espinielli · October 17, 2017 15:14
diff --git a/.gitignore b/.gitignore
 .Rproj.user
 .Rhistory
 .RData
 .Ruserdata
diff --git a/Readme.md b/Readme.md
diff --git a/Readme.Rmd b/Readme.Rmd
 ---
 title: "Polygon are in R with sf"
 author: "Enrico Spinielli"
 date: "October 15, 2017"
 output:
  html_document:
    keep_md: TRUE
 ---

 ```{r setup, include=FALSE}
 knitr::opts_chunk$set(echo = TRUE)
 ```


 Source `polygon_area.R` and you will get the answer in ${km}^2$.

 There are two CSV files for the polygons.
 Polygons are "closed", i.e. first and last point are the same.

 The area of the full polygon is $22597969\ {km}^2$
 while the area of the simplified one is $27412031\ {km}^2$.

 Here is the map of the two (red = full polygon, blue = simple polygon).

 ![](polys.png)
diff --git a/full_polygon.csv b/full_polygon.csv
 73.00000;0.00000
 73.00000;0.00000
 82.00000;0.00000
 82.00000;32.00000
 81.00000;32.00000
 81.00000;35.00000
 74.04500;35.00000
 74.00000;32.08333
 70.16667;32.08333
 70.13333;31.98333
 70.00000;31.13333
 69.79472;30.81861
 69.53333;30.83333
 69.54167;30.56667
 69.67222;30.13333
 69.65833;30.08333
 69.42194;30.02778
 69.33333;29.53333
 69.30833;29.49444
 69.01667;29.05000
 68.94083;28.57083
 68.91667;28.41667
 68.87500;28.80333
 68.50333;28.45833
 68.10000;29.33333
 67.70000;30.00000
 67.20389;29.40111
 66.96667;29.08333
 66.70000;29.61667
 66.39722;29.75861
 66.16667;29.86694
 66.02194;29.95444
 65.66667;30.16667
 65.58361;29.81556
 65.05639;29.62583
 64.93333;29.61667
 64.70000;30.08333
 64.23333;30.50000
 63.73333;30.01667
 63.24111;31.17444
 63.14667;31.26500
 63.00000;31.50000
 62.95000;31.55000
 62.42167;31.10833
 61.91944;30.27861
 61.80000;30.08333
 61.72167;29.94750
 61.55111;29.65250
 61.43333;29.45000
 61.25333;29.11361
 61.07583;28.75694
 60.85833;28.33833
 60.75000;28.16667
 60.36528;27.67528
 60.34500;27.64944
 60.33167;27.62806
 60.23333;27.47500
 60.22333;27.45667
 60.20028;27.29306
 60.19389;27.22111
 60.17167;26.94639
 60.16139;26.83861
 60.15250;26.75889
 60.14972;26.71694
 60.14417;26.66139
 60.13333;26.55000
 60.07611;26.39028
 60.07028;26.37444
 59.94556;26.03500
 59.88333;25.86667
 59.86667;25.97500
 59.85167;26.07833
 59.85000;26.08917
 59.83750;26.17389
 59.79639;26.44806
 59.78944;26.49333
 59.75528;26.72139
 59.74694;26.77667
 59.61167;27.63667
 59.47167;28.04333
 59.45667;28.09944
 59.38611;28.19667
 59.18639;27.88917
 59.05139;27.77111
 58.84333;27.46778
 58.80028;27.38278
 58.70000;27.41667
 58.48861;27.49611
 58.32944;27.51472
 58.03833;27.62000
 57.90000;27.81667
 57.83000;27.55972
 57.60000;27.38333
 57.55000;27.70000
 57.38028;27.68583
 56.75167;27.90167
 56.50500;28.12833
 56.16667;28.15000
 55.87417;30.01889
 55.80000;30.48972
 55.58333;30.94806
 55.28000;30.86139
 55.19167;30.96472
 54.66833;31.04139
 54.50333;31.08472
 54.36500;31.12917
 54.21667;31.33139
 54.09472;31.49333
 53.50278;32.27333
 53.21667;32.46667
 52.96833;31.35972
 52.08139;31.95139
 52.27500;32.67333
 52.35000;33.31000
 52.32167;33.89833
 52.00000;34.11667
 51.96667;34.16667
 51.70000;34.50000
 51.65000;34.08333
 51.23333;34.45000
 51.07167;35.33000
 50.85000;35.43333
 50.81583;35.44861
 50.37167;35.64667
 50.35500;35.69833
 50.32139;36.29333
 50.31667;36.40833
 50.31333;36.48500
 50.31667;36.82833
 50.43333;37.46667
 50.30167;37.64000
 50.30083;37.64083
 50.09194;37.76000
 49.90861;38.04278
 49.93028;38.14667
 49.95000;38.17861
 50.06611;38.19250
 50.07500;38.22667
 49.74167;39.50000
 49.61250;40.15167
 49.56306;40.20750
 49.53194;40.07000
 49.36667;40.16667
 48.51833;39.86333
 48.19500;39.94333
 48.12833;39.89167
 47.95000;39.80833
 47.83333;39.67500
 47.85667;39.21833
 47.81667;38.91667
 47.55500;38.31333
 47.11167;38.22333
 46.98333;38.33333
 46.78333;37.50000
 46.65833;37.42167
 46.57333;37.36833
 45.63833;36.79667
 45.50444;36.71611
 45.45000;36.68333
 45.37833;36.68333
 45.35000;36.64667
 45.30667;36.59000
 45.24500;36.59500
 45.20500;36.53333
 45.15917;36.54389
 45.15333;36.54500
 45.07167;36.57167
 45.00000;36.59167
 44.93667;36.61000
 44.82917;36.62444
 44.51667;36.66667
 44.35000;36.63333
 44.03667;36.55833
 43.74167;36.49167
 43.25000;36.38333
 42.73222;36.26639
 42.72500;36.50000
 42.72000;36.61667
 42.70889;36.91472
 42.70333;37.12000
 42.68333;37.66667
 42.68222;37.71222
 42.65333;37.80833
 42.18389;39.40306
 41.90000;40.33333
 41.79917;40.65639
 41.69750;40.97861
 41.60000;41.28194
 41.54889;41.44972
 41.51667;41.54861
 41.48361;41.65500
 41.49750;41.70889
 41.48972;41.72167
 41.47500;41.71611
 41.46417;41.78167
 41.43472;41.82333
 41.46083;41.87889
 41.50000;41.90778
 41.52444;41.96556
 41.52528;41.97694
 41.50639;41.99250
 41.49417;42.04833
 41.51167;42.08694
 41.51417;42.18389
 41.49333;42.20417
 41.49389;42.28889
 41.47111;42.33389
 41.46639;42.40778
 41.44278;42.43917
 41.43917;42.47083
 41.44000;42.52056
 41.46833;42.51056
 41.51056;42.56972
 41.56167;42.57806
 41.57583;42.59611
 41.57833;42.78389
 41.57083;42.83861
 41.51667;42.79694
 41.42806;42.97889
 41.30333;43.19889
 41.25333;43.12528
 41.24694;43.19778
 41.17611;43.22722
 41.20222;43.37417
 41.17944;43.43778
 41.13333;43.46667
 41.09194;43.44972
 41.05972;43.47083
 41.02750;43.47194
 40.98556;43.59944
 40.93306;43.67139
 40.84444;43.67611
 40.84000;43.68500
 40.81194;43.71333
 40.73611;43.74889
 40.70778;43.73639
 40.68139;43.74917
 40.58750;43.68694
 40.56556;43.64972
 40.56250;43.64694
 40.52750;43.64694
 40.53667;43.63111
 40.52083;43.63528
 40.52694;43.62417
 40.50639;43.58333
 40.47750;43.54750
 40.45694;43.55639
 40.41806;43.62083
 40.38556;43.60972
 40.34528;43.59250
 40.27111;43.63917
 40.25694;43.68167
 40.22444;43.68222
 40.22083;43.65889
 40.16417;43.71389
 40.14833;43.66139
 40.11556;43.66472
 40.07972;43.71889
 40.07944;43.76972
 40.01833;43.90556
 40.03083;44.11250
 40.01972;44.17139
 40.03500;44.19806
 40.04528;44.27889
 40.03167;44.29889
 40.02861;44.33972
 40.00000;44.37556
 40.00000;44.41917
 39.96444;44.48861
 39.90361;44.55750
 39.87722;44.56444
 39.85056;44.59694
 39.82556;44.60167
 39.38333;44.45000
 39.32333;44.08667
 38.90972;44.20833
 38.32222;44.50417
 38.04889;44.29972
 37.89722;44.23611
 37.70833;44.62667
 37.10833;44.66667
 36.94167;44.26667
 37.30556;44.16667
 37.22472;43.64056
 37.35000;43.21667
 37.37639;43.11833
 37.30556;42.82361
 37.24889;42.64972
 37.08333;42.33333
 37.26667;42.25000
 37.10333;41.79111
 37.00000;41.50000
 37.07222;41.23028
 37.03333;41.19861
 37.03333;40.83333
 36.66667;39.33333
 36.70861;39.02833
 36.66667;38.75000
 36.90000;38.36667
 36.64889;37.38306
 36.65000;37.06389
 36.83333;36.66667
 36.78444;36.64139
 36.50000;36.58750
 36.23333;36.70000
 36.16667;36.36667
 35.86667;36.18333
 35.88333;36.03333
 35.91667;35.66667
 35.55000;35.53333
 35.19333;35.71667
 34.58333;35.75000
 34.53833;35.28667
 34.48333;35.05000
 34.36667;34.87444
 34.24500;34.74667
 34.03167;34.62139
 33.94556;34.60389
 33.89167;34.59167
 33.83194;34.58333
 33.64889;34.63306
 33.16667;34.93333
 33.10000;34.86667
 33.10000;34.71667
 33.09083;34.60306
 32.85750;34.55361
 32.78167;34.54389
 32.71667;34.53333
 32.68056;34.42750
 32.61389;34.35444
 32.50583;34.18806
 32.49472;34.17083
 32.33500;34.05528
 32.16944;33.99250
 31.91667;33.98333
 31.83333;34.00000
 31.82500;34.00194
 32.21667;33.10000
 32.63333;32.08333
 32.80861;31.66194
 33.10000;30.95000
 33.50000;30.00000
 33.71389;28.75000
 33.80000;28.26667
 33.92389;27.62306
 33.95167;27.33333
 34.00000;27.16667
 34.00000;24.16667
 34.33333;23.58333
 34.33333;11.50000
 37.50000;11.50000
 37.59278;11.29417
 37.64167;11.20000
 37.67361;11.11389
 37.68333;11.10000
 37.74278;10.95917
 37.76944;10.90861
 37.81944;10.78667
 37.88917;10.62861
 38.03889;10.28639
 38.25472;9.78722
 38.39528;9.45639
 38.58333;9.01667
 38.60306;8.96500
 38.63306;8.89222
 38.64444;8.86528
 38.65750;8.83667
 38.68417;8.77194
 38.79500;8.49944
 39.00000;8.00000
 39.00000;4.68500
 38.48028;3.94972
 38.33333;3.75000
 38.26056;3.55000
 38.21333;3.42194
 38.13194;3.20194
 38.11306;3.15139
 37.90250;2.58944
 37.80361;2.32889
 37.71667;2.12500
 37.44167;1.50000
 37.27472;1.12389
 36.91667;0.10000
 36.87111;-0.02361
 36.45361;-1.02361
 36.40500;-1.13778
 36.25222;-1.49500
 35.88333;-2.02500
 35.83333;-2.00000
 35.83333;-7.38333
 35.96667;-7.38333
 35.96667;-12.00000
 35.54639;-12.31250
 35.00000;-12.71167
 34.00000;-13.42722
 33.19028;-13.97972
 33.00000;-14.12333
 32.25000;-14.61667
 32.00000;-14.80111
 31.50000;-15.75000
 31.42139;-16.03278
 31.40694;-16.55694
 31.45000;-16.80000
 31.48306;-16.94056
 31.50250;-16.99500
 31.65000;-17.41667
 31.68306;-17.45694
 31.83333;-17.71667
 32.33111;-18.13028
 32.98333;-18.40000
 33.92500;-18.06917
 34.16667;-17.80000
 35.52056;-16.23444
 36.19444;-15.39028
 36.50000;-15.00000
 37.00000;-15.00000
 38.00000;-15.00000
 38.50000;-15.00000
 39.00000;-15.00000
 39.50000;-15.00000
 40.00000;-15.00000
 41.00000;-15.00000
 42.00000;-15.00000
 42.50000;-14.00000
 43.00000;-13.00000
 45.00000;-13.00000
 45.00000;-8.75000
 48.57333;-8.75000
 49.00000;-15.00000
 57.00000;-15.00000
 57.00000;-10.00000
 61.00000;-10.00000
 61.00000;0.00000
 73.00000;0.00000
diff --git a/polygon_area.R b/polygon_area.R
 #  install.packages(c("tidyverse", "sf", "units", "mapview")

 library(tidyverse)
 library(sf)
 library(units)
 library(mapview)

 # list of point defining the polygon (last point equal to first one)
 poly_full_csv <- read_delim(
  "full_polygon.csv",
  delim = ";",
  col_names = c("lat", "lon"),
  col_types = "dd")

 # from list of points to SF polygon
 poly_full <- poly_full_csv %>%
  select(lon, lat) %>% 
  as.matrix() %>%
  list() %>%
  st_polygon()


 poly_simple_csv <- read_delim(
  "simple_polygon.csv",
  delim = ";",
  col_types = "dd", col_names = FALSE
 ) %>% rename(lon = X2, lat = X1)


 poly_simple <- poly_simple_csv %>%
  select(lon, lat) %>% 
  as.matrix() %>%
  list() %>%
  st_polygon()

 ps <- st_sf(a = 1, geometry = st_sfc(poly_simple)) %>%
  st_set_crs(4326)

 pf <- st_sf(a = 1, st_sfc(poly_full)) %>%
  st_set_crs(4326)

 pf %>% st_area() %>% set_units(km^2)
 ps %>% st_area() %>% set_units(km^2)

 mapview(pf, color = "white", col.regions = "red") + mapview(ps)
diff --git a/polygonarea.Rproj b/polygonarea.Rproj
 Version: 1.0

 RestoreWorkspace: Default
 SaveWorkspace: Default
 AlwaysSaveHistory: Default

 EnableCodeIndexing: Yes
 UseSpacesForTab: Yes
 NumSpacesForTab: 2
 Encoding: UTF-8

 RnwWeave: knitr
 LaTeX: pdfLaTeX
diff --git a/polys.png b/polys.png
diff --git a/simple_polygon.csv b/simple_polygon.csv
 81.07095264;-1.249340377
 82.15928065;20.49622637
 79.98098991;37.36859498
 36.99425199;44.74575178
 33.9395891;25.52224348
 35.61426157;-6.585536566
 36.32646554;-12.62765374
 39.68569469;-15.69204363
 81.07095264;-1.249340377
	---
	title: "Polygon are in R with sf"
	author: "Enrico Spinielli"
	date: "October 15, 2017"
	output:
	html_document:
	keep_md: TRUE
	---

	```{r setup, include=FALSE}
	knitr::opts_chunk$set(echo = TRUE)
	```


	Source `polygon_area.R` and you will get the answer in ${km}^2$.

	There are two CSV files for the polygons.
	Polygons are "closed", i.e. first and last point are the same.

	The area of the full polygon is $22597969\ {km}^2$
	while the area of the simplified one is $27412031\ {km}^2$.

	Here is the map of the two (red = full polygon, blue = simple polygon).

	![](polys.png)
	73.00000;0.00000
	73.00000;0.00000
	82.00000;0.00000
	82.00000;32.00000
	81.00000;32.00000
	81.00000;35.00000
	74.04500;35.00000
	74.00000;32.08333
	70.16667;32.08333
	70.13333;31.98333
	70.00000;31.13333
	69.79472;30.81861
	69.53333;30.83333
	69.54167;30.56667
	69.67222;30.13333
	69.65833;30.08333
	69.42194;30.02778
	69.33333;29.53333
	69.30833;29.49444
	69.01667;29.05000
	68.94083;28.57083
	68.91667;28.41667
	68.87500;28.80333
	68.50333;28.45833
	68.10000;29.33333
	67.70000;30.00000
	67.20389;29.40111
	66.96667;29.08333
	66.70000;29.61667
	66.39722;29.75861
	66.16667;29.86694
	66.02194;29.95444
	65.66667;30.16667
	65.58361;29.81556
	65.05639;29.62583
	64.93333;29.61667
	64.70000;30.08333
	64.23333;30.50000
	63.73333;30.01667
	63.24111;31.17444
	63.14667;31.26500
	63.00000;31.50000
	62.95000;31.55000
	62.42167;31.10833
	61.91944;30.27861
	61.80000;30.08333
	61.72167;29.94750
	61.55111;29.65250
	61.43333;29.45000
	61.25333;29.11361
	61.07583;28.75694
	60.85833;28.33833
	60.75000;28.16667
	60.36528;27.67528
	60.34500;27.64944
	60.33167;27.62806
	60.23333;27.47500
	60.22333;27.45667
	60.20028;27.29306
	60.19389;27.22111
	60.17167;26.94639
	60.16139;26.83861
	60.15250;26.75889
	60.14972;26.71694
	60.14417;26.66139
	60.13333;26.55000
	60.07611;26.39028
	60.07028;26.37444
	59.94556;26.03500
	59.88333;25.86667
	59.86667;25.97500
	59.85167;26.07833
	59.85000;26.08917
	59.83750;26.17389
	59.79639;26.44806
	59.78944;26.49333
	59.75528;26.72139
	59.74694;26.77667
	59.61167;27.63667
	59.47167;28.04333
	59.45667;28.09944
	59.38611;28.19667
	59.18639;27.88917
	59.05139;27.77111
	58.84333;27.46778
	58.80028;27.38278
	58.70000;27.41667
	58.48861;27.49611
	58.32944;27.51472
	58.03833;27.62000
	57.90000;27.81667
	57.83000;27.55972
	57.60000;27.38333
	57.55000;27.70000
	57.38028;27.68583
	56.75167;27.90167
	56.50500;28.12833
	56.16667;28.15000
	55.87417;30.01889
	55.80000;30.48972
	55.58333;30.94806
	55.28000;30.86139
	55.19167;30.96472
	54.66833;31.04139
	54.50333;31.08472
	54.36500;31.12917
	54.21667;31.33139
	54.09472;31.49333
	53.50278;32.27333
	53.21667;32.46667
	52.96833;31.35972
	52.08139;31.95139
	52.27500;32.67333
	52.35000;33.31000
	52.32167;33.89833
	52.00000;34.11667
	51.96667;34.16667
	51.70000;34.50000
	51.65000;34.08333
	51.23333;34.45000
	51.07167;35.33000
	50.85000;35.43333
	50.81583;35.44861
	50.37167;35.64667
	50.35500;35.69833
	50.32139;36.29333
	50.31667;36.40833
	50.31333;36.48500
	50.31667;36.82833
	50.43333;37.46667
	50.30167;37.64000
	50.30083;37.64083
	50.09194;37.76000
	49.90861;38.04278
	49.93028;38.14667
	49.95000;38.17861
	50.06611;38.19250
	50.07500;38.22667
	49.74167;39.50000
	49.61250;40.15167
	49.56306;40.20750
	49.53194;40.07000
	49.36667;40.16667
	48.51833;39.86333
	48.19500;39.94333
	48.12833;39.89167
	47.95000;39.80833
	47.83333;39.67500
	47.85667;39.21833
	47.81667;38.91667
	47.55500;38.31333
	47.11167;38.22333
	46.98333;38.33333
	46.78333;37.50000
	46.65833;37.42167
	46.57333;37.36833
	45.63833;36.79667
	45.50444;36.71611
	45.45000;36.68333
	45.37833;36.68333
	45.35000;36.64667
	45.30667;36.59000
	45.24500;36.59500
	45.20500;36.53333
	45.15917;36.54389
	45.15333;36.54500
	45.07167;36.57167
	45.00000;36.59167
	44.93667;36.61000
	44.82917;36.62444
	44.51667;36.66667
	44.35000;36.63333
	44.03667;36.55833
	43.74167;36.49167
	43.25000;36.38333
	42.73222;36.26639
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	# install.packages(c("tidyverse", "sf", "units", "mapview")

	library(tidyverse)
	library(sf)
	library(units)
	library(mapview)

	# list of point defining the polygon (last point equal to first one)
	poly_full_csv <- read_delim(
	"full_polygon.csv",
	delim = ";",
	col_names = c("lat", "lon"),
	col_types = "dd")

	# from list of points to SF polygon
	poly_full <- poly_full_csv %>%
	select(lon, lat) %>%
	as.matrix() %>%
	list() %>%
	st_polygon()


	poly_simple_csv <- read_delim(
	"simple_polygon.csv",
	delim = ";",
	col_types = "dd", col_names = FALSE
	) %>% rename(lon = X2, lat = X1)


	poly_simple <- poly_simple_csv %>%
	select(lon, lat) %>%
	as.matrix() %>%
	list() %>%
	st_polygon()

	ps <- st_sf(a = 1, geometry = st_sfc(poly_simple)) %>%
	st_set_crs(4326)

	pf <- st_sf(a = 1, st_sfc(poly_full)) %>%
	st_set_crs(4326)

	pf %>% st_area() %>% set_units(km^2)
	ps %>% st_area() %>% set_units(km^2)

	mapview(pf, color = "white", col.regions = "red") + mapview(ps)
	Version: 1.0

	RestoreWorkspace: Default
	SaveWorkspace: Default
	AlwaysSaveHistory: Default

	EnableCodeIndexing: Yes
	UseSpacesForTab: Yes
	NumSpacesForTab: 2
	Encoding: UTF-8

	RnwWeave: knitr
	LaTeX: pdfLaTeX
	81.07095264;-1.249340377
	82.15928065;20.49622637
	79.98098991;37.36859498
	36.99425199;44.74575178
	33.9395891;25.52224348
	35.61426157;-6.585536566
	36.32646554;-12.62765374
	39.68569469;-15.69204363
	81.07095264;-1.249340377