geographiclib (version 0.4.0)

polarstereo_fwd: Polar Stereographic projection

Description

Convert geographic coordinates to/from Polar Stereographic projection. This conformal projection is used for polar regions and is the basis for the Universal Polar Stereographic (UPS) system.

Usage

polarstereo_fwd(x, northp, k0 = 0.994)
polarstereo_rev(x, y, northp, k0 = 0.994)

Value

Data frame with columns:

• For forward conversion:

  • x: Easting in meters from pole

  • y: Northing in meters from pole

  • convergence: Grid convergence in degrees

  • scale: Scale factor at the point

  • lon, lat: Input coordinates (echoed)

  • northp: Hemisphere indicator (echoed)

• For reverse conversion:

  • lon: Longitude in decimal degrees

  • lat: Latitude in decimal degrees

  • convergence: Grid convergence in degrees

  • scale: Scale factor at the point

  • x, y: Input coordinates (echoed)

  • northp: Hemisphere indicator (echoed)

Arguments

x

For forward conversion: a two-column matrix or data frame of coordinates (longitude, latitude) in decimal degrees. For reverse conversion: numeric vector of x (easting) coordinates in meters.

northp

Logical indicating hemisphere: TRUE for north polar, FALSE for south polar. Can be a vector for different hemispheres per point.

k0

Scale factor at the pole. Default is 0.994 (UPS standard). Use k0 = 1 for true stereographic.

y

Numeric vector of y (northing) coordinates in meters (reverse only).

Details

The Polar Stereographic projection is a conformal azimuthal projection centered on either pole. It is ideal for mapping polar regions because:

• It preserves local angles and shapes

• Directions from the pole are true

• Scale distortion is minimal near the pole

UPS (Universal Polar Stereographic) The default k0 = 0.994 corresponds to the UPS system used by:

• NATO military mapping

• EPSG:32661 (UPS North) and EPSG:32761 (UPS South)

• High-latitude extensions of UTM

UPS is used for latitudes poleward of 84°N and 80°S.

Common scale factors:

• k0 = 0.994: UPS standard

• k0 = 1.0: True stereographic (scale = 1 at pole)

• k0 = 0.97276901289: NSIDC Sea Ice Polar Stereographic

See Also

utmups_fwd() for automatic UTM/UPS selection based on latitude.

Examples

# Antarctic stations
stations <- cbind(
  lon = c(166.67, 77.97, -43.53, 0),
  lat = c(-77.85, -67.60, -60.72, -90)
)
polarstereo_fwd(stations, northp = FALSE)

# Arctic points
arctic <- cbind(lon = c(0, 90, 180, -90), lat = c(85, 85, 85, 85))
polarstereo_fwd(arctic, northp = TRUE)

# True stereographic (k0 = 1)
polarstereo_fwd(stations, northp = FALSE, k0 = 1.0)

# NSIDC Sea Ice projection
polarstereo_fwd(stations, northp = FALSE, k0 = 0.97276901289)

# South Pole is at origin
sp <- polarstereo_fwd(c(0, -90), northp = FALSE)
sp$x  # 0
sp$y  # 0

# Round-trip conversion
fwd <- polarstereo_fwd(stations, northp = FALSE)
polarstereo_rev(fwd$x, fwd$y, northp = FALSE)