  In arXiv:math/0311139, as evidence for his conjecture in birational log
geometry, Kawamata constructed a family of derived equivalences between toric
orbifolds. In arXiv:0911.4711, we showed that the derived category of a toric
orbifold is naturally identified with a category of polyhedrally-constructible
sheaves on R^n. In this paper we investigate and reprove some of Kawamata's
results from this perspective.
