[Proj] The world of ECEF aka geocentric coordinates

Noel Zinn ndzinn at comcast.net
Tue Feb 3 13:25:23 EST 2009

The 4th edition of the Manual of Photogrammetry (1980) page 485 section (phew!) gives the equations and refers to this as
"geocentric-local vertical".  I believe ESRI uses the same name for this
coordinate conversion in their software.

Bugayevskiy and Snyder (1995) on page 3 section 1.1.2 (right up front in
their "Map Projections A Reference Manual") call this the "topocentric
horizon coordinate system" and give different equations than the Manual of
Photogrammetry (due to a different, more cumbersome derivation).  In fact,
both citations are equivalent mathematically with a little additional

EPSG terminology is "topocentric coordinate system".  See section 2.2.2 of
Guidance Note 7-2 at www.epsg.org which offers forward and reverse

Now, it turns out that if you throw away the U of this ENU of this
coordinate system you have the (exact) ellipsoidal form of a perspective map
projection, the orthographic. Unfortunately, Bugayevskiy and Snyder, after a
cumbersome derivation that tosses the high order terms of the series they
invoke, offer an approximate form of the ellipsoidal orthographic on page
116 (when the exact form was stated on page 3). 

I vote for topocentric coordinates. 

Noel Zinn

-----Original Message-----
From: proj-bounces at lists.maptools.org
[mailto:proj-bounces at lists.maptools.org] On Behalf Of Gerald I. Evenden
Sent: Tuesday, February 03, 2009 11:20 AM
To: PROJ.4 and general Projections Discussions
Subject: Re: [Proj] The world of ECEF aka geocentric coordinates

On Tuesday 03 February 2009 11:43:00 am Clifford J Mugnier wrote:
> Local Space Rectangular (LSR) is the approximately  60-70 year old
> terminology used in computational photogrammetry.
> Polyhedric (Polyeder in Dutch or German) is the 19th century terminology
> for the "projection."  (Also known as the "Tampico Datum" from the 1920s
> 1930s.)
> C. Mugnier

If age has priority, it would seem to be a winner but "Rectangular' seem a 
little open to interpretation.

> From: proj-bounces at lists.maptools.org on behalf of Karney, Charles
> Sent: Tue 03-Feb-09 04:19
> While we're at it, what's the consensus for the terminology for the
> Cartesian system with origin at z = 0 tangent to ellipsoid, z up, y
> north?  Choices so far:
>     local Cartesian
>     ENU
>     topocentric

I do have trouble with ENU because of the conflict introduced with 
Easting-Northing as part of its name and the same usage of EN with 
cartographic projections.

There is nothing in the other names that mentions the property of the XY
being tangential to the ellipsoid although the U[p] might imply such.
does not cut it with me as it has too much baggage with other usage.

How about "[Ellipsoid] Tangential Cartesian" or ETC.

Hey, man!  That's got it!

> It seems that topocentric is the best, and this doesn't tie you down to
> Cartesian coordinates.  Transforming to polar gives azimuth-elevation-
> distance.
> --
> Charles Karney <ckarney at sarnoff.com>
> Sarnoff Corporation, Princeton, NJ 08543-5300

The whole religious complexion of the modern world is due
to the absence from Jerusalem of a lunatic asylum.
-- Havelock Ellis (1859-1939) British psychologist
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