing = c(1, 1), triangular = FALSE, rand.dir = FALSE)

`x`	A `SpatialPolygons` or `SpatialPolygonsDataFrame` object. This object must contain at least 1 polygon. If it contains more than 1 polygon, the SSS sample is drawn from the union of all polygons. Holes are respected.
`n`	Sample size. Number of locations to draw from the union of all polygons contained in `x`.
`spacing`	A vector of length 2 containing the RELATIVE spacing of grid points in the horizontal (X) and vertical (Y) directions. See details.
`triangular`	Boolean scalar specifying whether to produce a rectangular (`triangular==FALSE`) or triangular (`triangular==TRUE`) grid. See Details.
`rand.dir`	Either a boolean scalar specifying whether to randomly orient the grid's horizontal axis (`rand.dir==TRUE`) or not (`rand.dir==FALSE`), or a user-specified fixed direction for the horizontal axis. If FALSE, orientation of the grid is parallel to the X and Y axes. If TRUE, the X axis of the grid is randomly rotated by an angle between -pi/4 (-45 degrees) and pi/4 (45 degrees). If `rand.dir` is a number, the grid is rotated by that many radians. No range check is performed on user-specified `rand.dir`, so for example, rotation by `pi/8` is equivalent to rotation by `pi/8 + 2*pi`. User-specified, but random, direction of the grid can be specified by `rand.dir = runif(1,0,pi)`. Note, relative spacing of the grid cells is computed prior to rotation.

The projection system of the input shape object (x) is not considered. But, a projected coordinate system is necessary to obtain correct spacing on the ground. The author STRONGLY recommends converting x to a UTM coordinate system prior to calling this function.

Spacing (size and shape of grid cells) is determined by n and spacing. If spacing is not given, grid spacing is equal in X and Y directions, which produces square grid cells. In this case, grid spacing is delta (= sqrt(A/n), where A = area of union of all polygons in x.

Relative shape of grid cells is controlled by the spacing vector. If spacing = c(rx, ry), spacing in X and Y directions is spacing*delta/rev(spacing), where delta = sqrt(A/n). Conceptually, a square cell of size delta^2 is "stretched" multiplicatively by rx in the X direction and ry in the Y direction. After stretching, the area of each cell remains delta^2 while the relative lengths of the (rectangular) cell sides is 1 to (ry/rx)^2. That is, vertical dimension of each cell is (ry/rx)^2 times the horizontal dimension. Vice versa, the horizontal dimension is (rx/ry)^2 times the vertical.

In general, realized sample size is not fixed. Across multiple calls, realized sample size will not always equal n. Across an infinite number of calls, the average sample size will be n

In all cases, the grid is randomly shifted in the X and Y directions, before rotation (if called for). The amount of the random shift is less than the X and Y extent of cells, and is returned as an attribute of the sample.

A SpatialPointsDataFrame containing locations in the SSS sample, in row-wise order starting in the south (see sampleID, row, col in returned data frame). Attributes of the sample points (in the embedded data frame) are as follows:

sampleID: A unique identifier for every sample point. For rectangular grids, sampleID is incremented west to east by row from the south. For triangular grids, sampleID is assigned west to east to points in every other row from the south. Then, starts over in the southwest and assigns ID's to previously-skipped rows.
row: Row number of the sampled point in the grid. Row numbers are the vertical indices of the grid in a direction perpendicular to the (potentially rotated) main horizontal axis. Cell (1,1) is in the lower left (southwest) corner of the shape's bounding box. Thus, row 1 is defined along the lower (southern) boundary of the shape's bounding box. Points in row 1 may not be inside the shape and therefore may not appear in the sample. Consequently, the lowest row appearing in the sample may not be 1. Visualize row i with points(samp[samp$row==i,]).
col: Column number of the sampled point in the grid. Column numbers are the horizontal indices of the grid in a direction parallel to the (potentially rotated) main horizontal axis. Cell (1,1) is in the lower left (southwest) corner of the shape's bounding box. Thus, column 1 is defined along the left (western) boundary of the shape's bounding box. Points in column 1 may not be inside the shape and therefore may not appear in the sample. Consequently, the lowest column appearing in the sample may not be 1. Visualize column i with points(samp[samp$col==i,]).
geometryID: The ID of the polygon in x which each sample point falls. 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:

frame: Name of the input sampling frame.
frame.type: Type of resource in sampling frame. (i.e., "polygon").
sample.type: Type of sample drawn. (i.e., "SSS").
spacing.m: A vector of length 2 giving the dimensions of cells in units of the coordinates of x. (e.g., meters). This is the final delta computed above. Each cell has size prod(spacing.m) = Area / n.
rand.dir: The (potentially randomly chosen) direction for the grid's horizontal axis. This is in radians between -pi/4 and pi/4. rand.dir = 0 corresponds to no rotation (i.e., rand.dir = FALSE).
rand.shift: The random shift of the grid. This is a vector of length 2 containing the random shifts in the horizontal and vertical directions before rotation. The random shift in both directions is chosen between 0 and the corresponding element of the spacing.m attribute (described above).
triangular: TRUE or FALSE depending on whether the output grid is triangular or rectangular, respectively.

Trent McDonald

bas.polygon, sdraw

# A square grid oriented east-west
WA.samp <- sss.polygon( WA, 100 )   
plot( WA )
points( WA.samp )

# A rectangular grid oriented east-west, with relative spacing c(0.667, 1.5),
# or 1 to 2.25.
WA.samp <- sss.polygon( WA, 100, spacing=c(2,3) )   
plot( WA )
points( WA.samp )

# A rectangular grid oriented east-west, with x spacing = 2*(y spacing). 
WA.samp <- sss.polygon( WA, 100, spacing=c(sqrt(2),1) )   

# A rectangular grid, random orientation, with y spacing = 3*(x spacing)
WA.samp <- sss.polygon( WA, 100, spacing=c(1,sqrt(3)), rand.dir=TRUE )   

# A triangular grid oriented east-west
WA.samp <- sss.polygon( WA, 100, triangular=TRUE )   

# A triangular grid oriented east-west, with relative spacing c(.667,1.5)
WA.samp <- sss.polygon( WA, 100, spacing=c(2,3), triangular=TRUE )