[OSRS-PROJ] Re: On the Ellipsoidal Transverse Mercator

[Strebe at aol.com]

Gerald Evenden <gerald.evenden at verizon.net> writes:

> A question here, are we talking about the Gauss-Kruger model or some
> other construct?  Dozier, Lee are dealing with the Gauss-Kruger model.

There is no other construct. If the projection maps the ellipsoid conformally 
such that the central meridian everywhere is unity, and the map is not 
interrupted along the central meridian, then the map is the ellipsoidal transverse 
Mercator = Gauss Kruger. All methods yield the same results if they are pursued 
with unbounded accuracy. That is true of any conformal projection: if you 
supply a boundary condition, then you have specified the entire conformal map.

> The description below contains exotic concepts and lacks sufficent
> detail for review.  Without detailed, published description it remains
> an unfounded claim.

No, Mr. Evenden, the description is complete and mundane. Anyone who 
understands both the transverse Mercator and complex analysis would recognize it as a 
legitimate path to the ellipsoidal transverse Mercator. Your insecure 
insistence upon a published description is your loss, not mine; I and probably many 
other people reading this list are perfectly capable of generating correct maps 
with it. I have wheedled Wallis to publish. It's none of my concern if he does 
not and it is not my place to publish his method. I'm afraid you'll have to 
waffle through Dozier's account, since the best I can supply is references to 
Snyder, Dozier, and Lee, Dr. Wallis's name and location, source code, 
distortion analyses, comparisons with UTM coordinates, and images.

> Dr. Wallis claims that the publication of his transverse mercator
> is pending.

It will be awhile, he has told me, since it seems what he is writing is a 
book that goes far beyond just a method for generating the ellipsoidal transverse 
Mercator. It would not satisfy you anyway, since I do not expect it will be 
peer-reviewed.

> Apparently the map is segmented.
> 
It is not segmented. Two tombstones meet foot-to-foot, and two sets of such 
conjoined tombstones meet side-by-side. The tombstone shape is the classical 
simple rectangle with one end rounded as a semicircle.

> Note: Wallis only refers to mapping the N -or- S hemispheres
> whereas general concept of TM has no difficulty in the N-S
> direction but rather in the E-W direction.

Bizarre interpretation. Wallis clearly states that the entire north or south 
hemisphere is mapped. He's not talking about "direction"; he's talking about 
the extent of the map. The spherical transverse Mercator cannot map the entire 
north or south hemisphere.

> BTW: is there a plotted example of this version of the transverse
> mercator available on the web somewhere?

No, but if someone were to supply a place to deposit it, I would be happy to 
supply some. I can't imagine why you would be interested in pictures of 
unfounded claims, though. And there is no such thing as "this version"; all 
transverse Mercators are the same.

All who might be interested and don't find themselves consumed by 
pathological skepticism, or who understand the method and therefore have no need for 
skepticism, feel free to contact me with questions.

Regards,

daan Strebe
Geocart author
<A HREF="http://www.mapthematics.com">http://www.mapthematics.com</A>
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