The correct choice of function and derivative reconstruction filters is paramount to obtaining highly accurate renderings. Most filter choices are limited to a set of commonly used functions, and the visualization practitioner has so far no way to state his preferences in a convenient fashion. Much work has been done towards the design and specification of filters using frequency based methods. However, for visualization algorithms it is more natural to specify a filter in terms of the smoothness of the resulting reconstructed function and the spatial reconstruction error. Hence, in this paper, we present a methodology for designing filters based on spatial smoothness and accuracy criteria. We first state our design criteria and then provide an example of a filter design exercise. We also use the filters so designed for volume rendering of sampled data sets and a synthetic test function. We demonstrate that our results compare favorably with existing methods.

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