I was recently asked to print out a fabric pattern that could be used to cover a sphere, about the size of a ping pong ball, for the purposes of re-creating a favorite cat toy (quite important). Thinking this over, I realized that this was basically a map projection problem-- and could probably be solved by scaling an interrupted sinusoidal projection to match the geometry of a ping pong ball. Below are some R functions, and examples of how this endeavor evolved. Thanks to Greg Snow for this helpful post on the R-mailing list, describing how to preserve linear measurement when composing a figure in R. So far the pattern doesn't quite fit.
It looks like it was not the printer's fault-- I had used the wrong radius for a ping pong ball: 16mm instead of 19mm or 20mm (there are 38mm and 40mm diameter ping pong balls). Updated files are attached.