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Several interpolation algorithms have been developed to create homogeneous gridfields from heterogeneously distributed data. A shortcoming in most of these algorithms is the assumption that data field concentrations are fairly homogeneous over the grid field area. The method for constructing the weight functions as discussed here overcomes this problem by including a variable dependent on the concentration of data points in the weight function. A rainfall data field for South Africa is compiled by this algorithm. The concentration of climate stations in South Africa varies significantly.