# NAME

Geo::Coordinates::UTM - Perl extension for Latitiude Longitude conversions.

# SYNOPSIS

use Geo::Coordinates::UTM;

my (\$zone,\$easting,\$northing)=latlon_to_utm(\$ellipsoid,\$latitude,\$longitude);

my (\$latitude,\$longitude)=utm_to_latlon(\$ellipsoid,\$zone,\$easting,\$northing);

my (\$zone,\$easting,\$northing)=mgrs_to_utm(\$mgrs);

my (\$latitude,\$longitude)=mgrs_to_latlon(\$ellipsoid,\$mgrs);

my (\$mgrs)=utm_to_mgrs(\$zone,\$easting,\$northing);

my (\$mgrs)=latlon_to_mgrs(\$ellipsoid,\$latitude,\$longitude);

my @ellipsoids=ellipsoid_names;

my(\$name, \$r, \$sqecc) = ellipsoid_info 'WGS-84';

# DESCRIPTION

This module will translate latitude longitude coordinates to Universal Transverse Mercator(UTM) coordinates and vice versa.

## Mercator Projection

The Mercator projection was first invented to help mariners. They needed to be able to take a course and know the distance traveled, and draw a line on the map which showed the day's journey. In order to do this, Mercator invented a projection which preserved length, by projecting the earth's surface onto a cylinder, sharing the same axis as the earth itself. This caused all Latitude and Longitude lines to intersect at a 90 degree angle, thereby negating the problem that longitude lines get closer together at the poles.

## Transverse Mercator Projection

A Transverse Mercator projection takes the cylinder and turns it on its side. Now the cylinder's axis passes through the equator, and it can be rotated to line up with the area of interest. Many countries use Transverse Mercator for their grid systems.

## Universal Transverse Mercator

The Universal Transverse Mercator(UTM) system sets up a universal world wide system for mapping. The Transverse Mercator projection is used, with the cylinder in 60 positions. This creates 60 zones around the world. Positions are measured using Eastings and Northings, measured in meters, instead of Latitude and Longitude. Eastings start at 500,000 on the centre line of each zone. In the Northern Hemisphere, Northings are zero at the equator and increase northward. In the Southern Hemisphere, Northings start at 10 million at the equator, and decrease southward. You must know which hemisphere and zone you are in to interpret your location globally. Distortion of scale, distance, direction and area increase away from the central meridian.

UTM projection is used to define horizontal positions world-wide by dividing the surface of the Earth into 6 degree zones, each mapped by the Transverse Mercator projection with a central meridian in the center of the zone. UTM zone numbers designate 6 degree longitudinal strips extending from 80 degrees South latitude to 84 degrees North latitude. UTM zone characters designate 8 degree zones extending north and south from the equator. Eastings are measured from the central meridian (with a 500 km false easting to insure positive coordinates). Northings are measured from the equator (with a 10,000 km false northing for positions south of the equator).

UTM is applied separately to the Northern and Southern Hemisphere, thus within a single UTM zone, a single X / Y pair of values will occur in both the Northern and Southern Hemisphere. To eliminate this confusion, and to speed location of points, a UTM zone is sometimes subdivided into 20 zones of Latitude. These grids can be further subdivided into 100,000 meter grid squares with double-letter designations. This subdivision by Latitude and further division into grid squares is generally referred to as the Military Grid Reference System (MGRS). The unit of measurement of UTM is always meters and the zones are numbered from 1 to 60 eastward, beginning at the 180th meridian. The scale distortion in a north-south direction parallel to the central meridian (CM) is constant However, the scale distortion increases either direction away from the CM. To equalize the distortion of the map across the UTM zone, a scale factor of 0.9996 is applied to all distance measurements within the zone. The distortion at the zone boundary, 3 degrees away from the CM is approximately 1%.

## Datums and Ellipsoids

Unlike local surveys, which treat the Earth as a plane, the precise determination of the latitude and longitude of points over a broad area must take into account the actual shape of the Earth. To achieve the precision necessary for accurate location, the Earth cannot be assumed to be a sphere. Rather, the Earth's shape more closely approximates an ellipsoid (oblate spheroid): flattened at the poles and bulging at the Equator. Thus the Earth's shape, when cut through its polar axis, approximates an ellipse. A "Datum" is a standard representation of shape and offset for coordinates, which includes an ellipsoid and an origin. You must consider the Datum when working with geospatial data, since data with two different Datum will not line up. The difference can be as much as a kilometer!

# EXAMPLES

A description of the available ellipsoids and sample usage of the conversion routines follows

## Ellipsoids

The Ellipsoids available are as follows:

1 Airy
2 Australian National
3 Bessel 1841
4 Bessel 1841 (Nambia)
5 Clarke 1866
6 Clarke 1880
7 Everest 1830 (India)
8 Fischer 1960 (Mercury)
9 Fischer 1968
10 GRS 1967
11 GRS 1980
12 Helmert 1906
13 Hough
14 International
15 Krassovsky
16 Modified Airy
17 Modified Everest
18 Modified Fischer 1960
19 South American 1969
20 WGS 60
21 WGS 66
22 WGS-72
23 WGS-84
24 Everest 1830 (Malaysia)
25 Everest 1956 (India)
26 Everest 1964 (Malaysia and Singapore)
27 Everest 1969 (Malaysia)
28 Everest (Pakistan)
29 Indonesian 1974
30 Arc 1950
30 NAD 27
30 NAD 83

## ellipsoid_names

The ellipsoids can be accessed using ellipsoid_names. To store thes into an array you could use

``     my @names = ellipsoid_names;``

## ellipsoid_info

Ellipsoids may be called either by name, or number. To return the ellipsoid information, ( "official" name, equator radius and square eccentricity) you can use ellipsoid_info and specify a name. The specified name can be numeric (for compatibility reasons) or a more-or-less exact name. Any text between parentheses will be ignored.

``````     my(\$name, \$r, \$sqecc) = ellipsoid_info 'wgs84';
my(\$name, \$r, \$sqecc) = ellipsoid_info 'WGS 84';
my(\$name, \$r, \$sqecc) = ellipsoid_info 'WGS-84';
my(\$name, \$r, \$sqecc) = ellipsoid_info 'WGS-84 (new specs)';
my(\$name, \$r, \$sqecc) = ellipsoid_info 23;``````

## latlon_to_utm

Latitude values in the southern hemisphere should be supplied as negative values (e.g. 30 deg South will be -30). Similarly Longitude values West of the meridian should also be supplied as negative values. Both latitude and longitude should not be entered as deg,min,sec but as their decimal equivalent, e.g. 30 deg 12 min 22.432 sec should be entered as 30.2062311

The ellipsoid value should correspond to one of the numbers above, e.g. to use WGS-84, the ellipsoid value should be 23

For latitude 57deg 49min 59.000sec North longitude 02deg 47min 20.226sec West

using Clarke 1866 (Ellipsoid 5)

``     (\$zone,\$east,\$north)=latlon_to_utm('clarke 1866',57.803055556,-2.788951667)``

returns

``````     \$zone  = 30V
\$east  = 512543.777159849
\$north = 6406592.20049111``````

## latlon_to_utm_force_zone

On occasions, it is necessary to map a pair of (latitude, longitude) coordinates to a predefined zone. This function allows to select the projection zone as follows:

``````     (\$zone, \$east, \$north)=latlon_to_utm('international', \$zone_number,
\$latitude, \$longitude)``````

For instance, Spain territory goes over zones 29, 30 and 31 but sometimes it is convenient to use the projection corresponding to zone 30 for all the country.

Santiago de Compostela is at 42deg 52min 57.06sec North, 8deg 32min 28.70sec West

``    (\$zone, \$east, \$norh)=latlon_to_utm('international',  42.882517, -8.541306)``

returns

``````     \$zone = 29T
\$east = 537460.331
\$north = 4747955.991``````

but forcing the conversion to zone 30:

``````    (\$zone, \$east, \$norh)=latlon_to_utm_force_zone('international',
30, 42.882517, -8.541306)``````

returns

``````    \$zone = 30T
\$east = 47404.442
\$north = 4762771.704``````

## utm_to_latlon

Reversing the above example,

``     (\$latitude,\$longitude)=utm_to_latlon(5,'30V',512543.777159849,6406592.20049111)``

returns

``````     \$latitude  = 57.8030555601332
\$longitude = -2.7889516669741

which equates to

latitude  57deg 49min 59.000sec North
longitude 02deg 47min 20.226sec West``````

## latlon_to_mgrs

Latitude values in the southern hemisphere should be supplied as negative values (e.g. 30 deg South will be -30). Similarly Longitude values West of the meridian should also be supplied as negative values. Both latitude and longitude should not be entered as deg,min,sec but as their decimal equivalent, e.g. 30 deg 12 min 22.432 sec should be entered as 30.2062311

The ellipsoid value should correspond to one of the numbers above, e.g. to use WGS-84, the ellipsoid value should be 23

For latitude 57deg 49min 59.000sec North longitude 02deg 47min 20.226sec West

using WGS84 (Ellipsoid 23)

``     (\$mgrs)=latlon_to_mgrs(23,57.8030590197684,-2.788956799)``

returns

``     \$mgrs  = 30VWK1254306804``

## mgrs_to_latlon

Reversing the above example,

``     (\$latitude,\$longitude)=mgrs_to_latlon(23,'30VWK1254306804')``

returns

``````     \$latitude  = 57.8030590197684
\$longitude = -2.788956799645``````

## mgrs_to_utm

``````    Similarly it is possible to convert MGRS directly to UTM

(\$zone,\$easting,\$northing)=mgrs_to_utm('30VWK1254306804')

returns

\$zone = 30V
\$easting = 512543
\$northing = 6406804``````

## utm_to_mgrs

``````    and the inverse converting from UTM yo MGRS is done as follows

(\$mgrs)=utm_to_mgrs('30V',512543,6406804);

returns
\$mgrs = 30VWK1254306804``````

# AUTHOR

Graham Crookham, grahamc@cpan.org

# THANKS

Thanks go to the following:

Felipe Mendonca Pimenta for helping out with the Southern hemisphere testing.

Michael Slater for discovering the Escape \Q bug.

Mark Overmeer for the ellipsoid_info routines and code review.

Lok Yan for the >72deg. N bug.

Salvador Fandino for the forced zone UTM and additional tests

Matthias Lendholt for modifications to MGRS calculations

Peder Stray for the short MGRS patch

Copyright (c) 2000,2002,2004,2007,2010,2013 by Graham Crookham. All rights reserved.

This package is free software; you can redistribute it and/or modify it under the same terms as Perl itself.