I will first briefly mention some of my research related to biomedical image analysis, somewhat hinting at my general interest in Grassmannians (the manifold of lower dimensional subspaces in Euclidean space). The actual talk is about the problem of selecting good collections of lower dimensional subspaces, where “good" is supposed to mean “better distributed than random points". Indeed, we verify that cubature points on Grassmannians cover better than random points. We also numerically construct such deterministic cubature points. To further support our theoretical findings, we present numerical experiments on the approximation of Sobolev functions on Grassmannians from finitely many sampling points. The numerical results are in accordance with the theoretical findings.