[OSRS-PROJ] Pseudo X/Y values, forward and reverse
Clifford J Mugnier
cjmce at lsu.edu
Thu Jan 30 21:22:09 PST 2003
William,
Yes, it counts in BOTH directions. I'm currently writing the chapter on
"Object Space Coordinate Systems" for the new 5th edition of the "Manual of
Photogrammetry," and I'm including up to the 7th derivative in both direct
and inverse transformations. Why weren't greater expansions included into
PROJ4? It's not a topic of general interest in cartography. Cartographers
generally ignore such things, including the late John P. Snyder. John was
only interested in what was germain to the U.S. Geological Survey and the
scales of maps that they produced. John was never interested in geodetic
stuff. John avoided datums and such things.
WGS84 was a topic of vague interest at the time, NAD83 was just coming on
line, and cartographic interests were beginning to be getting into GIS
applications at the time. Remember now, that was 20 years ago! When it
came to private consulting stuff, John used my software (GRIDS 2.0)with the
full 15th derivative implementations in both direct and inverse for
transverse Mercator. USGS stuff was nice, but when it came to "real world"
applications, well ...
What's one of the rarest books ever printed? Try TM 5-241-10 "Universal
Transverse Mercator Grid EXTENSION OF ZONE TO ZONE TRANSFORMATION TABLES."
Sept, 1962, 642 pp.
No, I'm not going to fax a copy. Yes, it has the only copy (ever) of the
equations to the 15th derivative.
Conoco in Ponca City, OK., purchased a copy of my 7th derivative equations
of the Gauss-Krueger Transverse Mercator transformation back in 1988-1989.
The man's name was Grady Lewis. It ran in MS-DOS. Small world! Ten years
earlier than that, both Conoco and Phillips purchased the same stuff in
HP-67 and (later) HP-41CV programs for the same thing.
Cliff
Clifford J. Mugnier (cjmce at LSU.edu)
Chief of Geodesy
Center for GeoInformatics
LOUISIANA STATE UNIVERSITY
Dept. of Civil Engineering
CEBA 3223A
Baton Rouge, LA 70810
Facsimiile (225) 578-8652
Voice (225) 578-8536
Beep (504) 382-4371
------------------------------------------------------------
http://www.ASPRS.org/resources.html
http://www.ce.LSU.edu/~mugnier/
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Cliff,
Thank you, this is making more sense now. The number of derivatives used
in the algorithm limits how far from the central meridian that you can go
and still expect to return to the same lat/long. Is this only on the
inverse calculation or is this on the forward calculation as well. In
other words, do the calculated x/y values from the forward projection
suffer in accuracy? Also, was there some reason why they did not carry out
the formula with more derivatives in PROJ4?
William Hersman
ConocoPhillips, Alaska
"Clifford J Mugnier" <cjmce at lsu.edu>
Sent by: owner-osrs-proj at remotesensing.org
01/30/2003 01:53 PM
Any replies will be addressed to: osrs-proj
To: osrs-proj at remotesensing.org
cc:
Subject: Re: [OSRS-PROJ] Pseudo X/Y values, forward and reverse
Frank,
It's the implementation. I think John P. Snyder's book and formulae were
used for PROJ4. That would mean that the formulae for TM are to the 5th
derivative. That barely gets to +/- 3 degrees from the central meridian.
7th derivative gets almost to 4 degrees difference. Fifteenth derivative
gets to +/- 24 degrees from the central meridian with 1 mm "round-trip"
computational accuracy.
Cliff Mugnier
LOUISIANA STATE UNIVERSITY
William Hersman wrote:
> Input -175.1234589 59.7654305 DD
> Return -4054878.4814 2990301.082 ASP 4 FEET
> Input -4054878.4814 2990301.082 ASP 4 FEET
> Return -175.1487387 59.7638269 DD
William,
It would clearly help alot if you could provide the details of the
coordinate system. I tried this:
warmerda at gdal2200[237]% proj -I -v +init=nad27:5004 +units=ft
#Transverse Mercator
# Cyl, Sph&Ell
# +init=nad27:5004 +units=ft +proj=tmerc +datum=NAD27 +lon_0=-150 +lat_0=54
# +k=.9999 +x_0=152400.3048006096 +y_0=0 +no_defs +ellps=clrk66
# +nadgrids=conus,ntv1_can.dat
-4054905.40 2990291.47 (input)
175d7'10.261"W 59d45'56.295"N (output)
warmerda at gdal2200[238]% proj -v +init=nad27:5004 +units=ft
#Transverse Mercator
# Cyl, Sph&Ell
# +init=nad27:5004 +units=ft +proj=tmerc +datum=NAD27 +lon_0=-150 +lat_0=54
# +k=.9999 +x_0=152400.3048006096 +y_0=0 +no_defs +ellps=clrk66
# +nadgrids=conus,ntv1_can.dat
175d7'10.261"W 59d45'56.295"N (input)
-4054186.84 2990083.90 (output)
I see there is an over 700 ft difference in the positions. Far more than
I would have expected. In this case the longitude is 25 degrees away from
the central meridian for the zone, but I wouldn't have thought the
reversibility of the equations would have been so poor at that distance.
Cliff, you mentioned that the TM coordinates would not be reversible at
great distances. Is this the nature of the TM equations or a weakness in
their implementation with PROJ.4?
Best regards,
--
---------------------------------------+--------------------------------------
I set the clouds in motion - turn up | Frank Warmerdam,
warmerdam at pobox.com
light and sound - activate the windows | http://pobox.com/~warmerdam
and watch the world go round - Rush | Geospatial Programmer for Rent
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