[R-sig-Geo] DEM interpolation with Delaunay triangulation

[Edzer Pebesma]

On 11/20/2011 11:02 PM, Rolf Turner wrote:
> On 21/11/11 04:30, gianni lavaredo wrote:
>> Dear Researchers,
>>
>> I am looking a package o method to interpolate a point data.frame (x,y,z)
>> with Delaunay triangulation  (Trianguled interpoaltion network) and
>> create
>> a polygons data,frame o a raster. I know there are several fuction in
>> library RSAGA, spatstat (with "deldir"), library geometry.
> 
> I have no idea what you're on about.  If you could make your question
> clearer and more specific I might be able to make some suggestions
> as to how you could use spatstat/deldir.
> 
> An explicit simple (toy) example might help.

I have wondered this myself too -- the issue is the so-called TIN,
triangular interpolation network. Say, we have (field) observations
(x,y,z), we form a delanay triangulation on all (x,y) pairs, and we want
to obtain the prediction of z for an arbitrary (x0,y0) pair, based on
the linear trend surface fit through the three (x1,y1), (x2,y2), (x3,y3)
points that form the triangle in which (x0,y0) falls.

You could do, of course, a linear trend surface using three nearest
neighbours, e.g. by

require(gstat)
loadMeuse()
x = krige(log(zinc)~x+y, meuse, meuse.grid, nmax=3)
spplot(x[1],col.regions=bpy.colors(),
	sp.layout=list("sp.points", meuse))


but that takes the three nearest observations, which don't need to be
the three points in the triangle (and often, they are not, because
meuse.grid contains points outside the convex hull of the meuse
observation locations).

> 
>     cheers,
> 
>         Rolf Turner
> 
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-- 
Edzer Pebesma
Institute for Geoinformatics (ifgi), University of Münster
Weseler Straße 253, 48151 Münster, Germany. Phone: +49 251
8333081, Fax: +49 251 8339763  http://ifgi.uni-muenster.de
http://www.52north.org/geostatistics      e.pebesma at wwu.de