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: [email protected] [mailto:[email protected]] On Behalf Of Tuomas Aakala Sent: Thursday, February 24, 2011 10:35 AM To: [email protected] 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 ______________________________________________ [email protected] 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. ______________________________________________ [email protected] 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.
