This has been a good learning discussion for me!
Thanks Loyal and Math Teacher for the good comments.
I have nothing against the LDP design site mentioned above, but I don't know if it's cut out for this kind of work. It might be, but I don't know.
Loyal, post: 353729, member: 228 wrote: Roadie,
How did your weekend "project" turn out?
Nothing quite like number games to burn a few days off.
Loyal
Hi Loyal,
I didn't have access to software over the weekend so I was just mentally planning it. I finally have some time now to play around with it in Carlson. I'll let you know. Thanks for all the input!
RB
Success!
RoadBurner, post: 353441, member: 6168 wrote: I have a site with a local system, and we've put state plane coordinates on the same points. I can convert entities back and forth easily in cad using a lisp I wrote (simple shift, one scale factor, no rotation). No problem for me. But the client wants to be able to convert as well with their GIS software. I've provided several points in both systems that they can use to define a custom projection, but they're having trouble getting things to even come close. Back in the day, I played around with custom projections in TrimNet, but I don't have anything like that now. If I did, I could figure out a projection that works. I was mainly just wondering if that website was any good before referring the client to them.
Thanks for the input ya'll 🙂
RoadBurner, is the client using ArcGIS software? If they are, you should be able to create a custom projected coordinate system definition for them. This works in ArcGIS because it supports a 2 std parallel Lambert conformal conic projection with an added scale factor (that was added to support the single std parallel case). If you convert from SPCS
E = final spcs easting
N = final spcs northing
x = "raw" LCC coordinate before original FE applied
y = "raw" LCC coordinate before original FN applied
sf = scale factor to convert to local system
dE = east shift
dN = north shift
local_east = local easting
local_north = local northing
Usual Lambert equations:
E = FE + x
N = FN + y
Conversion to local from SPCS:
local_east = dE + sf * E
local_north = dN + sf * N
Substitute:
local_east = dE + sf * (FE + x)
local_north = dN + sf * (FN + y)
Collect terms:
local_east = dE + sf * FE +sf * x
local_north = dN + sf * FN + sf * y
new false easting = dE + sf * FE
new false northing = dN + sf * FN
So define a new Lambert conformal conic PCS using the new false easting/northing values and the scale factor. Probably will only work with Esri/ArcGIS software because of our quirk of allowing a scale factor with a 2st parallel case.
Thanks, Melita : )
Melita, would you answer a couple of questions for an old retired math teacher? I derive Lambert conformal systems using James Stem's methodology in NGS Manual 5. With a little manipulation, his equations can be used to derive "single parallel" systems.
Anyway, here are my questions. What is the purpose of multiplying a false easting or false northing by a scale factor? And how do you derive a "single parallel" Lambert conformal conic projection without first stating the latitude of the central (single) parallel?
Thanks for the insight.
MathTeacher, post: 354416, member: 7674 wrote: Melita, would you answer a couple of questions for an old retired math teacher? I derive Lambert conformal systems using James Stem's methodology in NGS Manual 5. With a little manipulation, his equations can be used to derive "single parallel" systems.
Anyway, here are my questions. What is the purpose of multiplying a false easting or false northing by a scale factor? And how do you derive a "single parallel" Lambert conformal conic projection without first stating the latitude of the central (single) parallel?
Thanks for the insight.
Various grid-to-ground / combined scale factor adjustments are done to the "final" State Plane or UTM coordinate values. If I want to adjust the projection parameters, I need to figure out the adjusted false easting and false northing values plus if there was an existing scale factor what the new scale should be. Let's take a UTM zone with a combined scale factor adjustment of 0.999458. The new parameters would be:
false easting: 499729.0
false northing: 0.0
new scale factor: 0.9990582168
On your second question, if I'm interpreting correctly, that's a terminology mistake. I had a big argument with a developer (who should know better!) about it a few days ago, in fact. I often say that there are two variants of Lambert conformal conic--the two standard parallel case and a single standard parallel plus scale factor case. However, as you pointed out, that's not right. The so-called "single standard parallel case" is actually just a scale factor plus central/origin latitude case. It creates two implicit standard parallels which can be calculated if the scale factor is less than one. (If it's greater than one, the conic is now above the ellipsoid surface and the equations to calculate the standard parallels won't resolve.
Most non-US Lambert conformal conic definitions are central/origin latitude plus scale factor.
Melita
Melita,
Fascinating. You multiply the ground system's combined factor by the UTM false easting to get a custom false easting. Then you multiply the combined factor by the UTM central meridian scale factor (0.9996) to get a custom scale factor. So you never consider the ellipsoid at all. You just assign an easting to the UTM central meridian that is consistent with the given combined factor.
Loyal raises the state plane to coincide with the ground at a point not on the central parallel. Using his data, I would develop a Lambert projection with central meridian at, say, 40 deg 12 min and raised to ground.
Here's a local projection method on the NCDOT web site. This one adjusts State Plane northings and eastings by dividing distances by the local combined factor. One point's coordinates are the same on both SPC and the local system, so the link to an ellipsoid is lost. It will work, though, for one project.
Coordinate scenes abound; how on earth do you keep up with them?
I don't! I just keep being surprised by the latest variation. Several state DOTs are now following MN's and WI's lead and publishing at least partial LDPs. The latest I've seen was Indiana.
Changing the projection parameters only makes it easier for software to handle--once you start messing with the ellipsoid parameters you have to decide how to handle the datum/geographic coordinate reference system and any transformations connected to it.
A developer I work with started working on the Esri projection engine around 1998. He thought, "Oh, I'll work on it for a few years, then I'll be done and will work on something else." He's still working on it (and loves it).
MathTeacher, post: 354502, member: 7674 wrote: Melita,
Fascinating. You multiply the ground system's combined factor by the UTM false easting to get a custom false easting. Then you multiply the combined factor by the UTM central meridian scale factor (0.9996) to get a custom scale factor. So you never consider the ellipsoid at all. You just assign an easting to the UTM central meridian that is consistent with the given combined factor.Loyal raises the state plane to coincide with the ground at a point not on the central parallel. Using his data, I would develop a Lambert projection with central meridian at, say, 40 deg 12 min and raised to ground.
Here's a local projection method on the NCDOT web site. This one adjusts State Plane northings and eastings by dividing distances by the local combined factor. One point's coordinates are the same on both SPC and the local system, so the link to an ellipsoid is lost. It will work, though, for one project.
https://connect.ncdot.gov/resources/Location/Manual Documents/Local Project Coordinate System.pdf
Coordinate scenes abound; how on earth do you keep up with them?
Thanks for the link.
Your welcome, Adam. There are more procedural and policy documents on the Location and Surveys page at the NCDOT web site. Some of those may be helpful to as well. You can get there using "NCDOT location and surveys" as a Google search term.
Great discussion and so glad to see surveyors talking about Low Distortion Projections (LDP). I held for a long time out of personal stubborness, but LDP's are the way to go. You really don't need to be a geodesist or math wizard to implement them. The software does the math for you. BTW Shawn Billings wrote two excellent articles about how to go about it that are independent of software, simply the concepts and methodology.
Loyal's Rules for LDP Design (in descending order of importance):
First: don't (ever) screw with the Ellipsoid definition!
As soon as you mess around with the defining parameters of the NAD83 (GRS80) Ellipsoid, you are no longer working with NAD83 ANYTHING... As Melita pointed out above, this lands you in the quagmire of dealing with the geocentric 'T' offsets (and maybe Rotations and Scale as well). Mike Potterfield once said (paraphrased): ÛÏUsing a custom ellipsoid to solve grid to ground issues, is like using an H-Bomb to kill flies!Û
Second: If you REALLY want to generate a Coordinate System (definition) that REALLY [actually] relates (geometrically) with a State Plane (or UTM) System (developed Surface & Grid Bearings), then you REALLY need to start with the formal Definition (parameters) of THAT [underlying] SPC/UTM System. I personally see little wisdom in such ÛÏthings,Û and generally refer to them as ÛÏpsuedo-Low Distortion ProjectionsÛ (pLDPs). HOWEVER, the continued ÛÏmodifrinkinicationÛ of SPC systems by DOTs, Engineers, and many Surveyors, forces ÛÏusÛ to deal with this Coordinate Alchemy from time to time.
Third: Try NOT to mix Projection ÛÏTYPESÛ (square pegs in round holes - cylinders, cones, tangent planes). Although one can (quite easily) generate an Un-rectified Oblique Mercator (Hotine) Projection that ÛÏworksÛ very well on a SMALL Scale ÛÏmodifiedÛ Transverse Mercator or Lambert SPC, it WILL start to fall apart (at some point), as you move further from the ÛÏsweet-spot.Û Don't paint yourself into a corner!
Last (but not least), avoid the temptation to get TOO clever! No matter how much you massage the data (or refine your Projection Parameters), you are never going to remove ALL distortion... there is a point of diminishing returns. However, don't be too ÛÏquick-n-dirtyÛ either. ÛÏEverything should be made as simple as possible, but not simpler.Û (Albert Einstein)
In closing...Meta Data, Metadata, METADATA! Leave BIG footprints, and others will follow (if they can't, then it isn't YOUR fault).
Loyal
