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Generate geographic coordinates given a vertex in a sphere

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I need a way to get the geographic coordinates (longitude and latitude) of a selected vertex in a sphere. Does anybody know of any material on this subject? Thanks.

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Geographic coordinates are virtually the same as spherical polar coordinates. The differences are superficial:
1. It is often assumed that the normalised altitude (cf. radius) is 1.
2. Angles are taken to run from 0° to 360° and -90° to 90°, using imperial degrees-minutes-seconds rather than 0 to 2p in a decimal expansion.

Assuming the sphere is centred at the origin (if it isn't, translate), has radius r, and has poles at (0, r, 0) and (0, -r, 0):

φ = arccos(y/r)
θ = arctan(z/x)

(If you're working in C or C++, you should want to use atan2(y, x) rather than atan(y/x)).

This will get you to spherical polar coordinates. To convert this to geographics:

lat = φ * (180 / Pi) - 90
lon = θ * (180 / Pi)

The conversion into minutes has as much to do with string-processing as mathematics, so I take it you're not interested.


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