# Point Rotation Result

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I need a way to take a point and find out where it would be after a rotation about an axis. Anybody know any resources? Thanks, Michael

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An equation to rotate a vector v about a unit-length axis n by an angle t is:
v' = cos(t)(v-(v.n)n)+sin(t)(nXv)+(v.n)n
The derivation involves separating v into components perpendicular and parallel to n, rotating the perpendicular portion, and then re-composing.

The equation is more commonly expressed in matrix form. Googling for 'axis angle matrix' will mostly likely turn up the algorithm for constructing this matrix (just be aware of row vs. column vector issues).

The equivalent quaternion equation is:
v' = q*v*q~
Where v and v' are quaternions whose real part is arbitrary (usually 0) and whose imaginary part corresponds to the vector in question. Note that the above is for quaternions using 'standard' multiplication order; if you were using, say, the DirectX quaternion class, the order of multiplication would be reversed.

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