Getting started with distanamo

Introduction

This package allows you to create distance cartograms (or distance anamorphoses, hence the name).

Distance cartograms are a type of cartogram that deforms the layers of a map according to the distances between a set of source points and a set of image points.

This is done by extending (by interpolation) to the layer(s) of the study area (territorial divisions, network…) the local displacement between the source coordinates and the image coordinates, derived from the distances between each pair of homologous points (source / image points).

The relation between the source points and the image points, and thus the relative position of the image points compared to the source points, must depend on the studied theme (such as positions in access time for which this package provides some helper functions to generate the image points from the durations between the points).

Usage

Basics

To use this package you need to provide two sets of homologous points : source points and image points. They are used to create an interpolation grid that will be used to deform the layer(s) of interest.

library(sf)

## Linking to GEOS 3.12.1, GDAL 3.8.4, PROJ 9.4.0; sf_use_s2() is TRUE

library(distanamo)
# Read source points, image points and the background layer to deform
source_pts <- st_read(
  dsn = system.file("gpkg/data-prefecture.gpkg", package = "distanamo"),
  layer = 'prefecture', quiet = TRUE
)
image_pts <- st_read(
  dsn = system.file("gpkg/data-prefecture.gpkg", package = "distanamo"),
  layer = 'image-points', quiet = TRUE
)
background_layer <- st_read(
  dsn = system.file("gpkg/data-prefecture.gpkg", package = "distanamo"),
  layer = 'departement', quiet = TRUE
)

# Create the interpolation grid
igrid <- dc_create(
  source_points = source_pts, 
  image_points = image_pts, 
  precision = 2, 
  bbox = st_bbox(background_layer)
)

# Use it to deform our layer of interest
deformed_background <- dc_interpolate(igrid, background_layer)

# Display the deformed layer
plot(st_geometry(deformed_background))

# Display useful information
summary(igrid)

## Summary of the interpolation grid:
## Number of cells: 441 
## Precision: 50462.76 (α = 2) 
## Deformation strength: 1.041534 
## Mean absolute error: 3734.717 
## RMSE (interp - image): 4989.972 
## RMSE x (interp - image): 4060.84 
## RMSE y (interp - image): 2899.896 
## RMSE (interp - source): 42725.87 
## RMSE x (interp - source): 32080.25 
## RMSE y (interp - source): 28219.8 
## R squared: 0.9997285

# Plot information about the interpolation grid
par(mfrow = c(2, 2))
plot(igrid, ask = FALSE)
par(mfrow = c(1, 1))

Adjusting the image points to the source points

In some cases, you may want to adjust the image points to the source points using an affine or a Euclidean transformation.

For example, here, if the image points represent locations in spatial cognition (and thus are not directly comparable to the source points, aren’t in the same coordinate system, etc.), you need to adjust them to the source points.

pos_result <- dc_adjust(
    source_points = source_pts,
    image_points = image_pts,
    adjustment_type = "euclidean"
)

# Create the interpolation grid
igrid <- dc_create(
  source_points = pos_result$source_points,
  image_points = pos_result$image_points,
  precision = 2.0, 
  bbox = st_bbox(background_layer)
)

This is also what is done internally when using the dc_generate_positions_from_durations function (see below) after it has performed a Principal Coordinates Analysis (PCoA) on the duration matrix.

Generating image points from a reference point and durations from the reference point to all the other points

Optionally you can provide a layer of source points and matrix of duration between the points.

This duration matrix will be used to extract the duration between a reference point and all the other points, allowing to use the dc_move_from_reference_point function to move closer / farther points from the reference point depending on if they can be reached faster or slower of the mean speed (between the reference point and all the others).

The cartogram obtained by this method qualifies the unipolar accessibility of a location (the reference point used in the dc_move_from_reference_point function). It’s also sometimes referred to as a centered time cartogram.

# Read source points and layer to be deformed
source_pts <- st_read(
  dsn = system.file("gpkg/data-prefecture.gpkg", package = "distanamo"),
  layer = 'prefecture', quiet = TRUE
)
background_layer <- st_read(
  dsn = system.file("gpkg/data-prefecture.gpkg", package = "distanamo"),
  layer = 'departement', quiet = TRUE
)
bbox <- sf::st_bbox(background_layer)

# Read durations between points
d <- read.csv(system.file("csv/mat.csv", package = "distanamo"), row.names = 1)
d[1:5, 1:5]

##                 RODEZ LE.PUY.EN.VELAY POITIERS VALENCE CRETEIL
## RODEZ             0.0           173.4    307.3   252.8   414.1
## LE PUY-EN-VELAY 173.1             0.0    337.6   112.3   358.8
## POITIERS        307.7           336.8      0.0   402.5   213.3
## VALENCE         252.6           114.1    402.6     0.0   353.4
## CRETEIL         414.7           359.0    214.5   354.4     0.0

dv <- d['GRENOBLE', ]
# So we have only the duration between GRENOBLE and all the other points
dv[1:5]

##          RODEZ LE.PUY.EN.VELAY POITIERS VALENCE CRETEIL
## GRENOBLE 311.7           172.2      413      64   352.3

source_pts$durations <- as.double(dv)

ref_point <- subset(source_pts, source_pts$NOM_COM == "GRENOBLE")
other_points <- subset(source_pts, !source_pts$NOM_COM == "GRENOBLE")

# Move points to create the image points layer
positioning_result <- dc_move_from_reference_point(
  reference_point = ref_point,
  other_points = other_points,
  duration_col_name = "durations",
  factor = 1
)

# Create the interpolation grid
igrid <- dc_create(
  positioning_result$source_points,
  positioning_result$image_points,
  2.0,
  bbox
)

# Deform the target layer
deformed_background <- dc_interpolate(igrid, background_layer)

# Display the deformed layer
plot(st_geometry(deformed_background))

A popular way of representing this type of cartogram is to add concentric circles (separated by a constant time) around the reference point. This can be done using the dc_concentric_circles function and the result of the dc_move_from_reference_point function (note that the steps parameter is the time, in the same unit as the durations, between each circle).

circles <- dc_concentric_circles(
  positioning_result,
  steps = list(60, 120, 180)
)
plot(st_geometry(deformed_background))
plot(st_geometry(circles), add = TRUE)

Generating image points from a durations matrix between all the points

Optionally you can provide a matrix of durations between all the points as well as the positions of the source points and use the dc_generate_positions_from_durations function to generate the image points.

This function will perform Principal Coordinates Analysis (PCoA, a form a Multidimensional scaling) on the duration matrix to generate the positions of the points in a 2D space. It will then adjust these points (using an affine or a Euclidean transformation) to the source points to generate the final image points that can be used to create the interpolation grid.

The cartogram obtained by this method qualifies the global accessibility (or the multipolar accessibility) of a territory.

# Read source points and layer to be deformed
source_pts <- st_read(
  dsn = system.file("gpkg/data-prefecture.gpkg", package = "distanamo"),
  layer = 'prefecture', quiet = TRUE
)
background_layer <- st_read(
  dsn = system.file("gpkg/data-prefecture.gpkg", package = "distanamo"),
  layer = 'departement', quiet = TRUE
)

# Read durations between points
d <- read.csv(system.file("csv/mat.csv", package = "distanamo"), row.names = 1)

pos_result <- dc_generate_positions_from_durations(d, source_pts)

# Display useful information about the result of the positioning
summary(pos_result)

## Summary of the multipolar displacement result:
## Min displacement: 2349.236 [m] 
## Mean displacement: 34569.15 [m] 
## Max displacement: 108405.5 [m] 
## Transformation matrix:
##      358.1063 1126.673 673162.7 
##      -1170.315 396.8617 6619705 
## Scale: 1208.994 
## RMSE: 39842.59 
## RMSE x: 25310.6 
## RMSE y: 30770.21

plot(pos_result)

# Create the interpolation grid
igrid <- dc_create(
  pos_result$source_points,
  pos_result$image_points,
  2.0,
  sf::st_bbox(background_layer)
)

summary(igrid)

## Summary of the interpolation grid:
## Number of cells: 441 
## Precision: 50462.76 (α = 2) 
## Deformation strength: 0.9896468 
## Mean absolute error: 5015.278 
## RMSE (interp - image): 5765.391 
## RMSE x (interp - image): 4292.306 
## RMSE y (interp - image): 3849.135 
## RMSE (interp - source): 38103.94 
## RMSE x (interp - source): 24114.01 
## RMSE y (interp - source): 29502.97 
## R squared: 0.999635

par(mfrow=c(2,2))
plot(igrid, ask = FALSE)
par(mfrow=c(1,1))

# Deform the target layer
deformed_background <- dc_interpolate(igrid, background_layer)

plot(st_geometry(deformed_background))

Deforming multiple layers at once

If you want to deform multiple layers in parallel with an interpolation grid, you can use the dc_interpolate_parallel function.

result_layers <- dc_interpolate_parallel(
  igrid,
  list(layer1, layer2, layer3)
)

More information about the method and references

This package is a port of the Darcy standalone software regarding the bidimensional regression and the backgrounds layers deformation.
All credit for the contribution of the method goes to Colette Cauvin (Théma - Univ. Franche-Comté) and for the reference Java implementation goes to Gilles Vuidel (Théma - Univ. Franche-Comté).

The method is also available as a QGIS plugin (GitHub repository / QGIS plugin repository).

This R package is a wrapper around the Rust library distance-cartogram-rs which can be used directly from Rust.

About the method

Cauvin, C. (2005). A systemic approach to transport accessibility. A methodology developed in Strasbourg: 1982-2002. Cybergeo: European Journal of Geography. DOI: 10.4000/cybergeo.3425.
Cauvin, C., & Vuidel, G. (2009). Darcy 2.0 - Mode d’emploi (https://thema.univ-fcomte.fr/productions/software/darcy/download/me_darcy.pdf).
Tobler, W. R. (1994). Bidimensional regression. Geographical Analysis, 26(3), 187-212. DOI: 10.1111/j.1538-4632.1994.tb00320.x
Bronner, A. C. (2023). Cartogrammes, anamorphoses : des territoires transformés. In Traitements et cartographie de l’information géographique, ISTE Group (pp.231-271). DOI: 10.51926/ISTE.9161.ch7.

About distance (or time) cartograms in general: their usability, the other methods to create them, etc.

Ullah, R., Mengistu, E., van Elzakker, C. & Kraak, M. (2016). Usability evaluation of centered time cartograms. Open Geosciences, 8(1), 337-359. DOI: 10.1515/geo-2016-0035.
Hong, S., Kim, Y. S., Yoon, J. C., & Aragon, C. (2014). Traffigram: distortion for clarification via isochronal cartography. In Proceedings of the SIGCHI Conference on Human Factors in Computing Systems (pp. 907–916). Association for Computing Machinery. DOI: 10.1145/2556288.2557224.
Ullah, R., Kraak, M. J., & Van Elzakker, C. (2013). Using cartograms to explore temporal data: do they work. GeoViz, 2013.
Ullah, R., & Kraak, M. J. (2014). An alternative method to constructing time cartograms for the visual representation of scheduled movement data. Journal of Maps, 11(4), 674–687. DOI: 10.1080/17445647.2014.935502.
Hong, S., Kocielnik, R., Min-Joon Yoo, Battersby, S., Juho Kim, & Aragon, C. (2017). Designing interactive distance cartograms to support urban travelers. In 2017 IEEE Pacific Visualization Symposium (PacificVis) (pp. 81-90).
Shimizu, E. and Inoue, R. (2009). A new algorithm for distance cartogram construction. International Journal of Geographical Information Science 23(11): 1453-1470. DOI: 10.1080/13658810802186882.