# [OSRS-PROJ] Pseudo X/Y values, forward and reverse

William Hersman Willy.Hersman at conocophillips.com
Thu Jan 30 18:58:30 EST 2003

```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

"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
# +k=.9999 +x_0=152400.3048006096 +y_0=0 +no_defs +ellps=clrk66
-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
# +k=.9999 +x_0=152400.3048006096 +y_0=0 +no_defs +ellps=clrk66
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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