SwiftyGeographicLib

Swift wrapper for Charles Karney's C++ library for geodesics. See Karney's GeographicLib project.

Description

Current Implementation

Geodesic

• Geodesic.direct
• Geodesic.arcDirect
• Geodesic.inverse

The shortest path between two points (p1 & p2) on the ellipsoid having locations specified by p1 at (lat1, lon1) and p2 at (lat2, lon2) is called the geodesic. Its length between p1 and p2 is s12 and the geodesic from p1 to p2 has forward azimuths az1 and az2 at the two end points.

Traditionally two geodesic problems are considered, direct and inverse.

The Direct Problem

Given lat1, lon1, s12, az1, determine lat2, lon2, and az2. This is solved by the function direct().

Example: Starting at New York JFK airport (lat=40.63972222, lon=-73.77888888), head on an initial bearing of 51.37288858° for a distance on 5,554,344m - compute the location of p2 and final forward azimuth on the WGS84 ellipsoid.

import SwiftyGeographicLib
let dirResult = direct(p1: (lat: 40.63972222, lon: -73.77888888), az1: 51.37287886, s12: 5554344.26)
let p2Lat = dirResult.lat2         // 51.477500002 - lat of London Heathrow (LHR) airport
let p2Lon = dirResult.lon2         // -0.461388897 - lon of London Heathrow (LHR) airport
let p2FwdAzimuth = dirResult.az2   // 107.97130748 - forward bering at LHR

The ArcDirect variant

Similar the Direct problem, but instead of specifying the distance s12 between the points, specify the central angle a12 between the points.

import SwiftyGeographicLib
let dirResult = arcDirect(p1: (lat: 40.6, lon: -73.8), az1: 51.19888284557982, a12: 49.94131021789904)
let p2Lat = dirResult.lat2         // 51.6 - lat of p2 (nr. London Heathrow (LHR) airport)
let p2Lon = dirResult.lon2         // -0.5 - lon of p2 (nr. London Heathrow (LHR) airport)
let p2FwdAzimuth = dirResult.az2   // 107.82177673551425 - forward bering at p2

The Inverse Problem

Given lat1, lon1, lat2, lon2, determine s12, az1, and az2. This is solved by the function inverse().

Example: Starting at New York JFK airport (lat=40.63972222, lon=-73.77888888) and ending at London Heathrow airport (lat=51.4775, lon=-0.46138888) - compute distance s12 and forward azimuths az1 and az2 on the WGS84 ellipsoid.

import SwiftyGeographicLib
let invResult = inverse(p1: (lat: 40.63972222, lon: -73.77888888), p2: (lat: 51.4775, lon: -0.46138888))
let dist = invResult.s12          // 5554344.26   - dist between JFK to LHR
let p1FwdAzimuth = invResult.az1  // 51.37287886  - forward bearing at JFK
let p2FwdAzimuth = invResult.az2  // 107.97130749 - forward bering at LHR

Gnomonic

• Gnomonic.forward
• Gnomonic.reverse

Gnomonic Forward

Forward projection from geographic to gnomonic.

import SwiftyGeographicLib
let origin = (lat: 48.0 + 50.0/60.0, lon: 2.0 + 20.0/60.0)  // Paris
let point  = (lat: 50.9, lon: 1.8)                          // Calais
let fwd = SwiftyGeographicLib.forward(origin: origin, point: point, ellipsoid: WGS84)
let x = fwd.x                 // x = -37543.66988338346
let y = fwd.y                 // y = 230103.21385030495

Gnomonic Reverse

Reverse projection from gnomonic to geographic.

import SwiftyGeographicLib
let origin = (lat: 48.0 + 50.0/60.0, lon: 2.0 + 20.0/60.0)  // Paris
let point  = (x: -38e3, y: 230e3) 
let rev = SwiftyGeographicLib.reverse(origin: origin, point: point, ellipsoid: WGS84)
let lat = rev.lat                 // lat = 50.89904
let lon = rev.lon                 // lon = 1.79353

Swift Package Management

dependencies: [
        .package(url: "https://github.com/firecrestHorizon/SwiftyGeographicLib.git", branch: "main"),
    ],

WGS as default ellipsoid and overriding WGS84

The package will use WGS84 as the default datum (semi-major axis, a = 6,378,137.0 m; flattening f = 1/298.257223563) Other ellipsoids can be used by overrding the default ellipsoid a & f values.

Example for ETRS89:

let ETRS89 = (a: 6378137.0, f: 1 / 298.257222101)
let dirResult = direct(p1: (lat: 51.21, lon: 3.456), az1: 23.344, s12: 10000, ellipsoid: ETRS89)