  Let {(Z_i,W_i):i=1,...,n} be uniformly distributed in [0,1]^d * G(k,d), where
G(k,d) denotes the space of k-dimensional linear subspaces of R^d. For a
differentiable function f from [0,1]^k to [0,1]^d we say that f interpolates
(z,w) in [0,1]^d * G(k,d) if there exists x in [0,1]^k such that f(x) = z and
vec{f}(x) = w, where vec{f}(x) denotes the tangent space at x defined by f. For
a smoothness class F of H\"older type, we obtain probability bounds on the
maximum number of points a function f in F interpolates.
