WEFOUNDA Manual if Spherical and Practical Astronomy Embracing the General Problems of Spherical Astronomy, the Special Applications to Nautical Astronomy, and the Theory and Use of Fixed and Portable Astronomical Instruments. Volume I i Spherical Astronomy

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The spherical distributions generate random vectors, located on a spherical surface. They can be used as random directions, for example in the steps of a random walk.

This function returns a random direction vector v = ( x , y , z ) in three dimensions. The vector is normalized such that |v|^2 = x^2 + y^2 + z^2 = 1 . The method employed is due to Robert E. Knop (CACM 13, 326 (1970)), and explained in Knuth, v2, 3rd ed, p136. It uses the surprising fact that the distribution projected along any axis is actually uniform (this is only true for 3 dimensions).