# Tag Info

## Hot answers tagged ellipsoid

25

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 ...

15

The elevation above the ellipsoid (ellipsoidal height) is the elevation above a mathematical model that approximates the shape of the earth. The current most common one is WGS84. These are the elevations that you'd get from a GPS. Orthometric heights are measured above the geoid or equipotential surface, that is, the surface of equal gravity. MSL is "mean ...

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Ian's answer is incorrect. WGS84 approximates Earth by an elipsoid, which is basically a deformed sphere. EGM96 is a more complex model based on the gravitational force of the Earth (which is not constant) that defines what "sea level" or "up/down" mean, a smooth but irregular shape called "geoid". WGS84 is the elipsoid that best fits that geoid, and this ...

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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. ...

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Geographic distance can be described in a number of ways, depending on the surface abstraction used: For flat surface models, Euclidean distance is appropriate. For spherical surface models, you would probably use great-circle distance. For ellipsoidal surface models geodesic distance may be more appropriate, as the shortest distance between two points on ...

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No, a datum and ellipsoid are not equivalent. For a loose definition, think of the ellipsoid as defining size and shape. The datum then fixes that ellipsoid to the earth. NAD83 (various realizations) and WGS (another set of realizations) use almost the same ellipsoid GRS80/WGS84, and were originally designed in the 1980s to be equivalent. Since then, NAD83 ...

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The question concerns what kinds of curves deserve an implicitly exact representation rather than a discretized approximation. The crux of the matter is this: to be successful, the class of curves you support in this manner must be closed under the class of curve- and polygon-creation operations supported in the GIS. These operations include: Buffering....

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Dan, You may be interested in some of the work I've been doing on geodesics. This is described in this preprint. In particular, note: The direct and inverse geodesics problems may be solved to machine precision. This means about 15 nm for double precision. I can switch to long doubles, add an extra term in the series, and get accuracy of 6 pm. Note in ...

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Ultimately, because all extensive features are given by curves and those curves are approximated by line segments (when projected) or geodesic segments (when not projected), any errors are due to the fact that a line segment joining two projected points likely deviates (at least a little) from the projection of a geodesic between those two points. The ...

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Summary The short answer is that you take a weighted average of the coordinates to combine independent unbiased measurements of a given location. The weights are proportional to a particular quantitative expression of the precision of each measurement. The weights further determine confidence intervals for the coordinates. Those intervals can themselves ...

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I have done this before using forward azimuths, here is a link that has descriptions and algorithms that may be helpful: Inverse/Forward Utilities A forward azimuth calculates a new point that is a specified distance and compass bearing from a starting point. The basic idea is that you have a point in Lat/Lon and you calculate a series of forward azimuths ...

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An ellispoid is a mathematical model of the earth that approximates its three dimensional shape. See this definition. Elevation on top of the ellipsoid is 0, but since it's just an approximation one can be above or below the ellipsoid at any given point. "Elevation above the surface of the ellipsoid" is the distance between the measurement and the 0 value of ...

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GeographicLib includes classes to compute the geoid height via interpolation on a grid of values (the Geoid class) and via summing the spherical harmonic sum (the GravityModel class). The interpolation method is pretty straightforward; see the associated documentation, Geoid height. I agree that the NGA programs for computing the geoid height via spherical ...

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The term horizontal datum is used because it is more easily flattened into 2 dimensions and more useful for finding locations on a flat plane (compared to a vertical datum). As in the ESRI post you referenced (image below), the Earth's surface is very uneven, so modeling this very difficult. The "ellipsoid" used in horizontal datums is close approximation ...

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The answer is ~10001.966km (see Wolfram and sigurdhu) The fixed JavaScript Implementation gives me 10001.959km. Close enough. JavaScript was introducing errors at a precision bigger than 16 digits at Math.pow(0.5, digits)

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This is the answer to @Dan's question about using the auxiliary sphere to solve intersection problems. No, the auxiliary sphere doesn't let you solve for intersections directly. The problem is that the mapping from the ellipsoid to the sphere depends on the geodesic (e.g., its azimuth at the equator). Thus the auxiliary sphere is good for solving for a ...

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

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You need to define exactly what you mean by "move due east"! If you follow a rhumb line (aka a loxodrome) you will always be travelling east be following a parallel of latitude not be going in a straight line (ie, not the shortest path) stay at the same latitude If you follow a great circle (aka a geodesic or orthodrome), one that is initially heading ...

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The python code for EllipseCircumference given on wikipedia is right. Your translation into Javascript, however, is wrong. The python statement x, y = 0.5 * (x + y), math.sqrt(x * y) does the assignments in parallel and so it is not equivalent to x = 0.5 * (x + y); y = math.sqrt(x * y) but to t = x; x = 0.5 * (t + y); y = math.sqrt(t * y) Make ...

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This answer isn't a single command, but I'll put it in to get the ball rolling. Use gdalwarp to resample the geoid grid, then gdal_calc.py to shift the original raster. gdalwarp -s_srs epsg:4326 -t_srs epsg:26910 -r cubic -tr 10 10 -tap HT2_0.gtx HT2_0_resampled.tif gdal_calc.py -A original.tif -B HT2_0_resampled.tif --calc="A+B" --outfile=shifted.tif If ...

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An "ellipsoid" is a mathematical approximation of the shape of the Earth. Many different ellipsoids exist, but the two most widely used today are the GRS80 and the WGS84, which attempt to provide a best-fit across the globe. Heights were traditionally referenced to MSL, but with satellite and other technologies, we can often do better in terms of accuracy. ...

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The first workflow and the first step of the second workflow are doing the same thing. They're unprojecting the data from the LCC-based projected coordinate reference system (CRS) to its sphere-based geographic CRS. ...Originally I thought the second step of the second workflow was doing a datum transformation between the sphere and the NAD83 datum (based ...

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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. ...

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A "horizontal datum" references the 2D horizontal portion of a set of coordinates. Take these coordinates: Latitude: 29.27452 North Longitude: 102.32512 West Elevation: 110 meters If I said "The horizontal datum is WGS84" and that's all, then I've introduced ambiguity in my coordinates. And if there's one thing GIS professionals hate, it's ambiguity. ...

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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)....

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Aha! I fixed the bug by setting P->a to authalic radius and P->ra to 1/P->a in the code below. FORWARD(e_healpix_forward); // ellipsoid lp.phi = auth_lat(P, lp.phi, 0); return healpix_sphere(lp); } ... ENTRY1(healpix, apa) if (P->es) { P->apa = pj_authset(P->es); // For auth_lat(). P->qp = pj_qsfn(1.0, P->e, P->one_es)...

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What about "2D distance"? That's a term i've used as opposed to 3D distance (your slope distance)

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Here is a C# library for calculating geoid EGM96 undulations: https://github.com/MatejFranceskin/GeoidHeightsDotNet Available also as Nuget packet: GeoidHeightsDotNet

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Pardon if I'm cross-posting a link from Stack Overflow. I asked a similar question on Stack Overflow with regards how to do the calculations for an IOS application. I actually ended up answering my own question but I've posted a link here which gives you both C and Objective C code to complete this task. Code is here: http://stackoverflow.com/questions/...

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