Shifting .dwg file to align with a shapefile
I'm trying to integrate data in a .dwg file collected by surveyors into an ArcView 10.2 project I have projected as NAD83 UTM Zone 10 N. The survey data is in an undefined coordinate system but I have values for the translation parameters, which are below as described by the surveyors.
Which utilities can perform this transformation?
Our surveys were based on a local assumed coordinate system. To translate our local coordinates to UTM, you will have to (1) apply a scale factor to your UTM mapping coordinates of 0.99960196 and (2) apply the following shifts in northings and eastings : ΔN = 5 441 341.306 & ΔE = 491 604.143. After going thru this procedure, you will have a list of UTM mapping coordinates.
If I understood the surveyor's directions correctly, you should be able to make a custom projected coordinate reference system for the CAD data.
Let's say that standard UTM coordinates are calculated like this:
e = fe + k0 * x n = fn + k0 * y
where e = UTM easting, n = UTM northing, k0 = 0.9996, fe = 500000.0, fn = 0.0, and x and y are the proto-projected coordinates. The direction say to do:
e * sf - 491604.143 n * sf - 5441341.306
where sf = 0.99960196
Do a substitution:
(fe + k0 * x) * sf - 491604.143 (k0 * y) * sf - 5441341.306
(sf * fe) + (sf * k0) * x - 491604.143 (sf * k0) * y - 5441341.306
local grid x = 0.999202119216 * x + 7996.916608 local grid y = 0.999202119216 * y - 5441341.306
So create a new projected CRS based on transverse Mercator with a scale factor = 0.999202119216, false easting = 7996.916608, and false northing = 5441341.306
Note: If the data's not lining up and looks like it's too small, try using the inverse of sf instead, 1.00039819849893 and rerun the equations above to calculate the new values.
You might ask the surveyors in your next contract to return grid coordinates IN UTM or State Plane instead.
The surveyor wording is a bit unclear, and I have not done this on UTM yet, so without testing and verifying this, I cant be certain i have it right, but the formula is correct. May just need a slight tweak (i.e. subtracting the shift values instead of adding OR using the inverse of the scaling instead of the actual).
Take your current UTM Northing (0.0) or Easting (500000), multiply by the scale factor the surveyor provided (0.99960196), then add the shift value the surveyor provided. The resulting values should be entered into the Northing or Easting values in a new modified Projected Coordinate Systems Properties dialog for the UTM Zone 10N properties.
(Easting * Scale Factor)+Easting Shift = New Easting (Northing * Scale Factor)+Northing Shift = New Northing OR (500000*0.99960196)+491604.143 = 991405.123 (0.0*0.99960196)+5441341.306 = 5441341.306
I don't know how accurate you have to be in your maps but georeferencing should get you close. The how to is referencing an older version of arc but it should be basically the same as performing this in 10.2