Ground to Grid from State Plane with rotation and scale CAD data

[Matt_Trebesch]

I need help figuring out how to get CAD data that has a shift, rotation and scale factor based on this projection. NAD_1983_StatePlane_Montana_FIPS_2500_Feet_Intl
WKID: 2256

 Basically I have a drawing that is based on the above projection, but it has a coordinate truncation (shift), scale factor AND rotation set to the CAD .dwg provided.  

Ordinarily, I would create a world file that could take 2 coordinate pairs and then that would georeference the CAD drawing.  That worked when I simply had a coordinate shift.  (often the engineers would truncate coordinates to make the designs space smaller in CAD)

Now I'm given data with a scale factor AND a rotation included with coordinate truncation.

How do I get this CAD drawing to reside in map projected space?  What's the best way to do that?

Basically, I was provided a PDF control table and info as well as whatever they used to set the ground to grid translation in AutoCAD.       (they gave a screen shot)

I think I can figure out the scale factor - but the rotation is problematic to me - I'm presuming it's rotating on the origin? 

I want to add this CAD data to a map with other projected data so I can digitize data from it.

Any advice is appreciated.

[DanPatterson]

About georeferencing CAD data—ArcGIS Pro | Documentation

Limitations of CAD dataset section

Georeferencing a CAD dataset is limited to a two-point transformation using the similarity transformation method. 

probably doesn't help if you are looking for a quick solution

[Matt_Trebesch]

Dan, yes, I realize that limitation to transformation of a CAD drawing, but the solution I'm seeking is to project, or otherwise.   That said, this IS a 2 point solution, if I can take into account the rotation and scale.   Sort of reversing from a ground to grid editing solution. 

This is a linear shift, rotation and scale, there is no skew.

The end result will be a linear similarity/affine, if I could somehow find the coordinate pair.   Anyhow, I understand the limitation of the CAD transformation.    Technically you can MANUALLY add a shift or rotation:

https://pro.arcgis.com/en/pro-app/latest/help/data/cad/georeferencing-cad-data.htm

see the "Rotate, move, or scale the dataset" section.

But I'm hoping to take the given rotation/shift/scale data I have and use it than to manually fudge this thing.

I have to believe there is a way to take a CAD drawing that is in a projection and has the ground to grid properties defined and get it into a projected coordinate space.   

It might not be through the CAD georeferencing tool, either.

This can't be a new idea, or problem..  especially for those of us that work with  CAD data from engineers in the civil engineering world.

Hopefully one of them sees this!!!