Geo::Ellipsoid - longitude and latitude calculations using an ellipsoid model
my $geo = Geo::Ellipsoid->new(ellipsoid => 'NAD27',
angle_unit => 'degrees');
my @origin = ( 37.619002, -122.374843 ); # SFO
my @dest = ( 33.942536, -118.408074 ); # LAX
# range and bearing from one location to another
my ( $range, $bearing ) = $geo->to( @origin, @dest );
$range = $geo->range( @origin, @dest );
$bearing = $geo->bearing( @origin, @dest );
# destination given start point, range, and bearing
my ( $lat, $lon ) = $geo->at( @origin, 2000, 45.0 );
# approximate displacement given one location and a destination
my ( $x, $y ) = $geo->displacement( @origin, @dest );
# approximate location given one location and displacement
my @pos = $geo->location( $lat, $lon, $x, $y );
Accurate latitude/longitude calculations.
Geo::Ellipsoid performs geometrical calculations on the surface of an ellipsoid. An ellipsoid is a three-dimension object formed from the rotation of an ellipse about one of its axes. The approximate shape of the earth is an ellipsoid, so Geo::Ellipsoid can accurately calculate distance and bearing between two widely-separated locations on the earth's surface.
The shape of an ellipsoid is defined by the lengths of its semi-major and semi-minor axes. The shape may also be specified by the flattening ratio f as:
f = ( semi-major - semi-minor ) / semi-major
which, since f is a small number, is normally given as the reciprocal of the flattening 1/f.
The shape of the earth has been surveyed and estimated differently at different times over the years. The two most common sets of values used to describe the size and shape of the earth in the United States are 'NAD27', dating from 1927, and 'WGS84', from 1984. United States Geological Survey topographical maps, for example, use one or the other of these values, and commonly-available Global Positioning System (GPS) units can be set to use one or the other. See "DEFINED ELLIPSOIDS" below for the ellipsoid survey values that may be selected for use by Geo::Ellipsoid.
The new() constructor may be called with a hash list to set the value of the ellipsoid to be used, the value of the units to be used for angles and distances, and whether or not the output range of longitudes and bearing angles should be symmetric around zero or always greater than zero. The initial default constructor is equivalent to the following:
my $geo = Geo::Ellipsoid->new(
ellipsoid => 'WGS84',
angle_unit => 'radians' ,
distance_unit => 'meter',
longitude_symmetric => 0,
bearing_symmetric => 0,
The constructor arguments may be of any case and, with the exception of the ellipsoid value, abbreviated to their first three characters. Thus, ( UNI => 'DEG', DIS => 'FEE', Lon => 1, ell => 'NAD27', bEA => 0 ) is valid.
Returns a list with the names all known ellipsoids.
Set the angle unit used by the Geo::Ellipsoid object. The unit may also be set in the constructor of the object. The allowable values are 'degrees' or 'radians'. The default is 'radians'. The unit value is not case sensitive and may be abbreviated to 3 letters. The unit of angle apply to both input and output latitude, longitude, and bearing values.
Set the distance unit used by the Geo::Ellipsoid object. The unit of distance may also be set in the constructor of the object. The recognized values are 'meter', 'kilometer', 'mile', 'nm' (nautical mile), or 'foot'. The default is 'meter'. The value is not case sensitive and may be abbreviated to 3 letters.
For any other unit of distance not recognized by this method, pass a numerical argument representing the length of the distance unit in meters. For example, to use units of furlongs, call
The distance conversion factors used by this module are as follows:
Unit Units per meter
Set the ellipsoid to be used by the Geo::Ellipsoid object. See "DEFINED ELLIPSOIDS" below for the allowable values. The value may also be set by the constructor. The default value is 'WGS84'.
Sets the ellipsoid parameters to the specified semi-major axis (given in meters) and reciprocal flattening. A zero value for the reciprocal flattening will result in a sphere for the ellipsoid, and a warning message will be issued.
$geo->set_custom_ellipsoid( 'sphere', 6378137, 0 );
If called with no argument or a true argument, sets the range of output values for longitude to be symmetric around zero, i.e., in the range [-pi,+pi) radians, [-180,180) degrees etc. depending on the angle unit.
If called with a false or undefined argument, sets the output angle range to be non-negative, i.e., [0,2*pi) radians, [0, 360) degrees etc. depending on the angle unit.
If called with no argument or a true argument, sets the range of output values for bearing to be symmetric around zero, i.e., in the range [-pi,+pi) radians, [-180,180) degrees etc. depending on the angle unit.
If called with a false or undefined argument, sets the output angle range to be non-negative, i.e., [0,2*pi) radians, [0,360) degrees etc. depending on the angle unit.
Sets the defaults for the new() constructor method. Call with key, value pairs similar to new.
ellipsoid => 'GRS80',
angle_unit => 'degrees',
distance_unit => 'kilometer',
longitude_symmetric => 1,
bearing_symmetric => 0
Keys and string values (except for the ellipsoid identifier) may be shortened to their first three letters and are case-insensitive:
uni => 'deg',
ell => 'GRS80',
dis => 'kil',
lon => 1,
bea => 0
Returns the name of the ellipsoid.
Returns the equatorial radius in meters.
Returns the polar radius in meters.
Returns the geocentric radius in meters, given a geocentric latitude. The geocentric latitude is the angle between the equatorial plane and the radius from centre to the point on the surface.
Returns the flattening.
Returns the eccentricity.
Returns true if the longitude is symmetric around zero, and false otherwise.
Returns true if the bearing is symmetric around zero, and false otherwise.
Returns the angle unit, i.e., the unit for latitude, longitude, and bearing.
Returns the distance unit.
Returns a list consisting of the distance unit per angle of latitude and longitude (degrees or radians) at the specified latitude. These values may be used for fast approximations of distance calculations in the vicinity of some location.
( $lat_scale, $lon_scale ) = $geo->scales($lat0);
$x = $lon_scale * ($lon - $lon0);
$y = $lat_scale * ($lat - $lat0);
Returns the range in distance units between two specified locations given as latitude, longitude pairs.
my $dist = $geo->range( $lat1, $lon1, $lat2, $lon2 );
my $dist = $geo->range( @origin, @destination );
Returns the bearing in degrees or radians from the first location to the second. Zero bearing is true north.
my $bearing = $geo->bearing( $lat1, $lon1, $lat2, $lon2 );
Returns the list (latitude,longitude) in degrees or radians that is a specified range and bearing from a given location.
my( $lat2, $lon2 ) = $geo->at( $lat1, $lon1, $range, $bearing );
In list context, returns (range, bearing) between two specified locations. In scalar context, returns just the range.
my( $dist, $theta ) = $geo->to( $lat1, $lon1, $lat2, $lon2 );
my $dist = $geo->to( $lat1, $lon1, $lat2, $lon2 );
Returns the (x,y) displacement in distance units between the two specified locations.
my( $x, $y ) = $geo->displacement( $lat1, $lon1, $lat2, $lon2 );
NOTE: The x and y displacements are only approximations and only valid between two locations that are fairly near to each other. Beyond 10 kilometers or more, the concept of X and Y on a curved surface loses its meaning.
Returns the list (latitude,longitude) of a location at a given (x,y) displacement from a given location.
my @loc = $geo->location( $lat, $lon, $x, $y );
The following ellipsoids are defined in Geo::Ellipsoid, with the semi-major axis in meters and the reciprocal flattening as shown. The default ellipsoid is WGS84.
Ellipsoid Semi-Major Axis (m.) 1/Flattening
--------- ------------------- ---------------
AIRY 6377563.396 299.3249646
AIRY-MODIFIED 6377340.189 299.3249646
AUSTRALIAN 6378160.0 298.25
BESSEL-1841 6377397.155 299.1528128
CLARKE-1880 6378249.145 293.465
EVEREST-1830 6377276.345 290.8017
EVEREST-MODIFIED 6377304.063 290.8017
FISHER-1960 6378166.0 298.3
FISHER-1968 6378150.0 298.3
GRS80 6378137.0 298.25722210088
HOUGH-1956 6378270.0 297.0
HAYFORD 6378388.0 297.0
IAU76 6378140.0 298.257
KRASSOVSKY-1938 6378245.0 298.3
NAD27 6378206.4 294.9786982138
NWL-9D 6378145.0 298.25
SOUTHAMERICAN-1969 6378160.0 298.25
SOVIET-1985 6378136.0 298.257
WGS72 6378135.0 298.26
WGS84 6378137.0 298.257223563
The methods should not be used on points which are too near the poles (above or below 89 degrees), and should not be used on points which are antipodal, i.e., exactly on opposite sides of the ellipsoid. The methods will not return valid results in these cases.
The conversion algorithms used here are Perl translations of Fortran routines written by LCDR L. Pfeifer NGS Rockville MD that implement T. Vincenty's Modified Rainsford's method with Helmert's elliptical terms as published in "Direct and Inverse Solutions of Ellipsoid on the Ellipsoid with Application of Nested Equations", T. Vincenty, Survey Review, April 1975.
The Fortran source code files inverse.for and forward.for may be obtained from
Peter John Acklam, <firstname.lastname@example.org> (current maintainer)
Jim Gibson, <Jim@Gibson.org> (original author)
See LIMITATIONS, above.
There are currently no known bugs.
Please report any bugs or feature requests via https://github.com/pjacklam/p5-Geo-Ellipsoid/issues.
Old bug reports and feature requests can be found at http://rt.cpan.org/NoAuth/Bugs.html?Dist=Geo-Ellipsoid.
You can find documentation for this module with the perldoc command.
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Copyright 2016-2021 Peter John Acklam, current maintainer.
Copyright 2005-2008 Jim Gibson, all rights reserved.
This program is free software; you can redistribute it and/or modify it under the same terms as Perl itself.
To install Geo::Ellipsoid, copy and paste the appropriate command in to your terminal.
perl -MCPAN -e shell
For more information on module installation, please visit the detailed CPAN module installation guide.