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Reconstruction of gradients from sampled data is a crucial task in volume visualization. Gradients are used, for instance, as normals for surface shading or for classification in standard ray casting techniques. Using the ideal derivative reconstruction filter, which can be derived from the ideal function reconstruction filter, is impracticable because of its infinite extend. Simply truncating the filter leads to problems due to discontinuities at the edges. To overcome these problems several windows have been defined, which are discussed in this paper with respect to gradient estimation.

Keywords: volume visualization, reconstruction, gradient, filter, frequency response

There is a lot of perhaps unnecessary lore about choice of a window function, and practically every function that rises from zero to a peak and then falls again has been named after someone.

in Numerical Recipes in C [17]