<HTML dir=ltr><HEAD><TITLE>Re: [Proj] Ellipsoidal Orthographic</TITLE>
<META content="text/html; charset=unicode" http-equiv=Content-Type>
<META name=GENERATOR content="MSHTML 8.00.7600.16821"></HEAD>
<BODY>
<DIV dir=ltr id=idOWAReplyText8412>
<DIV dir=ltr><FONT color=#000000 size=2 face="Times New Roman">Charles,</FONT></DIV>
<DIV dir=ltr><FONT size=2></FONT> </DIV>
<DIV dir=ltr><FONT size=2>Using the closed form for the geocentric inverse is OK for surface mapping, but for a more universal application that will work with aerial photography and particularly with satellite imagery, the closed form deteriorates with altitude above the ellipsoid. The iterative form will accommodate orbital imagery altitudes with no loss in computational precision. That's a significant consideration since the "Oil Patch" indeed uses orbital imagery in their exploration activities.</FONT></DIV>
<DIV dir=ltr><FONT size=2></FONT> </DIV>
<DIV dir=ltr><FONT size=2>Cliff</FONT></DIV>
<DIV dir=ltr><FONT color=#000000 size=2 face="Times New Roman"></FONT> </DIV></DIV>
<DIV dir=ltr id=idSignature26522>
<DIV><FONT color=#000000 size=2 face="Times New Roman"><SPAN style="FONT-SIZE: 10pt">
<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>
<DIV dir=ltr><BR>
<HR tabIndex=-1>
<FONT size=2 face=Tahoma><B>From:</B> proj-bounces@lists.maptools.org on behalf of Charles Karney<BR><B>Sent:</B> Tue 28-Jun-11 12:59<BR><B>To:</B> PROJ.4 and general Projections Discussions<BR><B>Subject:</B> Re: [Proj] Ellipsoidal Orthographic<BR></FONT><BR></DIV>
<DIV>
<P><FONT size=2>Noel,<BR><BR>You use an iterative method to solve for the reverse projection. But<BR>the reverse projection can be written in closed form. Recovering the 3d<BR>position [x,y,z] from the easting and northing entails solving a<BR>quadratic equation, so that you get 2 or 0 (or exceptionally 1) root, as<BR>expected.<BR><BR>I can provide you with the outline of the solution if you want.<BR><BR> --Charles<BR><BR><BR>On 06/28/11 07:43, Noel Zinn (cc) wrote:<BR>> 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>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></BODY></HTML>