<HTML><FONT FACE=arial,helvetica><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2">Dear Mr. Engsager:<BR>
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It is unfortunate we were unable to see you in Durban at the ICA conference.<BR>
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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.<BR>
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We should compare calculated coordinates. Please contact me directly if you are able to spend a little time on this.<BR>
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Regards,<BR>
daan Strebe<BR>
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In a message dated 10/16/03 3:17:59 AM, ke@kms.dk writes:<BR>
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<BLOCKQUOTE CITE STYLE="BORDER-LEFT: #0000ff 2px solid; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px; PADDING-LEFT: 5px" TYPE="CITE"></FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2">Dear Colleagues</FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2"><BR>
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</FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2">I have got a notise from one of my colleagues at National Survey and Cadastre,</FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2"><BR>
</FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2">Denmark, that some discussions on Ellipsoidal Transverse Mercator is going on.</FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2"><BR>
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</FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2">REF.: "Some Conformal Mapping and Transformations for Geodesy and Cartography",</FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2"><BR>
</FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2"> by Knud Poder and Kartsen Engsager, Geodetic Division, KMS, Denmark 1998.</FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2"><BR>
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</FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2">The basics of the problem has been solved by R. König und K.H: Weise in 1951.</FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2"><BR>
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</FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2">The transformation of Geotetic Coordinates (ellipsoidal) may be transformed to Transversal</FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2"><BR>
</FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2">coordinates in three steps ::</FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2"><BR>
</FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2"> </FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2"><BR>
</FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2"> 1) Geodetic coord. (phi, lambda) are transformed to a Gaussian Sphere using a fourth</FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2"><BR>
</FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2"> degree Clenshaw summation giving Gaussian Coord. (PHI, LAMBDA).</FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2"><BR>
<BR>
</FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2"> 2) Gaussian coord. (PHI, LAMBDA) are transformed to Complex Gaussian coord (Y, X).</FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2"><BR>
</FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2"> (The formulas are in principle the same as used in Mecator Mapping).</FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2"><BR>
<BR>
</FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2"> 3) Complex Gaussian coord (Y,X) are transformed to Transversal coord (N, E) using</FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2"><BR>
</FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2"> a fourth degree Comples Clenshaw summation, - concatenated by a scaling.</FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2"><BR>
<BR>
</FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2">The opposit direction transforms from Transversal coord. (N,E) to Geodetic coord (phi, lambda).</FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2"><BR>
<BR>
</FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2">This transformation is done with an accuracy better than 3e-5 m for E < 4000 km !!!!</FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2"><BR>
</FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2">This transformation passes the Noth/Southpole without any difficulties. In our GIS system the</FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2"><BR>
</FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2">earth is shown more times rolling around the central meridian of the Transversal Mercator !!!</FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2"><BR>
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</FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2">I hope taht you are able to take these informations into consideration when making guidelines</FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2"><BR>
</FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2">for using the Transverse Mercator mapping.</FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2"><BR>
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