This package contains a C++ implementation of the RecMap algorithm [1], [2] to draw maps according to given statistical values. These so-called cartograms or value-by-area-maps may be used to visualize any geospatial-related data, e.g., political, economic or public health data. The input consists of a map represented by overlapping rectangles. This map is defined by the following parameters for each map region:
The (x, y) coordinates represent the center of the minimal bounding boxes (MBB), The coordinates of the MBB are derived by adding or subtracting the (dx, dy) tuple accordingly. The tuple (dx, dy) also defines the ratio of the map region. The statistical values define the desired area of each map region.
The output is a rectangular cartogram where the map regions are:
The construction heuristic places the rectangles in a way that important spatial constraints, in particular
are tried to be preserved.
The ratios are preserved, and the area of each region corresponds to the as input given statistical value z.
The graphic below depicts a typical example of a rectangular cartogram drawing.
attach the package
look into for documentation
state
Facts and Figures
DatasetThe rectangles have to overlap to compute the dual graph. This enables to generate valid input having only the (x, y) coordinates of the map region.
The index order of the input map has an impact to the resulting cartogram. This algorithmic property is caused due to the computation of the dual graph. In [1] a genetic algorithm was applied as metaheuristic. Due to the limited computing resources on the CRAN check systems, we do not use all the potential of the metaheuristic.
Study the examples of the reference manual ?recmapGA
on
how the GA package
can be used.
The topology error is an indicator of the deviation of the neighborhood relationships. The error is computed by counting the differences between dual graphs or adjacency graphs of map and cartogram
The relative positions error measures the angle difference between all region centers.
The output is a data.frame
object.
## x y dx dy z name dfs.num
## 1 -86.12445 24.40204 3.201992 2.697824 227.17614 Alabama 31
## 2 -123.13242 29.61981 3.939586 3.257613 337.50407 Arizona 38
## 3 -85.30009 39.65352 3.265364 2.683509 230.44305 Arkansas 33
## 4 -131.42392 31.53933 4.341915 3.488740 398.36290 California 37
## 5 -122.00152 23.21422 3.965671 3.095895 322.87304 Colorado 47
## 6 -53.13517 41.31657 1.896954 1.418697 70.77429 Connecticut 19
## topology.error relpos.error relposnh.error
## 1 4 0.2265446 0.5912115
## 2 4 0.2041032 0.7446224
## 3 6 0.4400093 0.8416664
## 4 3 0.1353180 0.1454522
## 5 8 0.5045327 0.9388417
## 6 3 0.1937878 0.4808290
smp <- c(29, 22, 30, 3, 17, 8, 9, 41, 18, 15, 38, 35, 21, 23, 19, 6, 31, 32, 20,
28, 48, 4, 13, 14, 42, 37, 5, 16, 36 , 43, 25, 33, 12, 7, 39, 44, 2, 47,
45, 46, 24, 10, 1,11 ,40 ,26 ,27 ,34)
op <- par(mfrow = c(1 ,1), mar = c(0, 0, 0, 0), bg = NA)
plot(Cartogram.Area <- recmap(M[smp, ]),
col.text = 'black', lwd = 2)
## values
## number of map regions 48.00000
## area error 0.13000
## topology error NA
## relative position error NA
## screen filling [in %] 113.77072
## xmin -124.93741
## xmax -66.26565
## ymin 25.35365
## ymax 50.81868
## values
## number of map regions 48.00000
## area error 0.00000
## topology error 156.00000
## relative position error 0.09000
## screen filling [in %] 39.74965
## xmin -131.88541
## xmax -26.73219
## ymin 17.21867
## ymax 57.88620
state.x77[, 'Population']
op <- par(mfrow = c(1 ,1), mar = c(0, 0, 0, 0), bg = NA)
usa$z <- state.x77[, 'Population']
M <- usa[!usa$name %in% c("Hawaii", "Alaska"), ]
plot(Cartogram.Population <- recmap(M[order(M$x), ]),
col.text = 'black', lwd = 2)
# index order
smp <- c(20,47,4,40,9,6,32,33,3,10,34,22,2,28,15,12,39,7,42,45,19,13,43,30,24,
25,11,17,37,41,26,29,21,35,8,36,14,16,31,48,46,38,23,18,1,5,44,27)
op <- par(mfrow = c(1 ,1), mar = c(0, 0, 0, 0), bg = NA)
plot(Cartogram.Population <- recmap(M[smp,]), col.text = 'black', lwd = 2)
state.x77[, 'Income']
usa$z <- state.x77[, 'Income']
M <- usa[!usa$name %in% c("Hawaii", "Alaska"), ]
op <- par(mfrow = c(1 ,1), mar = c(0, 0, 0, 0), bg = NA)
plot(Cartogram.Income <- recmap(M[order(M$x),]),
col.text = 'black', lwd = 2)
state.x77[, 'Frost']
usa$z <- state.x77[, 'Frost']
M <- usa[!usa$name %in% c("Hawaii", "Alaska"), ]
op <- par(mfrow = c(1 ,1), mar = c(0, 0, 0, 0), bg = NA)
gaControl("useRcpp" = FALSE)
Frost <- recmapGA(M, seed = 1)
plot(Frost$Cartogram,
col.text = 'black', lwd = 2)
## Length Class Mode
## GA 1 ga S4
## Map 6 data.frame list
## Cartogram 10 recmap list
## Summary 13 data.frame list
More interactive examples using state.x77
data are
available by running the code snippet below.
Checkerboards provide examples of sets of map regions which do not have ideal cartogram solutions according to Definition 1 [3].
op <- par(mar = c(0, 0, 0, 0), mfrow = c(1, 3), bg = NA)
plot(checkerboard8x8 <- checkerboard(8),
col=c('white','white','white','black')[checkerboard8x8$z])
# found by a greedy randomized search
index.greedy <- c(8, 56, 18, 5, 13, 57, 3, 37, 62, 58, 7, 16, 40, 59, 17, 34,
29, 41, 46, 27, 54, 43, 2, 21, 38, 52, 31, 20, 28, 48, 1, 22,
55, 11, 25, 19, 50, 10, 24, 53, 47, 30, 45, 44, 32, 35, 51,
15, 64, 12, 14, 39, 26, 6, 42, 33, 4, 36, 63, 49, 60, 61, 9,
23)
plot(Cartogram.checkerboard8x8.greedy <- recmap(checkerboard8x8[index.greedy,]),
col = c('white','white','white','black')[Cartogram.checkerboard8x8.greedy$z])
# found by a genetic algorithm
index.ga <- c(52, 10, 27, 63, 7, 20, 32, 18, 47, 28, 6, 55, 11, 61, 38, 50, 5,
21, 36, 34, 2, 22, 3, 1, 29, 57, 43, 4, 51, 58, 31, 49, 44, 25,
59, 33, 17, 40, 8, 41, 26, 37, 19, 56, 45, 35, 62, 53, 24, 64,
30, 15, 39, 12, 60, 48, 16, 23, 46, 42, 13, 54, 14, 9)
plot(Cartogram.checkerboard8x8.ga <- recmap(checkerboard8x8[index.ga,]),
col = c('white','white','white','black')[Cartogram.checkerboard8x8.ga$z])
The work on RecMap was initiated by understanding the limits of
contiguous cartogram drawing [3] and after
studying the visualizations drawn by Erwin Raisz [4]. The purpose of the first implementation
[1] was a feasibility check on how
computer-generated rectangular cartograms with zero area error could
look like. The recmap
R package on CRAN provides a
rectangular cartogram algorithm to be used by any R user. Now, it is
easy to generate input (e.g., no complex polygon mesh), the code is
maintainable (less than 500 lines of C++-11
code), and the
algorithm is made robust to the price of not having all features
implemented (simplified local placement; no empty space error;
no MP1 variant). Recent research publications on rectangular cartogram
drawing include [5], [6], [7], [8]. However, according to a recent publication
[9], recmap
remains the only
rectangular cartogram algorithm that ‘maintains zero cartographic
error’. The interested reader can find more details on the package usage
and its implementation in [2].
## R version 4.4.1 (2024-06-14)
## Platform: x86_64-pc-linux-gnu
## Running under: Ubuntu 24.04.1 LTS
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## Matrix products: default
## BLAS: /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3
## LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.26.so; LAPACK version 3.12.0
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## time zone: Etc/UTC
## tzcode source: system (glibc)
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods
## [7] base
##
## other attached packages:
## [1] recmap_1.0.17 sp_2.1-4 Rcpp_1.0.13
## [4] GA_3.2.4 iterators_1.0.14 foreach_1.5.2
## [7] tufte_0.13
##
## loaded via a namespace (and not attached):
## [1] crayon_1.5.3 cli_3.6.3 knitr_1.48
## [4] rlang_1.1.4 xfun_0.47 highr_0.11
## [7] jsonlite_1.8.8 buildtools_1.0.0 htmltools_0.5.8.1
## [10] maketools_1.3.0 sys_3.4.2 sass_0.4.9
## [13] rmarkdown_2.28 grid_4.4.1 evaluate_0.24.0
## [16] jquerylib_0.1.4 fastmap_1.2.0 yaml_2.3.10
## [19] lifecycle_1.0.4 compiler_4.4.1 codetools_0.2-20
## [22] lattice_0.22-6 digest_0.6.37 R6_2.5.1
## [25] bslib_0.8.0 tools_4.4.1 cachem_1.1.0