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23

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 ...


10

WGS84, according to: http://support.google.com/earth/bin/answer.py?hl=en&answer=148110 Cheers, Ryan


8

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 ...


8

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. ...


6

It's been a year and nobody will care, but just in case someone arrives here... Actually 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 ...


6

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: ...


4

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 ...


4

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 ...


4

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 ...


3

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 ...


3

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 ...


3

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 ...


3

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)


2

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 ...


2

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 ...


1

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 ...


1

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. ...


1

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 ...


1

a quick google of the two will lead you to http://en.wikipedia.org/wiki/World_Geodetic_System From that page: Updates and new standards The latest major revision of WGS 84 is also referred to as "Earth Gravitational Model 1996" (EGM96), first published in 1996, with revisions as recent as 2004. This model has the same reference ellipsoid as WGS 84, but has ...


1

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, ...


1

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


1

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: ...



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