From exact correspondence data to conformal transformations in closed form using Vahlen matrices

We derive a method to determine a conformal transformation in nD in closed form given exact correspondences between data. We show that a minimal dataset needed for correspondence is a localized vector frame and an additional point.
In order to determine the conformal transformation we use the representation of the conformal model of geometric algebra by Vahlen matrices, which helps reduce the problem to purely Euclidean geometric algebra computations, as well as structure the solution into geometrically interpretable components.
We give a closed form solution for the general case of conformal (resp. anti-conformal) transformations, which preserve (resp. reverse) angles locally, as well as for the important special case when it is known that the conformal transformation is a rigid body motion, which preserves angles globally. Rigid body motions are also known as Euclidean transformations.