Ubuntu Manpage: Geo::Coordinates::OSGB - Convert coordinates between Lat/Lon and the British National Grid

Provided by: libgeo-coordinates-osgb-perl_2.06-1_all

NAME

       Geo::Coordinates::OSGB - Convert coordinates between Lat/Lon and the British National Grid

       An implementation of co-ordinate conversion for England, Wales, and Scotland based on
       formulae published by the Ordnance Survey of Great Britain.

       These modules will convert accurately between an OSGB national grid reference and lat/lon
       coordinates based on the OSGB geoid model.  (For an explanation of what a geoid model is
       and why you should care, read the Theory section below.) The OSGB geoid model fits
       mainland Britain very well, but is rather different from the international WGS84 model
       that has rapidly become the de facto universal standard model thanks to the popularity of
       GPS devices and maps on the Internet.  So, if you are trying to translate from an OSGB
       grid reference to lat/lon coordinates that can be used in Google Earth, Wikipedia, or some
       other Internet based tool, you will need to do two transformations: first translate your
       grid ref into OSGB lat/lon; then nudge the result into WGS84.  Routines are provided to do
       both of these operations, but they are only approximate.  The inaccuracy of the
       approximation varies according to where you are in the country but may be as much as
       several metres in some areas.

       To get more accurate results you need to combine this module with its companion
       Geo::Coordinates::OSTN02 which implements the transformation that now defines the
       relationship between GPS survey data based on WGS84 and the British National Grid.  Using
       this module you should be able to get results that are accurate to within a few
       centimetres, but it is slightly slower and requires more memory to run.

       Note that the OSGB (and therefore this module) does not cover the whole of the British
       Isles, nor even the whole of the UK, in particular it covers neither the Channel Islands
       nor Northern Ireland.  The coverage that is included is essentially the same as the
       coverage provided by the OSGB "Landranger" 1:50000 series maps.

VERSION

       Examine $Geo::Coordinates::OSGB::VERSION for details.

SYNOPSIS

         use Geo::Coordinates::OSGB qw(ll_to_grid grid_to_ll);

         # Basic conversion routines
         ($easting,$northing) = ll_to_grid($lat,$lon);
         ($lat,$lon) = grid_to_ll($easting,$northing);

DESCRIPTION

       These modules provide a collection of routines to convert between coordinates expressed as
       latitude & longtitude and map grid references, using the formulae given in the British
       Ordnance Survey's excellent information leaflet, referenced below in the Theory section.
       There are some key concepts explained in that section that you need to know in order to
       use these modules successfully, so you are recommended to at least skim through it now.

       The module is implemented purely in Perl, and should run on any Perl platform.

       In this description `OS' means `the Ordnance Survey of Great Britain': the British
       government agency that produces the standard maps of England, Wales, and Scotland.  Any
       mention of `sheets' or `maps' refers to one or more of the 204 sheets in the 1:50,000
       scale `Landranger' series of OS maps.

       This code is fine tuned to the British national grid system.  You could use it elsewhere
       but you would need to adapt it.  Some starting points for doing this are explained in the
       Theory section below.

SUBROUTINES/METHODS

The following functions can be exported from the "Geo::Coordinates::OSGB" module:

grid_to_ll ll_to_grid

shift_ll_into_WGS84 shift_ll_from_WGS84

parse_grid
parse_trad_grid format_grid_trad
parse_GPS_grid format_grid_GPS
parse_landranger_grid format_grid_landranger

parse_ISO_ll format_ll_trad
format_ll_ISO

None of these is exported by default, so pick the ones you want or use an ":all" tag to
import them all at once.

use Geo::Coordinates::OSGB ':all';

ll_to_grid(lat,lon)
When called in a void context, or with no arguments "ll_to_grid" does nothing.

When called in a list context, "ll_to_grid" returns two numbers that represent the
easting and the northing corresponding to the latitude and longitude supplied.

The parameters can be supplied as real numbers representing decimal degrees, like this

my ($e,$n) = ll_to_grid(51.5, 2.1);

Following the normal convention, positive numbers mean North or East, negative South
or West. If you have data with degrees, minutes and seconds, you can convert them to
decimals like this:

my ($e,$n) = ll_to_grid(51+25/60, 0-5/60-2/3600);

Or you can use a single string in ISO 6709 form, like this:

my ($e,$n) = ll_to_grid('+5130-00005/');

To learn exactly what is matched by this last option, read the source of the module
and look for the definition of $ISO_LL_PATTERN. Note that the neither the "+" or "-"
signs at the beginning and in the middle, nor the trailing "/" may be omitted.

If you have trouble remembering the order of the arguments, or the returned values,
note that latitude comes before longitude in the alphabet too, as easting comes before
northing.

The easting and northing will be returned as a whole number of metres from the point
of origin of the British Grid (which is a point a little way to the south-west of the
Scilly Isles).

If you want the result presented in a more traditional grid reference format you
should pass the results to one of the grid formatting routines, which are described
below. Like this.

$gridref = format_grid_trad(ll_to_grid(51.5,-0.0833));
$gridref = format_grid_GPS(ll_to_grid(51.5,-0.0833));
$gridref = format_grid_landranger(ll_to_grid(51.5,-0.0833));

However if you call "ll_to_grid" in a scalar context, it will automatically call
"format_grid_trad" for you.

It is not needed for any normal work, but "ll_to_grid()" also takes an optional
argument that sets the ellipsoid model to use. This normally defaults to `OSGB36',
the name of the normal model for working with British maps. If you are working with
the highly accurate OSTN02 conversions supplied in the companion module in this
distribution, then you will need to produce pseudo-grid references as input to those
routines. For these purposes you should call "ll_to_grid()" like this:

my $pseudo_gridref = ll_to_grid(51.2, -0.4, 'WGS84');

and then transform this to a real grid reference using "ETRS89_to_OSGB36()" from the
companion module. This is explained in more detail below.

format_grid_trad(e,n)
Formats an (easting, northing) pair into traditional `full national grid reference'
with two letters and two sets of three numbers, like this `TQ 102 606'. If you want
to remove the spaces, just apply "s/\s//g" to it.

$gridref = format_grid_trad(533000, 180000); # TQ 330 800
$gridref =~ s/\s//g; # TQ330800

If you want the individual components call it in a list context.

($sq, $e, $n) = format_grid_trad(533000, 180000); # (TQ,330,800)

Note the easting and northing are truncated to hectometers (as the OS system demands),
so the grid reference refers to the lower left corner of the relevant 100m square.

format_grid_GPS(e,n)
Users who have bought a GPS receiver may initially have been puzzled by the unfamiliar
format used to present coordinates in the British national grid format. On my Garmin
Legend C it shows this sort of thing in the display.

TQ 23918
bng 00972

and in the track logs the references look like this "TQ 23918 00972".

These are just the same as the references described on the OS sheets, except that the
units are metres rather than hectometres, so you get five digits in each of the
easting and northings instead of three. So in a scalar context "format_grid_GPS()"
returns a string like this:

$gridref = format_grid_GPS(533000, 180000); # TQ 33000 80000

If you call it in a list context, you will get a list of square, easting, and
northing, with the easting and northing as metres within the grid square.

($sq, $e, $n) = format_grid_GPS(533000, 180000); # (TQ,33000,80000)

Note that, at least until WAAS is working in Europe, the results from your GPS are
unlikely to be more accurate than plus or minus 5m even with perfect reception. Most
GPS devices can display the accuracy of the current fix you are getting, but you
should be aware that all normal consumer-level GPS devices can only ever produce an
approximation of an OS grid reference, no matter what level of accuracy they may
display. The reasons for this are discussed below in the section on Theory.

format_grid_landranger(e,n)
This routine does the same as "format_grid_trad", but it appends the number of the
relevant OS Landranger 1:50,000 scale map to the traditional grid reference. Note
that there may be several or no sheets returned. This is because many (most) of the
Landranger sheets overlap, and many other valid grid references are not on any of the
sheets (because they are in the sea or a remote island. This module does not yet cope
with the detached insets on some sheets.

In a list context you will get back a list like this: (square, easting, northing,
sheet) or (square, easting, northing, sheet1, sheet2) etc. There are a few places
where three sheets overlap, and one corner of Herefordshire which appears on four maps
(sheets 137, 138, 148, and 149). If the GR is not on any sheet, then the list of
sheets will be empty.

In a scalar context you will get back the same information in a helpful string form
like this "NN 241 738 on OS Sheet 44". Note that the easting and northing will have
been truncated to the normal hectometre three digit form. The idea is that you'll use
this form for people who might actually want to look up the grid reference on the
given map sheet, and the traditional GR form is quite enough accuracy for that
purpose.

parse_trad_grid(grid_ref)
Turns a traditional grid reference into a full easting and northing pair in metres
from the point of origin. The grid_ref can be a string like 'TQ203604' or 'SW 452
004', or a list like this "('TV', '435904')" or a list like this "('NN', '345',
'208')".

parse_GPS_grid(grid_ref)
Does the same as "parse_trad_grid" but is looking for five digit numbers like 'SW
45202 00421', or a list like this "('NN', '34592', '20804')".

parse_landranger_grid(sheet, e, n)
This converts an OS Landranger sheet number and a local grid reference into a full
easting and northing pair in metres from the point of origin.

The OS Landranger sheet number should be between 1 and 204 inclusive (but I may extend
this when I support insets). You can supply "(e,n)" as 3-digit hectometre numbers or
5-digit metre numbers. In either case if you supply any leading zeros you should
'quote' the numbers to stop Perl thinking that they are octal constants.

This module will croak at you if you give it an undefined sheet number, or if the grid
reference that you supply does not exist on the sheet.

In order to get just the coordinates of the SW corner of the sheet, just call it with
the sheet number. It is easy to work out the coordinates of the other corners,
because all OS Landranger maps cover a 40km square (if you don't count insets or the
occasional sheet that includes extra details outside the formal margin).

parse_grid(grid_ref)
Attempts to match a grid reference some form or other in the input string and will
then call the appropriate grid parsing routine from those defined above. In
particular it will parse strings in the form '176-345210' meaning grid ref 345 210 on
sheet 176, as well as 'TQ345210' and 'TQ 34500 21000' etc. You can in fact always use
"parse_grid" instead of the more specific routines unless you need to be picky about
the input.

grid_to_ll(e,n) or grid_to_ll(grid_ref)
When called in list context "grid_to_ll()" returns a pair of numbers representing
longitude and latitude coordinates, as real numbers. Following convention, positive
numbers are North and East, negative numbers are South and West. The fractional parts
of the results represent fractions of degrees.

When called in scalar context it returns a string in ISO longitude and latitude form,
such as '+5025-00403/' with the result rounded to the nearest minute (the formulae are
not much more accurate than this). In a void context it does nothing.

The arguments must be an (easting, northing) pair representing the absolute grid
reference in metres from the point of origin. You can get these from a grid reference
string by calling "parse_grid()" first.

An optional last argument defines the geoid model to use just as it does for
"ll_to_grid()". This is only necessary is you are working with the pseudo-grid
references produced by the OSTN02 routines. See Theory for more discussion.

format_ll_trad(lat, lon)
Takes latitude and longitude in decimal degrees as arguments and returns a string like
this

N52:12:34 W002:30:27

In a list context it returns all 8 elements (hemisphere, degrees, minutes, seconds for
each of lat and lon) in a list. In a void context it does nothing.

format_ll_ISO(lat, lon)
Takes latitude and longitude in decimal degrees as arguments and returns a string like
this

+5212-00230/

In a list context it returns all 6 elements (sign, degrees, minutes for each of lat
and lon) in a list. In a void context it does nothing.

parse_ISO_ll(ISO_string)
Reads an ISO 6709 formatted location identifier string such as '+5212-00230/'. To
learn exactly what is matched by this last option, read the source of the module and
look for the definition of $ISO_LL_PATTERN. Note that the neither the "+" or "-"
signs at the beginning and in the middle, nor the trailing "/" may be omitted. These
strings can also include the altitude of a point, in metres, like this:
'+5212-00230+140/'. If you omit the altitude, 0 is assumed.

In a list context it returns ($lat, $lon, $altitude). So if you don't want or don't
need the altitude, you should just drop it, for example like this:

my ($lat, $lon) = parse_ISO_ll('+5212-00230/')

In normal use you won't notice this. In particular you don't need to worry about it
when passing the results on to "ll_to_grid", as that routine looks for an optional
altitude after the lat/lon.

shift_ll_from_WGS84(lat, lon, altitude)
Takes latitude and longitude in decimal degrees (plus an optional altitude in metres)
from a WGS84 source (such as your GPS handset or Google Earth) and returns an
approximate equivalent latitude and longitude according to the OSGM02 model. To
determine the OSGB grid reference for given WGS84 lat/lon coordinates, you should call
this before you call "ll_to_grid". Like so:

($lat, $lon, $alt) = shift_ll_from_WGS84($lat, $lon, $alt);
($e, $n) = ll_to_grid($lat,$lon);

You don't need to call this to determine a grid reference from lat/lon coordinates
printed on OSGB maps (the so called "graticule intersections" marked in pale blue on
the Landranger series).

This routine provide a fast approximation; for a slower, more accurate approximation
use the companion Geo::Coordinates::OSTN02 modules.

shift_ll_into_WGS84(lat, lon, altitude)
Takes latitude and longitude in decimal degrees (plus an optional altitude in metres)
from an OSGB source (such as coordinates you read from a Landranger map, or more
likely coordinates returned from "grid_to_ll()") and adjusts them to fit the WGS84
model.

To determine WGS84 lat/lon coordinates (for use in Wikipedia, or Google Earth etc) for
a given OSGB grid reference, you should call this after you call "grid_to_ll()". Like
so:

($lat, $lon) = grid_to_ll($e, $n);
($lat, $lon, $alt) = shift_ll_into_WGS84($lat, $lon, $alt);

This routine provide a fast approximation; for a slower, more accurate approximation
use the companion Geo::Coordinates::OSTN02 modules.

THEORY

The algorithms and theory for these conversion routines are all from A Guide to Coordinate
Systems in Great Britain published by the OSGB, April 1999 (Revised Dec 2010) and
available at http://www.ordnancesurvey.co.uk/.

You may also like to read some of the other introductory material there. Should you be
hoping to adapt this code to your own custom Mercator projection, you will find the paper
called Surveying with the National GPS Network, especially useful.

The routines are intended for use in Britain with the Ordnance Survey's National Grid,
however they are written in an entirely generic way, so that you could adapt them to any
other ellipsoid model that is suitable for your local area of the earth. There are other
modules that already do this that may be more suitable (which are referenced in the "See
Also" section), but the key parameters are all defined at the top of the module.

$ellipsoid_shapes{OSGB36} = [ 6377563.396, 6356256.910 ];
use constant ORIGIN_LONGITUDE => RAD * -2; # lon of grid origin
use constant ORIGIN_LATITUDE => RAD * 49; # lat of grid origin
use constant ORIGIN_EASTING => 400000; # Easting for origin
use constant ORIGIN_NORTHING => -100000; # Northing for origin
use constant CONVERGENCE_FACTOR => 0.9996012717; # Convergence factor

The ellipsoid model is defined by two numbers that represent the major and minor radius
measured in metres. The Mercator grid projection is then defined by the other five
parameters. The general idea is that you pick a suitable point to start the grid that
minimizes the inevitable distortion that is involved in a Mercator projection from
spherical to Euclidean coordinates. Such a point should be on a meridian that bisects the
area of interest and is nearer to the equator than the whole area. So for Britain the
point of origin is 2W and 49N (in the OSGB geoid model) which is near the Channel Islands.
This point should be set as the "ORIGIN_LONGITUDE" and "ORIGIN_LATITUDE" parameters (as
above) measured in radians. Having this True Point of Origin in the middle and below (or
above if you are antipodean) minimizes distortion but means that some of the grid values
would be negative unless you then also adjust the grid to make sure you do not get any
negative values in normal use. This is done by defining the grid coordinates of the True
Point of Origin to be such that all the coordinates in the area of interest will be
positive. These are the parameters "ORIGIN_EASTING" and "ORIGIN_NORTHING". For Britain
the coordinates are set as 400000 and -100000, so the that point (0,0) in the grid is just
to the south west of the Scilly Isles. This (0,0) point is called the False Point of
Origin. The fifth parameter affects the convergence of the Mercator projection as you get
nearer the pole; this is another feature designed to minimize distortion, and if in doubt
set it to 1 (which means it has no effect). For Britain, being so northerly it is set to
slightly less than 1.

The British National Grid
One consequence of the True Point of Origin of the British Grid being set to
"+4900-00200/" is that all the vertical grid lines are parallel to the 2W meridian; you
can see this on the appropriate OS maps (for example Landranger sheet 184), or on the
"plotmaps.pdf" picture supplied with this package. The effect of moving the False Point
of Origin to the far south west is that all grid references always positive.

Strictly grid references are given as whole numbers of metres from this point, with the
easting always given before the northing. For everyday use however, the OSGB suggest that
grid references need only to be given within the local 100km square as this makes the
numbers smaller. For this purpose they divide Britain into a series of 100km squares
identified in pair of letters: TQ, SU, ND, etc. The grid of the big squares actually
used is something like this:

HP
HU
HY
NA NB NC ND
NF NG NH NJ NK
NL NM NN NO NP
NR NS NT NU
NW NX NY NZ
SC SD SE TA
SH SJ SK TF TG
SM SN SO SP TL TM
SR SS ST SU TQ TR
SV SW SX SY SZ TV

SW covers most of Cornwall, TQ London, and HU the Shetlands. Note that it has the neat
feature that N and S are directly above each other, so that most Sx squares are in the
south and most Nx squares are in the north.

Within each of these large squares, we only need five digit coordinates --- from (0,0) to
(99999,99999) --- to refer to a given square metre. For daily use however we don't
generally need such precision, so the normal recommended usage is to use units of 100m
(hectometres) so that we only need three digits for each easting and northing --- 000,000
to 999,999. If we combine the easting and northing we get the familiar traditional six
figure grid reference. Each of these grid references is repeated in each of the large
100km squares but for local use with a particular map, this does not usually matter.
Where it does matter, the OS suggest that the six figure reference is prefixed with the
identifier of the large grid square to give a `full national grid reference', such as
TQ330800. This system is described in the notes of in the corner of every Landranger
1:50,000 scale map.

Modern GPS receivers can all display coordinates in the OS grid system. You just need to
set the display units to be `British National Grid' or whatever similar name is used on
your unit. Most units display the coordinates as two groups of five digits and a grid
square identifier. The units are metres within the grid square (although beware that the
GPS fix is unlikely to be accurate down to the last metre).

Geoid models
This section explains the fundamental problems of mapping a spherical earth onto a flat
piece of paper (or computer screen). A basic understanding of this material will help you
use these routines more effectively. It will also provide you with a good store of
ammunition if you ever get into an argument with someone from the Flat Earth Society.

It is a direct consequence of Newton's law of universal gravitation (and in particular the
bit that states that the gravitational attraction between two objects varies inversely as
the square of the distance between them) that all planets are roughly spherical. (If they
were any other shape gravity would tend to pull them into a sphere). On the other hand,
most useful surfaces for displaying large scale maps (such as pieces of paper or screens)
are flat. There is therefore a fundamental problem in making any maps of the earth that
its curved surface being mapped must be distorted at least slightly in order to get it to
fit onto the flat map.

This module sets out to solve the corresponding problem of converting latitude and
longitude coordinates (designed for a spherical surface) to and from a rectangular grid
(for a flat surface). This projection is in itself is a fairly lengthy bit of maths, but
what makes it extra complicated is that the earth is not quite a sphere. Because our
planet spins about a vertical axis, it tends to bulge out slightly in the middle, so it is
more of an oblate spheroid than a sphere. This makes the maths even longer, but the real
problem is that the earth is not a regular oblate spheroid either, but an irregular lump
that closely resembles an oblate spheroid and which is constantly (if slowly) being
rearranged by plate tectonics. So the best we can do is to pick an imaginary regular
oblate spheroid that provides a good fit for the region of the earth that we are
interested in mapping. The British Ordnance Survey did this back in 1830 and have used it
ever since as the base on which the National Grid for Great Britain is constructed. You
can also call an oblate spheroid an ellipsoid if you like. The general term for an
ellipsoid model of the earth is a "geoid".

The first standard OSGB geoid is known as "Airy 1830" after the year of its first
development. It was revised in 1936, and that version, generally known as OSGB36, is the
basis of all current OSGB mapping. In 2002 the model was redefined (but not functionally
changed) as a transformation from the international geoid model WGS84. This redefinition
is called OSGM02. For the purposes of these modules (and most other purposes) OSGB36 and
OSGM02 may be treated as synonyms.

The general idea is that you can establish your latitude and longitude by careful
observation of the sun, the moon, the planets, or your GPS handset, and that you then do
some clever maths to work out the corresponding grid reference using a suitable geoid.
These modules let you do the clever maths, and the geoid they use is the OSGM02 one. This
model provides a good match to the local shape of the Earth in the British Isles, but is
not designed for use in the rest of the world; there are many other models in use in other
countries.

In the mid-1980s a new standard geoid model was defined to use with the fledgling global
positioning system (GPS). This model is known as WGS84, and is designed to be a
compromise model that works equally well for all parts of the globe (or equally poorly
depending on your point of view --- for one thing WGS84 defines the Greenwich observatory
in London to be not quite on the zero meridian). Nevertheless WGS84 has grown in
importance as GPS systems have become consumer items and useful global mapping tools (such
as Google Earth) have become freely available through the Internet. Most latitude and
longitude coordinates quoted on the Internet (for example in Wikipedia) are WGS84
coordinates.

One thing that should be clear from the theory is that there is no such thing as a single
definitive set of coordinates for every unique spot on earth. There are only
approximations based on one or other of the accepted geoid models, however for most
practical purposes good approximations are all you need. In Europe the official
definition of WGS84 is sometime referred to as ETRS89. For all practical purposes in
Western Europe the OS advise that one can regard ETRS89 as identical to WGS84 (unless you
need to worry about tectonic plate movements).

Practical implications
If you are working exclusively with British OS maps and you merely want to convert from
the grid to the latitude and longitude coordinates printed (as faint blue crosses) on
those maps, then all you need from these modules are the plain "grid_to_ll()" and
"ll_to_grid()" routines. On the other hand if you want to produce latitude and longitude
coordinates suitable for Google Earth or Wikipedia from a British grid reference, then you
need an extra step. Convert your grid reference using "grid_to_ll()" and then shift it
from the OSGB model to the WGS84 model using "shift_ll_into_WGS84()". To go the other way
round, shift your WGS84 lat/lon coordinated into OSGB, using "shift_ll_from_WGS84()",
before you convert them using "ll_to_grid()".

If you have a requirement for really accurate work (say to within a millimetre or two)
then you need to use the OS's transformation matrix called OSTN02. This monumental work
published in 2002 re-defined the British grid in terms of offsets from WGS84 to allow
really accurate grid references to be determined from really accurate GPS readings (the
sort you get from professional fixed base stations, not from your car's sat nav or your
hand-held device). The problem with it is that it defines the grid in terms of a
deviation in three dimensions from a pseudo-grid based on WGS84 and it does this
separately for every square km of the country, so the data set is huge and takes a second
or two to load even on a fast machine. Nevertheless a Perl version of OSTN02 is included
as a separate module in this distribution just in case you really need it (but you don't
need it for any "normal" work). Because of the way OSTN02 is defined, the sequence of
conversion and shifting works differently from the approximate routines described above.

Starting with a really accurate lat/lon reading in WGS84 terms, you need to transform it
into a pseudo-grid reference using "ll_to_grid()" using an optional argument to tell it to
use the WGS84 geoid parameters instead of the default OSGB parameters. The
Geo::Coordinates::OSTN02 package provides a routine called "ETRS89_to_OSGB36()" which will
shift this pseudo-grid reference into an accurate OSGB grid reference. To go back the
other way, you use "OSGB36_to_ETRS89()" to make a pseudo-grid reference, and then call
"grid_to_ll()" with the WGS84 parameter to get WGS84 lat/long coordinates.

($lat, $lon, $height) = (51.5, -1, 10);
($x, $y) = ll_to_grid($lat, $lon, 'WGS84');
($e, $n, $elevation) = ETRS89_to_OSGB36($x, $y, $height);

($x, $y, $z) = OSGB36_to_ETRS89($e, $n, $elevation);
($lat, $lon) = grid_to_ll($x, $y, 'WGS84');

EXAMPLES

         # to import everything try...
         use Geo::Coordinates::OSGB ':all';

         # Get full coordinates in metres from GR
         ($e,$n) = parse_trad_grid('TQ 234 098');

         # Latitude and longitude according to the OSGB geoid (as
         # printed on OS maps), if you want them to work in Google
         # Earth or some other tool that uses WGS84 then adjust results
         ($lat, $lon) = grid_to_ll($e, $n);
         ($lat, $lon, $alt) = shift_ll_into_WGS84($lat, $lon, $alt);
         # and to go the other way
         ($lat, $lon, $alt) = shift_ll_from_WGS84($lat, $lon, $alt);
         ($e, $n) = ll_to_grid($lat,$lon);
         # In both cases the elevation is in metres (default=0m)

         # Reading and writing grid references
         # Format full easting and northing into traditional formats
         $gr1 = format_grid_trad($e, $n);      # "TQ 234 098"
         $gr1 =~ s/\s//g;                      # "TQ234098"
         $gr2 = format_grid_GPS($e, $n);       # "TQ 23451 09893"
         $gr3 = format_grid_landranger($e, $n);# "TQ 234 098 on Sheet 176"
         # or call in list context to get the individual parts
         ($sq, $e, $n) = format_grid_trad($e, $n); # ('TQ', 234, 98)

         # parse routines to convert from these formats to full e,n
         ($e,$n) = parse_grid('TQ 234 098');
         ($e,$n) = parse_grid('TQ234098'); # spaces optional
         ($e,$n) = parse_grid('TQ',234,98); # or even as a list
         ($e,$n) = parse_grid('TQ 23451 09893'); # as above..

         # You can also get grid refs from individual maps.
         # Sheet between 1..204; gre & grn must be 3 or 5 digits long
         ($e,$n) = parse_grid(176,123,994);

         # With just the sheet number you get GR for SW corner
         ($e,$n) = parse_grid(184);

         # Reading and writing lat/lon coordinates
         ($lat, $lon) = parse_ISO_ll("+52-002/");
         $iso = format_ll_ISO($lat,$lon);    # "+520000-0020000/"
         $str = format_ll_trad($lat,$lon);   # "N52:00:00 W002:00:00"

BUGS AND LIMITATIONS

       The conversions are only approximate.   So after

         ($a1,$b1) = grid_to_ll(ll_to_grid($a,$b));

       neither "$a==$a1" nor "$b==$b1". However "abs($a-$a1)" and "abs($b-$b1)" should be less
       than 0.00001 which will give you accuracy to within a metre. In the middle of the grid
       0.00001 degrees is approximately 1 metre.  Note that the error increases the further away
       you are from the central meridian of the grid system.

       The "format_grid_landranger()" does not take account of inset areas on the sheets.  So if
       you feed it a reference for the Scilly Isles, it will tell you that the reference is not
       on any Landranger sheet, whereas in fact the Scilly Isles are on an inset in the SW corner
       of Sheet 203.  There is nothing in the design that prevents me adding the insets, they
       just need to be added as extra sheets with names like "Sheet 2003 Inset 1" with their own
       reference points and special sheet sizes.  Collecting the data is another matter.

       Not enough testing has been done.  I am always grateful for the feedback I get from users,
       but especially for problem reports that help me to make this a better module.

DIAGNOSTICS

       Should this software not do what you expect, then please first read this documentation,
       secondly verify that you have installed it correctly and that it passes all the
       installation tests on your set up, thirdly study the source code to see what it's supposed
       to be doing, fourthly get in touch to ask me about it.

CONFIGURATION AND ENVIRONMENT

       There is no configuration required either of these modules or your environment. It should
       work on any recent version of perl, on any platform.

DEPENDENCIES

       None.

INCOMPATIBILITIES

       None known.

LICENSE AND COPYRIGHT

       Copyright (C) 2002-2013 Toby Thurston

       OSTN02 transformation data is freely available but remains Crown Copyright (C) 2002

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

AUTHOR

       Toby Thurston -- 04 Oct 2013

       toby@cpan.org