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<DIV dir=ltr><FONT color=#000000 size=2 face="Times New Roman">Noel,</FONT></DIV>
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<DIV dir=ltr><FONT size=2>Facing a July 1 deadline for a new edition of the <STRONG><EM>Manual</EM></STRONG>, but I'll try to look up some hoary details afterwards. I've got Jordan-Eggert as well as Helmert, Driencourt & Laborde, and some others that probably have the citations you need in various languages.</FONT></DIV>
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<DIV dir=ltr><FONT size=2>I am pretty certain that the original equations did not even come close to the LSR on the ellipsoid. My contention is that the LSR is <STRONG><EM><U>equivalent</U></EM></STRONG> to the <EM><STRONG><U>intention</U></STRONG></EM> of the Polyhedric/Polyeder for the ellipsoid. The old stuff always employed <EM>equivalent spheres</EM>, anyway. That's where so much of the stuff came from back then that is now screwy-looking. A few hold-outs are like the Rosenmund Oblique Cyllindrical and the Krovak Oblique Conic.</FONT></DIV>
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<DIV dir=ltr><FONT size=2>Cliff</FONT></DIV>
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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.<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" /><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 3531</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] <o:p></o:p></SPAN></DIV>
<DIV style="MARGIN: 0in 0in 0pt" class=MsoNormal><SPAN style="FONT-SIZE: 10pt">Cell: (225) 328-8975 [Academic & Research]<o:p></o:p></SPAN></DIV>
<DIV style="MARGIN: 0in 0in 0pt" class=MsoNormal><SPAN style="FONT-SIZE: 10pt">Honorary Life Member of the <o:p></o:p></SPAN></DIV>
<DIV style="MARGIN: 0in 0in 0pt" class=MsoNormal><SPAN style="FONT-SIZE: 10pt">Louisiana Society of Professional Surveyors <o:p></o:p></SPAN></DIV>
<DIV style="MARGIN: 0in 0in 0pt" class=MsoNormal><SPAN style="FONT-SIZE: 10pt">Fellow Emeritus of the ASPRS <o:p></o:p></SPAN></DIV>
<DIV style="MARGIN: 0in 0in 0pt" class=MsoNormal><SPAN style="FONT-SIZE: 10pt">Member of the Americas Petroleum Survey Group<o:p></o:p></SPAN></DIV><BR></SPAN></FONT></DIV></DIV>
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<FONT size=2 face=Tahoma><B>From:</B> proj-bounces@lists.maptools.org on behalf of Noel Zinn (cc)<BR><B>Sent:</B> Wed 29-Jun-11 09:33<BR><B>To:</B> PROJ.4 and general Projections Discussions<BR><B>Subject:</B> Re: [Proj] Ellipsoidal Orthographic<BR></FONT><BR></DIV>
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<P style="MARGIN: 0in 0in 0pt" class=MsoNormal>Cliff has saved me a trip to the "old-timey" library by sending me a PDF of the relevant chapter of the 2004 Manual of Photogrammetry.<SPAN> </SPAN>The LSR equations are there as they were in 1980 by the name of geocentric local vertical (see Ellipsoidal Orthographic presentation).<SPAN> </SPAN>There is also the statement, "When <I>h0 </I><SPAN>= 0</SPAN>, and used only in a 2-dimensional case, it is equivalent to the old European <I>Müffling </I>or Polyeder (Polyhedric) projection commonly found in 18<SPAN>th </SPAN>and 19<SPAN>th </SPAN>century maps compiled with plane table and alidade."<SPAN> </SPAN>As noted previously, Cliff has asserted similarly here and in other forums.<SPAN> </SPAN></P>
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<P style="MARGIN: 0in 0in 0pt" class=MsoNormal>You're peerless at what you do, Cliff, but what I mean by "beef" is more than an assertion, but corroboration in the form (for example) of a photocopy of some hoary document in Dutch or in von <SPAN>Müffling penmanship from your geodetic antiquarium.<SPAN> </SPAN>When you were working for ONI in the eighties, I was doing a similar job for NCS.<SPAN> </SPAN>You'll remember that our clients' motto was "trust but verify".<SPAN> </SPAN></SPAN></P>
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<P style="MARGIN: 0in 0in 0pt" class=MsoNormal>One issue is whether von <SPAN>Müffling was using the LSR equations, but the other issue is whether he realized he was dealing with the ellipsoidal orthographic.<SPAN> </SPAN>Have the authors of the Manual of Photogrammetry realized that?<SPAN> </SPAN>It's not mentioned.<SPAN> </SPAN>It first dawned on me in 2005.<SPAN> </SPAN>I don't know when ESRI made the connection, but Dave Burrows communicated it to me 2007 and ESRI knew it before then.<SPAN> </SPAN>I wish I knew if these were Snyder's equations for the ellipsoidal orthographic back in 1979, which he choose not to share.</SPAN></P>
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<P style="MARGIN: 0in 0in 0pt" class=MsoNormal><SPAN>Noel</SPAN></P>
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<DIV style="FONT-FAMILY: 'Calibri'; COLOR: #000000; FONT-SIZE: 12pt">Noel Zinn, Principal, Hydrometronics LLC<BR>+1-832-539-1472 (office), +1-281-221-0051 (cell)<BR>noel.zinn@hydrometronics.com (email)<BR>http://www.hydrometronics.com (website)<BR></DIV>
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<DIV><B>From:</B> <A title=ndzinn@comcast.net href="mailto:ndzinn@comcast.net">Noel Zinn (cc)</A> </DIV>
<DIV><B>Sent:</B> Tuesday, June 28, 2011 5:14 PM</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] Ellipsoidal Orthographic</DIV></DIV></DIV>
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<DIV>Thanks, Cliff. A search of “Polyhedric <SPAN>Müffling” turns up a trail of your postings in many forums, but no “beef” (equations). I’m off to the library tomorrow to find the 2004 photogrammetry manual. Cheers.</SPAN></DIV>
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<DIV style="FONT-FAMILY: 'Calibri'; COLOR: #000000; FONT-SIZE: 12pt">Noel Zinn, Principal, Hydrometronics LLC<BR>+1-832-539-1472 (office), +1-281-221-0051 (cell)<BR>noel.zinn@hydrometronics.com (email)<BR>http://www.hydrometronics.com (website)<BR></DIV>
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<DIV><B>From:</B> <A title=cjmce@lsu.edu href="mailto:cjmce@lsu.edu">Clifford J Mugnier</A> </DIV>
<DIV><B>Sent:</B> Tuesday, June 28, 2011 9:20 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] Ellipsoidal Orthographic</DIV></DIV></DIV>
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<DIV dir=ltr><FONT color=#000000 size=2 face="Times New Roman">I have always considered the identical equations to represent the Polyhedric projection (also known as the <SPAN style="FONT-FAMILY: 'Times New Roman','serif'; FONT-SIZE: 10pt">Müffling projection</SPAN>). At large scales 1:100,000, 1:50,000 it seems to fit perfectly in my personal experience. My first experience with the Local Space Rectangular was in 1968 at Army Map Service for the photo-triangulation of the Apollo Lunar Landing Map series. It's a standard transformation in many photogrammetric photo-triangulation software packages. See my treatment of the Polyhedric/<SPAN style="FONT-FAMILY: 'Times New Roman','serif'; FONT-SIZE: 10pt">Müffling projection</SPAN> in the <EM>Manual of Photogrammetry</EM>, 5th edition, 2004, Chapter 3, Section 3.1.2.2, page 189. John Snyder and I did discuss that back in the 1980s, and I explained to him that this was exactly what I used to solve the infamous "Tampico Datum" problem of Mexico when I was doing some consulting work over at Offshore Navigation, Inc. back then.</FONT></DIV>
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<DIV style="MARGIN: 0in 0in 0pt" class=MsoNormal><SPAN style="FONT-SIZE: 10pt" lang=DE>Clifford J. Mugnier, C.P., C.M.S.</SPAN></DIV>
<DIV style="MARGIN: 0in 0in 0pt" class=MsoNormal><SPAN style="FONT-SIZE: 10pt">Chief of Geodesy,</SPAN></DIV>
<DIV style="MARGIN: 0in 0in 0pt" class=MsoNormal><B><SPAN style="FONT-VARIANT: small-caps; FONT-SIZE: 10pt">Center for GeoInformatics</SPAN></B></DIV>
<DIV style="MARGIN: 0in 0in 0pt" class=MsoNormal><SPAN style="FONT-SIZE: 10pt">Department of Civil Engineering </SPAN></DIV>
<DIV style="MARGIN: 0in 0in 0pt" class=MsoNormal><SPAN style="FONT-SIZE: 10pt">Patrick F. Taylor Hall 3531</SPAN></DIV>
<DIV style="MARGIN: 0in 0in 0pt" class=MsoNormal><B><SPAN style="FONT-SIZE: 10pt">LOUISIANA STATE UNIVERSITY </SPAN></B></DIV>
<DIV style="MARGIN: 0in 0in 0pt" class=MsoNormal><SPAN style="FONT-SIZE: 10pt">Baton Rouge, LA<SPAN> </SPAN>70803</SPAN></DIV>
<DIV style="MARGIN: 0in 0in 0pt" class=MsoNormal><SPAN style="FONT-SIZE: 10pt">Voice and Facsimile:<SPAN> </SPAN>(225) 578-8536 [Academic] </SPAN></DIV>
<DIV style="MARGIN: 0in 0in 0pt" class=MsoNormal><SPAN style="FONT-SIZE: 10pt">Voice and Facsimile:<SPAN> </SPAN>(225) 578-4578 [Research] </SPAN></DIV>
<DIV style="MARGIN: 0in 0in 0pt" class=MsoNormal><SPAN style="FONT-SIZE: 10pt">Cell: (225) 328-8975 [Academic & Research]</SPAN></DIV>
<DIV style="MARGIN: 0in 0in 0pt" class=MsoNormal><SPAN style="FONT-SIZE: 10pt">Honorary Life Member of the </SPAN></DIV>
<DIV style="MARGIN: 0in 0in 0pt" class=MsoNormal><SPAN style="FONT-SIZE: 10pt">Louisiana Society of Professional Surveyors </SPAN></DIV>
<DIV style="MARGIN: 0in 0in 0pt" class=MsoNormal><SPAN style="FONT-SIZE: 10pt">Fellow Emeritus of the ASPRS </SPAN></DIV>
<DIV style="MARGIN: 0in 0in 0pt" class=MsoNormal><SPAN style="FONT-SIZE: 10pt">Member of the Americas Petroleum Survey Group</SPAN></DIV><BR></SPAN></FONT></DIV></DIV>
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<FONT size=2 face=Tahoma><B>From:</B> proj-bounces@lists.maptools.org on behalf of Noel Zinn (cc)<BR><B>Sent:</B> Tue 28-Jun-11 06:43<BR><B>To:</B> PROJ.4 and general Projections Discussions<BR><B>Subject:</B> [Proj] Ellipsoidal Orthographic<BR></FONT><BR></DIV>
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<P><FONT size=2>The only equations for the ellipsoidal orthographic that I've ever found<BR>published (in a book or journal) are those of Bugayevskiy and Snyder (1995),<BR>which are complicated and (the authors acknowledge) truncated. Following<BR>EPSG Guidance Note 7, Part 2, I've prepared a presentation on the<BR>ellipsoidal orthographic that offers simple, exact equations. The<BR>derivation also suggests that the ellipsoidal orthographic is unique among<BR>projections, being transitional between distorted cartography in 2D and<BR>undistorted visualization in 3D on a computer in ECEF or ENU (topocentric)<BR>coordinates. A link to the presentation follows:<BR><BR><A href="http://www.hydrometronics.com/downloads/Ellipsoidal%20Orthographic%20Projection.pdf">http://www.hydrometronics.com/downloads/Ellipsoidal%20Orthographic%20Projection.pdf</A><BR><BR>Does anyone in this group have other sources of information on the<BR>ellipsoidal orthographic?<BR><BR>Noel<BR><BR>PS - Scroll the page if it presents in black<BR><BR>Noel Zinn, Principal, Hydrometronics LLC<BR>+1-832-539-1472 (office), +1-281-221-0051 (cell)<BR>noel.zinn@hydrometronics.com (email)<BR><A href="http://www.hydrometronics.com/">http://www.hydrometronics.com</A> (website)<BR><BR><BR>_______________________________________________<BR>Proj mailing list<BR>Proj@lists.maptools.org<BR><A href="http://lists.maptools.org/mailman/listinfo/proj">http://lists.maptools.org/mailman/listinfo/proj</A><BR></FONT></P></DIV>
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