Could the Chinese have Produced Charts for Columbus and Magellan?

In a work of popular history published in 2009, Gavin Menzies claims that maps and other knowledge passed to Europe in 1434 inspired the exploration of a route to Asia by travelling westward across the Atlantic, and that, together with the wealth brought from the New World, this knowledge sparked the Renaissance in Europe. Stripped of any claims that are entirely unnecessary to believe that the Chinese had an important role in kickstarting the Renaissance, the plausibility rests in the claim that the Chinese had the knowledge, and instruments of sufficient accuracy, to produce maps that could have been useful to explorers such as Columbus and Magellan. This paper explores that question, and concludes that the Chinese probably did have the ability to produce maps that indicated longitude by the end of the thirteenth century, but had probably lost it by the sixteenth century. It is therefore impossible to be certain whether they could have produced useful navigational aids in the early fifteenth century.