Oblique Mercator transformation

Howdy,

Good that you are using the Stem text. Rather than trying to match your state GIS tool, why not compare your Mathcad results with the output of NGS toolkit item SPCS83?

Are you sure your code is using natural log rather than log10?

Cheers and good luck,

DMM

Mike - thanks for the tip. Yep,definitely using natural log (ln).

These obviously aren't state plane coords, as MI uses 3 zones of lambert conformal projections for SPC. But state agencies (environmental quality, natural resources, etc) not entirely concerned with survey grade precision use the oblique mercator for simplicity of a single zone, state-wide. I have concerns/curiousity w/ how they are deriving these 'GeoRef' coords from geodetic lat & long values.

Howdy again,

Aha. Another single zone system. Does this document describe your system?

http://www.michigan.gov/documents/DNR_Map_Proj_and_MI_Georef_Info_20889_7.pdf

I will review it and post comments if anything seems of note. Last class on projections was a loooong time ago.

Cheers,

DMM

I dunno Butch, I think Mike is right about testing your program using the NGS Program SPC83.

I took a quick look at the Michigan link that Mike posted above, and it looks like a retified Oblique Transverse Mercator to me (but I might have missed something, it was a quick look).

Alaska Zone 1 (5001) is also an Oblique Transverse Mercator (the ONLY SPC zone that is), so it might be worth a shot. Try a couple of stations in Southeast Alaska, and see how it works.

Loyal

Yep, I used this document for the false northings / eastings, scale, azimuth of skew, lat & long @ origin etc. I'm not sure I can use the NGS tool kit to compare results, since I can't force it to select this GeoRef projection system & its values. It will (I assume) default to the actual established SPC system for the lat & long I plug in, which will be the Lambert conformal for any lat / long value in MI.

This is kind of why I'm pursuing this, since I'd like a method to verify values in this GeoRef system since any monkey can obtain & plug in Gps Lat / Long values.

Loyal, the info I dug up on this system indicates it as a Hotine Skew Orthomorphic projection. It was developed by a Dr. Ralph Moore Berry @ University of Michigan in 1972 to encompass the whole of MI & the territorial waters of the Great Lakes in a single zone. Heres an informative link:
http://www.rsgis.msu.edu/pdf/mi_coordinate_systems.pdf

I will compare my model to the Alaska Zone through the NGS toolkit & see what I find.

My understanding is that the “Oblique Transverse Mercator Projection” used in Alaska Zone 1, and the “Hotine Skew Orthomorphic projection” (aka. “rectified skew orthomorphic,” Hotine 1947) are one in the same (USGS PP-1395, Snyder 1987).

I just checked my copy of Projctr (a coordinate transformation program from the 1980s that I still use from time to time), and it also bears this out.

That being the case, I would think that you could use the NGS SPC83 program and some values (NGS Data Sheets) in Southeast Alaska to test your algorithms for consistency with the NGS results.

I don't have much (if any) use for rectified Oblique Transverse Mercator Projections (I haven't worked in Southeast Alaska since the mid-80s, or Michigan since the early 80s), but I do use the UN-rectified Hotine Oblique Mercator from time to time for special applications.

Loyal

My model is still hanging up by a 100 m + or - compared to NGS for Alaska 5001 zone. I just found the Snyder / USGS publication online. He presents exponential functions over Hotine's hyperbolic functions (as presented in the NGS Stem text also), which was likely a big deal back then in terms of computing speed. So, I'll try a new model w/ Synder's equations & see if I can get something to agree.

Interesting thread . . .

I have helpful information that I'm willing to share. I've used the Oblique Mercator equations since 1972 when I was an undergrad at the University of Michigan and worked with Ralph Moore Berry on the Michigan Geo-Ref System.

During the summer of 1983 I worked at NGS on transformation equations to be used on on the NAD83. My contribution is acknowledged on page iv of the Stem publication NOAA Manual NOS NGS 5.

I prepared a paper presented at the 1985 ASCE Spring Convention in Denver, Colorado, which describes the "new" version of transformation equations for Lambert Conic Conformal, the Transverse Mercator, UTM, and Oblique Mercator projections. That paper includes a detailed flow chart, a complete algorithm, and a listing of a FORTRAN progam that performs transformations on any of the 4 projections. I still have an "execute" file of that progam which may, or may not, run on current computers - you know, finding a computer old enough to run it may be a problem.

Source documents include:

1. U.S. Lake Survey Miscellaneous Paper 70-4 by Ralph Moore Berry and Valdis Bormanis dated September 1970 and titled, "Plane Coordinate Survey System for the Great Lakes Based Upon the Hotime Skew Orthomorphic Projection. It is one and the same as the Oblique Mercator Projection. Berry gave it that name in recognition of the work done by Brig. Martin Hotine's work on "The orthomophic Projection of the Spheroid." I can provide a .pdf of that document.

2. While working at NGS summer 1983 I was given an algorithm compiled by NGS Geodesist, T. Vincenty. Those equations are essentially those used in NGS Manual 5. If you really need them, I can scan and provide those as well.

3. As far as I know, the equations for the Oblique Mercator Projection appearing in Manual 5 are OK. Yes, they are a challenge to program because of hyperbolic trig functions, natural logarithms etc. But if you tenacious, your diligence should pay off.

With regard to matching GIS software, I'd not hesitate to ask them to provide a copy of the alogoriths used. I had a similar argument with Hewlett Packard in 1981 when their programmable calculator failed to perform state plane coordinate transformations correctly. But, don't expect them to ever admit their mistakes. Somehow, the fault always lies elsewhere.

Hope this is helpful.

Earl F. Burkholder, PS, PE, F.ASCE
Global COGO, Inc.
Las Cruces, NM 88003
www.globalcogo.com
eburk@globalcogo.com

There are three versions of the Oblique Mercator projection in use. The oldest is the Rosenmund projection used to this day in Switzerland. It is a "double projection" in that the cyllinder is first is projected onto a sphere, thereafter to the ellipsoid. It is used nowhere else. The second is the Laborde projection developed by General Jean Laborde when he was in Madagascar. It is also a "double projection," but is more involved than the Rosenmund because of how Laborde eventually gets to the ellipsoid. (Laborde was later chased out of Madagascar after he was found in bed with another man's wife. He later co-authored a book on geometric geodesy & projections while in Paris - Traite des Projections by Driencourt & Laborde.) The third and most widely used is the Hotine Rectified Skew Transverse Mercator developed by Brigadier Martin Hotine while he was seconded to the Survey of India after WWII when he developed it for Malaya and Borneo. It was published in several numbers of "Empire Survey Review" as The Orthomorphic Projection of the Spheroid.

Hotine's RSO is actually used in two different forms, depending on how one describes the oblique aspect, be it based on an oblique line between two points or on a single azimuth at the equator. It too, is a "double projection," but rather than projecting it to an intermediate sphere, he projects it to an intermediate figure known as an "aposphere," a figure akin to a turnip.

The best and most straightforward treatment of the Hotine RSO is indeed in Stem's book which is available in pdf format from the NGS website. If your transformation does not match Stem, your transformation is wrong - it is the official national standard of transformations of ALL State Plane Coordinate Projections for NAD83.

The projections programmed in the HP-67/97 Application Pac were specifically for NAD1927, and were based on the equations published in SP-67 by Charles N. Claire. They were not intended to be mathematically correct; they were intended to be reasonably close to transformations according to the little blue books of projection tables published by USC&GS - some of these which were based on Geocentric Latitude as later discovered and published by John P. Snyder in the 1980s.

Thanks Cliff, it is always good to learn more about the background and important details.

Great reply, thanks Earl!

I'm going to plug the Hotine equations from Stem into Excel; I think its going to work far better (and easier) than the software I'm using, MathCad. If I don't get good agreement, I can post the spreadsheet for any curious tinkerers out there.

> Interesting thread . . .
>
> I have helpful information that I'm willing to share. I've used the Oblique Mercator equations since 1972 when I was an undergrad at the University of Michigan and worked with Ralph Moore Berry on the Michigan Geo-Ref System.
>
> During the summer of 1983 I worked at NGS on transformation equations to be used on on the NAD83. My contribution is acknowledged on page iv of the Stem publication NOAA Manual NOS NGS 5.
>
> I prepared a paper presented at the 1985 ASCE Spring Convention in Denver, Colorado, which describes the "new" version of transformation equations for Lambert Conic Conformal, the Transverse Mercator, UTM, and Oblique Mercator projections. That paper includes a detailed flow chart, a complete algorithm, and a listing of a FORTRAN progam that performs transformations on any of the 4 projections. I still have an "execute" file of that progam which may, or may not, run on current computers - you know, finding a computer old enough to run it may be a problem.
>
> Source documents include:
>
> 1. U.S. Lake Survey Miscellaneous Paper 70-4 by Ralph Moore Berry and Valdis Bormanis dated September 1970 and titled, "Plane Coordinate Survey System for the Great Lakes Based Upon the Hotime Skew Orthomorphic Projection. It is one and the same as the Oblique Mercator Projection. Berry gave it that name in recognition of the work done by Brig. Martin Hotine's work on "The orthomophic Projection of the Spheroid." I can provide a .pdf of that document.
>
> 2. While working at NGS summer 1983 I was given an algorithm compiled by NGS Geodesist, T. Vincenty. Those equations are essentially those used in NGS Manual 5. If you really need them, I can scan and provide those as well.
>
> 3. As far as I know, the equations for the Oblique Mercator Projection appearing in Manual 5 are OK. Yes, they are a challenge to program because of hyperbolic trig functions, natural logarithms etc. But if you tenacious, your diligence should pay off.
>
> With regard to matching GIS software, I'd not hesitate to ask them to provide a copy of the alogoriths used. I had a similar argument with Hewlett Packard in 1981 when their programmable calculator failed to perform state plane coordinate transformations correctly. But, don't expect them to ever admit their mistakes. Somehow, the fault always lies elsewhere.
>
> Hope this is helpful.
>
> Earl F. Burkholder, PS, PE, F.ASCE
> Global COGO, Inc.
> Las Cruces, NM 88003
> www.globalcogo.com
> eburk@globalcogo.com

This Place is Da Bomb!!!:good:

SPCS83 source code is available

Howdy,

Don't forget that the source code for SPCS83 is available for review. Of course, it is in FORTRAN which might be difficult to decipher.

http://www.ngs.noaa.gov/PC_PROD/SPCS83/

Good luck.

DMM

There is still a plain jane Fortran that ships with most Linux distributions and FreeBSD. Your code will probably run with little or no modification.