cffk/scratch

scratch repository

Octave/MATLAB implementation of GeographicLib

Contents:

• Introduction
• Installation
• Function summary
• Changes
• Other links

Introduction

This toolbox provides native MATLAB implementations of a subset of the C++ library, GeographicLib. Key components of this toolbox are

• Geodesics, direct, inverse, area calculations.
• Projections, transverse Mercator, polar stereographic, etc.
• Grid systems, UTM, UPS, MGRS.
• Geoid lookup, egm84, egm96, egm2008 geoids supported.
• Geometric transformations, geocentric, local cartesian.
• Great ellipse, direct, inverse, area calculations.

All the functions are vectorized and so offer speeds comparable to compiled C++ code when operating on arrays.

Some common features of these functions:

• Angles (latitude, longitude, azimuth, meridian convergence) are measured in degrees.
• Distances are measured in meters, areas in meters^2.
• Latitudes must lie in [-90, 90]. Latitudes outside this range are treated in NaNs
• The ellipsoid is specified as [a, e], where a = equatorial radius and e = eccentricity. The eccentricity can be pure imaginary to denote a prolate ellipsoid.
• Keep |e| < 0.2 (i.e., |f| <= 1/50) for full double precision accuracy.

There is some overlap between this toolbox and MATLAB's Mapping Toolbox. However, this toolbox offers:

• better accuracy;
• treatment of oblate and prolate ellipsoid;
• guaranteed convergence for geoddistance;
• calculation of area and differential properties of geodesics;
• ellipsoidal versions of the equidistant azimuthal and gnomonic projections.

Installation

The Octave/MATLAB packages are available on SourceForge and MATLAB Central.

Tha Octave package can be installed with the command

pkg install geographiclib-octave-M.N.tar.gz
pkg load geographiclib

The MATLAB toolbox can be installed with the command

matlab.addons.install geographiclib_toolbox-M.N.mltbx

Function summary

Click on the function name for the definition of the function.

Geodesics

• geoddistance - Distance between points on an ellipsoid
• geodreckon - Point at specified azimuth, range on an ellipsoid
• geodarea - Surface area of polygon on an ellipsoid

Projections

• tranmerc_fwd - Forward transverse Mercator projection
• tranmerc_inv - Inverse transverse Mercator projection
• polarst_fwd - Forward polar stereographic projection
• polarst_inv - Inverse polar stereographic projection
• eqdazim_fwd - Forward azimuthal equidistant projection
• eqdazim_inv - Inverse azimuthal equidistant projection
• cassini_fwd - Forward Cassini-Soldner projection
• cassini_inv - Inverse Cassini-Soldner projection
• gnomonic_fwd - Forward ellipsoidal gnomonic projection
• gnomonic_inv - Inverse ellipsoidal gnomonic projection

Grid systems

• utmups_fwd - Convert to UTM/UPS system
• utmups_inv - Convert from UTM/UPS system
• mgrs_fwd - Convert UTM/UPS coordinates to MGRS
• mgrs_inv - Convert MGRS to UTM/UPS coordinates

Geoid lookup

• geoid_height - Compute the height of the geoid above the ellipsoid
• geoid_load - Load a geoid model

Geometric transformations

• geocent_fwd - Conversion from geographic to geocentric coordinates
• geocent_inv - Conversion from geocentric to geographic coordinates
• loccart_fwd - Convert geographic to local cartesian coordinates
• loccart_inv - Convert local cartesian to geographic coordinates

Great ellipses

• gedistance - Great ellipse distance on an ellipsoid
• gereckon - Point along great ellipse at given azimuth and range

Utility

• defaultellipsoid - Return the WGS84 ellipsoid
• ecc2flat - Convert eccentricity to flattening
• flat2ecc - Convert flattening to eccentricity
• geographiclib_test - The test suite for the geographiclib package
• geographiclib_signtest - Another test suite

Documentation

• geoddoc - Geodesics on an ellipsoid of revolution
• projdoc - Projections for an ellipsoid
• gedoc - Great ellipses on an ellipsoid of revolution

Changes

See the change log.

Other links

• GeographicLib.
• Implementations in other languages.
• How to install the geoid datasets.
• C. F. F. Karney, Transverse Mercator with an accuracy of a few nanometers, J. Geodesy 85(8), 475–485 (2011), preprint.
• C. F. F. Karney, Algorithms for geodesics, J. Geodesy 87(1), 43–55 (2013).