Design of accurate and smooth filters for function and derivative reconstruction
Torsten Bert Möller, Klaus D. Mueller, Yair Kurzion, Raghu Machiraju, Roni Yagel · 2002
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.