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26

This summarizes my understanding of some of the basic ideas. Because it is hard to find all of them clearly described and summarized in one place, I could be wrong or misleading about some of them: comments and corrections are welcome. "Geoids" are approximations to a surface of gravitational equipotential. The geoid is a hypothetical Earth surface ...


18

So there are two pieces to what someone might call a Coordinate System The first is a Geographic Coordinate System or GCS, which is what WGS84 falls under. The definition given by ESRI states that a GCS uses a three-dimensional spherical surface to define locations on the earth. Basically, a GCS is used to define your real world points on a 3 dimensional ...


11

No, GPS does not 'correct' for continental drift per se. GPS can be (and is) used to measure drift. Drift is accounted for in the model of the earth used, aka datum or reference ellipsoid. GPS uses the World Geodetic System, or WGS, and most units report coordinates in the initial version established in 1984 (aka WGS84 coordinates). That model, and others ...


11

This answer is divided into multiple sections: Analysis and Reduction of the Problem, showing how to find the desired point with "canned" routines. Illustration: a Working Prototype, giving working code. Example, showing examples of the solutions. Pitfalls, discussing potential problems and how to cope with them. ArcGIS implementation, comments about ...


10

Internally, ST_Buffer(geography, ...) uses a fixed projection guess with _ST_BestSRID, which are typically UTM zones or whatever makes sense to the algorithm. This is why you see the differences, because they are different projections that are not optimized for the location of the points. For simple point buffers, you could use a custom azimuthal ...


9

I am not a Geodesy expert, but far as I understand it, the geoid, is the shape that the surface of the oceans would take under the influence of gravity alone. It is the surface at which the intensity of gravity is the same. The Problem isn't that it is difficult to describe mathematically, but it might be impossible to predict correctly and accurately. ...


8

One thing to keep in mind is that lat/long is geodetic and not geocentric: If we were to calculate elevation as a radius from the center of the ellipse, our elevation lat/long would be different than our horizontal lat/long! This is why there are two different datums. The horizontal datum is just a smooth ellipse, because it's easier to do trig functions ...


7

I admire your enthusiasm but have to say you're not defining anything new. The simplest geographic/geodetic models of the earth are perfect spheres/globes. The only "difference" between that simple old system and your "new" system being that heights, instead of measured relative to the surface of the fixed-radius (R) sphere/globe, are now relative to the ...


7

The heights on google earth refer to EGM96 and are, therefore, Geoidal heights. The lat/long are referred to the WGS 84 ellipsoid.


7

One could use either kind of latitude to locate points on the WGS 84 ellipsoid (used by the NED) or any other ellipsoid, but "everybody knows" that the values will always be given as geodetic latitudes. However, it is surprisingly hard to find an authoritative statement to that effect! Before we go on, it helps to understand that although a datum ...


6

It looks like you've done everything correctly. You can evaluate the errors from each method by performing the inverse calculations to find the distance given the origin and destination coordinates, then evaluate the residuals of distances. This is a round-trip exercise. # For Vincenty's method: geopy_inv_dist = geopy.distance.vincenty(origin, destination)....


5

If the wheels are pointing straight ahead, you are taking the shortest route toward some point directly ahead and thus following a great circle (or geodesic). If you wish to cross each meridian at exactly the same azimuth each time (and thus follow a rhumb line), you would have to gradually steer slightly more towards the meridian as you progress. Generally,...


5

This is not a map of the Earth. This is a map of a spheric world, whose Radius = 1 (dimensionless). In this map, a spheric triangle was drawn. The vertices of the triangle are: N North pole. 1 Start point of a travel. 2 End point of a travel. The travel was started with initial azimuth alpha_1, and traveled a distance s. The distance, on the ...


3

Without knowing the projection, or datum of the monuments, the only way to transform them correctly would be through a great deal of trial, and error. Given the latitude of the area you are in, the Northing is too small to be in UTM meters, or feet, unless the first digit of the coordinate has been removed for space saving. Knowing where the monuments are ...


3

Interesting to find that my math illiterate solution did the job with 5 minutes of thought and coding, wouldn't the flattening factor have to be considered rather than a perfect elliptical model? double pRad = 6356.7523142; double EqRad = 6378.137; return pRad + (90 - Math.Abs(siteLatitude)) / 90 * (EqRad - pRad)...


3

I was curious to see how quickly @cffk's approach converges on a solution, so I wrote a test using arcobjects, which produced this output. Distances are in meters: 0 longitude: 0 latitude: 90 Distances: 3134.05443974188 2844.67237777542 3234.33025754997 Diffs: 289.382061966458 -389.657879774548 -100.27581780809 1 longitude: 106.906152157596 ...


3

As you note, this problem arises in determining maritime boundaries; it's often referred to as the "tri-point" problem and you can Google this and find several papers addressing it. One of these papers is by me(!) and I offer an accurate and rapidly convergent solution. See Section 14 of http://arxiv.org/abs/1102.1215 The method consists of the ...


3

The difference is defined by the datum shift between the two reference ellipsoids. The shift itself is defined with a transformation (7 param. Helmert, 4 param,....) using 3D cartesian coordinates (X, Y, Z) which are calculated from ellipsoid coordinates (lat, lng, elevation). The transformation (parameters) is usually derived from a set of points which ...


3

The question is pretty complicated. What you are asking about is calculations on the surface of the Earth, which is called spherical trigonometry. To get even more precise you need to use an ellipsoidal model of the Earth. I'd suggest you use a program that can already do this for you, but if you want to do it yourself, here's a link to start on. The ...


3

The geopy pull request fixes your issue with geopy. You will need to install the python package geographiclib first with pip install geographiclib


3

I don't think there are practical limitations to ned2geodetic. The conversion from LLA to ECEF coordinates has closed form solution. The rotation of NED vector to ECEF has closed form solution. Vector addition in ECEF is trivial. Conversion of ECEF coordinates to LLA as implemented in Matlab is not closed form solution. However, the algorithm employed is ...


2

The answer depends on what you are interested in and therefore what you mean by 'earth's surface'. The Geoid is the equipotential surface (in terms of gravitational potential). The ellipsoid is a geometric approximation of the irregular land-sea (physical) surface. Given the irregularities even in the physical surface, no ellipsoid can ever do a perfect job. ...


2

Yes, you must use an ellipsoid (or other mathematical surfaces). the reason is that the Geoid is a Physical surface (defined as the equipotential surface of gravity strength field). Simple meaning - it has no mathematical formula (another simple meaning - it is a surface at the height of the mean sea level that if you put a drop of water on it it wont move)....


2

From mkennedy, the answer: "it's NAD 27 state plane zone, so already in US survey feet . . . I used US NGS programs to look up the state plane zone, then to test converting the xy points to lat/lon."


2

I know the question has answered already, but allow me to show you something cool for future use: A live Google map where you can move the edge markers affecting the great circle and rhumb line same time. Here is the link: Great circle article!


2

I would much rather suggest doing it manually since the math is simple. This will be much faster than using so many potentially complex methods. public static Point createPointInDistanceAtAngle(Point anchor, double distance, double angle) { double dx = distance * Math.cos(Math.toRadians(angle)); double dy = ...


2

One place to start is the bibliography provided by the geographiclib of Charles Karney. This starts at the begining with: I. Newton, Philosophiae Naturalis Principia Mathematica (3rd edition, Roy. Soc., 1726), Book 3, Prop. 19, Prob. 3, pp. 412–416. https://books.google.com/books?id=0xYOAAAAQAAJ&pg=PA412 English translation: Newton's ...


2

If two ellipsoids share the same origin and axes (both use Greenwich and the same North pole), but have different axes lengths, only the geodetic latitude will change between the two. This is true because geodetic latitude is defined as a line perpendicular to the ellipsoid surface. However, you shouldn't normally think in terms of the ellipsoids, but of ...


2

EPSG/WKID number 4326 relates to WGS84 Geographic, with units in degrees. The ellipsoid is extremely similar to GRS80, with only a slight difference in one of the axes. This is the code and system that the Global Navigation Satellite System (GNSS) is based on (also known as GPS, for the American constellation of satellites). GNSS/GPS satellites are ...


2

A quadrangle? Yes, it is named: spheroidal quadrangle.


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