[Proj] Extended range TM usage

[Gerald I. Evenden]

On Tuesday 26 August 2008 12:14:37 pm Clifford J Mugnier wrote:
> The most common rational reasons include GIS applications of
> hydrocarbon-producing regions.  For example, the entire Gulf of Mexico,
> significant portions of Siberia, the Persian Gulf, etc.  The key word is
> "region."  There are numerous cartographic uses for this in Reservoir
> Engineering as well as maintenance of lease blocks data bases, etc.

My question here is what was the rational for choosing TM and, in particular, 
elliptical TM?  Was the shape of the region considered?  Were other 
projections like Stereographic or Lambert Conic considered?

> The military has ALWAYS recognized this need and actually published a
> special book on Zone-to-Zone transformations.

Indeed, I often ran into geologist spanning UTM zones and thus the AMS sheets 
that they were using as base maps and thus ended up giving us computer map 
makers fits.  NMD (National Mapping Division) would kludge up a base map for 
them from pasted together mylar sheets.  But, you cannot extend the TM 
projection and expect it to overlay sheets from a different 
zone---because---the scale of the projection rapidly deteriorates at 
increased distance from the CM and is not the same scale as a sheet from the 
adjacent zone.  Thus computer generated maps with extended zones would not 
match AMS sheets not having the same CM.

> I seem to write about these valid rational reasons periodically, and I
> think I do so in this discussion list.

Because it keeps coming up and I do not think some people realize the 
problems.

> If you don't want to implement this sort of thing and are looking for a
> reason not to do so, use sunrise tomorrow as an excuse.

As long as user's recognize that extending the range of TM will create charts 
that *do not* overlay regions *not exactly* computed in the same manner, then 
no problem.  Current libproj4 allows a fairly wide TM extent.  BUT no user 
shall come and complain that a map area generated on one CM will not match a 
map generated on another CM.  That is: UTM sheets will not match extended TM 
when the extended TM's CM is not the same as the UTM sheet.

Secondly, *do not* complain if distances taken from extended TM grid at 
extended distances from the TM do not seem to match real distances.  The 
scale factor goes to hell as one gets further and further from the CM.

Given the scale problems there seems little reason to even bother with the 
ellptical TM and just use spherical TM with a radius that gives a "close 
enough for ... " accuracy.  That's what they have in practice have now.

Again, I try to be a good rope maker and I want to be sure that users have 
enough to hang themselves.  The added TMs give the user a choice of the color 
of the hemp.

Of course, the least area outlines come up.  As I recall, we digitized the 
zones into geographic so they could be plotter anywhere, anyway.  We had to 
do it because of the irregular shape near the shore line.

It's getting late.

> Cliff Mugnier
> LOUISIANA STATE UNIVERSITY
...
-- 
The whole religious complexion of the modern world is due
to the absence from Jerusalem of a lunatic asylum.
-- Havelock Ellis (1859-1939) British psychologist