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With "Geographic coordinate system" we only get the location, no rotations or anything. Translated into latitude and longitude.

Where with "Spherical coordinate system", we should be able to get the exact position, including rotations.

The spherical coordinates of a point P are defined as follows:

  • the radius or radial distance is the Euclidean distance from the origin O to P.
  • the inclination (or polar angle) is the angle between the zenith direction and the line segment OP.
  • the azimuth (or azimuthal angle) is the signed angle measured from the azimuth reference direction to the orthogonal projection of the line segment OP on the reference plane.

Now, if I'd want to get my position on Earth with Spherical coords:

  • the center of the core of Earth is the origin
  • radius from core to sea level + elevation above/below sea level is the radius
  • inclination: angle between zenith direction and angle taken from my perspective, vertical point of view (imagine a ray coming out of the center of your pupil)
  • azimuth: same as with compass, angle from the North Pole.

P.S. The inclination part wouldn't be correct in this case, because the point is measured exactly on Earth's surface and inclination- from my point of view. But for the idea, that should be enough. (Yes, yes, we can add to radius the distance from "ground" to center of my "pupil" to get the exact point of view in space, while taking the measurements in stature)

As for the gravity attractor thing, that was meant in order to get the position anywhere in the universe. Keeping in mind that it should be measured by using the origin of the center of the nearest, strongest object with a gravitation field in whom you reside.

Are my assumptions correct?

P.S. Please bear with me, I'm not native English speaker. Though, I'm giving my best to chain up all the crazy words/terms (like stature) while not losing the idea what I'm trying to express.

Hope I've made myself clear this time...

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It's not at all clear (to me, at least) what you're asking here... could you explain it in a different way? –  David Z Nov 18 '11 at 5:48
    
And leave out mentioning of some "attractor" (gravitational or other) that is totally misplaced! What about the rotations in the headline? Forgotten some lines later? –  Georg Nov 18 '11 at 9:38
    
@DavidZaslavsky, the question has been edited. –  joltmode Nov 18 '11 at 13:29
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What do you mean when you say "we only get the location, no rotations or anything"? –  mcandril Nov 18 '11 at 16:27
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It sounds like you're asking about both a position and an orientation. –  David Z Nov 19 '11 at 1:24

1 Answer 1

Regardless of the coordinate system, 3 coordinates describe either a point or a plane (in 3D), 4 coordinates a line (in 3D) and 5 coordinates a screw. To get a rigid body orientation you need either an additional 3 angles (euler angles), or 4 coordinates (quarternion), or 9 coordinates (rotation matrix). The last two also need constraints between the coordinates to make them work.

It gets interesting when you look at rigid bodies using 6 dimensional twists and wrenches, which are 5 dimensional screws plus a magnitude. (ref: http://en.wikipedia.org/wiki/Screw_theory).

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