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Scale factor AND coordinate shift   Paul Petersen Feb 01, 2007
Re: Scale factor AND coordinate shift   Melita Kennedy Feb 01, 2007
Re: Scale factor AND coordinate shift   Paul Petersen Feb 01, 2007
Re: Scale factor AND coordinate shift   Melita Kennedy Feb 02, 2007
Re: Scale factor AND coordinate shift   Paul Petersen Feb 02, 2007
Re: Scale factor AND coordinate shift   R Wyllie Feb 23, 2007
Re: Scale factor AND coordinate shift   Melita Kennedy Feb 23, 2007
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Subject Scale factor AND coordinate shift 
Author Paul Petersen 
Date Feb 01, 2007 
Message I am currently building a GIS database, and the engineers involved in the project have requested that we use their Modified State Plane Projection. Here are the details:

*Based off of Colorado Central Zone (0502), NAD83 (ft)
*Project Combined factor = 0.999706760
*Reciprocal = 1.000293326
*Coordinates are truncated by subtracting the following:
-1,000,000 from Modified SP Northing values
-2,000,000 from Modified SP Easting values

It can be summed up as:
Custom Northing = SP Northing x 1.000263326 - 1,000,000
Custom Easting = SP Easting x 1.000263326 - 2,000,000

This seems like it should be pretty straight-forward, but I have been banging my head against ArcGIS trying to get the new data to line up against data in an unmodified projection. I can get points to project properly against other data by applying the inverse of the formula on the shape field in the field calculator, but I need to apply the modifications as a projection file (ie I don't want to actually reproject any data)!

I have not had success defining this new projection as a .prj. I have posted my best attempt at it below. I have simply subtracted 1,000,000 from the false northing and 2,000,000 from the false easting, and applied a scale_factor of 1.000293326, but the data is not lining up correctly.

What I THINK is going on is that ArcMap may be applying the false northing/easting first, and THEN the scale factor. It needs to be the other way around: scale factor first, and then coordinate truncation. I think that's why the field calculator is working, because I can control the order of the modification. I'm grasping at straws here...

Does anyone has any ideas on what I can do to properly define this projection? Thanks for any help or comments. 
 
Projection: Lambert_Conformal_Conic
False_Easting: 1000000.000316
False_Northing: -0.000004
Central_Meridian: -105.500000
Standard_Parallel_1: 38.450000
Standard_Parallel_2: 39.750000
Scale_Factor: 1.000293
Latitude_Of_Origin: 37.833333
Linear Unit: Foot_US (0.304801)
 
   
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Subject Re: Scale factor AND coordinate shift 
Author Melita Kennedy 
Date Feb 01, 2007 
Message In the mathematics, the scale factor is applied first, then the false easting/northing.

So back up to the original false easting and northing values. Multiple them by the scale factor, and then subtract off the shifts.

Melita 
  Melita Kennedy
ESRI Product Specialist 
   
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Subject Re: Scale factor AND coordinate shift 
Author Paul Petersen 
Date Feb 01, 2007 
Message Thanks for the response. How do I set this mathematical order in the projection file? What I do is enter the "Modify" dialog for the Stateplane projection, then subtract the offsets from the false easting and northing, and set the scale factor parameter there as well. However, the data does not line up proper.

When I "manually" reproject the new data by using the field calculator in ArcMap, the data lines up perfectly with standard Stateplane data. To convert the new data to standard stateplane I simply ADD the offset to the coordinates and then DIVIDE by scale factor (ie perform the equation backwards to convert the coordinates). So I know the formula the engineers sent me is fundatmentally correct, but I just can't get it to work by defining a projection in ArcCatalog and letting ArcMap reproject on the fly. 
   
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Subject Re: Scale factor AND coordinate shift 
Author Melita Kennedy 
Date Feb 02, 2007 
Message You can't set the order. You need to multiply the original false easting/northing by the scale factory, then subtract the 2mill/1mill:

3000000*1.000293326 = 3000879.978 - 2000000 = 1000879.978
1000000*1.000293326 = 1000293.326 - 1000000 = 293.326

and include the scale factor in the definition, of course.

Hope this helps,
Melita 
  Melita Kennedy
ESRI Product Specialist 
   
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Subject Re: Scale factor AND coordinate shift 
Author Paul Petersen 
Date Feb 02, 2007 
Message Melita,
That was the trick! Thank you so much! 
   
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Subject Re: Scale factor AND coordinate shift 
Author R Wyllie 
Date Feb 23, 2007 
Message I too am having a problem with custom projections. Our office is split with some Geomedia users and other ArcGIS users. I can not get their custom projection to work in ArcGIS. I have most of the parameters set correctly, however they have shifted their storage space and that is my issue. Here is the storage space:

Horizontal storage unit = .0003048m
Vertical storage unit = .00001m
Storage Center:
X = 304800.00m
Y = 222063.90m
Height = 0.00m

Projection Space:
Lambert Conformal Conic
Longitude of Origin = -93.500deg
Latitude of Origin = 40.000deg
Standard Parallel 1 = 40.375
Standard Parallel 2 = 43.625deg
False Easting (X) = 304800.00m
False Northing (Y) = 0.00m

Geographic Space:
Datum = North American 1983

I would appreciate any help any getting a prj file created of the above situation. Thanks! 
   
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Subject Re: Scale factor AND coordinate shift 
Author Melita Kennedy 
Date Feb 23, 2007 
Message I'm not sure if this will work or not.

First try modifying the base coordinate system and change the linear unit to a custom one with the conversion value:

0.0003048 (meters/unit)

Make sure the false easting value is also changed. It should change automatically when you change the unit.

Check the data after you change it. Is the data the correct relative size? If it is, but is still shifted, you'll have to do some fiddling with the storage center values. Try using zero for the false easting and the unit-converted y storage center value, made negative.

Melita 
  Melita Kennedy
ESRI Product Specialist