[R] Easting and northing cf. Latitude and longitude

(Ted Harding) Ted.Harding at nessie.mcc.ac.uk
Fri Jun 22 11:07:14 CEST 2001

On 22-Jun-01 Patrick Connolly wrote:
> I think I've seen this discussed here before but it doesn't seem to
> appear in the archive.
> I am using the map package which so far has been fine for my purposes.
> Some people I work with have GPS type data that defines positions as
> number of metres not degrees.  I don't know how much the system
> varies, but in New Zealand, they are referred to as Eastings and
> Northings.
> What I would like to know is how complicated it is to convert between
> such data and the normal latitude and longitude that the map package
> uses.  I assume various datum points are used for different parts of
> the world, and knowing the appropriate one and the definition of a
> "northing" and an "easting", the conversion would be relatively
> straight forward.

Errr, sort of ... , though to some extent this depends on the
accuracy you seek.

I implemented such a conversion for Lat-Long/Eastings-Northings
years ago, for the UK Ordnance Survey Grid (which uses E & N),
using the method & formulae published by the OS in a little
booklet (program written in C -- nasty-looking piece of work, since
it is basically a transcription of their formulae). I can send you
the C code for this, as an example, if you wish.

For such a method, you will, strictly speaking, need to know,
for your own national mapping agency:

-- the major and minor semi-axes for the reference ellipsoid
-- the Long. & Lat., and E and N, of the "True Origin"
-- the scale factor on the "central meridian"
-- the map projection they use to generate plane maps
   from Lat & Long data, i.e. the "National Projection"

(the reference ellipsoid may also be called the "map datum").
Nowadays, there is also a complication in that "The Meridian"
is no longer what it used to be, being now defined by satellite
data (and allegedly superior through being immune to continental
drift and similar sabotage of reference points rigidly attached
to dry land). So, in fact, there is a choice of meridians, too ...

There is a further complication in that the GPS system actually
used to generate the data you get, may have been set up to use
some other reference system; so you need to find out what this
was. It may then turn out that you do not have access to the
formulae defining the relationship between their Lat & Long
and your E & N, unless you can find out the relationship
netween their Lat & Long and your National Lat & Long.

The National Projection ( [Lat,Long]->[E,N] ) is defined by
a series of formulae which depend on your Nation; in this
direction it is a one-pass operation. The inversion of it
( [E,N]->[Lat,Long] ) involves an iterative solution. You
should be able to find out from your national mapping agency
how their projection is defined.

Good luck!

E-Mail: (Ted Harding) <Ted.Harding at nessie.mcc.ac.uk>
Fax-to-email: +44 (0)870 167 1972
Date: 22-Jun-01                                       Time: 10:07:14
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