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!

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