Low rank interpolation of boundary spline curves

The coefficients of a tensor-product spline surface in R-d with m x 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. (C) 2017 Elsevier B.V. All rights reserved.