[OSRS-PROJ] Re: Concerning calumny and the ellipsoidal transverse Mercator

[Gerald I. Evenden]

On Sat, 2003-08-23 at 19:53, Strebe at aol.com wrote:
> Gerald I. Evenden <gerald.evenden at verizon.net> writes:
> 
>   I wrote:
> > > Because the finite nature of the ellipsoidal transverse Mercator
> > is so
> > > rarely known, and because no numeric solutions have ever been
> > > published, and because there is no geodetic need for such a
> > > projection, it is entirely likely that I have produced the only
> > images
> > > of the projection ever made. I would be happy to make some
> > available
> > > if anyone is interested.
> 
> > It is difficult for me to refrain from becoming a bit sarcastic here
> > as your story sounds like a tabloid exposure.  I will remain a
> > sceptic until I see peer review publication.
> 
> So, I offered to supply the mathematics of the scenario, which is the
> final authority. However, you prefer to see an annotation in a
> peer-reviewed journal. Presumably that is because you do not feel
> qualified to analyze the mathematics. If that is so then it seems odd
> that you feel qualified to dispense skepticism, not to mention
> ridicule.

Absolutely, and without apologies.  No, I am not a mathematician
and never claimed to be but I always react to unsubstantiated claims.
One should *always* be from Missouri and have a "show me attitude." 
In this case I would rely upon review and consensus among of the
cartographic community.  If I had the equations, I would code them
and check them out with various numeric procedures.

> Here is one reference; I imagine there are more, probably in Lee's and
> Thompson's papers:
> 
> "The transverse Mercator projection is one of the most extensively
> used in large scale topographic mapping. Closed equations of chiefly
> academic interest are given here, rearranged from Lee's and Thompson's
> work with the Gauss-Krüger ellipsoidal adaptation of Lambert's
> original work. In this version, the map is conformal everywhere, and
> the central meridian is standard. The entire map is finite, unlike the
> spherical version which extends to infinity."
> 
> -- J.P. Snyder, "Calculating Map Projections for the Ellipsoid", The
> American Cartographer, Vol. 6, No. 1, April 1979.

Quite interesting.  But it amazes me that Snyder seems to ignore
this work in his later publications.  I suppose one reason is that
the finite and extended limits are of no use in small scale mapping
as there is no need for ellipsoidal calculations at these scales
and distortions limiting usefulness.  Nonetheless, it would be helpful
the have the math available---"for academic reasons."  One thing
that bothers me in the above quote is "central meridian is standard"
and does that mean the scale is constant along the CM?

I need bibliography for Lee/Thompson as the general bib titles
are too vague to be sure if they point to the applicable articles.
Getting an article from through my local library typically takes
more than 30 days.

> > As for conformity, its application is limited to large-scale
> > cadastral mapping.  Conformity is a concept which only
> > applies to the infinitesimal region about a point.  At a distance
> > distortion is quickly apparent and eventually becomes extreme.
> > Conformal projection for global presentations is most useful to
> > demonstrate the limitation of conformal projections.
> 
> Not so. Conformal maps of any extent are useful for showing accurate
> shapes over short distances. The shapes of (for example) small
> islands, short coastline segments, or provincial boundaries are
> correct on any conformal map. That is a valuable property. It is also
> true that local directions are correct once north has been
> established. I encourage you to loosen up your thinking a bit.
> Rigidity is not rigor.

The only region where shape of finite objects is reasonable is near
the zone of tangency.  For example, Greenland looks ridiculous
on a Mercator map.

> > As for the Peter's projection (a perverse use of the well known
> > cylindrical equal area) it has been severely criticized by well
> > know cartographers.
> 
> Peters made all sorts of ridiculous claims concerning "his"
> projection. On the other hand, cylindrical equal-area projections do
> have reasonable, if limited, uses. For instance, if you need a single,
> basic projection whose central meridian must be able to move freely
> without changing the shapes of mapped objects, then you are restricted
> to cylindrical projections. You yourself recommend equal-area
> projections; hence Peters must be useful. Yes, that's a limited use,
> but any small-scale projection is limited in use.

The Peters projection is a special case of the general equal-area
cylindrical projection where the latitude of true scale is set
to about 50° latitude.  Usage is reasonable in vicinity of this
latitude but the trouble arose when the UN decided to use this
as their world map and a storm of criticism arose from some well
known cartographers because of the excessive extortion for the
global display.  As I recall, a rational for its use was because
third world people in equatorial regions would not feel inferior
to the non-equatorial countries whose size was exaggerated by the
Mercator projection.

The cylindrical equal-area is certainly applicable in certain
applications where other factors are involved---like matching
the charts when sliding the CM.  But for general use without
special requirements, I generally go to the pseudocylindicals. 

There are many factors that go into choosing an appropriate
projection and many of these factors have contributed to the hundreds
of different projections we may choose from.  The global display
remains the most difficult and thus accounts for most of the
mapping attempts.

	<material deleted>
> 
> Regards,
> 
> daan Strebe
> Geocart author
> http://www.mapthematics.com/
-- 
Gerald I. Evenden <gerald.evenden at verizon.net>

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