Low rank interpolation of boundary spline curves

The coefficients of a tensor-product spline surface in Rd with m×n control points form a tensor of order 3 and dimension (m,n,d). Motivated by applications in isogeometric analysis we analyze the rank of this tensor. In particular, we propose a new construction for low rank tensor-product spline surfaces from given boundary curves. While the results of this construction are generally not affinely invariant, we propose a simple standardization procedure that guarantees affine invariance for d=2. In addition we provide a detailed comparison with existing constructions of spline surfaces from boundary data.