  We study metric properties of maximal framed representations of fundamental
groups of surfaces in symplectic groups over real closed fields, interpreted as
actions on Bruhat-Tits buildings endowed with adapted Finsler norms. We prove
that the translation length can be computed as intersection with a geodesic
current, give sufficient conditions guaranteeing that such a current is a
multicurve, and, if the current is a measured lamination, construct an
isometric embedding of the associated tree in the building. These results are
obtained as application of more general results of independent interest on
positive crossratios and actions with compatible barycenters.
