[R] weighted Voronoi diagrams

[rex.dwyer at syngenta.com]

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

______________________________________________
R-help at r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.




message may contain confidential information. If you are not the designated recipient, please notify the sender immediately, and delete the original and any copies. Any use of the message by you is prohibited.