Create a projection that scales CAD from Ground to Grid about 0,0

11-19-2014 12:33 PM
New Contributor

I have been working with adding in a scale factor parameter but am not able to figure out how to scale about the origin.  Our survey standards require us to scale our data from 0,0.  I need to create a projection that will reduce CAD data from ground back to grid, scaling about 0,0 of the grid.

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Esri Notable Contributor

If the "grid" coordinate system is a state plane or UTM zone, you should be able to incorporate the grid-to-ground value into a custom projected coordinate system.

Here's something I wrote up several years ago on the old forums. It's set up for a Lambert-based state plane zone, but a transverse Mercator zone would be easier, start with the equations and replace LCC with TM, and the original sf is not equal to 1.0.

There are 2 main 'styles' of Lambert conic (LCC):

1. 2 standard parallels

2. 1 std parallel + scale factor (sf)

In ArcGIS, the math will handle both, and in fact, you can conflate them to:

2 std parallels + scale factor

The math is really:

fe + sf*(LCC x)

fn + sf*(LCC y)

where fe/fn are false easting/northing, sf is scale factor, and LCC x/y is the 'raw' coordinates. However, for a LCC-based SPCS zone, sf is 1.0

If the Combined Adjustment Factor (grid-to-ground) is applied to the final state plane coordinates, you would get:

CAF*(fe + (LCC x))

CAF*(fn + (LCC y))

So rewrite:

CAF*fe + CAF*(LCC x)

CAF*fn + CAF*(LCC y)

Due to how the UI works, you'll need to copy down the existing parameter values. Then when you're modifying the PCS, change the "projection" to something else and then back to Lambert_conformal_conic". That will add in the scale factor parameter.

Set the sf = CAF, and multiply the existing fe/fn by the CAF for the new values.


Occasional Contributor III

Thank you this is just what I was looking for!  I didn't realize I had to apply the scale factor to the false easting as well.  Unfortunately I don't think I can do this exact same thing in AutoCAD Civil 3D, which is what I really need to do, but it works beautifully in ArcGIS!

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New Contributor III

So to clarify for my brain, I multiply the existing values by my CAF. The fn, fe, and sf?

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Esri Notable Contributor

Yes, that's correct.

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