  We consider the popular and classical method of alternating projections for
finding a point in the intersection of two closed sets. By situating the
algorithm in a metric space, equipped only with well-behaved geodesics and
angles (in the sense of Alexandrov), we are able to highlight the two key
geometric ingredients in a standard intuitive analysis of local linear
convergence. The first is a transversality-like condition on the intersection;
the second is a convexity-like condition on one set: "uniform approximation by
geodesics."
