Question

I wish to create a 2D set of N points (typically 1e2 – 1e4) in a square with the following constraints:

• there should be a minimal distance between all points (hard core exclusion zone)

• the number of points filling the square is given in advance (or a close estimate), as I want to obtain a fixed density (I can adjust a little the size of the square afterwards if necessary).

• the pattern should be reasonably “random”

• a fast solution is preferred

I used rStrauss in the package spatstat before, but i could never figure out how to reliably obtain a given number of points, and quite often the function would stall my machine for 10 minutes, presumably because the task was too hard. I’m guessing there may be a more suitable function for this.

## regular grid of 1e2 points in [-10, 10]^2
xy = expand.grid(x=seq(-10, 10, length=10), y=seq(-10, 10, length=10))
N = NROW(xy)

EDIT: as suggested in the answer

xyr = rSSI(r=0.1, N, win = owin(c(-10,10),c(-10,10)), N)
plot(xyr)

Answer 1

rSSI, also in the spatstat package, takes care of your issues, except possibly the speed, depending on your standards. It has a hardcore inhibition distance, and will hit a target number of points (or give up trying–you can set the threshold for giving up), and the placements are random. I don’t think it’s particularly fast, but I was able to create 1e6 points in the unit square with an inhibition distance of 1e-4 in about 30 seconds. The speed and success rate will depend heavily on your inhibition distance relative to the number of points.