voronoi

I have data in the form (x, y, z) where x and y are not on a regular grid. I wish to display a 2D colormap of these data, with intensity (say, grey scale) mapped to the z variable. An obvious solution is to interpolate (see below) on a regular grid, d <- data.frame(x=runif(1e3, 0, 30), y=runif(1e3, 0, 30)) d$z = (d$x - 15)^2 + (d$y - 15)^2 library(akima) d2 <- with(d, interp(x, y, z, xo=seq(0, 30, length = 30), yo=seq(0, 30, length = 50), duplicate="mean")) pal1 <- grey(seq(0,1,leng=500)) with(d2, image(sort(x), sort(y), z, useRaster=TRUE, col = pal1)) points(d$x, d$y, col="white", bg=grey(d$z

I've successfully implemented a way to generate Voronoi diagrams in 2 dimensions using Fortune's method. But now I'm trying to use it for nearest neighbor queries for a point (which is not one of the original points used to generate the diagram). I keep seeing people saying that it can be done in O(lg n) time (and I believe them), but I can't find a description of how it's actually done. I'm familiar with binary searches, but I can't figure out a good criteria to guarantee that upper bound. I also figured maybe it could have to do with inserting the point into the diagram and updating

I am trying to create Voronoi polygons (aka Dirichlet tessellations or Thiessen polygons) within a fixed geographic region for a set of points. However, I am having trouble finding a method in R that will bound the polygons within the map borders. My main goal is to get accurate area calculations (not simply to produce a visual plot). For example, the following visually communicates what I'm trying to achieve: library(maps) library(deldir) data(countyMapEnv) counties <- map('county', c('maryland,carroll','maryland,frederick', 'maryland,montgomery', 'maryland,howard'), interior=FALSE) x <- c(

I have points (e.g., lat, lon pairs of cell tower locations) and I need to get the polygon of the Voronoi cells they form. from scipy.spatial import Voronoi tower = [[ 24.686 , 46.7081], [ 24.686 , 46.7081], [ 24.686 , 46.7081]] c = Voronoi(towers) Now, I need to get the polygon boundaries in lat,lon coordinates for each cell (and what was the centroid this polygon surrounds). I need this Voronoi to be bounded as well. Meaning that the boundaries don't go to infinity, but rather within a bounding box. Given a rectangular bounding box, my first idea was to define a kind of intersection

I'm working on a game where I create a random map of provinces (a la Risk or Diplomacy). To create that map, I'm first generating a series of semi-random points, then figuring the Delaunay triangulations of those points. With that done, I am now looking to create a Voronoi diagram of the points to serve as a starting point for the province borders. My data at this point (no pun intended) consists of the original series of points and a collection of the Delaunay triangles. I've seen a number of ways to do this on the web, but most of them are tied up with how the Delaunay was derived. I'd love

I'm looking for a simple (if exists) algorithm to find the Voronoi diagram for a set of points on the surface of a sphere. Source code would be great. I'm a Delphi man (yes, I know...), but I eat C-code too. Jason S Here's a paper on spherical Voronoi diagrams . Or if you grok Fortran (bleah!) there's this site . Update in July 2016: Thanks to a number of volunteers (especially Nikolai Nowaczyk and I), there is now far more robust / correct code for handling Voronoi diagrams on the surface of a sphere in Python. This is officially available as scipy.spatial.SphericalVoronoi from version 0.18