[Proj] URGENT Non-existent Projection Definition (Oblique Mercator RSO Natural Origin)

Fri Jan 26 19:59:58 EST 2007

Hello everyone,

I am emailing to push for the addition of the coordinate system known as
the Rectified Skew Orthomorphic Oblique Mercator Natural Origin
(sometimes known as Hotine Oblique Mercator Natural Origin).  I have
come to the conclusion that this projection is not capable of being
defined properly in the current version of Proj.  This email is very
urgent as it applies to not only Alaska State Plane zone 1 but also
Michigan Georef (the most widely used projection for freely available
data in the state of Michigan).  This projection problem has been posted
multiple times over the course of more than 2 years and has still not
been fixed.  If you read through prior posts, you will see that a proper
solution has never been developed although Melita Kennedy has made it
known that ArcMap does support this projection.  Additionally, I have
supplied the code for this transformation in the form of Visual Basic
Code on a previous post which is not as accurate as it could be with the
proper help from this group.  The transformation algorithm is available
via EPSG's website but may contain a small error for the computation of
gamma or some other parameter.  Please note the urgency of this problem,
as this deficiency hinders the users of most open source mapping
software (Mapguide and Mapserver) for anyone in Michigan or Alaska.
Below is an outline of the correct transformation of an example
coordinate and also the incorrect transformation results from using
proj. 

Michigan Georef Meters as Defined in GPS Pathfinder Office (Uses a
Correct Transformation)

Datum Name= NAD 1983 (Conus)

Datum Method= Molodensky

Projection= Oblique Mercator Angle (RSO)

Positive Coordinate Direction= North and East

Central Latitude= 45Deg 18Min 33Sec North

Central Longitude= 86Deg 00Min 00Sec West

False Northing(meters)= -4354009.816

False Easting(meters)= 2546731.496

Scale Factor= 0.9996

Azimuth in Seconds= 1214120

Azimuth located at center of projection 

Origin located at Equator

Point 1 Georef Meters

665104.166 x correct

341261.925 y correct

Point 2 Georef Meters

662000.00 x correct

341000.00 y correct

Point 1 State Plane South Meters

4033461.471 x correct

233802.762 y correct

Point 2 State Plane South Meters

4030351.750 x correct

233602.528 y correct

Transformation using Autodesk Map 3D 2007 (Also uses a correct
transformation)

I imported a shapefile with the same 2 Georef Coordinates as the above
example.

The shapefile that was imported was defined according to Autodesk as
MI83-OB and transformed into the Michigan State Plane South Meters
Projection (MI83-S) and it also gave me the correct coordinates.

Point 1 State Plane South Meters

4033461.471 x correct

233802.762 y correct

Point 2 State Plane South Meters

4030351.750 x correct

233602.528 y correct

*Proj4 attempted RSO natural origin projection definitions

Michigan State Plane South Meters

This is the definition that I used to project my Michigan Georef Data
to.  Please also note that I changed the false easting (+x_0) to 4000000
(correct) instead of 3999999.99999###..(wrong false easting unless the
small variation is making up for something that happens in this
projection engine)

+proj=lcc +lat_1=43.66666666666667 +lat_2=42.1 +lat_0=41.5
+lon_0=-84.36666666666667 +x_0=4000000.0 +y_0=0 +ellps=GRS80
+datum=NAD83 +units=m

I used a few different variations of the omerc projection to try to
represent a natural origin RSO properly but could not get it to work
right.  I think this is because Proj does not support natural origins.
(Origin located at Equator)

*Here are my CS2CS point transformation examples and results of two
forward examples and two reverse examples

*This example has the parameter +no_uoff applied to the georef
definition

cs2cs +proj=omerc +k_0=0.9996 +alpha=337.25555555555556
+lat_0=45.30916666666667 +lonc=86.00000000000000 +no_uoff
+x_0=2546731.496 +y_0=-4354009.816 +ellps=GRS80 +datum=NAD83 +units=m
+to +proj=lcc +lat_1=43.66666666666667 +lat_2=42.1 +lat_0=41.5
+lon_0=-84.36666666666667 +x_0=4000000.0 +y_0=0 +ellps=GRS80
+datum=NAD83 +units=m

665104.166 341261.925

10038527.39 10152300.28

*This example does not have the parameter +no_uoff applied

cs2cs +proj=omerc +k_0=0.9996 +alpha=337.25555555555556
+lat_0=45.30916666666667 +lonc=86.00000000000000 +x_0=2546731.496
+y_0=-4354009.816 +ellps=GRS80 +datum=NAD83 +units=m +to +proj=lcc
+lat_1=43.66666666666667 +lat_2=42.1 +lat_0=41.5
+lon_0=-84.36666666666667 +x_0=4000000.0 +y_0=0 +ellps=GRS80
+datum=NAD83 +units=m

665104.166 341261.925

6630581.93 5400202.21

*This reverse example does not have the parameter +no_uoff applied

cs2cs +proj=lcc +lat_1=43.66666666666667 +lat_2=42.1 +lat_0=41.5
+lon_0=-84.36666666666667 +x_0=4000000.0 +y_0=0 +ellps=GRS80
+datum=NAD83 +units=m +to +proj=omerc +k_0=0.9996
+alpha=337.25555555555556 +lat_0=45.30916666666667
+lonc=86.00000000000000 +x_0=2546731.496 +y_0=-4354009.816 +ellps=GRS80
+datum=NAD83 +units=m

4033461.471 233802.762

238971.78 5627717.79

*This reverse example has the parameter +no_uoff applied (it apparently
doesn't matter when projecting TO oblique mercator)

cs2cs +proj=lcc +lat_1=43.66666666666667 +lat_2=42.1 +lat_0=41.5
+lon_0=-84.36666666666667 +x_0=4000000.0 +y_0=0 +no_uoff +ellps=GRS80
+datum=NAD83 +units=m +to +proj=omerc +k_0=0.9996
+alpha=337.25555555555556 +lat_0=45.30916666666667
+lonc=86.00000000000000 +x_0=2546731.496 +y_0=-4354009.816 +ellps=GRS80
+datum=NAD83 +units=m

4033461.471 233802.762

238971.78 5627717.79 

Again, it is very urgent that this projection be supported.  Thank you
all for your help.  If you have any questions please post them as soon
as possible.

Max Clever, L.S.I.T.

Staff Surveyor

Spicer Group, Inc.

230 S. Washington Avenue

Saginaw, MI  48607

Phone:  (989) 754-4065 ext. 5584

Cell:       (989) 989-928-8028

Fax:       (989) 754-4440

mailto: maxc at spicergroup.com <mailto:maxc at spicergroup.com> 

www.spicergroup.com

Spicer Group's Engineers, Surveyors, and Planners strive for perfection
in everything we do.  We take the best that exists & make it better.
When it doesn't exist, we design it!

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