[R] Boundaries and deldir

[p_connolly]

On 2015-02-03 00:46, Rolf Turner wrote:

[...]


> The deldir function creates a Delaunay triangulation/Dirichlet
> tessellation inside a "rectangular window" (denoted by "rw" in the
> argument list).  This is the only boundary invoked or involved.
> 
> The function plot.tile.list() will *plot* the Dirichlet tessellation
> "clipped" to a specified polygon.  But that is just for *plotting*.  I
> am not sure that I really understand the idea of a "boundary beyond
> which the triangulation ceases".  The Delaunay triangulation is a
> finite
> structure; its outer boundary is the convex hull of the set of points
> being triangulated.  You cannot confine it to a smaller region without
> losing some of those points.
> 
> If you can explain what you really want to do, perhaps I can help.

This should make it clearer:


Suppose we had trees planted at the following coordinates

x   <- c(2.3,3.0,7.0,1.0,3.0,8.0)
y   <- c(2.3,3.0,2.0,5.0,8.0,9.0)

We can get a plot of the layout and polygons that "belong" to each tree.

del <- deldir(x,y,list(ndx=2,ndy=2),c(0,10,0,10), plotit = TRUE, wl = 
'tess')

The areas of the polygons so drawn can be seen in this dataframe.

del$summary

Apart from those immediately adjacent to the corner (dummy) points,
the areas represent the amount of space the roots could grow at a
uniform rate before encountering a neighbouring tree's roots or a
notional concrete path as described by the dummy triangular points,
shown by this red square:

polygon(y=c(0,0,10,10,0), x=c(0,10, 10, 0, 0), border = "red")

My question relates to the possibility of doing something similar if
the notional path was described by this green polygon:

polygon(y=c(0.5, 1, 1.5, 9.5, 10, 8.5, 0.5),
         x=c(0.5, 8, 9.5, 9, 7, .7, 0.5), border = "green")

Judging by references to 'rw', a rectangular window, I suspect not.


Thanks for the help.

Patrick



> 
> cheers,
> 
> Rolf