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

Strebe at aol.com Strebe at aol.com
Fri Oct 17 01:44:16 EDT 2003

Dear Mr. Engsager:

It is unfortunate we were unable to see you in Durban at the ICA conference.

Thank you for the note below, which I read with great interest. I had not 
heard of this method before. I find that the graticules for the first two images 
generally match my own images of the complete ellipsoidal transverse Mercator. 
However, I also find that the spacing of the parallels in the images you 
supply does not match perfectly well all along the meridians: if they match at 
mid-latitudes, then they are too close to the pole at upper   and lower 
latitudes. If the problem were due to pixels that are not quite square on your monitor 
or mine, then I would expect the problem to occur along only one axis. 
Instead, it occurs in every direction. I tried various values for the ellipse's 
eccentricity but was unable to compensate for the discrepancy. Hence I must 
conclude that there is some other source of error; possibly in the implementation of 
the transformation or in the formulation.

We should compare calculated coordinates. Please contact me directly if you 
are able to spend a little time on this.

daan Strebe

In a message dated 10/16/03 3:17:59 AM, ke at kms.dk writes:

> Dear Colleagues
> I have got a notise from one of my colleagues at National Survey and 
> Cadastre,
> Denmark, that some discussions on Ellipsoidal Transverse Mercator is going 
> on.
> REF.:  "Some Conformal Mapping and Transformations for Geodesy and 
> Cartography",
>   by Knud Poder and Kartsen Engsager, Geodetic Division, KMS, Denmark 1998.
> The basics of the problem has been solved by R. König und K.H: Weise in 
> 1951.
> The transformation of Geotetic Coordinates (ellipsoidal) may be transformed 
> to Transversal
> coordinates in three steps ::
>     1)   Geodetic coord. (phi, lambda)  are transformed to a Gaussian Sphere 
> using a fourth
>                       degree Clenshaw summation giving Gaussian Coord. (PHI, 
>    2)  Gaussian coord. (PHI, LAMBDA) are transformed to Complex Gaussian 
> coord (Y, X).
>                      (The formulas are in principle the same as used in 
> Mecator Mapping).
>    3)  Complex Gaussian coord (Y,X)  are transformed to Transversal coord 
> (N, E) using
>                     a fourth degree Comples Clenshaw summation, - 
> concatenated by a scaling.
> The opposit direction transforms from Transversal coord. (N,E) to Geodetic 
> coord (phi, lambda).
> This transformation is done with an accuracy better than 3e-5 m for E < 4000 
> km !!!!
> This transformation passes the Noth/Southpole without any difficulties. In 
> our GIS system the
> earth is shown more times rolling around the central meridian of the 
> Transversal Mercator !!!
> I hope taht you are able to take these informations into consideration when 
> making guidelines
> for using the Transverse Mercator mapping.

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