  We show that Y. Cheung's general $Z$-continued fractions can be adapted to
give approximation by saddle connection vectors for any compact translation
surface. That is, we show the finiteness of his Minkowski constant for any
compact translation surface. Furthermore, we show that for a Veech surface in
standard form, each component of any saddle connection vector dominates its
conjugates. The saddle connection continued fractions then allow one to
recognize certain transcendental directions by their developments.
