Tensor-product spline interpolation to data on or near a family of lines

Algorithms exist for least-squares tensor-product splineapproximation to data (a) on a rectangular mesh, (b) on a family of parallel lines and (c) that is generally scattered. In contrast,direct algorithms for tensor-product splineinterpolation are available only for data type (a). The structure of the data in cases (a) and (b) is such that the corresponding algorithms are particularly efficient.