Access WGS84 ellipsoid parameters and perform ellipsoid-related calculations including auxiliary latitudes, radii of curvature, and meridian distances.
ellipsoid_params()
ellipsoid_circle(lat)
ellipsoid_latitudes(lat)
ellipsoid_latitudes_inv(lat, type)
ellipsoid_curvature(lat)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)
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
# WGS84 parameters
ellipsoid_params()
#> $a
#> [1] 6378137
#>
#> $f
#> [1] 0.003352811
#>
#> $b
#> [1] 6356752
#>
#> $e2
#> [1] 0.00669438
#>
#> $ep2
#> [1] 0.006739497
#>
#> $n
#> [1] 0.00167922
#>
#> $area
#> [1] 5.100656e+14
#>
#> $volume
#> [1] 1.083207e+21
#>
# Radius at different latitudes
ellipsoid_circle(c(0, 30, 45, 60, 90))
#> lat radius quarter_meridian meridian_distance
#> 1 0 6378137 10001966 0
#> 2 30 5528257 10001966 3320113
#> 3 45 4517591 10001966 4984944
#> 4 60 3197105 10001966 6654073
#> 5 90 0 10001966 10001966
# Compare auxiliary latitudes
ellipsoid_latitudes(c(0, 30, 45, 60, 90))
#> lat parametric geocentric rectifying authalic conformal isometric
#> 1 0 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
#> 2 30 29.91675 29.83364 29.87515 29.88900 29.83368 31.28104
#> 3 45 44.90379 44.80758 44.85568 44.87170 44.80768 50.22747
#> 4 60 59.91661 59.83308 59.87489 59.88879 59.83322 75.12340
#> 5 90 90.00000 90.00000 90.00000 90.00000 90.00000 Inf
# Radii of curvature
ellipsoid_curvature(c(0, 45, 90))
#> lat meridional transverse
#> 1 0 6335439 6378137
#> 2 45 6367382 6388838
#> 3 90 6399594 6399594