[Proj] Extended range TM usage

Duncan Agnew dagnew at ucsd.edu
Wed Aug 27 12:53:52 EDT 2008

```If an onlooker can weigh in on the extended TM debate, partly because I
think the debaters somewhat talk past each other...

Gerald is looking at the TM math as a projection--that is, something
that is used to create XY coordinates with the purpose of display (a
map on paper or on the screen). Given the finite resolution of any
display system he is right to say that spherical TM is often just
fine (scale error at most 1 part in 300). The best possible for a
physical
display might be 0.01 mm over 1 m for a hardcopy, which is 10**-5.
These numbers matter only if you wanted to actually make measurements
from the
map display itself, rather than (as in GIS) the numbers stored
internally.
How many people actually measure off maps to high precision, these days?
(Getting coordinates off doesn't count--eg, if using military maps in
UTM with
a 1-km graticule, how many people measure the distances to high
precision off
the map, as opposed to getting coordinates from the graticule and then
computing
the distance from the coordinates?)

Cliff is looking at the TM math as a grid system--that is, something
that is used to create XY coordinates to be used "as they stand"--eg,
for deciding if your region (defined by lat-long) overlaps mine (defined
by XY, according to some official or semi-official system). Then you and
I had better use the same math or we have a problem. So if customary
usage for defining property boundary coordinates (eg lease areas in the
Gulf of
Mexico) is ellipsoidal TM coordinates with a reference meridian 10
degrees
away, then there will be a need for an implementation of this
transformation,
however bizarre the scale may be.

For boundary work (though for little else), the precision had
best be
very high--though as a practitioner of geodetic GPS, I have to point
out that,
in practice, even claiming lat/long to better than a few centimeters is
problematic unless you take care to allow for tectonic motions.

Duncan Agnew

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