I would be interested in response from others about some of the currently methods of computing "ground" coordinates from grid coordinates. It seems to me there are two approaches commonly used and one is, in my opinion, wrong.
Various surveying textbooks clearly outline the method for computing "combined" factors of relating relatively short ground distances to grid distances between the same two points. (By "short" I mean a very small portion of the arc of an ellipsoidal distance, so small it can be considered a straight line rather than an arc). In other words the ratio of the average radius of the earth is compared to the radii of the distance from the ellipsoid to the ground and from the ellipsoid to the grid. This is clearly a valid method of computing a "short" ground distance from gird or vice-versa.
So one method of computing ground coordinates is to take the grid coordinate of a centrally located point up to the ground surface with the coordinate values unchanged for this central point. Ground values for other grid points are computed by differencing their coordinate values from this central point, multiplying the difference by the combined factor then adding the difference to the coordinate value of the central point to develop ground coordinate values. Of course these values will be close to the grid values with the differences becoming greater as one gets further and further away from the central point. To make the ground values appear distinct from the grid values some large constant offset is usually added or subtracted to the coordinate values. This approach makes sense to me and agrees with my understanding of the mathematics involved.
The second approach, which appears wrong to me, involves simply multiplying all of the project coordinates by this combined factor to generate ground values. Usually a large offset is likewise added to make them look different from the grid values. This in effect, is multiplying the coordinate values, which are distances from the coordinate system origin, by the combined factor. In other words the combined factor is being applying to a very long portion of the arc from the origin to the coordinate value rather than simply to a short ground distance near the center of the project site. I have seen some serious problems arising in surveys where users have gone back and forth between ground and grid by simply multiplying the coordinate values by the combined factor or its reciprocal. Regardless of my views, this is the approach taken by some manufacturers. Any comments from anyone else about this?
The second method appears to be common among DOT departments. Either works if there is good documentation of the method and constants (metadata) and people pay attention to it.
The problems that most often arise are due to someone seeing something that looks like SPC and assuming it is true (grid) SPC. To avoid that, I would recommend defining the ground coordinates as the scaled SPC (by whichever method) minus some millions and hundreds of thousands of feet. The resulting numbers are easy to convert back, but won't tempt someone to skip the conversion.
Mighty Moe is going to bash this approach, but I think we have agreed to differ.
I don't see a mathematical problem with either version. Method 1 allows for coordinates to be near true State Plane - great for using aerial images referenced to State Plane. Method 2 allows for more simplicity in metadata (rather than selecting a central project coordinate to scale from, use 0,0). The biggest issue related to Method 2 is significant digits. As you said, going back and forth will introduce small errors (like a Xerox copy of a copy of a copy of an original). Using more precision in the scale factor probably helps reduce the likelihood of distortion, but makes scaling a pain. Generally I like scale factors at the 1ppm precision. It's plenty practical for the purpose of scaling between a grid distance and a surface distance, but again, little bits of rounding can bite over long distances.
I prefer method 1, but with the caveat that I some kind of monumented control point is used as the origin of the scaling. That one location should have the same value in both grid and ground coordinates. I indicate this on the map.
"Forgive me Father, for I have sinned!"
"Yes, my son?"
"I scaled up to ground from the origin!"
"Oh hey, we'll have to get special dispensation from the Pope for that!"
Use of the term "wrong" implies it's a moral issue. It's not a moral issue. There are different ways to do things, each with their own advantages and disadvantages.
The different methods you describe are simply a difference of what you calling your "origin" point in my opinion. Another point to make your origin is the defined origin for your particular state plane zone. That might be 1,000,000.3,000,000. a couple of other things I have seen done (but more like 20 years ago) is, (1) just assigning your most southeast point a coordinate value such as 10,000, 20,000. This seems like a bad idea as well. and (2) I have seen project coordinates (after going through one of the scale factor iterations) get rotated by by the convergence angle to get it to a "true north" basis at one point.
Of the two methods you described, I see no value in doing one over the other. And you can get the same confusion or pollution if you keep going back and forth from State Plane to "Project" coordinates.
Another issue I have seen is when you truncate. If you truncate before applying the combined scale factor vs. applying you csf then truncating. If your going to truncate, I would do it after all the other hoops you jump through to get there.
edit: Oops, I meant to say the the most important thing to do is to document exactly and clearly what you did, so anyone can follow in your footsteps. Which method you use is minor compared to whether or not you document what you did.
Personally, I advocate only Method 2.
The main reason is that, unless coordinates are actually on a "state plane," there should be no similarity between the user's coordinates and "state plane." Too many times I've seen and been confronted with, and I've heard and agree with the term, "bastardized state plane coordinates." In each and every case, it led to confusion and unnecessary time and costs. If coordinates are not "state plane," don't make them look like "state plane."
As for the accuracy of the method results, it is the same in either case. Scale is scale and the only thing that is changed between the two methods is the point about which scale is determined. In the first method, the scale point is within the project area and in the second, it is the coordinate system origin.
To visualize or illustrate the point, assume you have a map image, using a slide projector or similar, projected onto a sphere. If you rotate the sphere about its center, the distances between points remains the same no matter how the sphere is rotated.
Method 2 was the long time practice in Oregon. Now we have LDPs, which are even better.
In Oklahoma we just used the State Plane without fussing with any scaling. When operating with RTK the procedure is obvious. When using the TS you simply set your dc to the appropriate zone and enter state plane coordinates as your control. dc takes care of scaling issues. Simple.
Bill93, post: 332552, member: 87 wrote: The second method appears to be common among DOT departments. Either works if there is good documentation of the method and constants (metadata) and people pay attention to it.
The problems that most often arise are due to someone seeing something that looks like SPC and assuming it is true (grid) SPC. To avoid that, I would recommend defining the ground coordinates as the scaled SPC (by whichever method) minus some millions and hundreds of thousands of feet. The resulting numbers are easy to convert back, but won't tempt someone to skip the conversion.
Mighty Moe is going to bash this approach, but I think we have agreed to differ.
Well, not me, but the DOT doesn't allow it.
I've used so much of their available control there is no real way of going back at this point.
I used to hate the multiplied coordinates for the reasons you mention, however, as data has become so available for computer systems it's become very useful to have that simple connection between ground and grid coordinates.
It's very easy to bring in a quad or ortho and multiply it up, or divide your file down to mesh everything together.
By doing it around a point besides 0,0 you introduce a messy set of steps.
And if you subtract or add to the coordinate then the connection is completely lost.
But at the end of the day they are just xy numbers, the real important numbers are the lats and longs (NAD83) that underpin it all.
If I'm going to "modify" state coordinate systems, I'm going to do it around 0,0, it makes everything much simpler.
Point of clarification...
Actually, when you Scale the Coordinates, you are NOT scaling from the projection ORIGIN, but in fact scaling from a ÛÏpointÛ defined by the False Northing and Easting assigned to the ÛÏorigin.Û
For Example:
Texas NAD83 South Zone:
Origin : Latitude 25å¡40' North, Longitude 98å¡30' West
False Northing: 5,000,000 Meters
False Easting: 300,000 Meters
So in fact, you are ÛÏscalingÛ from a point situate above the South Pacific Ocean (West of Peru) at about:
Latitude: 15å¡29'42.02231Û South
Longitude: 100å¡38'31.64140 West
Ellipsoid Height: ~ 1.9 million meters (~1,200 Miles)
Not that that really makes any difference, just saying...
Loyal
MightyMoe, post: 332587, member: 700 wrote: ....But at the end of the day they are just xy numbers, the real important numbers are the lats and longs (NAD83) that underpin it all....
That's exactly right. They are just X/Y coordinates. All we are doing is modifying the distances between the points to more closely reflect the measured distance between points. doing a mass-multiplication of coordinates is a quick and easy way to modify all those distances. And the next step is to make them not be SPC look-alikes.
MightyMoe, post: 332587, member: 700 wrote:
And if you subtract or add to the coordinate then the connection is lost...
All foms of mathematical violence can be undone be reversing the process. SPC northing / CAF + 100,000 = MOD northing - 100,000 ÌÑ CAF. The connection isn't lost if the Metadata is maintained.
Loyal, post: 332589, member: 228 wrote: Point of clarification...
Actually, when you Scale the Coordinates, you are NOT scaling from the projection ORIGIN, but in fact scaling from a ÛÏpointÛ defined by the False Northing and Easting assigned to the ÛÏorigin.Û
Loyal
Having difficulty understanding the "scaling from a ÛÏpointÛ defined by the False Northing and Easting assigned to the ÛÏorigin.Û If state plane coordinates are scaled by just multiplying by a factor, then the "False Northing and False Easting too would be scaled.[pre]
S = Scale
x = unscaled coordinate value
y = unscaled coordinate value
xs = scaled "x" coordinate value
ys = scaled "y" coordinate value
the point about which scale is determined
xsp = x scale point value
ysp = y scale point value
Then:
xs = S(x - xsp)
ys = S(y - ysp)
When scaling is computed about the origin, xsp = 0 and ysp = 0.
xs = S(x - 0) = Sx
ys = S(y - 0) = Sy
ie, scaling is accomplished by multiplying the coordinates by the scale factor
If scaling is computed about the False Northing (yFN) and False Easting (xFE)
xs = S(x - xFE)
ys = S(y - yFN)
Thus xs and ys are not equal respectively when scaling about the origin versus the False Northing and False Easting.[/pre]
Perhaps a little more explanation about the statement in your post?
MLSchumann, post: 332568, member: 471 wrote: Personally, I advocate only Method 2.
The main reason is that, unless coordinates are actually on a "state plane," there should be no similarity between the user's coordinates and "state plane." Too many times I've seen and been confronted with, and I've heard and agree with the term, "bastardized state plane coordinates." In each and every case, it led to confusion and unnecessary time and costs. If coordinates are not "state plane," don't make them look like "state plane."As for the accuracy of the method results, it is the same in either case. Scale is scale and the only thing that is changed between the two methods is the point about which scale is determined. In the first method, the scale point is within the project area and in the second, it is the coordinate system origin.
To visualize or illustrate the point, assume you have a map image, using a slide projector or similar, projected onto a sphere. If you rotate the sphere about its center, the distances between points remains the same no matter how the sphere is rotated.
We used to hold a NAD27 monument and then survey from it using ground distances, all the check into monuments were recalculated by using the scale factor between the two, adding it to the inversed distance and recalculating the monument's coordinate.
This was the preferred method back in the days of doing mine control.
This allowed the points to be scaled onto quad sheets and when they were available in digital form put into a drawing. But the main issue is they do "look" like state plane coordinates, the scaled from 0,0 coordinates do not, they are too far away from the real state plane point, they also are simple to convert back, a one step conversion. Not too simple to convert the scale from a project point type of coordinate, and really difficult when it's further truncated.
Loyal, post: 332589, member: 228 wrote: Point of clarification...
Actually, when you Scale the Coordinates, you are NOT scaling from the projection ORIGIN, but in fact scaling from a ÛÏpointÛ defined by the False Northing and Easting assigned to the ÛÏorigin.Û
For Example:
Texas NAD83 South Zone:
Origin : Latitude 25å¡40' North, Longitude 98å¡30' West
False Northing: 5,000,000 Meters
False Easting: 300,000 MetersSo in fact, you are ÛÏscalingÛ from a point situate above the South Pacific Ocean (West of Peru) at about:
Latitude: 15å¡29'42.02231Û South
Longitude: 100å¡38'31.64140 West
Ellipsoid Height: ~ 1.9 million meters (~1,200 Miles)Not that that really makes any difference, just saying...
Loyal
There's always that one guy in every group that just has to be technically precise with everything. 🙂
MLSchumann, post: 332596, member: 471 wrote: Loyal
Having difficulty understanding the "scaling from a ÛÏpointÛ defined by the False Northing and Easting assigned to the ÛÏorigin.Û If state plane coordinates are scaled by just multiplying by a factor, then the "False Northing and False Easting too would be scaled.[pre]
S = Scale
x = unscaled coordinate value
y = unscaled coordinate valuexs = scaled "x" coordinate value
ys = scaled "y" coordinate valuethe point about which scale is determined
xsp = x scale point value
ysp = y scale point valueThen:
xs = S(x - xsp)
ys = S(y - ysp)When scaling is computed about the origin, xsp = 0 and ysp = 0.
xs = S(x - 0) = Sx
ys = S(y - 0) = Sy
ie, scaling is accomplished by multiplying the coordinates by the scale factorIf scaling is computed about the False Northing (yFN) and False Easting (xFE)
xs = S(x - xFE)
ys = S(y - yFN)Thus xs and ys are not equal respectively when scaling about the origin versus the False Northing and False Easting.[/pre]
Perhaps a little more explanation about the statement in your post?
Loyal is commenting on the semantic issue of calling 0,0 the origin. Of course it's commonly thought of the origin point in say an autocad file, but in the state plane system the origin point will need a coordinate assigned which will allow plenty of room to move south and west from it. So by multiplying the coordinates you are using the grid point 0,0 but the coordinate at the state plane origin point will be larger by the assigned scale factor just as you are showing.
MLSchumann, post: 332596, member: 471 wrote: Loyal
Having difficulty understanding the "scaling from a ÛÏpointÛ defined by the False Northing and Easting assigned to the ÛÏorigin.Û If state plane coordinates are scaled by just multiplying by a factor, then the "False Northing and False Easting too would be scaled.[pre]
S = Scale
x = unscaled coordinate value
y = unscaled coordinate valuexs = scaled "x" coordinate value
ys = scaled "y" coordinate valuethe point about which scale is determined
xsp = x scale point value
ysp = y scale point valueThen:
xs = S(x - xsp)
ys = S(y - ysp)When scaling is computed about the origin, xsp = 0 and ysp = 0.
xs = S(x - 0) = Sx
ys = S(y - 0) = Sy
ie, scaling is accomplished by multiplying the coordinates by the scale factorIf scaling is computed about the False Northing (yFN) and False Easting (xFE)
xs = S(x - xFE)
ys = S(y - yFN)Thus xs and ys are not equal respectively when scaling about the origin versus the False Northing and False Easting.[/pre]
Perhaps a little more explanation about the statement in your post?
Pretty simple...
When you SCALE "coordinates," you are scaling from 0/0, NOT from the ORIGIN...Look at the projection parameters for ANY SPC Zone (UNLESS you are deducting the False Northing/East values from the Coordinates). I rest my case...Yes there are a few [partial] exceptions.
Loyal
Edit:
Check out:
As everybody here knows, I don't subscribe to the bastardization of State Plane (or UTM) Coordinate doctrine. If you want to work in SPC (or UTM), fine, great, wonderful, marvelous...but don't screw with the Coordinates! If you want to compute/return/show ÛÏground distancesÛ on your plat/description/plans, fine, great, wonderful marvelous... just divide (or multiply) the ÛÏgrid distanceÛ by whatever magic fudge factor blows your skirt up, BUT LEAVE the COORDINATES alone! I know some folks who do it this way (Real SPC/UTM Coordinates, w/scaled [ÛÏgroundÛ] distances), and I think that is the ÛÏbestÛ way to go. I know that the DOTS have ÛÏtheir way or the highwayÛ (pun intended), but if they are paying the bill, then they can order their steak any way they want it.
If you want ÛÏGround COORDINATES,Û then generate a coordinate system (with formal projection parameters w/ Datum, Units, etc.) in which the Developed Surface (grid), is reasonably coincident with the ground (give or take a few ppms will be at or below the signal to noise threshold and most any Total Station or GPS work done within the limits of most small projects...UNLESS you are in the mountains).
Loyal
Dang straight, Loyal. +1
Example:
State plane grid Inverse Pt. 1 - Pt. 2 5280.00 ft. Az= 0å¡00'00"
Pt 1 Pt.2
N=3756000.000 N=3761280.000
E=4949000.000 E=4949000.000
Inverse Scaled from Pt 1 = 5280.50 Az= 0å¡00'00"
Pt 1 Pt.2
N=3756000.000 N=3761280.503
E=4949000.000 E=4949000.000
Inverse Scaled from 0 = 5280.50 Az= 0å¡00'00
Pt 1 Pt.2
N=3756357.978 N=3761638.481
E=4949471.681 E=4949471.68
True ground dist= 5280.52
So to be technical both methods 1 and 2 and state plane grid are incorrect
Also the official LDP Grid Dist. happens to = 5280.57
