Optimal polynomial meshes and Caratheodory-Tchakaloff submeshes on the   sphere
  Using the notion of Dubiner distance, we give an elementary proof of the fact that good covering point configurations on the 2-sphere are optimal polynomial meshes. From these we extract Caratheodory-Tchakaloff (CATCH) submeshes for compressed Least Squares fitting. 
Paul Leopardi, Alvise Sommariva, Marco Vianello
math.NA