A K-affine real-valued function on the reals is a solution of y˘˘+ Ky = 0. A K-affine function on a metric space is a real-valued function which is K-affine along every geodesic with respect to arc length. A K-convex function is one which is supported tangentially below by a K-affine function at each point. The negative of a K-convex function is K-concave. These functions occur naturally on spaces with curvature bounded by K. On classical n-dimensional space of constant curvature K there is an n+1-dimensional linear space of K-affine functions, a fact which characterizes those spaces. Standard kinds of coordinates (polar, cylindrical, spherical) arise from special warped product constructions, in which a metric on a product space is given by scaling the metric on one factor by a K-affine function on the other. (This is joint work with Stephanie Alexander.)