GEODESY(2) GEODESY(2)
NAME
geodesy - Geodesy module
SYNOPSIS
include "geodesy.m";
geodesy := load Geodesy Geodesy->PATH;
# easting, northing
Eano: adt{
e: real;
n: real;
};
# latitude, longitude in radians
Lalo: adt{
la: real;
lo: real;
};
OSGB36, Ireland65, ED50, WGS84, ITRS2000, ETRS89: con iota;
Natgrid, IrishNatgrid, UTMEur, UTM: con iota;
init: fn(d: int, t: int, z: int);
format: fn(d: int, t: int, z: int);
os2en: fn(s: string): (int, Eano);
en2os: fn(en: Eano): string;
str2lalo: fn(s: string): (int, Lalo);
lalo2str: fn(lalo: Lalo): string;
str2en: fn(s: string): (int, Eano);
en2lalo: fn(en: Eano): Lalo;
lalo2en: fn(lalo: Lalo): Eano;
datum2datum: fn(lalo: Lalo, f: int, t: int): Lalo;
DESCRIPTION
Geodesy provides routines to deal with (some) terrestrial
coordinate systems.
Eastings and northings are defined by the Eano adt and are
measured in metres and latitude and longitude (which should
be in radians) by the Lalo adt. Latitude is in the range
-π/2 to π/2 radians and longitude in the range -π to π radi-
ans.
OSGB36 (Ordnance Survey Great Britain 1936), Ireland65 (Ire-
land 1965), ED50 (European Datum 1950), WGS84 (World Geode-
tic System 1984), ITRS2000 (International Terrestrial Refer-
ence System 2000), and ETRS89 (European Terrestrial Refer-
ence System 1989) are the current datums defined. Helmert
transformations are used to convert between them. Note that
Page 1 Plan 9 (printed 12/22/24)
GEODESY(2) GEODESY(2)
Ireland65 and ED50 are currently not supported and WGS84 and
ITRS2000 are considered equivalent.
Natgrid (National Grid), IrishNatgrid (Irish National Grid),
UTMEur (European Universal Transverse Mercator), and UTM
(Universal Transverse Mercator) are the current transverse
Mercator projections supported.
The following functions are provided
init The module should always be initialized first. The
parameters are the required datum (default WGS84),
transverse Mercator projection (default Natgrid) and
UTM zone (default 30) if appropriate. Negative values
or out of range values are ignored.
format
Parameters as above. Alters the current settings at any
time though care must be taken to ensure existing coor-
dinates are still treated as in their original form.
os2en
Converts an Ordnance Survey National Grid reference to
an easting, northing. The formats XYen, XYeenn,
XYeeennn, XYeeeennnn, XYeeeeennnnn, eenn, eeennn,
eeeennnn, eeeeennnnn and eeeeeennnnnn are allowed. Here
X and Y are upper case letters, e is an easting digit
and n is a northing digit. The reference can therefore
be rounded to the nearest decakilometre, kilometre,
hectometre, decametre or metre. The first element of
the returned tuple is zero if the string has an incor-
rect format.
en2os
Converts an easting, northing to an OS reference in the
form XYeeeeennnnn as above.
str2lalo
Converts a latitude/longitude string to a latitude,
longitude. The string may have the formats deg[N|S],
deg:min[N|S] or deg:min:sec[N|S] for latitude,
deg[E|W], deg:min[E|W] or deg:min:sec[E|W] for longi-
tude. The latitude must come first, then optional white
space, then the longitude. Degrees, minutes and sec-
onds may be integer or real. Format errors are indi-
cated as in os2en.
lalo2str
Converts a latitude, longitude to string format as
above. Seconds are given to two decimal places.
str2en
Page 2 Plan 9 (printed 12/22/24)
GEODESY(2) GEODESY(2)
Converts a string in OS or latitude/longitude format as
above to an easting, northing. Format errors indicated
as in os2en.
en2lalo
Converts an easting, northing to latitude, longitude
using the current transverse Mercator projection.If the
latter is UTM or UTMEur the current zone setting will
be used.
lalo2en
Converts latitude, longitude to an easting, northing
using the current transverse Mercator projection.
datum2datum
Approximate (Helmert) transformation of a latitude,
longitude between any of OSGB36, WGS84, ITRS2000 or
ETRS89. The `from' datum appears first in the parameter
list.
SOURCE
/module/math/geodesy.m
/appl/math/geodesy.b
BUGS
The module is heavily biased towards Great Britain.
Page 3 Plan 9 (printed 12/22/24)