A method of smooth bivariate interpolation for data given on a generalized curvilinear grid

Abstract

A method of locally bicubic interpolation is presented for data given at the nodes of a two-dimensional generalized curvilinear grid. The physical domain is transformed to a computational domain in which the grid is uniform and rectangular by a generalized curvilinear coordinate transformation. The metrics of the transformation are obtained by finite differences in the computational domain. Metric derivatives are determined by repeated application of the chain rule for partial differentiation. Given the metrics and the metric derivatives, the partial derivatives required to determine a locally bicubic interpolant can be estimated at each data point using finite differences in the computational domain. A bilinear transformation is used to analytically transform the individual quadrilateral cells in the physical domain into unit squares, thus allowing the use of simple formulas for bicubic interpolation.