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Spatial and spatio-temporal distributions of both physical and socioeconomic phenomena can be approximated by functions depending on location in a multi-dimensional space, as multivariate scalar, vector, or tensor fields. Typical examples are elevations, climatic phenomena, soil properties, population densities, fluxes of matter, etc. While most of these phenomena are characterised by measured or digitised point data, often irregularly distributed in space and time, visualisation, analysis, and modelling within a GIS are usually based on a raster representation. Moreover, the phenomena can be measured using various methods (remote sensing, site sampling, etc.) leading to heterogeneous datasets with different digital representations and resolutions which need to be combined to create a single spatial model of the phenomenon under study. Many interpolation and approximation methods were developed to predict values of spatial phenomena in unsampled locations (for reviews see Burrough 1986; Franke 1982a; Franke and Nielson 1991; Lam 1983; McCullagh 1988; Watson 1992; and for a discussion of Kriging and error, see Heuvelink, Chapter 14). In GIS applications, these methods have been designed to support transformations between different discrete and continuous representations of spatial and spatiotemporal fields, typically to transform irregular point or line data to raster representation, or to resample between different raster resolutions.