Given a special Lagrangian fibration $f:M \rightarrow B$ of a Calabi-Yau manifold $M$, one can associate to it two affine structures (symplectic and complex) on the base space $B$. A theorem of Hitchin says that there locally exists a convex function $K$ such that the coordinate system in one affine structure is mapped to the coordinate system in the other affine structure via the Legendre transform associated to $K$. Is it possible to see this theorem explicitly for elliptic curves and K3 surfaces? What is K for elliptic curves?