  We give a description (direct formulas) of all complex geodesics in a convex
tube domain in $\CC^n$ containing no complex affine lines, expressed in terms
of geometric properties of the domain. We next apply that result to give
formulas (a necessary condition) for extremal mappings with respect to the
Lempert function and the Kobayashi-Royden metric in a big class of bounded,
pseudoconvex, complete Reinhardt domains: for all of them in $\CC^2$ and for
those of them in $\CC^n$ which logarithmic image is strictly convex in
geometric sense.
