High Quality Content by WIKIPEDIA articles! In the theory of three-dimensional rotation, the Rodrigues rotation formula (named after Olinde Rodrigues) a formula for rotating a vector in space, given an axis and angle of rotation. If v is a vector in R3 and z is a unit vector describing an axis of rotation about which we want to rotate v by an angle ? (in a right-handed sense), the Rodrigues formula is: mathbf{v}_mathrm{rot} = mathbf{v} costheta + (mathbf{z} times mathbf{v})sintheta + mathbf{z} (mathbf{z} cdot mathbf{v}) (1 - costheta). By extension, this can be used to transform all three basis vectors to compute a rotation matrix from an axis-angle representation. In other words, the Rodrigues formula is an algorithm to compute the exponential map from so(3) to SO(3).

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