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<DIV><FONT face=Calibri>Muneendra Kumar and John Badekas may have been at Ohio
State at the same time. Molodensky was, indeed, from a previous
generation. I believe that Professor Badekas recently retired from the
National Technical University of Athens. He, too, was a photogrammetrist.
</FONT></DIV>
<DIV> </DIV>
<DIV><FONT face=Calibri>Noel Zinn, Principal, Hydrometronics
LLC<BR>+1-832-539-1472 (office), +1-281-221-0051 (cell)<BR><A
title="mailto:noel.zinn@hydrometronics.com
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(email)<BR><A
title="http://www.hydrometronics.com
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<DIV style="font-color: black"><B>From:</B> <A
title="mailto:cjmce@lsu.edu
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href="mailto:cjmce@lsu.edu">Clifford J Mugnier</A> </DIV>
<DIV><B>Sent:</B> Tuesday, October 12, 2010 9:37 AM</DIV>
<DIV><B>To:</B> <A title=proj@lists.maptools.org
href="mailto:proj@lists.maptools.org">PROJ.4 and general Projections
Discussions</A> </DIV>
<DIV><B>Subject:</B> Re: [Proj] Using Proj.4 to compress a
10-parameterMolodensky-Badekas datum shift into 7 parameters</DIV></DIV></DIV>
<DIV><BR></DIV>
<DIV dir=ltr id=idOWAReplyText72307>
<DIV dir=ltr><FONT color=#000000 size=2 face="Times New Roman">The "evaluation
point" is the Datum Origin, a rather important item. In regard to the
"unexplained" difference in ellipsoid height results, my guess is the
approximations made by the inverse algorithm from Geocentric
coordinates.</FONT></DIV>
<DIV dir=ltr><FONT size=2></FONT> </DIV>
<DIV dir=ltr><FONT size=2>Personally, I prefer the elegance of incorporating the
Datum Origin. </FONT></DIV>
<DIV dir=ltr><FONT size=2></FONT> </DIV>
<DIV dir=ltr><FONT size=2>I have also been told by Dr. Muneendra Kumar that
Badekas had nothing to do with Molodensky's original method. I
believe they were in school together at the same time, and Prof. Molodensky
preceeded them on another continent by some years if not decades.</FONT></DIV>
<DIV dir=ltr><FONT color=#000000 size=2
face="Times New Roman"></FONT> </DIV></DIV>
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<DIV><FONT color=#000000 size=2 face="Times New Roman"><SPAN
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<DIV style="MARGIN: 0in 0in 0pt" class=MsoNormal><SPAN
style="FONT-SIZE: 10pt; mso-ansi-language: DE" lang=DE>Clifford J. Mugnier,
C.P., C.M.S.<o:p></o:p></SPAN></DIV>
<DIV style="MARGIN: 0in 0in 0pt" class=MsoNormal><SPAN
style="FONT-SIZE: 10pt">Chief of Geodesy,<o:p></o:p></SPAN></DIV>
<DIV style="MARGIN: 0in 0in 0pt" class=MsoNormal><B><SPAN
style="FONT-VARIANT: small-caps; FONT-SIZE: 10pt">Center for
GeoInformatics<o:p></o:p></SPAN></B></DIV>
<DIV style="MARGIN: 0in 0in 0pt" class=MsoNormal><SPAN
style="FONT-SIZE: 10pt">Department of Civil Engineering <o:p></o:p></SPAN></DIV>
<DIV style="MARGIN: 0in 0in 0pt" class=MsoNormal><SPAN
style="FONT-SIZE: 10pt">Patrick F. Taylor Hall 3223A<o:p></o:p></SPAN></DIV>
<DIV style="MARGIN: 0in 0in 0pt" class=MsoNormal><B><SPAN
style="FONT-SIZE: 10pt">LOUISIANA STATE UNIVERSITY <o:p></o:p></SPAN></B></DIV>
<DIV style="MARGIN: 0in 0in 0pt" class=MsoNormal><SPAN
style="FONT-SIZE: 10pt">Baton Rouge, LA<SPAN style="mso-spacerun: yes">
</SPAN>70803<o:p></o:p></SPAN></DIV>
<DIV style="MARGIN: 0in 0in 0pt" class=MsoNormal><SPAN
style="FONT-SIZE: 10pt">Voice and Facsimile:<SPAN
style="mso-spacerun: yes"> </SPAN>(225) 578-8536 [Academic]
<o:p></o:p></SPAN></DIV>
<DIV style="MARGIN: 0in 0in 0pt" class=MsoNormal><SPAN
style="FONT-SIZE: 10pt">Voice and Facsimile:<SPAN
style="mso-spacerun: yes"> </SPAN>(225) 578-4578 [Research]
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style="FONT-SIZE: 10pt">Cell: (225) 238-8975 [Academic &
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<FONT size=2 face=Tahoma><B>From:</B> proj-bounces@lists.maptools.org on behalf
of Mikael Rittri<BR><B>Sent:</B> Tue 12-Oct-10 03:45<BR><B>To:</B> PROJ.4 and
general Projections Discussions<BR><B>Subject:</B> [Proj] Using Proj.4 to
compress a 10-parameter Molodensky-Badekas datum shift into 7
parameters<BR></FONT><BR></DIV>
<DIV><BR>
<P><FONT size=2>A Molodensky-Badekas datum shift is represented by 10
parameters.<BR>But it can be compressed to a 7-parameter
representation.<BR><BR>As Noel Zinn has explained (<A
href="http://lists.maptools.org/pipermail/proj/2010-October/005424.html">http://lists.maptools.org/pipermail/proj/2010-October/005424.html</A>),<BR>the
10-parameter representation has advantages over the 7-parameter<BR>one, for
people who derive, analyze and compare datum shifts.<BR><BR>But for people who
just use a datum shift to transform coordinates,<BR>the 7-parameter
representation gives the same results. In this<BR>limited sense, the compression
is lossless, which is useful if<BR>your software (like Proj.4) does not support
10-parameter M-B.<BR><BR>I learned how to do the compression from Melita Kennedy
(thanks<BR>again!). And I have now realized that one can persuade Proj.4
to<BR>do most of the work of the compression process. Since I
thought<BR>this is rather nice, I'd like to explain it by an
example.<BR><BR>Example: M-B datum shift EPSG:1096, "La Canoa to WGS 84
(2)",<BR>which has the same parameters as EPSG:1771, "La Canoa to REGVEN
(1)".<BR> <BR> Source ellipsoid:
International 1924.<BR> Target ellipsoid: WGS
84.<BR> <BR> dX =
-270.933 m<BR> dY = 115.599 m<BR> dZ =
-360.226 m<BR> RX = -5.266 arc sec<BR> RY =
-1.238 arc sec<BR> RZ = 2.381 arc
sec<BR> dS = -5.109 ppm<BR> eX =
2464351.59 m<BR> eY = -5783466.61 m<BR> eZ
= 974809.81 m<BR><BR>where eX,eY,eZ are the geocentric coordinates
of the so-called<BR>evaluation point.<BR><BR>In principle, the equivalent
7-parameter datum shift should have<BR>the same rotations RX, RY, RZ and the
same scale difference dS.<BR>But there is a catch: the sign convention for the
rotations.<BR>M-B uses the same sign convention as Coordinate Frame
Rotation,<BR>while cs2cs uses the opposite convention of the Position
Vector<BR>Transform, so we must negate the three rotations. So, in
cs2cs<BR>syntax, the 7-parameter datum shift we seek has the
form<BR><BR>
+towgs84=?,?,?,5.266,1.238,-2.381,-5.109<BR> <BR>To
find the question marks, we have to do three steps. <BR><BR>i) Make a
7-parameter "something" by temporarily replacing<BR> the question
marks by zeros. It is not really a datum<BR> shift, but we
might call it a 7-parameter compressor.<BR> Use it in a cs2cs
command like this<BR> <BR> >cs2cs -f "%.3f"
+proj=geocent +towgs84=0,0,0,5.226,1.238,-2.381,-5.109 +to +datum=WGS84
+proj=geocent<BR><BR> As input, use the evaluation point eX,eY,eZ of
the M-B datum shift:<BR><BR> 2464351.59
-5783466.61 974809.81<BR><BR> We get the
output<BR><BR> 2464278.090 -5783490.207
974643.507<BR><BR>ii) Now subtract the output row from the input row, and we
get<BR><BR>
73.500 23.597
166.303<BR><BR>iii) Then add the original dX,dY,dZ from the M-B datum
shift,<BR> which were -270.933,115.599,-360.226, and we
get<BR><BR>
-197.433 139.196
-193.923<BR> <BR>The last three values are the question marks in our
7-parameter<BR>datum shift.<BR><BR>To test it, we use the test point given in
section 2.4.4.1,<BR>pages 114-115, EPSG Guidance Note 7.2, <A
href="http://www.epsg.org/guides/docs/G7-2.pdf">http://www.epsg.org/guides/docs/G7-2.pdf</A><BR><BR>>cs2cs
+ellps=intl +proj=longlat
+towgs84=-197.433,139.196,-193.923,5.226,1.238,-2.381,-5.109 +to +datum=WGS84
+proj=longlat<BR>66d4'48.091"W 9d35'0.386"N
201.46<BR>66d4'54.705"W 9d34'49.001"N
180.499<BR><BR>According to GN 7.2, the result should have
been <BR><BR>66°04'54.705"W 9°34'49.001"N 180.51
m<BR><BR>so we have achieved a lossless compression - apart from
the<BR>unexplained difference of about 1.1 cm in the ellipoidal
height. <BR> <BR>Regards,<BR>Mikael Rittri<BR>Carmenta
AB<BR>Sweden<BR>www.carmenta.com<BR>_______________________________________________<BR>Proj
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