geodesy

Libraries of geodesy functions implemented in JavaScript – intended to serve as examples or starting-points for people wanting to develop geodesy applications (in JavaScript or other languages), though they can also be used as-is.

latlon.js

This is a library of geodesy functions for working with points and paths on (a spherical model of) the earth’s surface, including (orthodromic) great-circle geodesics and (loxodromic) rhumb lines. All calculations are done using spherical trigonometry.

The library includes the following functions:

• distanceTo destination point (using haversine formulation)
• bearingTo destination point
• finalBearingTo destination point
• midpointTo destination point
• destinationPoint following initial bearing for given distance
• intersection of two paths
• rhumbDistanceTo destination point
• rhumbBearingTo destination point
• rhumbDestinationPoint following given bearing for given distance
• rhumbMidpointTo destination point

Full details are available at www.movable-type.co.uk/scripts/latlong.html.

latlon-vincenty.js

Vincenty’s formulae for ‘direct and inverse solutions of geodesics on the ellipsoid’; these give distances and bearings on an ellipsoidal earth model accurate to within 0.5mm distance, 0.000015″ bearing.

The library includes the following wrapper functions:

• distanceTo destination point
• initialBearingTo destination point
• finalBearingTo destination point
• destinationPoint following initial bearing for given distance
• finalBearingOn initial bearing for given distance

The heaving lifting is done in two routines:

• direct (implementing the direct solution of geodesics on the ellipsoid)
• inverse (implementing the inverse solution of geodesics on the ellipsoid)

Full details are available at www.movable-type.co.uk/scripts/latlong-vincenty.html.

latlon-ellipsoid.js

Geodesy tools for an ellipsoidal earth model.

The LatLonE object incorporates not just latitude & longitude coordinates, but also the datum the lat/lon point is defined on.

LatLonE also holds ellipsoid parameters and Helmert transform parameters for translating between different datums (e.g. between OSGB36 & WGS-84).

The convertDatum function performs such translations between datums.

The library includes:

• ellipsoid parameters
• datum parameters (reference ellipsoid & Helmert transform parameters)
• convertDatum: convert lat/lon point to new datum
• toCartesian: convert lat/lon point to ECEF 3-d vector
• toLatLon: convert ECEF 3-d vector to lat/lon point

More information at www.movable-type.co.uk/scripts/latlong-convert-coords.html.

latlon-vectors.js

This is a library of functions for working with points and paths on (a spherical model of) the earth’s surface using a vector-based approach using ‘n-vectors’ (rather than the more common spherical trigonometry; a vector-based approach makes most calculations much simpler, and easier to follow, compared with trigonometric equivalents).

The library includes:

• distanceTo destination point
• bearingTo destination point
• midpointTo destination point
• destinationPoint following initial bearing for given distance
• intersection of two paths
• crossTrackDistanceTo great circle path
• enclosedBy polygon
• meanOf set of points

More information at www.movable-type.co.uk/scripts/latlong-vectors.html.

osgridref.js

Routines for converting between Ordnance Survey grid references and (OSGB-36) latitude/longitude coordinates, based on Ordnance Survey formulae.

The library includes:

• latLonToOsGrid: convert (OSGB) latitude/longitude to (numeric) OS grid reference
• osGridToLatLon: convert (numeric) OS grid reference to (OSGB) latitude/longitude
• parse standard format grid reference to numeric grid reference
• toString: convert numeric grid reference to standard format

More information at www.movable-type.co.uk/scripts/latlong-gridref.html.

utm.js, mgrs.js

Routines for converting between UTM (Universal Transverse Mercator) coordinates and latitude/longitude coordinates (WGS84 or any other ellipsoid datum), and between UTM and MGRS (Military Grid Reference System) grid references. Based on Karney 2011 ‘Transverse Mercator with an accuracy of a few nanometers’.

The libraries include:

• LatLonE.toUtm: convert (WGS84) latitude/longitude to UTM coordinate
• Utm.toLatLon: convert UTM coordinate to (WGS84) latitude/longitude
• Utm.toMgrs convert UTM coordinate to MGRS grid reference (including Norway and Svalbard exceptions)
• Mgrs.toUtm: convert MGRS grid reference to UTM coordinate

More information at www.movable-type.co.uk/scripts/latlong-utm-mgrs.html.

geo.js

Tools for converting between numeric degrees and degrees / minutes / seconds.

The library includes the following functions:

• parseDMS: parse string representing degrees/minutes/seconds into numeric degrees
• toLat: convert decimal degrees to latitude
• toLon: convert decimal degrees to longitude
• toBrng: convert decimal degrees to bearing

geohash.js

Geohash is now moved to its own repository, as this one is becoming bloated.

Documentation

Documentation for all these methods is available at www.movable-type.co.uk/scripts/js/geodesy/docs.