[Proj] Ellipsoidal Orthographic

Clifford J Mugnier cjmce at lsu.edu
Tue Jun 28 09:20:02 EST 2011

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, 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
Baton Rouge, LA  70803
Voice and Facsimile:  (225) 578-8536 [Academic] 
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Member of the Americas Petroleum Survey Group


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:


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


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 <http://www.hydrometronics.com/>  (website)

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