Problems of the week (optional)

Show that the tensor product B-splines are linearly independent and form a partition of unity (non-negative and sum to one) whenever the knot-vectors are p+1-regular. 

Show the precise smoothness properties of Tensor-product B-splines.

Extra challenge: Construct a periodic cubic spline space over a uniform knot-vector, by making the domain and/or the B-splines periodic (not by enforcing boundary-conditions). Demonstrate your construction by approximating a circle with C?2 continuity