  Two curves are affinely equivalent if there exists an affine mapping
transforming one of them onto the other. Thus, detecting affine equivalence
comprises, as important particular cases, similarity, congruence and symmetry
detection. In this paper we generalize previous results by the authors to
provide an algorithm for computing the affine equivalences between two
parametric curves of certain types, in any dimension. In more detail, the
algorithm is valid for rational curves, and for parametric curves with
non-rational but meromorphic components admitting a rational inverse. Unlike
other algorithms already known for rational curves, the algorithm completely
avoids polynomial system solving, and uses bivariate factoring, instead, as a
fundamental tool. The algorithm has been implemented in the computer algebra
system {\tt Maple}, and can be freely downloaded and used.
