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Provided a point three-dimensions, what is the simplest way to rotate this point about the origin so that it falls along the X-, Y-, or Z-axis?

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Define 'simplest'. Do you mean with just one rotation? Will any axis do, or do you want to be able to target X, Y or Z specifically? –  occulus Dec 19 '11 at 1:02
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first rotate along any of the axises until it falls into one of the XY, YZ or XZ planes then rotate along the other axis (perpendicular to the plane it is on) until it's on the axis you want

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