Create random points based in distance and boundary conditions - r

Question

In my example, I have:
# Packages
library(sf)
library(ggplot2)
# Create some points
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"
)
# Create a countour of the area
ch <- st_convex_hull(st_union(df.laea))
ggplot() +
geom_sf(data = ch, fill = "white", color = "black") +
geom_sf(data = df.laea,color = "black")
Now, I'd like to create 10 random points but the conditions are that this points must be inside the ch boundaries and a minimum distance of 10 meters of each df.laea points that exist inside this ch area.
Please, any help with it?

Answer 1

I think the only tricky thing here is that a simple st_difference() of your polygon and the buffered points will return ten polygons, each with one of the points removed. Thus you have to either use a for loop or reduce() to remove one buffered point after the other from the polygon. To use reduce() you have to transform the vector to a proper list of sf instead of an sfc vector. This is what I did below.
# Packages
library(sf)
library(ggplot2)
library(purrr)
ch_minus <- df.laea$geometry |>
st_buffer(10000) |>
{\(vec) map(seq_along(vec), \(x) vec[x])}() |> # Transform buffered points to reducible list
reduce(.init = ch, st_difference)
sampled_points <- st_sample(ch_minus, 10)
ch_minus |>
ggplot() +
geom_sf() +
geom_sf(data = sampled_points)

Answer 2

You can buffer the points by the distance you'd like, then intersect those polygons with the ch polygon. From there, use st_sample and the associated arguments to get the points you want.
Example code:
## buffer df.laea 10m
laea_buff <- st_buffer(df.laea, dist = 10000) #changed dist to 10km to make it noticable in plot
# area to sample from:
sample_area <- st_intersection(ch, laea_buff)
# sample above area, all within 10km of a point and inside the `ch` polygon
points <- st_sample(sample_area, size = 10)
#plotting:
ggplot() +
geom_sf(data = points, color = 'red') +
geom_sf(data = laea_buff, color = 'black', fill = NA) +
geom_sf(data = ch, color = 'black', fill = NA) +
geom_sf(data = sample_area, color = 'pink', fill = NA) +
geom_sf(data = df.laea, color = 'black', size = .5)
Created on 2023-02-14 by the reprex package (v2.0.1)

Answer 3

As a comment on the nice answer by shs: it is possible to first use a sf::st_combine() call on the df.laea object & merge the 10 points to a single multipoint geometry.
This, when buffered, will work as an input for the necessary sf::st_difference() call to form a sampling area with holes, removing the need for a for cycle / map & reduce call.
# Packages
library(sf)
library(ggplot2)
# Create some points
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"
)
# merge 10 points to 1 multipoing
mod_laea <- df.laea %>%
st_combine()
# sampling area = difference between hull and buffered points
sampling_area <- mod_laea %>%
st_convex_hull() %>%
st_difference(st_buffer(mod_laea, 10000))
# sample over sampling area
sampled_points <- st_sample(sampling_area, 10)
# a visual overview
ggplot() +
geom_sf(data = sampling_area, fill = "white", color = "black") +
geom_sf(data = df.laea, color = "black") +
geom_sf(data = sampled_points, color = "red", pch = 4)