geographiclib (version 0.4.0)

ellipsoid_params: WGS84 Ellipsoid parameters and calculations

Description

Access WGS84 ellipsoid parameters and perform ellipsoid-related calculations including auxiliary latitudes, radii of curvature, and meridian distances.

Usage

ellipsoid_params()
ellipsoid_circle(lat)
ellipsoid_latitudes(lat)
ellipsoid_latitudes_inv(lat, type)
ellipsoid_curvature(lat)

Value

• ellipsoid_params(): Named list with WGS84 parameters:

  • a: Equatorial radius (semi-major axis) in meters

  • f: Flattening

  • b: Polar radius (semi-minor axis) in meters

  • e2: First eccentricity squared

  • ep2: Second eccentricity squared

  • n: Third flattening

  • area: Surface area in square meters

  • volume: Volume in cubic meters

• ellipsoid_circle(): Data frame with columns:

  • lat: Input latitude

  • radius: Radius of the circle of latitude in meters

  • quarter_meridian: Distance from equator to pole along a meridian

  • meridian_distance: Distance from equator to the given latitude

• ellipsoid_latitudes(): Data frame with auxiliary latitudes:

  • lat: Input geographic latitude

  • parametric: Parametric (reduced) latitude

  • geocentric: Geocentric latitude

  • rectifying: Rectifying latitude

  • authalic: Authalic latitude

  • conformal: Conformal latitude

  • isometric: Isometric latitude

• ellipsoid_latitudes_inv(): Data frame with:

  • input: Input auxiliary latitude

  • geographic: Corresponding geographic latitude

• ellipsoid_curvature(): Data frame with radii of curvature:

  • lat: Input latitude

  • meridional: Meridional radius of curvature (M)

  • transverse: Transverse radius of curvature (N)

Arguments

lat

Numeric vector of geographic (geodetic) latitudes in decimal degrees.

type

Character string specifying the type of auxiliary latitude for inverse conversion. One of: "parametric", "geocentric", "rectifying", "authalic", "conformal", "isometric".

Details

The WGS84 ellipsoid is the reference surface used by GPS and most modern mapping systems. It is defined by:

• Equatorial radius: 6,378,137 m

• Flattening: 1/298.257223563

Auxiliary latitudes are different ways of measuring latitude that are useful in various map projections:

• Parametric: Used in ellipsoid parameterization

• Geocentric: Angle from center of ellipsoid

• Rectifying: Preserves distances along meridians

• Authalic: Preserves areas

• Conformal: Preserves angles/shapes

• Isometric: Used in Mercator projection

Examples

# WGS84 parameters
ellipsoid_params()

# Radius at different latitudes
ellipsoid_circle(c(0, 30, 45, 60, 90))

# Compare auxiliary latitudes
ellipsoid_latitudes(c(0, 30, 45, 60, 90))

# Radii of curvature
ellipsoid_curvature(c(0, 45, 90))