r - Control alpha blending / opacity of n overlapping areas

Question

I struggle to understand (and control) the blending of alphas - unfortunately, alpha values don't simply "add up" (0.5 + 0.5 is not 1). But how could I achieve that?

The aim is to define the (absolute) grey value of overlapping areas relative to the total number of observations. See example below.

I tried to set scale_alpha(range = c(0,1)) to no avail, maybe I did not use it correctly.

library(ggplot2)
library(ggforce)

grid_df = data.frame(x = c(1:2, 2.5), y = rep(1,3), r = 1)

ggplot()+
geom_circle(data = grid_df, mapping = aes(x0 = x,  y0 = y, r = r), alpha = 0.33, fill = 'black') + 
  coord_fixed() 

Answer 1

First off, +1 to @JonSpring—this is just an expansion of the idea at the end of their answer. If you make an sf object, you can easily get the intersections of polygons. What you end up plotting isn't the circles themselves, but the polygons that come from splitting apart the intersecting pieces.

Starting from your grid, make a point for each row, convert that to a sf data frame, then take the buffer of the points at the radius given in the column r. This turns each point into a circle centered at the point's coordinates, and is flexible for different radii. Between the 3 circles are 6 intersecting polygons, as shown in the result.

library(dplyr)
library(sf)
library(ggplot2)
library(ggforce)

grid_df <- data.frame(x = c(1:2, 2.5), y = rep(1,3), r = 1)

grid_sf <- grid_df %>%
  mutate(geometry = purrr::map2(x, y, ~st_point(c(.x, .y)))) %>%
  st_as_sf() %>%
  st_buffer(dist = .$r, nQuadSegs = 60) %>%
  st_intersection()

grid_sf
#> Simple feature collection with 6 features and 5 fields
#> geometry type:  GEOMETRY
#> dimension:      XY
#> bbox:           xmin: 0 ymin: 0 xmax: 3.5 ymax: 2
#> epsg (SRID):    NA
#> proj4string:    NA
#>       x y r n.overlaps origins                       geometry
#> 1   1.0 1 1          1       1 POLYGON ((1.5 0.1339746, 1....
#> 1.1 1.0 1 1          2    1, 2 POLYGON ((1.75 0.3386862, 1...
#> 2   2.0 1 1          1       2 MULTIPOLYGON (((2.258819 0....
#> 1.2 1.0 1 1          3 1, 2, 3 POLYGON ((2 1, 1.999657 0.9...
#> 2.1 2.0 1 1          2    2, 3 POLYGON ((3 1, 2.999657 0.9...
#> 3   2.5 1 1          1       3 MULTIPOLYGON (((3.5 1, 3.49...

Use that n.overlaps column that comes from st_intersection to assign alpha. By default, alpha will scale from 0 to 1, but I figure you don't actually want a 0 alpha for the outer, non-overlapped parts of circles, so I scale it to get a minimum alpha.

alpha_range <- range(grid_sf$n.overlaps) / max(grid_sf$n.overlaps)

grid_sf  %>%
  ggplot() +
  geom_sf(aes(alpha = n.overlaps), fill = "black") +
  scale_alpha(range = alpha_range)

Just to expand a bit further and make the different polygons a bit more clear, take a look with a discrete fill scale instead of alpha:

grid_sf  %>%
  ggplot() +
  geom_sf(aes(fill = as.factor(n.overlaps))) +
  scale_fill_brewer(palette = "YlGnBu")