  Motivated by the analogies between the projective and the almost quaternionic
geometries, we study the generalized planar curves and mappings. We follow,
recover, and extend the classical approach as developed by Mikes and Sinyukov.
Then we exploit the impact of the general results in the almost quaternionic
geometry. In particular we show, that the natural class of H--planar curves
coincides with the class of all geodesics of the so called Weyl connections and
preserving this class turns out to be the necessary and sufficient condition on
diffeomorphisms to become morphisms of almost quaternionic geometries.
