<html><head><style type='text/css'>p { margin: 0; }</style></head><body><div style='font-family: Arial; font-size: 12pt; color: #000000'><P class=MsoNormal style="MARGIN: 0in 0in 0pt"><FONT face="Times New Roman">Mikael,</FONT></P>
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<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><FONT face="Times New Roman">Thanks for these references on direct projection.<SPAN style="mso-spacerun: yes"> </SPAN>Weird, yes, in the sense of unusual, but clever and useful for the reasons stated by the authors.<SPAN style="mso-spacerun: yes"> </SPAN></FONT></P>
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<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><FONT face="Times New Roman">Regarding the least-squares adjustment for the new CM, scale on CM and false coordinates, linearization of the TM algorithm by <?xml:namespace prefix = st1 ns = "urn:schemas-microsoft-com:office:smarttags" /><st1:City w:st="on"><st1:place w:st="on">Taylor</st1:place></st1:City> expansion must be exceptionally ugly, but this can be simply accomplished numerically to achieve the same results.</FONT></P>
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<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><FONT face="Times New Roman">Regarding your questions:</FONT></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt 0.25in; TEXT-INDENT: -0.25in; mso-list: l0 level1 lfo1; tab-stops: list .25in"><SPAN style="FONT-FAMILY: Symbol; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol"><SPAN style="mso-list: Ignore">·<SPAN style="FONT: 7pt 'Times New Roman'"> </SPAN></SPAN></SPAN><FONT face="Times New Roman">It's clever.</FONT></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt 0.25in; TEXT-INDENT: -0.25in; mso-list: l0 level1 lfo1; tab-stops: list .25in"><SPAN style="FONT-FAMILY: Symbol; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol"><SPAN style="mso-list: Ignore">·<SPAN style="FONT: 7pt 'Times New Roman'"> </SPAN></SPAN></SPAN><FONT face="Times New Roman">Apparently used in <st1:country-region w:st="on"><st1:place w:st="on">Australia</st1:place></st1:country-region> by Featherstone (cited by the authors).</FONT></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt 0.25in; TEXT-INDENT: -0.25in; mso-list: l0 level1 lfo1; tab-stops: list .25in"><SPAN style="FONT-FAMILY: Symbol; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol"><SPAN style="mso-list: Ignore">·<SPAN style="FONT: 7pt 'Times New Roman'"> </SPAN></SPAN></SPAN><FONT face="Times New Roman">No geographic ambiguity implied in my opinion.<SPAN style="mso-spacerun: yes"> </SPAN>You'll notice the ellipsoid has also changed along with the new parameters already mentioned, an obvious requirement to reduce the residuals of the adjustment.<SPAN style="mso-spacerun: yes"> </SPAN></FONT></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt 0.25in; TEXT-INDENT: -0.25in; mso-list: l0 level1 lfo1; tab-stops: list .25in"><SPAN style="FONT-FAMILY: Symbol; mso-fareast-font-family: Symbol; mso-bidi-font-family: Symbol"><SPAN style="mso-list: Ignore">·<SPAN style="FONT: 7pt 'Times New Roman'"> </SPAN></SPAN></SPAN><FONT face="Times New Roman">What the authors have conjured is a TM on WGS84 that emulates a TM on Bessel (RT90) point by point within acceptable error limits.<SPAN style="mso-spacerun: yes"> </SPAN>But this is just an approximation, as is a 7-parameter similarity transformation for that matter.<SPAN style="mso-spacerun: yes"> </SPAN>The only definitive transformation is that achieved by a readjustment of available survey data (lots of trilateration in <st1:country-region w:st="on"><st1:place w:st="on">Sweden</st1:place></st1:country-region> apparently) with a new ellipsoidal model.<SPAN style="mso-spacerun: yes"> </SPAN>Only that will achieve the least sum of residuals squared.<SPAN style="mso-spacerun: yes"> </SPAN>Geographicals in 3D are closer to reality than anything we do in the plane.<SPAN style="mso-spacerun: yes"> </SPAN></FONT></P>
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<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><FONT face="Times New Roman">Again, thanks,</FONT></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><FONT face="Times New Roman">Noel</FONT></P>
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<P><BR>----- Original Message -----<BR>From: "Mikael Rittri" <Mikael.Rittri@carmenta.com><BR>To: "PROJ.4 and general Projections Discussions" <proj@lists.maptools.org><BR>Sent: Thursday, December 11, 2008 9:43:08 AM GMT -06:00 US/Canada Central<BR>Subject: [Proj] What about datum shift via direct projection?<BR><BR><BR>Gerald wrote: <BR>> While there seems to be lull in the hot debate about separation of <BR>> church and state ... er ... datum and projection,<BR>> [...] <BR>> Thus, why is it so necessary to bind the two operations so tightly as done<BR>> in the proj.4 distribution? I cannot find a precedence for this concept. <BR><BR>This post is not specifically about the PROJ.4 design (so I changed<BR>the Subject line), but it is about how much datums and projections <BR>can and should be separated. <BR><BR>There is method for datum shift that uses a direct projection. <BR><BR>As an example, the old Swedish Grid is traditionally defined <BR>on the Swedish RT90 datum (ellipsoid: Bessel 1841) and using a <BR>Transverse Mercator projection with <BR> central meridian: 15° 48' 29.8" E <BR> scale factor: 1<BR> false easting: 1500000 m <BR> false northing: 0 m<BR>( http://www.lantmateriet.se/templates/LMV_Page.aspx?id=4766&lang=EN ) <BR><BR>With this definition, one would need some datum shift method <BR>to transform between RT90 lon/lat and WGS84 lon/lat.<BR><BR>However, a simpler method, now recommended by the Swedish Land Survey<BR>instead of a 7-parameter shift, is to start from the WGS84 datum, and than<BR>tweak the projection parameters a little: just use a Transverse Mercator <BR>with <BR> central meridian: 15° 48' 22.624306" E <BR> scale factor: 1.00000561024<BR> false easting: 1500064.274 m<BR> false northing: -667.711 m<BR>( http://www.lantmateriet.se/templates/LMV_Page.aspx?id=5197&lang=EN ) <BR><BR>A paper describing this technique is <BR>http://www.fig.net/pub/fig2006/papers/ps05_03/ps05_03_04_engberg_lilje_0670.pdf .<BR><BR>So, I have some rather vague questions to the readers of this list:<BR>- What do you think of this technique?<BR>- Is anyone else using it? <BR>- Doesn't the technique imply that a projected coordinate system <BR> may have an ambiguous geographic coordinate system? For the Swedish Grid,<BR> I can think of the geographic coordinate system as RT90 lon/lat, if I use <BR> the traditional projection parameters. Or I can think of it as WGS84 lon/lat, <BR> if I use the direct projection instead.<BR>- If the correct answer to the previous question is "No, you fool", then what? <BR> If I wanted to express the Swedish Grid, datum-shifted by the direct projection,<BR> in Well-Know Text, then I would be forced to say that the geographic coordinate <BR> system is WGS84 lon/lat. But then the resulting CRS cannot be Swedish Grid, <BR> because Swedish Grid has traditionally RT90 lon/lat as its geographic coordinate <BR> system. <BR><BR>I think direct projections for datum shifts are efficient and easy to<BR>use, and normally as accurate as a 7-parameter shift. But when I try <BR>to fit this method into the traditional framework that separates datum <BR>shifts and projections, and which insists that each projected CRS<BR>has a unique geographic coordinate system, I run into problems.<BR><BR>Are these problems caused by inflexibility in the traditional framework? <BR>Or is the method of direct projection just weird? <BR>Or am I missing some good way to reconcile them? <BR> <BR>Best regards, <BR><BR>--<BR>Mikael Rittri<BR>Carmenta AB<BR>Box 11354<BR>SE-404 28 Göteborg<BR>Visitors: Sankt Eriksgatan 5<BR>SWEDEN<BR>mikael.rittri@carmenta.com<BR>www.carmenta.com<BR>_______________________________________________<BR>Proj mailing list<BR>Proj@lists.maptools.org<BR>http://lists.maptools.org/mailman/listinfo/proj<BR></P></P></div></body></html>