Geodetic and Geocentric

There are six functions that can help to convert between geodetic and geocentric representations. Notice that currently all Geodetic representations are based on the WGS84 reference ellipsoid.

ECEF to Geocentric

We can convert a position vector represented in an Earth-Centered, Earth-Fixed frame (ECEF) r_e to the Geocentric latitude, longitude, and distance from Earth's center using the following function:

ecef_to_geocentric(r_e::AbstractVector{T}) -> NTuple{3, float(T)}

which returns a tuple with:

• The Geocentric latitude [rad];
• The longitude [rad]; and
• The distance from the Earth's center [m].

julia> ecef_to_geocentric([7000, 0, 7000])(0.7853981633974483, 0.0, 9899.494936611665)
julia> ecef_to_geocentric([0, 0, 7000])(1.5707963267948966, 0.0, 7000.0)
julia> ecef_to_geocentric([7000, 0, 0])(0.0, 0.0, 7000.0)

Geocentric to ECEF

We can convert a Geocentric coordinate (latitude lat [rad], longitude lon [rad], and distance from Earth's center r [m]) to a vector represented in the Earth-Centered, Earth-Fixed (ECEF) frame using the following function:

geocentric_to_ecef(lat::Number, lon::Number, r::Number) -> SVector{3}

which returns a 3x1 vector.

julia> geocentric_to_ecef(0, 0, 7000e3)3-element StaticArraysCore.SVector{3, Float64} with indices SOneTo(3):
 7.0e6
 0.0
 0.0
julia> geocentric_to_ecef(pi / 2, 0, 7000e3)3-element StaticArraysCore.SVector{3, Float64} with indices SOneTo(3):
 4.286263797015736e-10
 0.0
 7.0e6
julia> geocentric_to_ecef(pi / 4, 0, 7000e3)3-element StaticArraysCore.SVector{3, Float64} with indices SOneTo(3):
 4.949747468305833e6
 0.0
 4.949747468305832e6

ECEF to Geodetic

We can convert a position vector represented in an Earth-Centered, Earth-Fixed frame (ECEF) r_e to the Geodetic latitude, longitude, and altitude using the following function:

ecef_to_geodetic(r_e::AbstractVector{T}) -> NTuple{3, float(T)}

which returns a tuple with:

• The Geodetic latitude [rad];
• The longitude [rad]; and
• The altitude above the reference ellipsoid [m].

julia> ecef_to_geodetic([6378137.0, 0, 0])(0.0, 0.0, 0.0)
julia> ecef_to_geodetic([0, 6378137.0, 0])(0.0, 1.5707963267948966, 0.0)
julia> ecef_to_geodetic([0, 0, 6378137.0])(1.5707963267948966, 0.0, 21384.685754820704)

Geodetic to ECEF

The Geodetic latitude lat [rad], longitude lon [rad], and altitude h [m] can be converted to a vector represented in an ECEF reference frame by the following function:

geodetic_to_ecef(lat::Number, lon::Number, h::Number) -> SVector{3}

which returns a 3x1 vector.

julia> geodetic_to_ecef(0, 0, 0)3-element StaticArraysCore.SVector{3, Float64} with indices SOneTo(3):
 6.378137e6
 0.0
 0.0
julia> geodetic_to_ecef(deg2rad(-22), deg2rad(-45), 0)3-element StaticArraysCore.SVector{3, Float64} with indices SOneTo(3):
  4.1835869067109847e6
 -4.1835869067109837e6
 -2.3744128953028163e6

Geocentric to Geodetic

Given a Geocentric latitude ϕ_gc [rad] and distance from the center of Earth r [m], one can obtain the Geodetic coordinates (Geodetic latitude and altitude above the reference ellipsoid - WGS84) using the following function:

geocentric_to_geodetic(ϕ_gc::Number, r::Number) -> Number, Number

in which returns a tuple with two values:

• The Geodetic latitude [rad]; and
• The altitude above the reference ellipsoid (WGS-84) [m].

julia> geocentric_to_geodetic(deg2rad(-22), 6378137.0)(-0.3863099329112617, 3013.9291869809385)
julia> geocentric_to_geodetic(0, 6378137.0)(0.0, 0.0)

Geodetic to Geocentric

Given a Geodetic latitude ϕ_gd [rad] and altitude above the reference ellipsoid h [m], one can obtain the Geocentric coordinates (Geocentric latitude and position from the center of Earth) using the following function:

geodetic_to_geocentric(ϕ_gd::Number, h::Number) -> Number, Number

which returns a tuple with two values:

• The Geocentric latitude [rad]; and
• The distance from the center of Earth [m].

julia> geodetic_to_geocentric(deg2rad(-22), 0)(-0.38164509973650357, 6.375157677217675e6)
julia> geodetic_to_geocentric(0, 0)(0.0, 6.378137e6)