Shape-preserving, multiscale interpolation by bi- and multivariate cubic L1 splines Original Research Article

We introduce a class of bi- and multivariate cubic L1 interpolating splines, the coefficients of which are calculated by minimizing the sum of the L1 norms of second derivatives. The focus is mainly on bivariate cubic L1 splines for C1 interpolation of data located at the nodes of a tensor-product grid. These L1 splines preserve the shape of data even when the data have abrupt changes in magnitude or spacing. Extensions to interpolation of regularly spaced and scattered bi- and multivariate data by cubic and higher-degree surfaces/hypersurfaces on regular and irregular rectangular/quadrilateral/hexahedral and triangular/tetrahedral grids are outlined.