Sistem Referensi Koordinat dan Proyeksi

Mengapa CRS Penting

library(sf)

# Two sf objects in the same CRS: operations work
nc <- read_sf(system.file('shape/nc.shp', package = 'sf'))

# sf will error or warn when CRS do not match during operations
# This is the CRS metadata attached to the object
crs <- st_crs(nc)
cat('EPSG:', crs$epsg, '\n')
cat('Input is geographic (lon/lat)?', st_is_longlat(nc), '\n')
cat('Units:', crs$units_gdal, '\n')

st_crs: Membaca Info CRS

library(sf)

nc <- read_sf(system.file('shape/nc.shp', package = 'sf'))

# Inspect the CRS object
crs <- st_crs(nc)
cat('Class:', class(crs), '\n')
cat('EPSG:', crs$epsg, '\n')
cat('Proj4:', substr(crs$proj4string, 1, 60), '...\n')

# Lookup a CRS by EPSG code
wgs84 <- st_crs(4326)
web_mercator <- st_crs(3857)

cat('\nWGS84 name:', wgs84$Name, '\n')
cat('Web Mercator name:', web_mercator$Name, '\n')

EPSG:4326 — WGS84

library(sf)

# Create points in WGS84 (GPS coordinates)
cities <- data.frame(
  city = c('London', 'Tokyo', 'Sydney', 'New York'),
  lon  = c(-0.118, 139.692, 151.209, -74.006),
  lat  = c(51.509,  35.689, -33.869,  40.713)
)

cities_sf <- st_as_sf(cities,
  coords = c('lon', 'lat'),
  crs    = 4326
)

cat('CRS:', st_crs(cities_sf)$Name, '\n')
cat('Units:', st_crs(cities_sf)$units_gdal, '\n')

# Naive distance in degrees (not meaningful for real distances)
d <- st_distance(cities_sf[1, ], cities_sf[2, ])
cat('London-Tokyo distance (degrees):', round(as.numeric(d), 2), '\n')

EPSG:3857 — Web Mercator

library(sf)

cities <- data.frame(
  city = c('London', 'Tokyo'),
  lon  = c(-0.118, 139.692),
  lat  = c(51.509,  35.689)
)
cities_sf <- st_as_sf(cities, coords = c('lon', 'lat'), crs = 4326)

# Transform to Web Mercator
cities_merc <- st_transform(cities_sf, 3857)

cat('WGS84 coords (degrees):\n')
print(st_coordinates(cities_sf))

cat('\nWeb Mercator coords (metres):\n')
print(st_coordinates(cities_merc))

# Distance is now in metres
d <- st_distance(cities_merc[1, ], cities_merc[2, ])
cat('\nLondon-Tokyo distance (km):', round(as.numeric(d) / 1000, 0), '\n')

st_set_crs: Menetapkan CRS

library(sf)

# Create geometry with NO CRS
pts <- st_sfc(
  st_point(c(-74.006, 40.713)),
  st_point(c(-87.629, 41.878))
)
cat('CRS before:', is.na(st_crs(pts)), '(NA = no CRS)\n')

# Assign WGS84 (no coordinate transformation)
pts_wgs84 <- st_set_crs(pts, 4326)
cat('CRS after assignment:', st_crs(pts_wgs84)$epsg, '\n')

# Compare with st_transform (DOES transform coordinates)
pts_sf    <- st_sf(id = 1:2, geometry = pts_wgs84)
pts_merc  <- st_transform(pts_sf, 3857)
cat('Original lon:', st_coordinates(pts_sf)[1, 'X'], '\n')
cat('Mercator X:  ', st_coordinates(pts_merc)[1, 'X'], '\n')

st_transform: Memproyeksikan Ulang

library(sf)

nc <- read_sf(system.file('shape/nc.shp', package = 'sf'))
cat('Original CRS:', st_crs(nc)$epsg, '\n')

# Re-project to WGS84
nc_wgs84 <- st_transform(nc, 4326)
cat('Transformed CRS:', st_crs(nc_wgs84)$epsg, '\n')

# Re-project to a local projected CRS (NC State Plane)
nc_stateplane <- st_transform(nc, 32119)  # NAD83 / North Carolina
cat('State Plane CRS:', st_crs(nc_stateplane)$Name, '\n')

# Area calculation is more accurate in a projected CRS
area_deg <- st_area(nc[1, ])
area_m2  <- st_area(nc_stateplane[1, ])
cat('Area (degrees^2):', format(area_deg, big.mark = ','), '\n')
cat('Area (m^2):      ', format(area_m2,  big.mark = ','), '\n')

Memilih Proyeksi yang Tepat

library(sf)

# Common EPSG codes cheat sheet
epsg_table <- data.frame(
  EPSG = c(4326, 3857, 4269, 32637, 27700),
  Name = c(
    'WGS84 (GPS, global)',
    'Web Mercator (web maps)',
    'NAD83 (North America geographic)',
    'UTM zone 37N (Middle East)',
    'British National Grid (UK)'
  ),
  Units = c('degrees', 'metres', 'degrees', 'metres', 'metres')
)

print(epsg_table, row.names = FALSE)

# Look up any EPSG online: https://epsg.io/<code>
cat('\nTip: use st_crs(epsg_code)$Name to verify a code\n')

String Proj4

library(sf)

nc <- read_sf(system.file('shape/nc.shp', package = 'sf'))

# WGS84 as Proj4 string
wgs84_proj4 <- '+proj=longlat +datum=WGS84 +no_defs'
nc_wgs84 <- st_transform(nc, crs = wgs84_proj4)

cat('Using Proj4 string:\n', wgs84_proj4, '\n')
cat('Result CRS EPSG:', st_crs(nc_wgs84)$epsg, '\n')

# Compare: equivalent to st_transform(nc, 4326)
cat('Same as EPSG 4326?',
    identical(st_crs(nc_wgs84), st_crs(st_transform(nc, 4326))), '\n')

Memeriksa Kesamaan CRS

library(sf)

# Two objects in different CRS
nc_nad27  <- read_sf(system.file('shape/nc.shp', package = 'sf'))
nc_wgs84  <- st_transform(nc_nad27, 4326)

cat('Same CRS?', st_crs(nc_nad27) == st_crs(nc_wgs84), '\n')

# Always check before join/overlay
align_crs <- function(a, b) {
  if (st_crs(a) != st_crs(b)) {
    message('CRS mismatch! Transforming b to match a.')
    b <- st_transform(b, st_crs(a))
  }
  list(a = a, b = b)
}

aligned <- align_crs(nc_nad27, nc_wgs84)
cat('After alignment - same CRS?',
    st_crs(aligned$a) == st_crs(aligned$b), '\n')

Menghitung Jarak dengan CRS

library(sf)

# City points in WGS84
cities <- data.frame(
  city = c('Paris', 'Berlin', 'Madrid', 'Rome'),
  lon  = c(2.350, 13.404, -3.702, 12.496),
  lat  = c(48.865, 52.520,  40.417, 41.902)
)
cities_sf <- st_as_sf(cities, coords = c('lon', 'lat'), crs = 4326)

# sf computes geodesic distances on WGS84 automatically
dist_matrix <- st_distance(cities_sf)
rownames(dist_matrix) <- cities$city
colnames(dist_matrix) <- cities$city

# Convert to km
dist_km <- round(as.numeric(dist_matrix) / 1000)
mat_km <- matrix(dist_km, 4, 4, dimnames = list(cities$city, cities$city))
print(mat_km)

Alur Kerja CRS Lengkap

library(sf)

# Load and assign CRS
nc <- read_sf(system.file('shape/nc.shp', package = 'sf'))
nc_wgs84 <- st_transform(nc, 4326)

# Re-project to NC State Plane (metres) for accurate areas
nc_proj <- st_transform(nc, 32119)

# Compute area per county in km2
nc_proj$area_km2 <- as.numeric(st_area(nc_proj)) / 1e6

# Top 5 largest counties
top5 <- nc_proj[order(-nc_proj$area_km2), c('NAME', 'area_km2')]
cat('5 Largest NC Counties (km2):\n')
print(head(as.data.frame(top5)[, c('NAME', 'area_km2')], 5))

# Back to WGS84 for output
nc_output <- st_transform(nc_proj, 4326)
cat('\nOutput CRS:', st_crs(nc_output)$epsg, '\n')

Pemeriksaan Cepat

Rangkuman: CRS dan Proyeksi

library(sf)
nc <- read_sf(system.file('shape/nc.shp', package = 'sf'))

# CRS pipeline
cat('Original:', st_crs(nc)$epsg, '\n')
nc_wgs84 <- st_transform(nc, 4326)
nc_proj  <- st_transform(nc_wgs84, 32119)
cat('WGS84:', st_crs(nc_wgs84)$epsg, '\n')
cat('Projected:', st_crs(nc_proj)$epsg, '\n')