| Geo-Coordinates-OSGB documentation | view source | Contained in the Geo-Coordinates-OSGB distribution. |
Geo::Coordinates::OSTN02 - An implementation of the OSGB's OSTN02 transformation
use Geo::Coordinates::OSTN02 qw/OSGB36_to_ETRS89 ETRS89_to_OSGB36/; ($x, $y, $z) = OSGB36_to_ETRS89($e, $n, $h); ($e, $n, $h) = ETRS89_to_OSGB36($x, $y, $z);
The purpose and use of these modules is described briefly in the companion Geo::Coordinates::OSGB modules. In essence they implement in Perl the Ordnance Survey's OSTN02 transformation which is part of the current definition of the British National Grid. You are strongly recommended to read the official public guides and other introductory documents that are published by the Ordnance Survey of Great Britain with a wealth of other technical information about the OSTN02 transformation.
The following functions can be exported from the Geo::Coordinates::OSTN02
module:
OSGB36_to_ETRS89
ETRS89_to_OSGB36
None is exported by default.
Transforms from normal OSGB36 grid references to a pseudo-grid based on the WGS84/ETRS89 geoid
model, which can then be translated to lat/long coordinates using grid_to_ll() with the 'WGS84'
parameter.
my $elevation = '100'; # in metres
my ($e, $n) = parse_grid_trad('TQ304293');
my ($x, $y, $z) = OSGB36_to_ETRS89($e, $n, $elevation);
my ($lat, $lon) = grid_to_ll($x, $y, 'ETRS89'); # or 'WGS84'
Elevation will default to 0 metres if you omit it.
Transforms WGS84/ETRS89 pseudo-grid coordinates into OSGB36 grid references.
my ($lat, $lon, $height) = (51.5, -1, 10); # Somewhere in London my ($x, $y) = ll_to_grid($lat, $lon, 'ETRS89'); # or 'WGS84' my ($e, $n, $elevation) = ETRS89_to_OSGB36($x, $y, $height);
Since 2002 the British Ordnance Survey have defined the UK national grid not as a projection from their own model of the earth (the Airy 1830 geoid, revised 1936, known as OSGB36), but as a simple table of calculated differences from a projection based on the European standard geoid ETRS89 (which is for Europe a functional equivalent of the international WGS84 geoid). This revision is known as OSGM02 and the transformation is called OSTN02.
The idea is that you project your WGS84 latitude and longitude coordinates into WGS84 (or ETRS89) pseudo-grid references, and then look up the appropriate three dimensional correction in the OS table, and add the results to your grid reference to give you a standard British National Grid reference that you can use with British OS maps. Going back the other way is slightly more complicated, as you have to work backwards, but a simple iteration will do the job. This package implements these lookups and adjustments. You give it a three dimensional grid reference (easting, northing, and altitude, all in metres) and the package returns it corrected from one system to the other.
The problem in the implementation is that the table is huge, and most of it is empty as the OS have chosen to leave the transformation undefined for areas that are off shore. So this package only works properly for grid references that are actually on one or more OS maps. The complete table (including all the 0 lines) contains nearly 1 million lines with six data points and a key. In text form as supplied by the OS that is about 36M bytes of table. By leaving out the lines where the transformation is undefined, omitting a couple of redundant fields, and storing everything as hex strings, this module brings the amount of data down to just over 6M bytes, which loads in about 1 second on my test system. It would be possible to compress the data down to 3M bytes by storing it as packed decimals, but then it would be difficult to include inline in this module, as it would break every time I edited it.
The data is stored below, after the __DATA__ line. Each line is 18 bytes long and represents the transformation parameters for an individual grid square of 1km by 1km. Each line contains five fields all expressed as hexadecimal integers.
Start Length Meaning
0 3 The northing of the square in km
3 3 The easting of the square in km
6 4 The x-offset in mm (easting)
10 4 The y-offset in mm (northing)
14 4 The z-offset in mm (elevation)
To keep the numbers small and positive the values given for the offsets are actually the amount that they exceed the respective smallest values in the data set. Currently these minima are x: 86275mm, y: -81603mm, and z: 43982mm. So when we read a line from the data we have to add these minima to the values, convert to decimal, and multiply by 1000 to get back to metres.
When you load the OSTN02 module, the first thing it does is to load all 309,798 lines into an array called @ostn_data by simply doing this.
our @ostn_data = <DATA>;
This is why it takes over a second to load the module, but once loaded it's all very fast.
When we need to find the data values for a given grid reference, we work out the appropriate
grid square by truncating the easting and northing to the next lowest whole kilometer,
and pass these as the argument to the _get_ostn_ref subroutine. This is the only subroutine that
actually touches the data.
The core of the subroutine is a binary search. We work out the key by converting the northing and easting to hexadecimal and concatenating them. We add leading zeros so that each value is exactly three bytes long and the combined key is exactly six bytes long. The maximum value for easting in the OSGB grid is 700km and for northing 1250km, which are 2BC and 4E2, so each fits into three bytes. (And by the time this is called we have already checked that the values don't exceed the maxima).
This works pretty quickly, the only slow bit is loading the array at the beginning, but it is much faster and needs *much* less memory than loading all the data into the hash. (This would be simpler, and is what the original version did, but it was too slow to be usable and meant that the tests failed on many smaller systems as part of CPAN testing). We do still use a hash, but only to cache lines that we've already found. Read the code for details. This only gives a tiny speed up in general, so I might remove it in future versions.
Loading the array takes about 1.2 seconds on my Windows machine (a 2.8G Hz Intel Pentium M processor with 2G byte of memory) and just under 0.5 seconds on my Linux system (a 2.8G Hz Intel Pentium 4 processor with 512M bytes of memory). I think this probably says more about speed of the disks I have (and probably the efficiency of Perl under Linux), but your results should be comparable. Once the data is loaded, calling the routines is reasonably quick.
Please report any to toby@cpan.org
See the test routines included in the distribution.
Toby Thurston --- 6 Nov 2008
toby@cpan.org
See Geo::Coordinates::OSGB for the main routines. =cut __DATA__ 00004f15ed000023f2 00005015fc000623ec 000051160a000b23e7 000052161d001523e2 0000531631002223de 0000541645002e23da 0000551659003a23d7 000056166d004523d4 0000571680005123d1 0000581695005d23ce 00005916a9006a23c9 00005a16bd007623c5 00005b16d1008223c1 00005c16e8008d23bd 00005d1700009923b9 00005e171900a423b5 00005f173100af23af 000060174900bb23aa 000061176200c623a3 000062177a00d1239c 000063179300dd2396 00104e15de001823fa 00104f15ec001d23f2 00105015fb002223ec 0010511609002823e6 0010521619002e23e1 001053162c003a23dc 0010541640004623d8 0010551655005223d5 0010561669005e23d2 001057167c006a23ce 0010581691007723cb 00105916a5008223c6 00105a16b8008e23c2 00105b16d0009923be 00105c16e900a623ba 00105d170100b123b6 00105e171a00bc23b1 00105f173200c823ac 001060174a00d323a6 001061176300de23a0 001062177b00ea2398 001063179400f52393 00106417ad0100238c 00204d15cf002f2403 00204e15dd003523fb 00204f15ec003a23f3 00205015fa003f23ed 0020511609004423e6 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