Figure 4.1 Geohashes and hierarchical indexing

figures

code

I made this figure by hand in Inkscape, which was kind of fun, if a little tedious, given all the repetition involved. Here I show what I could have done instead in R.

Code

library(dplyr)
library(tidyr)

The Z-order (Morton) and Hilbert curves

The first two are general indexing schemes with deep mathematical roots, so unsurprisingly there are R packages for working with them. The morton package is only available on github so you will need devtools to install it, while hilbert is on CRAN. Because I can, I’ve made these bigger than the laboriously hand-crafted examples in the book.

Code

library(morton)
library(hilbert)

# make a data frame to put the numbers in
df <- tibble(n = 1:1023) |>
  mutate(m1 = morton::fromMorton(n)[[1]],
         m2 = -morton::fromMorton(n)[[2]])

# the hilbert functions are hard to use with mutate, so 
# just use base R to make these
df$h1 <- hilbert::position(df$n, n = 10)[, 1] + 33 # an offset
df$h2 <- -hilbert::position(df$n, n = 10)[, 2]

That’s it—why didn’t I think of this earlier? And ggplot::geom_path() provides an easy way to plot the ‘curves’.

Code

library(ggplot2)

ggplot(df) + 
  geom_path(aes(x = m1, y = m2), linewidth = 0.25) + 
  geom_path(aes(x = h1, y = h2), linewidth = 0.25) + 
  coord_equal() + 
  theme_void()

H3 hexagons

If you like hexagons, you’ll love the h3forr package, which provides a spatial data friendly API for the H3 indexing scheme. There is an official H3 API for R but it focuses on the indexes and makes it harder work to fill spaces with hexagons, unlike the h3forr::polyfill() function.

Anyway, here goes:

Code

library(h3forr)
library(tmap)
library(sf)
library(maptiles)

Make a 20km square near Wellington, Aotearoa.

Code

square <- c(1.735e6 + 2e4 * c(0, 0, 1, 1, 0), 
            5.425e6 + 2e4 * c(0, 1, 1, 0, 0)) |>
  matrix(ncol = 2) |>
  list() |>
  st_polygon() |>
  st_sfc() |>
  st_sf(crs = 2193) |>
  st_transform(4326) # polyfill needs lat-lon

A convenience function to wrap hsforr::polyfill() so that we retrieve all hexes within a buffered area of the supplied data.

Code

get_hexes <- function(poly, resolution, distance) {
  poly |> 
    st_buffer(distance) |>
    polyfill(res = resolution) |> 
    h3_to_geo_boundary() |> 
    geo_boundary_to_sf()
}

Then get some hexagons.

Code

h3_4 <- get_hexes(square, 4, 10000)
h3_5 <- get_hexes(square, 5, 5000)
h3_6 <- get_hexes(square, 6, 2500)
h3_7 <- get_hexes(square, 7, 1500)
h3_8 <- get_hexes(square, 8, 1000)
h3_9 <- get_hexes(square, 9, 750)

And make a map. I’m using maptiles::get_tiles() to provide a base map.

Code

basemap <- get_tiles(square, zoom = 11, provider = "CartoDB.Positron")

tm_shape(basemap, bbox = square) + tm_rgb() +
  tm_shape(h3_4) + tm_borders(lwd = 5) +
  tm_shape(h3_5) + tm_borders(lwd = 3) +
  tm_shape(h3_6) + tm_borders(lwd = 2) +
  tm_shape(h3_7) + tm_borders(lwd = 1) +
  tm_shape(h3_8) + tm_borders(lwd = 0.5) +
  tm_shape(h3_9) + tm_borders(lwd = 0.35) +
  tm_credits(get_credit("CartoDB.Positron"), bg.color = "white",
             position = c("RIGHT", "BOTTOM"), bg.alpha = 0.5)

Code

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