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I'll start with the OGP definitions:

  • Geographic. A coordinate reference system based on a geodetic datum and using an ellipsoidal (including spherical) model of the Earth. This provides an accurate representation of the geometry of geographic features for a large portion of the Earth’s surface. Geographic coordinate reference systems can be two- or three-dimensional. A Geographic 2D CRS is used when positions of features are described on the surface of the ellipsoid through latitude and longitude coordinates; a Geographic 3D CRS is used when positions are described on, above or below the ellipsoid and includes height above the ellipsoid. [...]
  • Geocentric. A coordinate reference system based on a geodetic datum that deals with the Earth’s curvature by taking the 3D spatial view, which obviates the need to model the curvature. The origin of a geocentric CRS is at the centre of mass of the Earth.

In practice, I would identify the difference between, say, a Geographic-3D and a Geocentric CRS in the fact that the latter has a central point in the 3D space from which angles and elevation are computed (no ellipsoid is needed, Earth is spherical?), whereas the former refers to the datum/ellipsoid, i.e. latitudes, longitudes and heights are computed with respect to the ellipsoid.

Am I saying something wrong or missing something? Thanks.

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Re geocentric: The earth's shape doesn't change just because you use a different coordinate system! However, a geocentric system makes no attempt to model the earth's shape at all. It is nevertheless physically tied to the earth by means of the datum: knowing the center is not good enough. You also need to know (e.g.) where on the earth the x, y, and z axes poke through. The datum tells you that (or its equivalent). –  whuber Apr 17 '12 at 21:11
    
Thanks for the answer @whuber. Do you mean geocentric CRSs rely on a datum as well? So, again, the difference with a Geographic 3D? –  Campa Apr 18 '12 at 8:08
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1 Answer

up vote 4 down vote accepted

Geographic-3D relies on an ellipsoid (which can be a spheroid or a sphere), and locations are specified with latitude, longitude on the ellipsoid, and a distance above or below the surface of the ellipsoid.

Geocentric coordinates are 3D Cartesian coordinates, with the origin at the notional centre of the Earth (ellipsoid, geoid, or physical Earth), and points defined as X,Y,Z triplets. For most cartographic purposes, this is pretty useless because as the X and Y coordinates change, so your position above the Earth changes, as well as other fun non-spherical issues.

Think of them as the difference between 2D polar coordinates, and 2D Cartesian coordinates. They're both complete, unambiguous, and useful ways of expressing the location of something, depending on the problem you want to solve.

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Thanks so much @MerseyViking. One thing is still not completely clear though: linking a datum to a Geocentric CRS is 1. needed to define orientation of the axis (e.g. prime meridian defines direction of X), 2. needed when transforms to other CRSs are required. Missing something? I just would love to understand all the details. Thanks again! –  Campa Apr 18 '12 at 11:50
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(+1) In the last paragraph, a better analogy is between Cartesian and elliptic coordinates, because heights are not (usually) measured radially from the earth's center but upward from the surface. –  whuber Apr 18 '12 at 15:07
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