Spatial Analysis:02
Tzai-Hung Wen
2025-03-03
Spatial Data Handling
rm(list = ls()) # 清除任何現有的R物件之前執行批次工作的程式碼
library(sf)
library(tmap)
library(pals) # collection of color palettes
library(cartography) # classification methods
#setwd("C:/Wen_Files/SA_2024")
load("./data/Sample.RData")0. sf format and coordinates
class(blocks_sf)[1] "sf" "data.frame"head(blocks_sf)Simple feature collection with 6 features and 28 fields
Geometry type: POLYGON
Dimension: XY
Bounding box: xmin: 534687.6 ymin: 177306.3 xmax: 569625.3 ymax: 188464.6
Projected CRS: +proj=lcc +datum=NAD27 +lon_0=-72d45 +lat_1=41d52 +lat_2=41d12 +lat_0=40d50 +x_0=182880.3657607315 +y_0=0 +units=us-ft +no_defs +ellps=clrk66 +nadgrids=@conus,@alaska,@ntv2_0.gsb,@ntv1_can.dat
NEWH075H_ NEWH075H_I HSE_UNITS OCCUPIED VACANT P_VACANT P_OWNEROCC P_RENTROCC NEWH075P_
0 2 69 763 725 38 4.980341 0.393185 94.626474 2
1 3 72 510 480 30 5.882353 20.392157 73.725490 3
2 4 64 389 362 27 6.940874 57.840617 35.218509 4
3 5 68 429 397 32 7.459207 19.813520 72.727273 5
4 6 67 443 385 58 13.092551 80.361174 6.546275 6
5 7 133 588 548 40 6.802721 52.551020 40.646259 7
NEWH075P_I POP1990 P_MALES P_FEMALES P_WHITE P_BLACK P_AMERI_ES P_ASIAN_PI P_OTHER
0 380 2396 40.02504 59.97496 7.095159 87.020033 0.584307 0.041736 5.258765
1 385 3071 39.07522 60.92478 87.105177 10.452621 0.195376 0.521003 1.725822
2 394 996 47.38956 52.61044 32.931727 66.265060 0.100402 0.200803 0.502008
3 399 1336 42.66467 57.33533 11.452096 85.553892 0.523952 0.523952 1.946108
4 404 915 46.22951 53.77049 73.442623 24.371585 0.327869 1.420765 0.437158
5 406 1318 50.91047 49.08953 87.784522 7.435508 0.758725 0.834598 3.186646
P_UNDER5 P_5_13 P_14_17 P_18_24 P_25_34 P_35_44 P_45_54 P_55_64 P_65_74
0 12.813022 24.707846 7.888147 12.479132 16.026711 8.555927 5.759599 4.924875 4.048414
1 1.921198 2.474764 0.814067 71.149463 7.359166 4.037773 1.595571 1.758385 3.712146
2 10.441767 13.554217 5.722892 8.835341 17.670683 17.871486 8.734940 5.923695 7.931727
3 10.853293 17.739521 7.709581 12.425150 18.113772 10.853293 9.056886 6.287425 4.266467
4 6.229508 8.633880 2.950820 7.103825 17.267760 16.830601 8.415301 7.431694 14.426230
5 8.725341 8.194234 3.641882 10.091047 29.286798 12.898331 7.814871 7.814871 6.904401
P_75_UP geometry
0 2.796327 POLYGON ((540989.5 186028.3...
1 5.177467 POLYGON ((539949.9 187487.6...
2 3.313253 POLYGON ((537497.6 184616.7...
3 2.694611 POLYGON ((537497.6 184616.7...
4 10.710383 POLYGON ((536589.3 184217.5...
5 4.628225 POLYGON ((568032.4 183170.2...Extracing as a new layer
new_sf <- blocks_sf[,6]
new2_sf <- blocks_sf[1:3,]Attribute table
blocks_df <- as.data.frame(blocks_sf)
class(blocks_df)[1] "data.frame"head(blocks_df)Coordinate system
st_crs(blocks_sf)Coordinate Reference System:
User input: +proj=lcc +datum=NAD27 +lon_0=-72d45 +lat_1=41d52 +lat_2=41d12 +lat_0=40d50 +x_0=182880.3657607315 +y_0=0 +units=us-ft +no_defs +ellps=clrk66 +nadgrids=@conus,@alaska,@ntv2_0.gsb,@ntv1_can.dat
wkt:
BOUNDCRS[
SOURCECRS[
PROJCRS["unknown",
BASEGEOGCRS["unknown",
DATUM["North American Datum 1927",
ELLIPSOID["Clarke 1866",6378206.4,294.978698213898,
LENGTHUNIT["metre",1]],
ID["EPSG",6267]],
PRIMEM["Greenwich",0,
ANGLEUNIT["degree",0.0174532925199433],
ID["EPSG",8901]]],
CONVERSION["unknown",
METHOD["Lambert Conic Conformal (2SP)",
ID["EPSG",9802]],
PARAMETER["Latitude of false origin",40.8333333333333,
ANGLEUNIT["degree",0.0174532925199433],
ID["EPSG",8821]],
PARAMETER["Longitude of false origin",-72.75,
ANGLEUNIT["degree",0.0174532925199433],
ID["EPSG",8822]],
PARAMETER["Latitude of 1st standard parallel",41.8666666666667,
ANGLEUNIT["degree",0.0174532925199433],
ID["EPSG",8823]],
PARAMETER["Latitude of 2nd standard parallel",41.2,
ANGLEUNIT["degree",0.0174532925199433],
ID["EPSG",8824]],
PARAMETER["Easting at false origin",600000,
LENGTHUNIT["US survey foot",0.304800609601219],
ID["EPSG",8826]],
PARAMETER["Northing at false origin",0,
LENGTHUNIT["US survey foot",0.304800609601219],
ID["EPSG",8827]]],
CS[Cartesian,2],
AXIS["(E)",east,
ORDER[1],
LENGTHUNIT["US survey foot",0.304800609601219,
ID["EPSG",9003]]],
AXIS["(N)",north,
ORDER[2],
LENGTHUNIT["US survey foot",0.304800609601219,
ID["EPSG",9003]]]]],
TARGETCRS[
GEOGCRS["WGS 84",
DATUM["World Geodetic System 1984",
ELLIPSOID["WGS 84",6378137,298.257223563,
LENGTHUNIT["metre",1]]],
PRIMEM["Greenwich",0,
ANGLEUNIT["degree",0.0174532925199433]],
CS[ellipsoidal,2],
AXIS["latitude",north,
ORDER[1],
ANGLEUNIT["degree",0.0174532925199433]],
AXIS["longitude",east,
ORDER[2],
ANGLEUNIT["degree",0.0174532925199433]],
ID["EPSG",4326]]],
ABRIDGEDTRANSFORMATION["unknown to WGS84",
METHOD["NTv2",
ID["EPSG",9615]],
PARAMETERFILE["Latitude and longitude difference file","@conus,@alaska,@ntv2_0.gsb,@ntv1_can.dat",
ID["EPSG",8656]]]]st_crs(roads_sf)Coordinate Reference System:
User input: +proj=lcc +datum=NAD27 +lon_0=-72d45 +lat_1=41d52 +lat_2=41d12 +lat_0=40d50 +x_0=182880.3657607315 +y_0=0 +units=us-ft +no_defs +ellps=clrk66 +nadgrids=@conus,@alaska,@ntv2_0.gsb,@ntv1_can.dat
wkt:
BOUNDCRS[
SOURCECRS[
PROJCRS["unknown",
BASEGEOGCRS["unknown",
DATUM["North American Datum 1927",
ELLIPSOID["Clarke 1866",6378206.4,294.978698213898,
LENGTHUNIT["metre",1]],
ID["EPSG",6267]],
PRIMEM["Greenwich",0,
ANGLEUNIT["degree",0.0174532925199433],
ID["EPSG",8901]]],
CONVERSION["unknown",
METHOD["Lambert Conic Conformal (2SP)",
ID["EPSG",9802]],
PARAMETER["Latitude of false origin",40.8333333333333,
ANGLEUNIT["degree",0.0174532925199433],
ID["EPSG",8821]],
PARAMETER["Longitude of false origin",-72.75,
ANGLEUNIT["degree",0.0174532925199433],
ID["EPSG",8822]],
PARAMETER["Latitude of 1st standard parallel",41.8666666666667,
ANGLEUNIT["degree",0.0174532925199433],
ID["EPSG",8823]],
PARAMETER["Latitude of 2nd standard parallel",41.2,
ANGLEUNIT["degree",0.0174532925199433],
ID["EPSG",8824]],
PARAMETER["Easting at false origin",600000,
LENGTHUNIT["US survey foot",0.304800609601219],
ID["EPSG",8826]],
PARAMETER["Northing at false origin",0,
LENGTHUNIT["US survey foot",0.304800609601219],
ID["EPSG",8827]]],
CS[Cartesian,2],
AXIS["(E)",east,
ORDER[1],
LENGTHUNIT["US survey foot",0.304800609601219,
ID["EPSG",9003]]],
AXIS["(N)",north,
ORDER[2],
LENGTHUNIT["US survey foot",0.304800609601219,
ID["EPSG",9003]]]]],
TARGETCRS[
GEOGCRS["WGS 84",
DATUM["World Geodetic System 1984",
ELLIPSOID["WGS 84",6378137,298.257223563,
LENGTHUNIT["metre",1]]],
PRIMEM["Greenwich",0,
ANGLEUNIT["degree",0.0174532925199433]],
CS[ellipsoidal,2],
AXIS["latitude",north,
ORDER[1],
ANGLEUNIT["degree",0.0174532925199433]],
AXIS["longitude",east,
ORDER[2],
ANGLEUNIT["degree",0.0174532925199433]],
ID["EPSG",4326]]],
ABRIDGEDTRANSFORMATION["unknown to WGS84",
METHOD["NTv2",
ID["EPSG",9615]],
PARAMETERFILE["Latitude and longitude difference file","@conus,@alaska,@ntv2_0.gsb,@ntv1_can.dat",
ID["EPSG",8656]]]]st_crs(roads_sf) <- st_crs(blocks_sf)
st_crs(roads_sf)Coordinate Reference System:
User input: +proj=lcc +datum=NAD27 +lon_0=-72d45 +lat_1=41d52 +lat_2=41d12 +lat_0=40d50 +x_0=182880.3657607315 +y_0=0 +units=us-ft +no_defs +ellps=clrk66 +nadgrids=@conus,@alaska,@ntv2_0.gsb,@ntv1_can.dat
wkt:
BOUNDCRS[
SOURCECRS[
PROJCRS["unknown",
BASEGEOGCRS["unknown",
DATUM["North American Datum 1927",
ELLIPSOID["Clarke 1866",6378206.4,294.978698213898,
LENGTHUNIT["metre",1]],
ID["EPSG",6267]],
PRIMEM["Greenwich",0,
ANGLEUNIT["degree",0.0174532925199433],
ID["EPSG",8901]]],
CONVERSION["unknown",
METHOD["Lambert Conic Conformal (2SP)",
ID["EPSG",9802]],
PARAMETER["Latitude of false origin",40.8333333333333,
ANGLEUNIT["degree",0.0174532925199433],
ID["EPSG",8821]],
PARAMETER["Longitude of false origin",-72.75,
ANGLEUNIT["degree",0.0174532925199433],
ID["EPSG",8822]],
PARAMETER["Latitude of 1st standard parallel",41.8666666666667,
ANGLEUNIT["degree",0.0174532925199433],
ID["EPSG",8823]],
PARAMETER["Latitude of 2nd standard parallel",41.2,
ANGLEUNIT["degree",0.0174532925199433],
ID["EPSG",8824]],
PARAMETER["Easting at false origin",600000,
LENGTHUNIT["US survey foot",0.304800609601219],
ID["EPSG",8826]],
PARAMETER["Northing at false origin",0,
LENGTHUNIT["US survey foot",0.304800609601219],
ID["EPSG",8827]]],
CS[Cartesian,2],
AXIS["(E)",east,
ORDER[1],
LENGTHUNIT["US survey foot",0.304800609601219,
ID["EPSG",9003]]],
AXIS["(N)",north,
ORDER[2],
LENGTHUNIT["US survey foot",0.304800609601219,
ID["EPSG",9003]]]]],
TARGETCRS[
GEOGCRS["WGS 84",
DATUM["World Geodetic System 1984",
ELLIPSOID["WGS 84",6378137,298.257223563,
LENGTHUNIT["metre",1]]],
PRIMEM["Greenwich",0,
ANGLEUNIT["degree",0.0174532925199433]],
CS[ellipsoidal,2],
AXIS["latitude",north,
ORDER[1],
ANGLEUNIT["degree",0.0174532925199433]],
AXIS["longitude",east,
ORDER[2],
ANGLEUNIT["degree",0.0174532925199433]],
ID["EPSG",4326]]],
ABRIDGEDTRANSFORMATION["unknown to WGS84",
METHOD["NTv2",
ID["EPSG",9615]],
PARAMETERFILE["Latitude and longitude difference file","@conus,@alaska,@ntv2_0.gsb,@ntv1_can.dat",
ID["EPSG",8656]]]]Taiwan Coordinate System
TWCOUNTY <- st_read("./data/TaiwanCounty.shp", options="ENCODING=utf-8")options: ENCODING=utf-8
Reading layer `TaiwanCounty' from data source
`C:\Users\wenth\Desktop\WK02\data\TaiwanCounty.shp' using driver `ESRI Shapefile'
Simple feature collection with 19 features and 9 fields
Geometry type: MULTIPOLYGON
Dimension: XY
Bounding box: xmin: 147522.2 ymin: 2422005 xmax: 351690.1 ymax: 2799149
Projected CRS: TWD97 / TM2 zone 121st_crs(TWCOUNTY)Coordinate Reference System:
User input: TWD97 / TM2 zone 121
wkt:
PROJCRS["TWD97 / TM2 zone 121",
BASEGEOGCRS["TWD97",
DATUM["Taiwan Datum 1997",
ELLIPSOID["GRS 1980",6378137,298.257222101,
LENGTHUNIT["metre",1]]],
PRIMEM["Greenwich",0,
ANGLEUNIT["degree",0.0174532925199433]],
ID["EPSG",3824]],
CONVERSION["Taiwan 2-degree TM zone 121",
METHOD["Transverse Mercator",
ID["EPSG",9807]],
PARAMETER["Latitude of natural origin",0,
ANGLEUNIT["degree",0.0174532925199433],
ID["EPSG",8801]],
PARAMETER["Longitude of natural origin",121,
ANGLEUNIT["degree",0.0174532925199433],
ID["EPSG",8802]],
PARAMETER["Scale factor at natural origin",0.9999,
SCALEUNIT["unity",1],
ID["EPSG",8805]],
PARAMETER["False easting",250000,
LENGTHUNIT["metre",1],
ID["EPSG",8806]],
PARAMETER["False northing",0,
LENGTHUNIT["metre",1],
ID["EPSG",8807]]],
CS[Cartesian,2],
AXIS["easting (X)",east,
ORDER[1],
LENGTHUNIT["metre",1]],
AXIS["northing (Y)",north,
ORDER[2],
LENGTHUNIT["metre",1]],
USAGE[
SCOPE["Engineering survey, topographic mapping."],
AREA["Taiwan, Republic of China - between 120°E and 122°E, onshore and offshore - Taiwan Island."],
BBOX[20.41,119.99,26.72,122.06]],
ID["EPSG",3826]]Export/import shapefiles
st_write(blocks_sf,"blocks.shp", delete_layer = TRUE)Deleting layer `blocks' using driver `ESRI Shapefile'
Writing layer `blocks' to data source `blocks.shp' using driver `ESRI Shapefile'
Writing 129 features with 30 fields and geometry type Polygon.1. Mapping Spatial Objects
using plot
plot(blocks_sf)警告： plotting the first 10 out of 30 attributes; use max.plot = 30 to plot all
plot(blocks_sf["P_VACANT"], breaks = "jenks", nbreaks = 6)
#(blocks_sf$P_VACANT ?)
brewer.blues(6)[1] "#EFF3FF" "#C6DBEF" "#9ECAE1" "#6BAED6" "#3182BD" "#08519C"plot(blocks_sf["P_VACANT"], breaks = "jenks", nbreaks = 6, pal=brewer.blues(6))
using tmap package
quick tmap
qtm(blocks_sf, fill="orange", style="natural")
# colors()Qick tmap: choropleth
qtm(blocks_sf, fill="P_VACANT", fill.title="Vacant %", title="My Map 1")
Qick tmap: bubble map
qtm(blocks_sf, symbols.size="P_VACANT", symbols.title.size="Vacant %", title="My Bubble Map")
Overlay multiple plots
lyr1 <- qtm(blocks_sf, fill="P_VACANT", fill.title="Vacant %", title="My Map 1")
lyr_road <- tm_shape(roads_sf)+tm_lines(col="gray") # lines
lyr_crimes <- tm_shape(breach_sf)+tm_dots(col="red", size= 0.1) # points
# overlay multiple plots
lyr1 + lyr_road + lyr_crimes
Showing multiple plots/maps
library(grid)
# open a new plot page
grid.newpage()
# set up the layout
pushViewport(viewport(layout=grid.layout(1,2)))
# plot using the print command
print(lyr1, vp=viewport(layout.pos.col = 1))
print(lyr_road, vp=viewport(layout.pos.col = 2))
# dev.off() # close plotting device
2. Attribute Query
index <- (blocks_sf$P_VACANT > 10)
newblocks_sf <- blocks_sf[index,]
lyr3 <- qtm(newblocks_sf, fill="red", title="Vacant > 10%", style="natural")
lyr_bg <- qtm(blocks_sf, fill="grey")
lyr_bg + lyr3Note that tm_style("natural") resets all options set with tm_layout, tm_view, tm_format, or tm_legend. It is therefore recommended to place the tm_style element prior to the other tm_layout/tm_view/tm_format/tm_legend elements.
3. Calculating Fields
create a field
x <- st_area(blocks_sf) # unit: foot
library(units)
x2 <- set_units(x, km^2)
blocks_sf$AREA1 <- x2
colnames(blocks_sf) [1] "NEWH075H_" "NEWH075H_I" "HSE_UNITS" "OCCUPIED" "VACANT" "P_VACANT"
[7] "P_OWNEROCC" "P_RENTROCC" "NEWH075P_" "NEWH075P_I" "POP1990" "P_MALES"
[13] "P_FEMALES" "P_WHITE" "P_BLACK" "P_AMERI_ES" "P_ASIAN_PI" "P_OTHER"
[19] "P_UNDER5" "P_5_13" "P_14_17" "P_18_24" "P_25_34" "P_35_44"
[25] "P_45_54" "P_55_64" "P_65_74" "P_75_UP" "geometry" "AREA1"
[31] "POPDEN" remove a field
blocks_sf <- subset(blocks_sf, select = -c(AREA1))
colnames(blocks_sf) [1] "NEWH075H_" "NEWH075H_I" "HSE_UNITS" "OCCUPIED" "VACANT" "P_VACANT"
[7] "P_OWNEROCC" "P_RENTROCC" "NEWH075P_" "NEWH075P_I" "POP1990" "P_MALES"
[13] "P_FEMALES" "P_WHITE" "P_BLACK" "P_AMERI_ES" "P_ASIAN_PI" "P_OTHER"
[19] "P_UNDER5" "P_5_13" "P_14_17" "P_18_24" "P_25_34" "P_35_44"
[25] "P_45_54" "P_55_64" "P_65_74" "P_75_UP" "geometry" "POPDEN" calculating values
x2 <- set_units(x, km^2)
blocks_sf$AREA1 <- x2
blocks_sf$POPDEN <- blocks_sf$POP1990 / blocks_sf$AREA1
plot(blocks_sf["POPDEN"], breaks = "jenks", nbreaks = 6, pal= brewer.blues(6))
qtm(blocks_sf, fill="POPDEN", fill.title="Population Density", title="Popn Map", style="natural")
4. Detailed Settings for Mapping
breakv<- getBreaks(v = blocks_sf$P_OWNEROCC, nclass = 6, method = "jenks")
# classification method:"fixed", "sd", "equal", "pretty", "quantile", "kmeans",
# "hclust", "bclust", "fisher", "jenks", "dpih", "q6", "geom", "arith", "em", "msd"
tm_shape(blocks_sf) +
tm_polygons("P_OWNEROCC", title = "Owner Occ", palette = "-GnBu",
breaks = c(breakv),
legend.hist = T) +
tm_scale_bar(width = 0.22) +
tm_compass(position = c(0.8, 0.08)) +
tm_layout(frame = F, title = "New Haven",
title.size = 2, title.position = c(0.55, "top"),
legend.hist.size = 0.5)
5. Statistical Plots
Histogram
hist(blocks_sf$P_VACANT, breaks = 40, col = "grey",
border = "red",
main = "The histogram of vacant property percentages",
xlab = "percentage vacant", xlim = c(0,40))
using ggplot2: histogram
library(ggplot2)
blocks_df <- as.data.frame(blocks_sf)
head(blocks_df)
plot1<- ggplot(blocks_df) + aes(P_VACANT) +
geom_histogram(col = "red", fill = "grey", bins = 40) +
xlab("percentage vacant") +
labs(title = "The histogram of vacant property percentages")
plot1
Boxplot
boxplot(blocks_sf$P_WHIT, blocks_sf$P_BLACK, names=c("White", "Black"),
xlab="Race", ylab="Percentage")
using ggplot2: boxplot
library(reshape2)
block_prop <- melt(blocks_df[, c("P_WHITE", "P_BLACK", "P_AMERI_ES")])No id variables; using all as measure variableshead(block_prop)
plot2 <- ggplot(block_prop) +
aes(variable, value) +
geom_boxplot()
plot2
Showing map + plot
grid.newpage()
pushViewport(viewport(layout=grid.layout(1,2)))print(lyr1+lyr_crimes, vp=viewport(layout.pos.col = 1))
print(plot2, vp=viewport(layout.pos.col = 2))
#dev.off()
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