topic Create a projection that scales CAD from Ground to Grid about 0,0 in Coordinate Reference Systems Questions

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

RyanHillard — Wed, 19 Nov 2014 20:33:27 GMT

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.

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

DanPatterson_Retired — Thu, 20 Nov 2014 09:37:16 GMT

Not sure of what you are trying to do since this is apparently a surveying term(?). When you mean "scale" to mean scale in the geometry sense of "translate, rotate and scale" or are you looking to move (ie translate or shift) your coordinate reference system so that the bounding rectangle of your input data has a 0 (zero) origin? Scale implies changing the range of values to fit into a new bounding rectangle, ie if you data are currently in the range 1-11 you can translate to the origin by performing a shift of -1 giving you a new origin (range is now 0-10) and then scale it so that coordinates fit in the range 0-1 by scaling it by dividing them by 10. You new coordinate system would have an origin of 0,0 and be scaled to a maximum range of 1,1

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

RyanHillard — Wed, 07 Jan 2015 19:07:33 GMT

Dan, thank you for your help. To better describe our process...we obtain a project scale factor about the center of our project and apply said factor about the origin, for example, if I have a grid coordinate of 500000, 1500000 and a scale factor of 1.000098756, the ground coordinate will be 500049.378, 1500148.134. Once I have completed my cad work, other members of the team need to bring it into Arcmap. Because most resources are on State Plane Grid, I need to be able to import the cad file into Arcmap and reverse the scaling to move the linework back to the grid location.

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

MattMiley — Fri, 30 Jan 2015 16:45:11 GMT

I have the same problem, whats the best method for "scaling" a cad file from ground back to state plane?

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

MelitaKennedy — Fri, 30 Jan 2015 20:36:20 GMT

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.

Melita

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

RyanHillard — Fri, 30 Jan 2015 20:43:01 GMT

Matt,

If you need help applying what Melita has below, let me know. We have automated the process of creating a custom projection file.

Best Regards,

Ryan

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

RyanKelso — Tue, 03 Mar 2015 00:30:36 GMT

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!

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

KeithMortensen — Thu, 30 Jun 2016 16:34:03 GMT

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

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

MelitaKennedy — Fri, 01 Jul 2016 21:15:21 GMT

Yes, that's correct.

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

MarkHotz — Thu, 23 Mar 2017 22:46:45 GMT

Ryan:

I could certainly use some help getting this set up. I have CAD data based on local ground coordinates that needs to be converted to UTM. I have been able to convert the point data manually using the feature to point tool in ArcGIS, and then calculating the geometry to get the local Grid coordinates, export to Excel, and apply the scale factor and corrections (for us the correction was adding 6,000,000 m N and 410,000 m E, and our scale factor is 0.9996899303). I would then just import that back into ArcGIS after setting the data frame's coordinate system to UTM. It would be so much easier if I could package this in a projection file and just use that to convert this data. I have only been able to my cumbersome method with point data (i.e. where coordinates can be created for each point), so I'm looking for a better way.

I think my problem is that using Melita's formulae (below) I don't know where the Ground Coordinates originate to be able to to create the false easting and northing for the projection file.

Melita's formula from another discussion:

x = ground easting
y = ground northing

UTM-Easting = 1.00011264*x ←where does "x" originate?
UTM-Northing = 1.00011264*y + 6000000 ←where does "y" originate?

Now we start adjusting the UTM parameters

UTM-Easting = 500000 + 0.9996*w
UTM-Northing = 0.9996*z

where w and z are the "proto-coordinates" calculated by the transverse Mercator algorithm before the scale factor and false easting/northing parameters are applied.

1.00011264*x = 500000 + 0.9996*w ← I can deduce the value of "w", but where does it originate?
1.00011264*y + 6000000 = 0.9996*z ← I can also deduce the value of "z", but where does it originate?

x = 500000/1.00011264 + (0.9996/1.000111264)*w
y = -6000000/1.00011264 + (0.9996/1.000111264)*z

so new parameters for the coordinate system:

false easting = 499943.686343
false northing = 5999324.236118
scale factor = 0.99948741774
+ the other parameters for the UTM zone (central meridian = -123, latitude of origin = 0).

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

MelitaKennedy — Tue, 28 Mar 2017 21:11:42 GMT

Hi Mark,

Is the scale factor applied before or after the translation (false easting and northing) values? I'm going to assume before.

UTM_easting = 410,000 m E + 0.9996899303 * local_grid_easting

UTM_northing = 6,000,000 m N + 0.9996899303 * local_grid_northing

To define the custom coordinate system, we want to solve for the local_grid coordinates.

local_grid_easting = (UTM_easting - 410000 ) / 0.9996899303

local_grid_northing = (UTM_northing - 6000000 ) / 0.9996899303

UTM_easting and UTM_northing are actually:

UTM_easting = 500000 + 0.9996*w
UTM_northing = 0.9996*z

w and z are "proto-coordinates". That is, the latitude and longitude values have been converted to xy coordinates except that we haven't applied the UTM zone scale factor nor the false easting value of 500000 m. The ellipsoid, central meridian and latitude of origin values have been used so far. Substitute in:

local_grid_easting = ({500000 + 0.9996*w} - 410000 ) / 0.9996899303

local_grid_northing = ({0.9996*z} - 6000000 ) / 0.9996899303

local_grid_easting = 90027.9149 + 0.9999100418 * w

local_grid_northing = -6001860.9952 + 0.9999100418 * z

local grid parameters

false easting = 90027.9149

false northing = -6001860.9952

scale factor = 0.9999100418

central meridian = utm zone's

latitude of origin = 0.0

projection = transverse Mercator

Melita

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

MarkHotz — Mon, 03 Apr 2017 23:05:16 GMT

Melita:

My apologies for not responding sooner. I don't like it when I'm in the middle of something important (like this) but then get pulled away to do something far less important :-). Now I'm back working on this issue.

Thanks a million for demonstrating this using my own data though...this is very much appreciated. The only thing I don't quite understand though is where do I find the values for "w" and "z"? Are these perhaps the values of central meridian and latitude of origin for the UTM Zone I'm using? Also, is this for converting from UTM to Ground coordinates? If so, then it should be relatively simply for me to convert from Ground to UTM as well, correct?

Thanks again

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

MarkHotz — Tue, 04 Apr 2017 18:58:35 GMT

Melita:

I'm just trying to learn how these numbers were derived so I can replicate the process in the future. I defined my local grid projection based on the parameters above, but the lines are about 2000 m out to the north (slightly northeast). When I just calc the geometry in the attribute table (in excel) using the conversion parameters, and then import the Excel table back into ArcMap the geometry falls into place. I'm not doubting your math, but how could this then be out by 2000 m if it's using the same parameters? Knowing where and how "w" and "z" are derived would probably help I think. What do you think?

Thanks

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

TarigAhmed3 — Wed, 26 Sep 2018 15:28:47 GMT

Ryan,

Could you please share this automated process?