I have this data:

> head(points)
x y z
1 3477751 5888124 -10.09
2 3477751 5888126 -10.26
3 3477751 5888128 -10.45
4 3477751 5888130 -10.64
5 3477753 5888124 -10.19
6 3477753 5888126 -10.34

I tried the delaunay triangulation as follows:

> ppp <- ppp(x, y, window=owin(c(min(x), max(x)), c(min(y), max(y))))
> tess <- delaunay(ppp)

> tess$tiles[[1]]$bdry[[1]]
$x
[1] 3477751 3477753 3477751

$y
[1] 5888124 5888124 5888126

Is there a way to map the z column (of points) to the x/y coords of the
triangulation/triangles?

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