  On a convex body in a Euclidean space, we introduce a new variational
formulation for its Funk metric, a Finsler metric compatible with the
tautological Finsler structure of the convex body. We generalize the metric on
Teichmuller spaces with the Weil-Petersson distance function. A set of
similarities the resulting metric structure shares with Thurston's asymmetric
metric is noted.
