Tensor-guided interpolation on non-planar surfaces

In blended-neighbor interpolation of scattered data, a tensor field represents a model of spatial correlation that is both anisotropic and spatially varying. In effect, this tensor field defines a non-Euclidean metric, a measure of distance that varies with direction and location. The tensors may be derived from secondary data, such as images. Alternatively, when the primary data to be interpolated are measured on a nonplanar surface, the tensors may be derived from surface geometry, and the nonEuclidean measure of distance is simply geodesic. Interpolation of geophysical data acquired on a non-planar surface should be consistent with tensor fields derived from both surface geometry and any secondary data.