Design of accurate and smooth filters for function and derivative reconstruction

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, the authors present a methodology for designing filters based on spatial smoothness and accuracy criteria. They first state their design criteria and then provide an example of a filter design exercise. They also use the filters so designed for volume rendering of sampled data sets and a synthetic test function. They demonstrate that their results compare favorably with existing methods.