Wisconsin has had projections for individual counties (although some counties share) for a while now. Seems to be similar concept to Iowa.
Then the statement is inadequate, as the rate of change is zero along any given latitude, not just the standard parallels of the given two parallel Lambert example.
However, if the statement is related to scale factor, then it is perfectly adequate. The scale factor is unity at the standard parallels of the given two parallel Lambert example, but does not equal unity at an other place in the coordinate system.
So is the statement incorrect or is your myopic interpretation. Please enlighten those of us in the ignorant age.
Kent,
I was right with you up to the point you assigned a motive to the use of low distortion projections. In my experience, the people who develop and use them have a very good handle on projections and geodesy in general. The accommodation is a recognition that not everyone has (nor do they need) that knowledge.
I have great respect for your abilities. You do limit yourself by assigning motives and character traits to folks you haven't met. While I understand not everyone comes here for warm fuzzies, it is ludicrous to make every other post an insult to people who do things different than you...
Distortions
Elements of Cartography, Sixth Edition, Table of Contents:
> I am with Kent on all of this.
I know I'm on firm ground, then. Thank you, Cliff.
> I was right with you up to the point you assigned a motive to the use of low distortion projections.
Well, the whole appeal of the projections in which the CSF approaches 1.000000 is when dealing with folks who have difficulty working in other projections where the CSF doesn't equal 1.000000. I doubt very much that a majority of these folks are experts at map projections or even have a functional knowledge of them.
I just do math, but LDPs are an interesting issue. And Kent is not terribly wide of the mark with his reference to finding ways to accommodate for lack of knowledge. I don't know if he thinks that training should be improved or if people should seek to train themselves, but knowing more of the theory would help anyone.
One of the worrisome things is loss of fundamental knowledge when accommodations are put into place. To me, a good example is the ground coordinates issue. It's likely that the first person who divided a coordinate by a combined factor knew what he was doing, its advantages and disadvantages. But three layers down and three generations later, much of the understanding is lost.
I think that the LDP approach is better because it preserves the mathematical relationship between the reference ellipsoid and the plane. But disseminating and preserving the knowledge beyond a checklist of steps to complete is the real challenge.
hi kent
i sent you an email moments ago, i need a clarification from an earlier post.
Unmanned,
Leica sores all GNSS measurments in WGS84 Latitude Longitude Ellipspoid Height. The unit for anything stored in the database is metric. This way all GNSS measurements can be converted in any coordinate system attached to data job. Even if the attached coordinate system is changed the user can see values in new coordinate system on the fly if needed.
Again, with you to a point. There are a great number of end users who don't have a clue what a projection is. Others I work for hold PhD's and can compute circles around most of us. It is still rare for any of them to ask for anything other than ground on a finished product. It's not a matter of understanding, it's a matter of need. It makes no sense to have every user of a product convert to ground or figure corrected ground distances for each line. Let the person who was paid to produce a map do it once.
Minnesota too, but they modified the GRS80 ellipsoid rather than adjust the map projection parameters.
Minnesota county coordinate systems
Melita
I don't remember where I first saw distortion in terms of LDPs, but I just remembered where I saw it in terms of State Plane. It's in Stem's NGS 5 manual. Here's a cut and paste in two parts. I preserved the page numbers, but eliminated the diagram on page 19.
Note that in the last paragraph, Stem says that the map scale distortion is identical to the grid scale factor. Now, that surprised me today, but my paper copy of Stem has that area highlighted, so I knew it at one time. He also gives a formula for calculating "scale error" as a percent.
The changes that LDP folks made are to use the combined factor instead of the scale factor and calculate parts per million instead of parts per hundred. Then they called it "distortion", with no modifier.
I think that it's highly questionable as to whether elevation is distortion in the same sense that scale is. Mathematically, the two factors have different denominators, so they don't describe the same concept at all. There's no problem with multiplying them to get a combined factor, but they're very different entities.
That said, the entity that LDPers use their "distortion" to describe is a useful one. But, distortion is a misnomer for it.
Your questioning that term was on target.
Anyone who wishes to discuss the meaning of distortion with an open mind as it relates to LDP with Micheal Dennis be my guest. I think you will have met your match.
> The changes that LDP folks made are to use the combined factor instead of the scale factor and calculate parts per million instead of parts per hundred. Then they called it "distortion", with no modifier.
>
> I think that it's highly questionable as to whether elevation is distortion in the same sense that scale is. Mathematically, the two factors have different denominators, so they don't describe the same concept at all. There's no problem with multiplying them to get a combined factor, but they're very different entities.
>
> That said, the entity that LDPers use their "distortion" to describe is a useful one. But, distortion is a misnomer for it.
I agree that the focus of a well designed LDP is developing a combined factor that approaches unity (1). The combined factor is a fabrication of two independent values: grid factor (aka scale factor) and elevation factor (which is based on the ratio of the topographic height from the center of the Earth and the ellipsoid radius - not sea level). The fact that these two values (GF and EF) are independent of one another is convenient for developing an LDP because one can be manipulated (the grid factor) to offset the distortion(?) of the other (the elevation factor). Some refer to the combined factor as the combined scale factor. This should probably be avoided as it is a misnomer.
If the scale factor is technically a "distortion", then I don't see how the elevation factor is not a distortion. It's not based on a homogenous mathematical surface, like the ellipsoid and projection surface, but I don't see how that matters.
from the Iowa Manual:
"1.3. Why the Iowa State Plane Coordinate System is Deficient for Certain Modern Day Uses"
Kent will freak out!!!!!!!!!!!!!!
Thanks David,
That looked a bit above my pay grade too. True experts make complex things usable.
N
That's a fair question; I hope my answer does it justice.
Scale distortion is a result of the mathematics of map projections and is unique to the specific projection under consideration. Elevation effect on the difference between the calculated length of a line and its measured length is independent of the projection used.
Evidence of this appears in the plane coordinate section of NGS Data Sheets. Note that, while the scale factors for the state plane projection and the UTM projection are different, the elevation factors are the same.
Historically, map distortion has been limited to scale distortion only. In the LDP world, the term distortion includes the elevation effect along with scale distortion. Kent's objection, I think, is the expansion of the meaning of the term without explicitly saying that it was expanded.
Personally, I'm a stickler for consistency in terminology and definition. But LDP distortion is mathematically sound and extremely useful. In fact, it is one of the best one-number summaries of performance that I've come across in almost 50 years of work in applied mathematics.
The LDP world is not going to coin a new term, so when we read or hear distortion, we'll have to be conscious of its context.
Distortion IS
...as distortion DOES.
This semantic sideshow is only going to further confuse the confused.
Inasmuch as a properly designed and implemented LDP will have a DEVELOPED SURFACE "far" from the Ellipsoidal Surface (which of course is one of the advantages of an LDP), the "Elevation Factor" (which I prefer to call a vertical coefficient or 'vc') is a function of the difference between the [design] Ellipsoid Height of the Developed Surface, and the Ellipsoid Height of any given physical point (on the ground) that is within the LDP design limits (usually less than 10-40ppm depending on usage and local terrian). The "projection induced" scale factor (k) is generally in the 1-5ppm range (depending of course on how "BIG" the LDP is designed to be).
Soooo... under "normal" conditions, the COMBINED effect of Scale (k) and "height" (vc) can be kept to a minimum.
Sure....21 feet UP or DOWN (relative to the design height) still changes the 'vc' value by +/-1ppm, and the "local" 'k' value should be factored in, but in many (if not most) cases, this COMBINED "distortion" (grid-ground) should fall pretty close to trivial/non-trivial threshold (at least that's what we work towards with LDP design).
Just my 2-bits
Loyal
Oh Yeah..."A rose by any other name, is still a Finkweed"
Ed (Big Daddy) Roth
Ah. Ok, Teach. I see your point to a point. The elevation factor isn't a map distortion. Technically it is applied before any projection math takes place. It seems like a fine line, but it's a line. In practice you cannot have one (map projection) without the other (elevation factor).
Kent's weird and indefensible position was that a distortion is only the rate of change in scale factors. Mr. Stem's work and the very link Kent referenced both opposed this interpretation. Ironically he ridiculed any who dared hold a differing viewpoint. How embarrassing. He successfully hijacked an interesting thread about graphically visualizing map projection distortion with, as Loyal said, a sideshow. It will be interesting to see if he keeps at it or if he shows the good sense to express even a modicum of humility and apologizes.
Sorry, Teach. Just because you leave the classroom doesn't mean you leave the school yard. Lol.
Loyal can cram several dollars worth of knowledge in his 2 bits worth, can't he?
