[Proj] Ellipsoidal Orthographic

Wed Jun 29 07:33:52 PDT 2011

[Proj] Ellipsoidal OrthographicCliff 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.  The LSR equations are there as they were in 1980 by the name of geocentric local vertical (see Ellipsoidal Orthographic presentation).  There is also the statement, "When h0 = 0, and used only in a 2-dimensional case, it is equivalent to the old European Müffling or Polyeder (Polyhedric) projection commonly found in 18th and 19th century maps compiled with plane table and alidade."  As noted previously, Cliff has asserted similarly here and in other forums.  

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 Müffling penmanship from your geodetic antiquarium.  When you were working for ONI in the eighties, I was doing a similar job for NCS.  You'll remember that our clients' motto was "trust but verify".  

One issue is whether von Müffling was using the LSR equations, but the other issue is whether he realized he was dealing with the ellipsoidal orthographic.  Have the authors of the Manual of Photogrammetry realized that?  It's not mentioned.  It first dawned on me in 2005.  I don't know when ESRI made the connection, but Dave Burrows communicated it to me 2007 and ESRI knew it before then.  I wish I knew if these were Snyder's equations for the ellipsoidal orthographic back in 1979, which he choose not to share.

Noel

Noel Zinn, Principal, Hydrometronics LLC
+1-832-539-1472 (office), +1-281-221-0051 (cell)
noel.zinn at hydrometronics.com (email)
http://www.hydrometronics.com (website)

From: Noel Zinn (cc) 
Sent: Tuesday, June 28, 2011 5:14 PM
To: PROJ.4 and general Projections Discussions 
Subject: Re: [Proj] Ellipsoidal Orthographic

Thanks, Cliff.  A search of “Polyhedric 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.

Noel Zinn, Principal, Hydrometronics LLC
+1-832-539-1472 (office), +1-281-221-0051 (cell)
noel.zinn at hydrometronics.com (email)
http://www.hydrometronics.com (website)

From: Clifford J Mugnier 
Sent: Tuesday, June 28, 2011 9:20 AM
To: PROJ.4 and general Projections Discussions 
Subject: Re: [Proj] Ellipsoidal Orthographic

I have always considered the identical equations to represent the Polyhedric projection (also known as the Müffling projection).  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/Müffling projection in the Manual of Photogrammetry, 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.

Clifford J. Mugnier, C.P., C.M.S.
Chief of Geodesy,
Center for GeoInformatics
Department of Civil Engineering 
Patrick F. Taylor Hall 3531
LOUISIANA STATE UNIVERSITY 
Baton Rouge, LA  70803
Voice and Facsimile:  (225) 578-8536 [Academic] 
Voice and Facsimile:  (225) 578-4578 [Research] 
Cell: (225) 328-8975 [Academic & Research]
Honorary Life Member of the 
Louisiana Society of Professional Surveyors 
Fellow Emeritus of the ASPRS 
Member of the Americas Petroleum Survey Group

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From: proj-bounces at lists.maptools.org on behalf of Noel Zinn (cc)
Sent: Tue 28-Jun-11 06:43
To: PROJ.4 and general Projections Discussions
Subject: [Proj] Ellipsoidal Orthographic

The only equations for the ellipsoidal orthographic that I've ever found
published (in a book or journal) are those of Bugayevskiy and Snyder (1995),
which are complicated and (the authors acknowledge) truncated.  Following
EPSG Guidance Note 7, Part 2, I've prepared a presentation on the
ellipsoidal orthographic that offers simple, exact equations.  The
derivation also suggests that the ellipsoidal orthographic is unique among
projections, being transitional between distorted cartography in 2D and
undistorted visualization in 3D on a computer in ECEF or ENU (topocentric)
coordinates.  A link to the presentation follows:

http://www.hydrometronics.com/downloads/Ellipsoidal%20Orthographic%20Projection.pdf

Does anyone in this group have other sources of information on the
ellipsoidal orthographic?

Noel

PS - Scroll the page if it presents in black

Noel Zinn, Principal, Hydrometronics LLC
+1-832-539-1472 (office), +1-281-221-0051 (cell)
noel.zinn at hydrometronics.com (email)
http://www.hydrometronics.com (website)

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