Coordinate conversion with the GaussKrüger Projection
Overview
CoordinateConverterGK.jl is a Julia package for conversion between the Cartesian coordinates and the geographic coordinates for a point with the GaussKrüger Projection. The formulae are based on documents and publications of the Geospatial Information Authority of Japan (see References).
Usage
General use
Given a central meridian λ₀
and latitude of origin φ₀
(in degrees), Cartesian coordinates can be converted with the following code:
using CoordinateConverterGK
λ, φ = xy2lonlat(λ₀, φ₀, easting, northing)
where λ
and φ
are the converted longitude and latitude, easting
and northing
are the eastward and northward distances (in meters) from the origin, respectively.
A function yx2latlon
is available in the same manner:
φ, λ = yx2latlon(φ₀, λ₀, northing, easting)
Similarly, functions lonlat2xy
and latlon2yx
can convert geographic coordinates to Cartesian coordinates for a point.
x, y = lonlat2xy(λ₀, φ₀, λ, φ)
Japan Plane Rectangular Coordinate System
When the Japan Plane Rectangular Coordinate System is adopted,
functions such as xy2lonlat_ja
and lonlat2xy_ja
can omit the coordinates of origin λ₀
, φ₀
.
These functions require the zone number of interest (1 to 19) instead.
λ, φ = xy2lonlat_ja(9, easting, northing) # in case of zone IX
Examples
# ANSWER: lat = 36.10404755, lon = 140.08539843
julia> yx2latlon(36.0, 139.83333333, 11573.375, 22694.980)
(36.104047552508895, 140.08539842726532)
# ANSWER: y = 11543.6883, x = 22916.2436
julia> latlon2yx(36.0, 139.0+5.0/6.0, 36.103774791666666, 140.08785504166664)
(11543.688321484718, 22916.24355431881)
References

Kawase, K. (2013) Concise Derivation of Extensive Coordinate Conversion Formulae in the GaussKrüger Projection, Bulletin of the Geospatial Information Authority of Japan, 60, pp.1–6

Kawase, K. (2011) A More Concise Method of Calculation for the Coordinate Conversion between Geographic and Plane Rectangular Coordinates on the GaussKrüger Projection (in Japanese), 国土地理院時報, 121, pp.109–124.

https://vldb.gsi.go.jp/sokuchi/surveycalc/surveycalc/algorithm/bl2xy/bl2xy.htm

https://vldb.gsi.go.jp/sokuchi/surveycalc/surveycalc/algorithm/xy2bl/xy2bl.htm