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Description

It has been observed recently that tensor-product spline surfaces with low rank coefficients provide advantages for efficient numerical integration, which is important in the context of matrix assembly in isogeometric analysis. By exploiting the low-rank structure one may efficiently perform multivariate integration by a executing a sequence of univariate quadrature operations. This fact has motivated us to study the problem of creating such surfaces from given boundary curves. On the one hand, we reconsider the classical constructions, which include Coons surfaces. We analyze the rank of the resulting parameterizations. On the other hand, we propose a new coordinate-wise rank-2 interpolation algorithm and discuss its extension to the case of parametric boundary curves. Here we discuss the properties of the new construction, which include a permanence principle and the reproduction of bilinear surfaces. Special attention is paid to the property of affine invariance. This is joint work with Dominik Mokri\(\v{s}\).