Parsing SVG paths in R

I'm trying to crack an R workflow for parsing SVG paths, using this file on this webpage. I'm encountering artifacts in the positioning of resulting polygons:

Some of the countries do not align with their neighbours - e.g. US/Canada, US/Mexico, Russia/Asian neighbours. Since the effect hits the countries with more complex polygons it seems likely to be a problem to do with cumulative summing, but I'm unclear where the problem lies in my workflow, which is:

nodejs

I reproduce the full workflow here using R (for US/Canada), with an external call to nodejs:

require(dplyr)
require(purrr)
require(stringr)
require(tidyr)
require(ggplot2)
require(rvest)
require(xml2)
require(jsonlite)

# Get and parse the SVG
doc = read_xml('https://visionscarto.net/public/fonds-de-cartes-en/visionscarto-bertin1953.svg')

countries = doc %>% html_nodes('.country')
names(countries) = html_attr(countries, 'id')
cdi = str_which(names(countries), 'CIV') # unicode in Cote d'Ivoire breaks the code
countries = countries[-cdi]

# Extract SVG paths and parse with node's svg-path-parser module.
# If you don't have node you can use this instead (note this step might be the problem):
# d = read_csv('https://gist.githubusercontent.com/geotheory/b7353a7a8a480209b31418c806cb1c9e/raw/6d3ba2a62f6e8667eef15e29a5893d9d795e8bb1/bertin_svg.csv')

d = imap_dfr(countries, ~
message(.y)
svg_path = xml_find_all(.x, paste0("//*[@id='", .y, "']/d1:path")) %>% html_attr('d')
node_call = paste0("node -e "var parseSVG = require('svg-path-parser'); var d='", svg_path,
"'; console.log(JSON.stringify(parseSVG(d)));"")
system(node_call, intern = T) %>% fromJSON %>% mutate(country = .y)
) %>% as_data_frame()


# some initial processing
d1 = d %>% filter(country %in% c('USA United States','CAN Canada')) %>%
mutate(x = replace_na(x, 0), y = replace_na(y, 0), # NAs need replacing
relative = replace_na(relative, FALSE),
grp = (command == 'closepath') %>% cumsum) # polygon grouping variable

# new object to loop through
d2 = d1 %>% mutate(x_adj = x, y_adj = y) %>% filter(command != 'closepath')

# loop through and change relative coords to absolute
for(i in 2:nrow(d2))
if(d2$relative[i]) # cumulative sum where coords are relative
d2$x_adj[i] = d2$x_adj[i-1] + d2$x_adj[i]
d2$y_adj[i] = d2$y_adj[i-1] + d2$y_adj[i]
else # code M/L require no alteration
if(d2$code[i] == 'V') d2$x_adj[i] = d2$x_adj[i-1] # absolute vertical transform inherits previous x
if(d2$code[i] == 'H') d2$y_adj[i] = d2$y_adj[i-1] # absolute holrizontal transform etc



# plot result
d2 %>% ggplot(aes(x_adj, -y_adj, group = paste(country, grp))) +
geom_polygon(fill='white', col='black', size=.3) +
coord_equal() + guides(fill=F)


Any assistance appreciated. The SVG path syntax is specified at w3 and summarised more concisely here.

Edit (response to @ccprog)

Here is data returned from svg-path-parser for the H command sequence:

svg-path-parser

H

code command x y relative country
<chr> <chr> <dbl> <dbl> <lgl> <chr>
1 l lineto -0.91 -0.6 TRUE CAN Canada
2 l lineto -0.92 -0.59 TRUE CAN Canada
3 H horizontal lineto 189. NA NA CAN Canada
4 l lineto -1.03 0.02 TRUE CAN Canada
5 l lineto -0.74 -0.07 TRUE CAN Canada


Here is what d2 looks like for same sequence after the loop:

d2

code command x y relative country grp x_adj y_adj
<chr> <chr> <dbl> <dbl> <lgl> <chr> <int> <dbl> <dbl>
1 l lineto -0.91 -0.6 TRUE CAN Canada 20 199. 143.
2 l lineto -0.92 -0.59 TRUE CAN Canada 20 198. 143.
3 H horizontal lineto 189. 0 FALSE CAN Canada 20 189. 143.
4 l lineto -1.03 0.02 TRUE CAN Canada 20 188. 143.
5 l lineto -0.74 -0.07 TRUE CAN Canada 20 187. 143.


Does this not look ok?. When I look at raw values for y_adj for H and previous rows they are identical 142.56.

H

142.56

d = imap_dfr(countries, ~
message(.y)
svg_path = xml_find_all(.x, paste0("//*[@id='", .y, "']/d1:path")) %>% html_attr('d')
node_call = paste0("node -e "var parseSVG = require('svg-path-parser'); var d='", svg_path,
"'; console.log(JSON.stringify(parseSVG.makeAbsolute(parseSVG(d))));"")
system(node_call, intern = T) %>% fromJSON %>% mutate(country = .y)
) %>% as_data_frame() %>%
mutate(grp = (command == 'moveto') %>% cumsum)

d %>% ggplot(aes(x, -y, group = grp, fill=country)) +
geom_polygon(col='black', size=.3, alpha=.5) +
coord_equal() + guides(fill=F)


closepath

moveto

moveto

closepath

moveto

closepath

grp

relative

H

V

1 Answer
1

Look at your rendering of Canada, especially the southern coast of the Hudson sound. There is a very obvious error. Sieveing through the path data, I found the following sequence in the original data:

h-2.28l-.91-.6-.92-.59H188.65l-1.03.02-.74-.07-.75-.07-.74-.07-.74-.06.88 1.09


I've loaded your rendering result into Inkscape, and drawn the relevant part of the path on top, the arrow marking the segment drawn by the absolute H command. (The z command has been removed, that is the reason for the missing segment.) It is obvious that somewhere in there a segment is too long.

It turns out the absolute H corrects the previous (horizontal) error. Look at the preceding point: it is 198., 143., but it should be 191.76,146.07. The vertical error remains at about -3.6.

H

198., 143.

191.76,146.07

I've made a codepen that overlays the original path data with your rendering as precisely as possible. The path data have been divided into the (single-polygon) groups and converted to absolute by Inkscape. Unfortunately, the program cannot convert them to polygon primitives, so there are still V and H commands in there.

It shows this:

group0

I've made some visual measurements of that deviation (error ~0.05), and they ultimately give the clue:

group01: 0.44,-0.73
group02: 0.84,-1.12
group03: 2.04,-1.44
group04: 2.94,-1.73
group05: 2.60,-1.86
group06: 3.14,-2.38
group07: 3.68,-2.54
group08: 4.03,-3.35
group09: 4.87,-2.97
group10: 6.08,-3.50 (begin)
group10: 0.00,-3.53 (end)
group11: 1.08,-1.95
group12: 2.05,-2.45
group13: 2.89,-2.84
group14: 3.64,-3.67
group15: 4.48,-3.44
group16: 4.04,-3.99
group17: 4.32,-3.08
group18: 4.75,-2.75
group19: 5.72,-2.95
group20: 5.40,-3.11
group21: 6.02,-2.95
group22: 6.63,-4.14
group23: 6.85,-5.00
group24: 7.14,-4.86
group25: 7.72,-4.39
group26: 8.65,-4.75
group27: 9.49,-4.39
group28: 10.20,-4.44
group29: 11.13,-4.58


You are removing the closepath commands, and then compute the first point of the next group relative to the last explicit point of the last group. But closepath actually moves the ccurrent point: back to the position of the last moveto command. These may, but need not be identical.

closepath

closepath

moveto

I can't give you a ready script in R, but what you need to do is this: at the beginning of a new group, cache the position of the first point. At the beginning of the next group, compute the new first point relative to that cached point.

y

H

if(d2$code[i] == 'H') d2$y_adj[i] = d2$y_adj[i-1]

y

d

d2

198., 143.

191.76,146.07

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