Determining a versor in n-D geometric algebra from the known transformation of n vectors

Suppose we only know of some elements in a geometric algebra how a versor has transformed them, can we then reconstruct the unknown versor V?
We present an O(2(n)) method that works in n-D geometric algebra for n exact vector correspondences. This makes it usable for determining, for instance, a Euclidean rigid body motion in n-D from a frame correspondence providing the required n+2 conformal vectors as: the frame location, the n axis directions, and the invariance of the point at infinity. The method can only determine a full conformal transformation if the weights of the transformed entities are also observed.