[Proj] does proj.4 work with Hotine Oblique Mercator?

[Rick Graves]

Hey,

I am not sure that proj.4 is converting latitude and longitude into Hotine Oblique Mercator coordinates correctly.  (But I am a newbie at cartography and such, so please bear with me, I could be making a mistake.)

As a result of the 2010 census in the USA, many states have redrawn their congressional districts.  Michigan is one, and the shapefiles for their new districts were created using the Hotine Oblique Mercator projection to get the whole state onto one map with a minimum of overall distortion.  There is a map and explanation here:

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


One can download Michigan's new Congressional district shapefiles from here:

http://www.mcgi.state.mi.us/mgdl/?rel=thext&action=thmname&cid=9&cat=Legislative+Districts+2010+US+Congress


The included prj file has this info:

PROJCS["NAD83 / Michigan Oblique Mercator",
GEOGCS["NAD83",
    DATUM["North_American_Datum_1983",
SPHEROID["GRS 1980",6378137,298.257222101,
    AUTHORITY["EPSG","7019"]],
AUTHORITY["EPSG","6269"]],
    PRIMEM["Greenwich",0,
AUTHORITY["EPSG","8901"]],
    UNIT["degree",0.01745329251994328,
AUTHORITY["EPSG","9122"]],
    AUTHORITY["EPSG","4269"]],
UNIT["metre",1,
    AUTHORITY["EPSG","9001"]],
PROJECTION["Hotine_Oblique_Mercator"],
PARAMETER["latitude_of_center",45.30916666666666],
PARAMETER["longitude_of_center",-86],
PARAMETER["azimuth",337.25556],
PARAMETER["rectified_grid_angle",337.25556],
PARAMETER["scale_factor",0.9996],
PARAMETER["false_easting",2546731.496],
PARAMETER["false_northing",-4354009.816],
AUTHORITY["EPSG","3078"],
AXIS["X",EAST],
AXIS["Y",NORTH]]

This page has info on the Hotine Oblique Mercator:

http://www.remotesensing.org/geotiff/proj_list/hotine_oblique_mercator.html


Using that, I came up with this command to invoke proj:

proj +proj=omerc +lat_0=45.30916666666666 +lonc=-86 +alpha=337.25556 +k_0=0.9996 +x_0=2546731.496 +y_0=-4354009.816

I get a latitude and longitude for Ann Arbor Michigan of 42 15 N - 83 45 W here:

http://wiki.answers.com/Q/What_is_the_latitude_and_longitude_of_ann_arbor_mi


Plugging 42d15N 83d45W into proj, I get -7945305.71 17799792.28.  But the bounding box of the entire state's shape file is this:

161318.17712499946, 128066.04250000045, 791832.2827499993, 859206.8181249984


The values I get from proj are both out of bounds. 

Am I doing something wrong?

Thanks,

Rick Graves
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