sf: Generate random points with maximal distance condition - r

Question

I'd like to generate 100 random points but imposed a maximal distance around points using st_buffer() of size 1000 meters around each point, and eliminating any offending points. But, in my example:
library(sf)
# Data set creation
set.seed(1)
df <- data.frame(
gr = c(rep("a",5),rep("b",5)),
x = rnorm(10),
y = rnorm(10)
)
df <- st_as_sf(df,coords = c("x","y"),remove = F, crs = 4326)
df.laea = st_transform(df,
crs = "+proj=laea +x_0=4600000 +y_0=4600000 +lon_0=0.13 +lat_0=0.24 +datum=WGS84 +units=m")
st_bbox(df.laea)
#
# Random simulation of 100 point inside df.laea extent
sim_study_area <- st_sample(st_as_sfc(st_bbox(df.laea)), 100) %>% # random points, as a list ...
st_sf()
border_area <- st_as_sfc(st_bbox(df.laea))%>% # random points, as a list ...
st_sf()
# I'd like to imposed a maximal distance of 1000 meters around points and for this:
i <- 1 # iterator start
buffer_size <- 1000 # minimal distance to be enforced (in meters)
repeat( {
# create buffer around i-th point
buffer <- st_buffer(sim_study_area[i,], buffer_size)
offending <- sim_study_area %>% # start with the intersection of master points...
st_intersects(buffer, sparse = F) # ... and the buffer, as a vector
# i-th point is not really offending
offending[i] <- TRUE
# if there are any offending points left - re-assign the master points
sim_study_area <- sim_study_area[offending,]
if ( i >= nrow(sim_study_area)) {
# the end was reached; no more points to process
break
} else {
# rinse & repeat
i <- i + 1
}
} )
# Visualizantion of points create with the offending condition:
simulation_area <- ggplot() +
geom_sf(data = border_area, col = 'gray40', fill = NA, lwd = 1) +
geom_sf(data = sim_study_area, pch = 3, col = 'red', alpha = 0.67) +
theme_bw()
plot(simulation_area)
It's not OK result because a don't have 100 points and I don't know how I can fix it.
Please any ideas?
Thanks in advance,
Alexandre

Answer 1

I think that the easiest solution is to adopt one of the sampling functions defined in the R package spatstat. For example:
# packages
library(sf)
#> Linking to GEOS 3.9.0, GDAL 3.2.1, PROJ 7.2.1
# create data
set.seed(1)
df <- data.frame(
gr = c(rep("a",5),rep("b",5)),
x = rnorm(10),
y = rnorm(10)
)
df <- st_as_sf(df,coords = c("x","y"),remove = F, crs = 4326)
df.laea = st_transform(
df,
crs = "+proj=laea +x_0=4600000 +y_0=4600000 +lon_0=0.13 +lat_0=0.24 +datum=WGS84 +units=m"
)
Now we sample with a Simple Sequential Inhibition Process. Check ?spatstat.core::rSSI for more details.
sampled_points <- st_sample(
x = st_as_sfc(st_bbox(df.laea)),
type = "SSI",
r = 1000, # threshold distance (in metres)
n = 100 # number of points
)
# Check result
par(mar = rep(0, 4))
plot(st_as_sfc(st_bbox(df.laea)), reset = FALSE)
plot(sampled_points, add = TRUE, pch = 16)
# Estimate all distances
all_distances <- st_distance(sampled_points)
all_distances[1:5, 1:5]
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.00 57735.67 183205.74 189381.50 81079.79
#> [2,] 57735.67 0.00 153892.93 143755.73 61475.85
#> [3,] 183205.74 153892.93 0.00 62696.68 213379.39
#> [4,] 189381.50 143755.73 62696.68 0.00 194237.12
#> [5,] 81079.79 61475.85 213379.39 194237.12 0.00
# Check they are all greater than 1000
sum(all_distances < 1000)
#> [1] 100 # since the diagonal is full of 100 zeros
Created on 2021-08-12 by the reprex package (v2.0.0)
Check here (in particular the answer from Prof. Baddeley), the references therein, and the help page of st_sample for more details.