One way to do Dirichlet triangulations is to map point (x,y) to point
(x,y,x^2+y^2) (I think, it's been a while) and then find the convex hull of
these points in 3 dimensions. You can do the Voronoi diagram of circles by
mapping (x,y,r) to (x,y,x^2+y^2-r^2) I would try assigning an r to each point
so that the area of the circle (r^2) is proportional to the size of the
"subject tree". You will need to scale the r^2 values so that none of
the polygons disappear. See papers by Aurenhammer and/or Edelsbrunner from
around 1990. I've been out of the field for a long time, so there may be
more recent stuff. Hopefully, there is an R package for convex hull in three
dimensions. Possibly, there is someone in the CS department at UMn who does
"computational geometry" who could assist you. Maybe someone else
knows of an R package that will do exactly what you want.
HTH
Rex
-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
On Behalf Of Tuomas Aakala
Sent: Thursday, February 24, 2011 10:35 AM
To: r-help at r-project.org
Subject: [R] weighted Voronoi diagrams
Dear R-users,
Does anyone know how to do weighted Voronoi diagrams (Dirichlet
tesselation) in R? To be more specific, I have a set of coordinates for
tree locations on a plot, and I'm looking for a way to do the
tesselation so that the polygon size for each tree depends on the size
of the subject tree, and the size of its neighbors. So, the location of
the bisection between two trees would not necessarily be at the
midpoint, but determined by the tree sizes. I have looked through the
options in tripack and deldir-packages, but editing the functions in
those packages is beyond my skills.
Thanks,
Tuomas
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