Thin plate spline interpolation — grid

Fit a thin plate spline to the points with fields::Tps() and evaluate it at every cell.

Usage

grid_tps(
  x,
  value = NULL,
  grid = NULL,
  statistic = c("prediction", "se"),
  lon.lat = FALSE,
  ...
)

Arguments

x: coordinates, or coordinates carrying their value as z; see xyz_input()
value: one value per coordinate, or NULL to use the z of x
grid: a grid_spec() to interpolate onto, or NULL for a default one
statistic: "prediction" for the fitted surface, "se" for its standard error
lon.lat: the coordinates are longitude and latitude, so distances should be great circle ones; passed to fields::Tps()
...: passed to fields::Tps(), for instance lambda or m

Value

A guerrilla_grid with values.

Details

A thin plate spline is the surface that passes near the data while bending as little as possible, with a smoothing parameter deciding the trade between those two. It is the engine behind GDAL's -tps warping, so this is also what happens when you georeference an image from ground control points.

Unlike grid_barycentric() it fills the whole grid, including cells far outside the data, where the answer is extrapolation and should be read as such. statistic = "se" is how it tells you that: the standard error grows with distance from the data, so the two surfaces together say both what the method thinks and where it is guessing.

lon.lat is the one place in this package where what the coordinates mean changes the arithmetic. A spline bends in the plane of its coordinates, and a degree of longitude is not a degree of latitude anywhere but the equator. It is not guessed from the crs, because the guess would be wrong exactly when it mattered; say what you have.

Examples

xy <- cbind(runif(60), runif(60))
v <- sin(xy[, 1] * 6) + xy[, 2]
if (requireNamespace("fields", quietly = TRUE)) {
  plot(grid_tps(xy, v))
  ## and where it is guessing
  plot(grid_tps(xy, v, statistic = "se"))
}
#> Warning: 
#> Grid searches over lambda (nugget and sill variances) with  minima at the endpoints: 
#>   (GCV) Generalized Cross-Validation 
#>    minimum at  right endpoint  lambda  =  7.880521e-06 (eff. df= 56.99962 )

#> Warning: 
#> Grid searches over lambda (nugget and sill variances) with  minima at the endpoints: 
#>   (GCV) Generalized Cross-Validation 
#>    minimum at  right endpoint  lambda  =  7.880521e-06 (eff. df= 56.99962 )