Fit a plane within each Delaunay triangle

Triangulate the points, fit value ~ x + y by least squares to the three corners of each triangle, and evaluate that fit at the cells inside it.

Usage

grid_facet_lm(x, value = NULL, grid = NULL, duplicates = mean, ...)

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

duplicates

function used to combine values at repeated coordinates, or NULL to leave them alone

...

ignored

Value

A guerrilla_grid with values.

Details

This is the long way round to grid_barycentric(), and the two agree to floating point. Three points determine a plane, least squares through three points is that plane, and barycentric interpolation evaluates that same plane – so the expensive per-triangle lm() and the one vectorised tsearch() call compute the same surface. Worth seeing once.

It replaces the Delaunay half of facets(), which did this through spatstat and returned a point pattern rather than a grid.

The Voronoi half of facets() is not here, because it was not doing what it looked like it was doing. A Voronoi tile contains exactly one point by construction, so lm(value ~ x + y) on it fits an intercept and nothing else, and predicts that one point's value across the whole tile. That is nearest neighbour, computed the slowest way available. grid_voronoi() is the same answer under its right name.

See also

grid_barycentric() for the fast form of this, grid_voronoi() for what the Voronoi case really was.

Examples

xy <- cbind(runif(40), runif(40))
v <- xy[, 1] + xy[, 2]
plot(grid_facet_lm(xy, v))