Intersection of polygons in R using sf

I want to assess the degree of spatial proximity of each point to other equivalent points by looking at the number of others within 400m (5 minute walk).

I have some points on a map. I can draw a simple 400 m buffer around them. I want to determine which buffers overlap and then count the number of overlaps. This number of overlaps should relate back to the original point so I can see which point has the highest number of overlaps and therefore if I were to walk 400 m from that point I could determine how many other points I could get to.

I've asked this question in GIS overflow, but I'm not sure it's going to get answered for ArcGIS and I think I'd prefer to do the work in R.

This is what I'm aiming for https://www.newham.gov.uk/Documents/Environment%20and%20planning/EB01.%20Evidence%20Base%20-%20Cumulative%20Impact%20V2.pdf

To simplify here's some code

# load packages
library(easypackages)
needed<-c("sf","raster","dplyr","spData","rgdal",
          "tmap","leaflet","mapview","tmaptools","wesanderson","DataExplorer","readxl",
          "sp" ,"rgisws","viridis","ggthemes","scales","tidyverse","lubridate","phecharts","stringr")
easypackages::libraries(needed)

## read in csv data; first column is assumed to be Easting and second Northing
polls<-st_as_sf(read.csv(url("https://www.caerphilly.gov.uk/CaerphillyDocs/FOI/Datasets_polling_stations_csv.aspx")),
                coords = c("Easting","Northing"),crs = 27700)
polls_buffer_400<-st_buffer(plls,400)
polls_intersection<-st_intersection(x=polls_buffer_400,y=polls_buffer_400)
plot(polls_intersection$geometry)

That should show the overlapping buffers around the polling stations. What I'd like to do is count the number of overlaps which is done here:

polls_intersection_grouped<-polls_intersection%>%group_by(Ballot.Box.Polling.Station)%>%count()

And this is the bit I'm not sure about, to get to the output I want (which will show "Hotspots" of polling stations in this case) how do I colour things? How can I : asess the degree of spatial proximity of each point to other equivalent points by looking at the number of others within 400m (5 minute walk).

It's probably terribly bad form but here's my original GIS question https://gis.stackexchange.com/questions/328577/buffer-analysis-of-points-counting-intersects-of-resulting-polygons

Edit: this gives the intersections different colours which is great. plot(polls_intersection$geometry,col = sf.colors(categorical = TRUE, alpha = .5))

summary(lengths(st_intersects(polls_intersection)))

What am I colouring here? I mean it looks nice but I really don't know what I'm doing.

How can I : asess the degree of spatial proximity of each point to other equivalent points by looking at the number of others within 400m (5 minute walk).

Here is how to add a column to your initial sfc of pollings stations that tells you how many polling stations are within 400m of each feature in that sfc.

Note that the minimum value is 1 because a polling station is always within 400m of itself.

# n_neighbors shows how many polling stations are within 400m
polls %>% 
  mutate(n_neighbors = lengths(st_is_within_distance(polls, dist = 400)))

Similarly, for your sfc collection of intersecting polygons, you could add a column that counts the number of buffer polygons that contain each intersection polygon:

polls_intersection %>% 
  mutate(n_overlaps = lengths(st_within(geometry, polls_buffer_400)))

And this is the bit I'm not sure about, to get to the output I want (which will show "Hotspots" of polling stations in this case) how do I colour things?

If you want to plot these things I highly recommend using ggplot2. It makes it very clear how you associate an attribute like colour with a specific variable.

For example, here is an example mapping the alpha (transparency) of each polygon to a scaled version of the n_overlaps column:

library(ggplot2)
polls_intersection %>% 
  mutate(n_overlaps = lengths(st_covered_by(geometry, polls_buffer_400))) %>% 
  ggplot() + 
  geom_sf(aes(alpha = 0.2*n_overlaps), fill = "red") 

Lastly, there should be a better way to generate your intersecting polygons that already counts overlaps. This is built in to the st_intersection function for finding intersections of sfc objects with themselves.

However, your data in particular generates an error when you try to do this:

st_intersection(polls_buffer_400)

# > Error in CPL_nary_intersection(x) : 
#>  Evaluation error: TopologyException: side location conflict at 315321.69159061194 199694.6971799387.

I don't know what a "side location conflict" is. Maybe @edzer could help with that. However, most subsets of your data do not contain that conflict. For example:

# this version adds an n.overlaps column automatically:
st_intersection(polls_buffer_400[1:10,]) %>% 
  ggplot() + geom_sf(aes(alpha = 0.2*n.overlaps), fill = "red")