Typical and low-distortion map projections.

Single Transformation with ECEF

This entry is part 33 of 34 in the series Where Theory Meets Practice

We at xyHt think this topic is one surveyors should be talking about. Instead of placing this reader’s letter to us as a comment under Dr. Ghilani’s article (linked below), we are making it a post itself to encourage discussion underneath.  Editor Gavin Schrock, PLS, started us off, below. 

Professor Ghiliani’s article, Transformation of Observations (xyHt, March 2015), states that Low-distortion Map Projections have both advantages over State Plane Coordinates and disadvantages.  At a seminar on GPS this last summer a very bright surveyor presented an information-rich 8-hour program in New Mexico.  In it he extolled the virtues of Low-distortion Map Projections.  At one point as proud as punch he stated that Oregon now has a separate Low-distortion Map Projection for each of its 40 counties.  Can you imagine such a mess? He further stated that in one jurisdiction where the authority was checking the geodetic information required to be supplied on maps by land surveyors that something like 80% of the data submitted was in error. Surveyors are being asked to be accomplished geodesists.

Is the tail wagging the dog?

When I suggested that Earth Centered Earth Fixed Coordinates, ECEF, are one system worldwide and the only “conversion factor” is a single transformation involving two angles, he immediately agreed and said he would love to adopt such a system, “if the surveying community would agree.”

With Earth Centered Earth Fixed Coordinates we need just a single transformation.  If that is lost and on the ground bearings are available from existing points (sound familiar?), we can recreate the rotation and locate ourselves with the earlier work.  A single set of ECEF coordinates at one point and a rotation angle is all that a local surveyor need put on her or his plat to “geographically” reference the survey.

What is the job of the land surveyor?  To find the latitude and longitude and ellipsoidal height of each of our client’s corners?  I don’t think so.  But we have been captured by the technology.  When you get in your work truck do you care how fast the fuel pump motor is running?  You care about the speed of the vehicle but not so much the rotational rate of the tires.  Same with my surveying: I want ground distances and bearings and care little about the geodetic height of the point or the transformations any more than I care about the algorithms used to calculate sines and cosines.

We should be asking our software developers to allow us to do just this.  We work on the ground and let the software do the transformations and rotation.  Skip Low-distortion Map Projections and State Plane Coordinates. They are approximations, no matter how elegantly wrapped up in multidimensional equations. We are half-way there; we have the ECEF technology we just need to capture it.

Michael Daly
Arrow Engineering
Gallup, NM

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Single Transformation with ECEF” Comments

  1. Thank you for the thoughtful response. The very subject you bring up has been greatly weighing on my mind for many years. I’m a practicing surveyor and have been involved in our state’s reference framework and RTN for over a decade. There has not been a ground-swell in our state to create LDPs like Oregon did (and those mainly only cover highway corridors); as Dr. G pointed out, with varied terrain many LDPs would have to be very tiny. As an exercise I looked at how many it would take to cover WA while providing any gain over the limitations of instrumentation, or that would provide an advantage over the single CGF project zones that DOTs develop on an ad hoc basis – it would take over 300. LDP is the cause celebre’, and while they can be amazing at what they can do, at what point is there a diminishing return considering pitfalls, and in overlooking some perhaps better ways?

    I’ve been following Dr. Burkholder’s ECEF solutions for many years, and have reached out to him about developing content on the subject – I’ll bring that back up again. The irony is that many surveyors do not realize that a substantial amount of what is done for them in the background – the ghost in the machine – (i.e. GNSS pre-projection steps) is already working right there in the realm of xyz/ECEF).

    I’ve often wondered why this has not caught on more directly. And what I’ve found out in asking geo-types in various parts of the country and world is that it is not for lack of good math, but more of a perception nature. I’m not going to say there is any problem with global coords, no, but there is a challenge in getting folks jazzed about it. I’d be perfectly happy working in that realm, but like many there would always have to be some downstream planar outputs, and for a very practical reason – legacy systems of spatial reference and even coordinate systems are designed to mimic a spatial view of the world from the point of view of a human planted with their feet plumbed to the earth.

    If you look north, the other axis in NE, LL, et al, is perpendicular, and the up-down is coincident with the gravitational pull towards the center of mass (i.e. humans perceive elevation as which-way-the-water-flows; down, towards “sea level”). So humans have not evolved to be able to intuitively interpret xyz coords that do not have a tacit spatial relationship to the tangent of earths surface they occupy and perceive. Decreasing/ascending xyz vales can be off at odd angles from where they stand.

    I know that sounds a little abstract, and that all of the heavy lifting could be handled inside-the-machine, but humans are wired (even to the level of “place” and “border” cells in the hippocampus) to key off of horizon, levels in our ears, and visual temporal clues as to direction -xyz offers no direct perceptive connection.

    That aside – the move to the global reference framework in 2022 will (i.e dropping NAD83) by the NGS will enable GNSS observations to be able to resolve to ECEF without the intermediate steps. Could the years in between be a golden time for the broader adoption of global coordinates? (at least inside the machine). I’d be game to help further that conversation.

  2. Added Discussion: Projections
    The preparation of a survey plat or report serves two basic functions. One is that it provides information for others to enable them to find and see where improvements and monuments are located and to realized some relative spatial orientations among the improvements and monuments. The other function is for other persons who may need to retrace the work so as to be able to accurately position the replacement of improvements and monuments.

    As a consequence, it is imperative for the survey plat or report to present information in such a manner as to satisfy the requirements for interpretation by the layman as well as to provide accurate positional retracement information.

    The layman, as Gavin Schrock discusses, relates to mutually orthogonal directions of gravity or up-down, forward and backward and side to side or right and left. By facing in an appropriate direction, it is then possible for the layman to rotate this basic reference frame to some sort of North-South, East-West and elevation orientation. The survey plat or report should provide sufficient information to respond to this spatial relational issue so that the layman can, given appropriate lineal measurement units, be able to make a meaningful interpretation of that information.

    The other side of the coin, so to speak, is the information required by a person who may do a potential retracement. That information requires details and specifics often not revealed or presented in the interpreted information presented to the layman. A little more succinctly stated, the information needed to see where monuments are is not the same as the information needed to put monuments back where they originally were.

    Adding some to the distinction between the layman and the surveyor geodesist, one might say for the layman, the earth is flat and gravitational lines, the verticals, are parallel. For the geodesist, the earth’s surface is round and undulated and gravitational lines are not parallel.

    The tools, technologies and methods of surveyors have changed over time. Today, this means the knowledge and understanding of these changes is necessary and that its manifestations are realized. The surveyor can no longer rely on old measurement methods and presentations because of the new tools being used.

    The measuring tools and technology one uses changes the measurement methods and attendant presentations. The diameter of an orange measured with a pocket tape can be reported as nine centimeters. With a machinist’s tool such as a micrometer or vernier caliper, there becomes problems: which or how many diameters are to be measured? What is to be reported? 87.05, 93.37, 89.94cm etc? In former times a surveyor using a Gunter’s chain could measure to the nearest link the distance between two stones. However, today, using a total station, the problem becomes two-fold, one of determining what points on the stones are to be measured and the other what measurements to report? When the surveyor uses GPS for measuring, he or she encounters the same sort of problems. Where on the on the earth as in the orange’s ridges and dimples does he or she measure? The surveyor is no longer using layman tools but, those that provide measurement information once only in the domain of the geodesist. As a consequence, using geodetic tools, it is imperative that the surveyor learn, understand and use geodetic measuring techniques and attendant reporting and presentation.

    Low distortion projections, state plane coordinates and local coordinate systems so long as on-the-ground dimensions are presented serve well for purposes of the layman. This may or may not be the case when it is required to replace monuments as closely as possible to their original location. Unless all projection parameters, not to forget time and date, are provided, positionally accurate relocations may not be realized. The underlying reasons are that projections attempt to present reality orthogonally while in reality, reality is always in perspective. One only needs look at a photograph or an isometric drawing to grasp the concept.

    Adding earth-centered, earth-fixed (ECEF) coordinates overcomes the limitations of fixed projections. It makes it easy and convenient to select any other projection, to select a differing perspective. It provides for not only other projections but, as well, differing transformations. One may compare a projection to a picture of an object and earth-centered, earth-fixed coordinates as an actual object in one’s hands. Extracting measurements from the photograph is possible though probably is not as precise as doing the same on the object.

    Both, projections and earth-centered, earth-fixed (ECEF) coordinates are practical presentation methods and both should in many cases be used. The suggestion is definitely not a standard to be imposed. While the need to fulfill a client’s requirements must be met, it must not be overlooked that the results of one’s work today may be the only evidence available for someone else’s work in the future for the same or another client. It is a responsibility that normally aspires to the professional.

    Measurements have a low ranking as property boundary evidence. Perhaps it is because there are too many surveyors who not only do not know how to measure properly but, who do not know how to present their measurements. Education, reflection and discourse about this and other related issues could do much to add credibility to measurements as evidence.

  3. This topic deserves a lot of attention and discussion. In reverse order on the following web site, see items # 14, 30, 47, 54, and 69.


    • Gavin Schrock Gavin Schrock

      Yes, article #30 delves into the aspect I noted in my previous post; that of (pardon my lack of better term) “orientation heuristics” which many of the current conventions and projection approaches so readily accommodate.

      Some good reading: http://www.globalcogo.com/setepaper.pdf

  4. I am not sure about ECEF systems either since we are asking the surveyor to be a geodesist. The inverse computations of ECEF coordinates to a slant distance and azimuth is not exactly a simple formula and typical legal descriptions need this. Now if we are going to let the software do all the computations without an understanding of what it is doing then ECEF works but I have seen bugs in commercial software so how would the typical surveyor check it. SPCS has been working for surveyors for years. I am not sure there is a better alternative. But this is my opinion.

  5. Also we should remember that our measurements are captured in a local astronomical coordinate system (that is, with respect to gravity) and thus the observations need to be converted to geodetic observations which requires knowledge of the local deflection of the vertical. While our knowledge of this is getting better and will improve by 2022 or there about, it will never be perfect and thus using an ECEF coordinate leads to the same problem of approximations and expecting the surveyors to be geodesists.

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