[Fwd: Re: [Proj] Re: The Michigan Georef Projection Problem]

[Dylan Keon]

Max and other listers,

I am forwarding Melita's reply from yesterday to the list.

--Dylan


-------- Original Message --------
Subject: Re: [Proj] Re: The Michigan Georef Projection Problem
Date: Mon, 20 Dec 2004 12:39:54 -0800 (PST)
From: Melita Kennedy [ESRI-Redlands] <mkennedy at esri.com>
Reply-To: Melita Kennedy [ESRI-Redlands] <mkennedy at esri.com>
To: gerald.evenden at verizon.net, mkennedy2 at earthlink.net, keon at nacse.org
CC: mkennedy at esri.com

Hi Dylan, Jerry, and Frank

I'm not cc'ing to the list as I don't think I can post from this
e-mail account. Dylan, feel free to post all or part of my reply
on the list if you wish.

I think I understand what's happening, although I'm bit confused
because it means that the State Plane zone, Alaska zone 1, probably
isn't working either.

First off, here are a few test points from PROJ using this defn.

proj +proj=omerc +lat_0=45.309166667 +lonc=-86.0 +alpha=337.255555556
+k=0.9996 +x_0=2546731.496 +y_0=-4354009.816 +ellps=GRS80 +datum=NAD83
+units=m

86W 43N
2546756.16 -4610501.20
86W 44N
2626908.90 -4498940.28
86W 45.309166667N
0.00 0.00

and now the results from the ESRI Projection Engine

cymru{melita}: forward91 102123
Projection Engine Version 9.0 (Dec 15 2004)
-86 43
-85 44
-86 45.309166667
499864.50  272108.86
580017.24  383669.77
499839.83  528600.24

Quite a difference, eh?

Hotine, "Oblique Mercator", RSO, and whatever other names are in use
confused me for quite a while. The ESRI Projection Engine now has
6 variants to try to support this map projection. Partially, that's
because we've added different versions at different times as we've
come to understand the projection better.

Hotine 2 Pt Natural Origin
Hotine 2 Point Center
Hotine Azimuth Natural Origin
Hotine Azimuth Center

Rectified Skew Orthomorphic - Natural Origin
Rectified Skew Orthomorphic - Center

PROJ supports Two Point and Point/Azimuth cases. From what I'm
seeing in the results and in the documentation, they are what
ESRI calls the 'Center' cases. That is, the cartesian origin is
located at the 'center' of the projection, lonc and lat_0.

The ESRI Natural Origin cases have the cartesian origin where
the central line crosses the aposphere. This is almost the ellipsoid's
equator. Alaska zone 1 and Michigan GeoRef both use the natural
origin case of Point/Azimuth. That's why they have such large
negative false northings and large positive false eastings.

The ESRI version (and the PROJ versions) also rectify the projection
back to 'north'. The default proj setting is +no_rot (no rotation).
The azimuth is used for the rectifying angle.

Hmmm, I get different results if I use +no_rot versus when I omit
it. So perhaps +no_rot is a rectifying angle of zero.

The ESRI RSO implementation have the same Hotine parameters, plus
a rectifying angle. Although I haven't tested it, I believe this is
the same parameter as the +no_rot parameter. The standard RSO
definitions must have this parameter set, as the rectifying angle
is not the same as the azimuth.

Snyder talks somewhat about this in a footnote in _Map Projections:
A Working Manual_, but I (and the projection programmers here find
the entire section to be difficult to follow.

I think you can get the results you expect with these parameters:

proj +proj=omerc +lat_0=45.309166667 +lonc=-86.0 +alpha=337.255555556
+k=0.9996 +x_0=499839.8337 +y_0=528600.2398 +ellps=GRS80 +datum=NAD83
+units=m

Melita

-- 
Melita Kennedy
Product Specialist
ESRI, Inc.
mkennedy at esri.com

> Date: Mon, 20 Dec 2004 10:39:00 -0800
> From: Dylan Keon <keon at nacse.org>
> To: gerald.evenden at verizon.net, mkennedy2 at earthlink.net
> CC: proj at xserve.flids.com, mkennedy at esri.com
> Subject: Re: [Proj] Re: The Michigan Georef Projection Problem
> 
> On 12/18/2004 12:06 PM, Melita Kennedy wrote:
> > Max, 
> > 
> > Can you give some details on what the problems are? Obviously,  you aren't
> > getting the results you expect but would you post some samples and what
> > your expected results are? Can you narrow down the problem to Michigan
> > GeoRef to lat/lon? Does it look like you can project to Michigan GeoRef
> > from lat/lon? 
> 
> Melita and Gerald,
> 
> Not sure if this is helpful to either of you, but here is the link to 
> the problem I was having with Proj and Michigan GeoRef back in August: 
> http://xserve.flids.com/pipermail/proj/2004-August/001843.html
> 
> --Dylan
>