You can determine the 3D position for a star, , by using the distance from Earth, , as well as the right ascension, , and declination, , within the following formula.
Note this will yield positions within the Earth-centered inertial reference frame.
You can determine the 3D position for a star, p, by using the distance from Earth, R, as well as the right ascension, Omega, and declination, delta, within the following formula.
p=RbeginbmatrixcosOmegacosdelta sinOmegacosdelta sindelta endbmatrix
Note this will yield positions within the Earth-centered inertial reference frame.
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