[PROJ] Latitude of natural origin in Transverse Mercator

[Greg Troxel]

Javier Jimenez Shaw <j1 at jimenezshaw.com> writes:

> I have a question about Transverse Mercator.
> What is the impact of the parameter "Latitude of natural origin", compared
> with the "False Northing"? (apart from the fact that one is in degrees and
> the other in meters)
> Is there any difference on using a Latitude of natural origin of, let's
> say, 40 degrees, or compute the equivalent False Northing?

Snyder's Album [1] says that TM uses the equator.  I had never heard of
latitude of natural origin.  Snyder's Manual [2] seems to align with
equator only but I may have missed it.

It seems like there is some more complicated definition of TM.
ESRI [3] lists but does not explain latitude of natural origin.

I would guess that latitude of natural origin means that some other
latitute is used as the place in lat/lon that maps to 0 (before adding
the false northing).  But, it's an ellipsoidal projection and I can't
convince myself that this is equivalent to a different false northing.

To me, it seems wrong or at best confusing to interchange these
parameters even if it is equivalent, as one seems to be about how the
projection is done and the other is just about moving numbers away from
0 so they won't be negative.

I am curious how you were led to latitude of natural origin.


[1] https://www.usgs.gov/publications/album-map-projections
[2] https://pubs.usgs.gov/pp/1395/report.pdf
[3] https://desktop.arcgis.com/en/arcmap/latest/map/projections/transverse-mercator.htm