# [OSRS-PROJ] On the Ellipsoidal Transverse Mercator

Gerald I. Evenden gerald.evenden at verizon.net
Wed Oct 15 11:26:58 EDT 2003

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

On Wednesday 15 October 2003 12:10 am, Strebe at aol.com wrote:
> Since Mr. Evenden has not successfully implemented Dozier's ellipsoidal

Not entirely true.  Dozier's method agrees with standard TM Taylor series
developments such as Snyder as I commented before.  Where it fails is
extension to +/-90 in both axis and not machine precise near the
central meridian (where precise values are  easily obtained).

> transverse Mercator, and since no one has come forward with any information
> about Dozier's method or its reliability, I have decided to explain
> Wallis's method. This method yields the ellipsoidal transverse Mercator to
> arbitrary accuracy, covering the entire ellipsoid. For any eccentricity
> greater than zero, this map is finite. The greater the eccentricity, the
> smaller the area required by the map.

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

> The map is bilaterally symmetrical. Each quadrant has the shape of a
> tombstone. The base of each tombstone consists of half of the 0th and half
> of the 180th meridians. Two tombstones join base-to-base, and the
> combination of two then join the other two side-by-side. The outer boundary
> consists of much of the equator. Just how much depends on the eccentricity.
> The equator is also the joint between the two sets of bêche-bêche
> tombstones.

Interesting: "bêche-bêche."  Can't find the phrase in my plebean college
dictionary nor on a web search.  I seen too many different shaped tombstones
to understand the above descriptions.  Apparently the map is segmented.

> I describe the method below. The method is due primarily to Dr. David E.
> Wallis of Pasadena, California, USA. His innovation is to use the
> ellipsoidal polar stereographic as the primary projection of the ellipsoid
> to the plane. He treats the result as a complex space and applies a
> function to "straighten out" the primary meridian such that it retains
> constant scale. That is the definition of the transverse Mercator. My
> contribution is the simple iterative technique to determine "z", as set
> forth below.
<snip>
Oops!  I think we have let the cat out of the bag.  A google seach on
Dr. David E. Wallis yielded a web site for Glendale CA:
http://www.wallisphd.com/
which points to:
http://www.wallisphd.com/mercator.htm

I really suggest anyone interested in this problem to check this site
out.  Dr. Wallis claims that the publication of his transverse mercator
is pending.  Unfortunately no email address (interesting).

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.

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

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