What are simple features?

First and foremost, simple features comprise a file format for geospatial vector data, following the ISO 19125-1:2004 standard. The name in itself can be seen as a nickname, but the term also says it all: simple features are relatively easy to handle. Their implementation in R as developed in the sf package has enormous advantages compared to more traditional file formats for geospatial data in R²:

• They depict a flat-file structure: Any sf object is basically a rectangular table with features (i.e., observations or geometries) in the rows and attributes or variables in the columns.
• The only difference to other rectangular data is a so-called geometry column that defines each features’ geometry (point, lines, polygons, etc.). These may be supplemented with metadata, e.g., a definition the coordinate reference system of the geospatial data.
• A lot of techniques in the sf package which rely on the file format can be perfectly integrated in a tidyverse workflow using pipes (%>%) or dplyr verbs.

Please refer to this great resource on simple features in R if you are interested in more specifics of the data format.

Gathering geospatial data

To gather geospatial data, we use the osmdata package. This package facilitates the download of OpenStreetMap (OSM) data by providing a straightforward syntax for OSM data quires from the Overpass API. OSM is a community-driven open-access project for mapping geographical data. osmdata allows for the direct import of OSM data as sf objects. This makes it easy to collect and combine various layers of data and to use the data in conjunction with other R packages for the management, analysis, and visualization of geospatial data.

In the following, we illustrate the use of sf objects retrieved from osmdata queries by walking readers through the generation and visualization of a data set on streets, buildings, and population characteristics in Mannheim. Readers who would like to run these applications on their own machines should have the following packages installed:

## Save package names as a vector of strings
pkgs <- c("dplyr", "ggplot2", "ggnewscale", "ggsn", "osmdata", "sf", "z11") 

## Install uninstalled packages
if (!("z11" %in% installed.packages()))
  remotes::install_github("StefanJuenger/z11")
lapply(pkgs[!(pkgs %in% installed.packages())], install.packages)

## Load all packages to library and adjust options
lapply(pkgs, library, character.only = TRUE)

Mannheim’s boundaries from OpenStreetMap

We start by retrieving a boundary box that includes all of Mannheim’s area. We specify the requested boundaries using osmdata::getbb() and initialize the Overpass query using osmdata::opq(). The function osmdata::add_osm_feature() allows us to retrieve administrative boundaries (specified by key = "admin_level") within our boundary box at the municipal level, defined by the value argument. osmdata::osmdata_sf() ensures that the retrieved data is imported as an sf object.

In additional processing steps, we extract the polygon data of the administrative boundaries in our boundary box and filter those boundaries which belong to Mannheim (as opposed to neighboring cities and municipalities). We do this by defining a filter which selects only polygons associated with the city name. From our experience, it’s always a good idea to use the country’s language for the city name. Lastly, we select the polygon geometry information and convert the GIS coordinates to a specific coordinate reference system (CRS) using sf::st_transform(3035).

mannheim <-
  osmdata::getbb("Mannheim") %>% 
  osmdata::opq(timeout = 25*100) %>%
  osmdata::add_osm_feature(
    key = "admin_level", 
    value = "6"
  ) %>% 
  osmdata::osmdata_sf() %$% 
  osm_multipolygons %>% 
  dplyr::filter(name == "Mannheim") %>% # filter on city level
  dplyr::select(geometry) %>%
  sf::st_transform(3035) 

mannheim

## Simple feature collection with 1 feature and 0 fields
## geometry type:  MULTIPOLYGON
## dimension:      XY
## bbox:           xmin: 4206252 ymin: 2923007 xmax: 4218767 ymax: 2943155
## projected CRS:  ETRS89-extended / LAEA Europe
##                         geometry
## 1 MULTIPOLYGON (((4209130 293...

We can see that the resulting data is essentially a raw data table that comprises some metadata, such as the CRS. Thus, we can use standard data wrangling techniques in R. For instance, we can simply plot the boundary data using ggplot2’s geom_sf(). This gives us an otherwise empty shading of Mannheim’s boundaries:

ggplot(mannheim, fill = NA) +
  geom_sf() +
  ggsn::blank()

Adding data: Streets, buildings, and foreign-born residents

To fill this map with life, we gather additional data from OpenStreetMap. We start by retrieving additional geometries for streets and roads, which we store in the object roads. Our query is vastly similar to our initial one. Of course, the main difference is that we now request different features in osmdata::add_osm_feature(). As opposed to retaining polygonal data via osm_multipolygons, we now request lines depicting streets and roads via osm_lines. Lastly, we retain only those street and road data that intersect with the administrative boundaries of Mannheim and make sure that we keep linestring geometries only.

roads <-
  osmdata::getbb("Mannheim") %>% 
  osmdata::opq(timeout = 25*100) %>%
  osmdata::add_osm_feature(
    key = "highway", 
    value = c(
      "trunk", 
      "primary", 
      "secondary", 
      "tertiary"
      )
  ) %>% 
  osmdata::osmdata_sf() %$% 
  osm_lines %>% 
  dplyr::select(geometry) %>%
  sf::st_transform(3035) %>% 
  sf::st_intersection(mannheim) %>% 
  dplyr::filter(
    sf::st_is(., "LINESTRING")
    )

Next, we proceed similarly for data on a various types of buildings (specified per the value argument in osmdata::add_osm_feature()). As buildings have two-dimensional areal footprints (as opposed to roads, which can be represented by simple lines), we once again extract osm_polygons and retain only those buildings that intersect with the administrative boundaries of Mannheim.

buildings <-
  osmdata::getbb("Mannheim") %>% 
  osmdata::opq(timeout = 25*100) %>%
  osmdata::add_osm_feature(
    key = "building", 
    value = c(
      "apartments", "commercial", 
      "office", "cathredral", "church", 
      "retail", "industrial", "warehouse", 
      "hotel", "house", "civic", 
      "government", "public", "parking", 
      "garages", "carport", 
      "transportation", 
      "semidetached_house", "school", 
      "conservatory"
    )
  ) %>% 
  osmdata::osmdata_sf() %$% 
  osm_polygons %>%
  dplyr::select(geometry) %>%
  sf::st_transform(3035) %>% 
  sf::st_intersection(mannheim)

Lastly, we add data on the geospatial density of Mannheim’s foreign-born population. Toward this end, we use processed data from the 2011 German Census, aggregated at a geospatial raster of 1 sqkm grid cells. This data is available from Stefan’s z11 package. The variable itself is a standard measure for ethnic diversity, e.g., to investigate Allport’s hypothesis that contact between people of different groups reduces prejudices (Klinger et al. 2017). It also is helpful in inequality research when assessing whether foreign-born residents are, for example, more exposed to environmental hazards (Rüttenauer 2019).

We transform the raster data to sf-readable polygon data using the same CRS as before. This means that each 1 sqkm grid cell can now be plotted onto our existing map of Mannheim per the geometry information in foreign_born whereas the variable layer in foreign_born stores the percentage of foreign-born residents in each grid cell.

foreign_born <- 
  z11::z11_get_1km_attribute(Auslaender_A) %>% 
  raster::crop(mannheim) %>% 
  raster::rasterToPolygons() %>% 
  sf::st_as_sf() %>% 
  sf::st_transform(3035) %>% 
  sf::st_intersection(mannheim) %>% 
  dplyr::filter(layer > -1)

2D plots

Now that we have gathered all the data that we would like to include in our illustration, the question is how to best present the different types of geospatial information. A straightforward solution would be presenting separate plots, e.g., one for streets and buildings and one for the density of Mannheim’s foreign-born population. However, separating information across numerous plots makes it hard to relate information from different variables to one another. An alternative approach, shown below, involves flattening multiple data layers, i.e., collapsing many geospatial variables onto a single two-dimensional map.

This is easy enough to do in the current example, where coarse areal mappings (grid cells) are supplemented with much finer areal (buildings) and linear (streets) data. However, even the addition of one additional layer with coarse areal information – e.g., additional census information on the percentage of the senior population at the 1 sqkm grid cell level – would result in a visually indistinguishable overlay of information.

ggplot() +
  geom_sf(data = mannheim) +
  geom_sf(
    data = foreign_born,
    aes(fill = layer,
        alpha = 0.8), 
    color = NA
  ) +
  scale_fill_distiller(
    palette = "Greens", 
    direction = 1,
    guide = FALSE
  ) +
  geom_sf(data = roads) +
  geom_sf(data = buildings) +
  theme(legend.position = "none") +
  ggsn::blank() 

3D plots

An alternative to flattening multiple layers onto a two-dimensional map is using a three-dimensional vertical stacking of the layers. This allows us to show even large numbers of overlapping geometries in a single plot, which yields compact yet accessible visualizations of multiple pieces of geospatial information.

Mathematically, we can create such a map with shearing and rotating any point in our input data:

\[{[x,y]} \times \underbrace{\begin{bmatrix}2 & 0 \\ 1.2 & 1 \end{bmatrix}}_\text{Shear Matrix} \times \underbrace{\begin{bmatrix} \cos(\frac{\pi}{20}) & \sin(\frac{\pi}{20}) \\ -\sin(\frac{\pi}{20}) & \cos(\frac{\pi}{20})\end{bmatrix}}_\text{Rotation Matrix} \underbrace{(+ \begin{bmatrix}x\_add & y\_add \end{bmatrix})}_\text{Optional Additions}\]

We can also add an \(x\) or \(y\) offset value to move all points in two-dimensional space at the end of this operation.³

In order to use our sf data, stored in an inherently two-dimensional CRS, we need to devise an auxiliary function in R that allows us to shear and rotate these two-dimensional simple features such that they can be displayed in a three-dimensional space. It’s a basic and self-written implementation of the formula above.

#' Rotate simple features for 3D layers
#' Rotates a simple features layer using a shear matrix transformation on the 
#' \code{geometry} column. This can get nice for visualisation and works with
#' points, lines and polygons.
#'
#' @param data an object of class \code{sf}
#' @param x_add integer; x value to move geometry in space
#' @param y_add integer; x value to move geometry in space
#'
#' #' @importFrom magrittr %>%

rotate_sf <- function(data, x_add = 0, y_add = 0) {
  
  shear_matrix <- function (x) { 
    matrix(c(2, 1.2, 0, 1), 2, 2) 
  }
  
  rotate_matrix <- function(x) { 
    matrix(c(cos(x), sin(x), -sin(x), cos(x)), 2, 2) 
  }
  
  data %>% 
    dplyr::mutate(
      geometry = 
        .$geometry * shear_matrix() * rotate_matrix(pi / 20) + c(x_add, y_add)
    )
}

Now that the rotate_sf() function has been defined, we can use it to produce a figure that shows the information on streets and buildings in the base layer. On top of this base layer, we stack a semi-transparent raster that shows the density of the Mannheim foreign-born population.

ggplot() +
  geom_sf(data = rotate_sf(mannheim),
          fill = NA) +
  geom_sf(data = rotate_sf(roads)) +
  geom_sf(data = rotate_sf(buildings)) +
  geom_sf(data = rotate_sf(mannheim, y_add = 15000),
          fill = NA,
          color = "gray",
          alpha = 0.2) +
  geom_sf(
    data = rotate_sf(foreign_born, y_add = 15000),
    aes(fill = layer,
        alpha = .8),
    color = NA
  ) +
  scale_fill_distiller(palette = "Greens",
                       direction = 1,
                       guide = FALSE) +
  theme(legend.position = "none") +
  ggsn::blank()

Below, we show how this idea can be extended by introducing the share of the senior (aged 65+) population at the 1 sqm grid cell level as an additional layer. The 3D display allows us not only to present information on both the foreign-born population and the senior population at once, but also to relate the two variables to one another. In other words, with the stacked 3D display, we can visually inspect the association between two or more variables. This is a unique asset of this type of three-dimensional visualization as there is no straightforward equivalent in a two-dimensional map.

## Retrieve data
seniors <- 
  z11::z11_get_1km_attribute(ab65_A) %>% 
  raster::crop(mannheim) %>% 
  raster::rasterToPolygons() %>% 
  sf::st_as_sf() %>% 
  sf::st_transform(3035) %>% 
  sf::st_intersection(mannheim) %>% 
  dplyr::filter(layer > -1)

## Plot
ggplot() +
  geom_sf(data = rotate_sf(mannheim),
          fill = NA) +
  geom_sf(data = rotate_sf(roads)) +
  geom_sf(data = rotate_sf(buildings)) +
  geom_sf(
    data = rotate_sf(mannheim, y_add = 15000),
    fill = NA,
    color = "gray",
    alpha = 0.2
  ) +
  geom_sf(
    data = rotate_sf(foreign_born, y_add = 15000),
    aes(fill = layer,
        alpha = .8),
    color = NA
  ) +
  scale_fill_distiller(palette = "Greens",
                       direction = 1,
                       guide = FALSE) +
  new_scale_fill() +
  geom_sf(
    data = rotate_sf(mannheim, y_add = 30000),
    fill = NA,
    color = "gray",
    alpha = 0.2
  ) +
  geom_sf(data = rotate_sf(seniors, y_add = 30000),
          aes(fill = layer,
              alpha = .8),
          color = NA) +
  scale_fill_distiller(palette = "Reds",
                       direction = 1,
                       guide = FALSE) +
  theme(legend.position = "none") +
  ggsn::blank()