  The projection onto the intersection of sets generally does not allow for a
closed form even when the individual projection operators have explicit
descriptions. In this work, we systematically analyze the projection onto the
intersection of a cone with either a ball or a sphere. Several cases are
provided where the projector is available in closed form. Various examples
based on finitely generated cones, the Lorentz cone, and the the cone of
positive semidefinite matrices are presented. The usefulness of our formulae is
illustrated by numerical experiments for determining copositivity of real
symmetric matrices.
