Sparse Ferguson-Hermite Signed Distance Fields

Abstract

We investigate Hermite interpolation in the context of discrete signed distance field filtering. Our method uses tricubic Hermite interpolation to generate a C1 continuous approximation to the signed distance function of the input scene. Our representation is kept purely first order by setting the mixed partial derivatives to zero, similarly to how Ferguson constructed bicubic Hermite patches. Our scheme stores four scalars at each sample, the value of the signed distance function and its first three partial derivatives. We optimize storage by only storing voxels that enclose a volume boundary. We show that this provides both a significant reduction in storage and render times compared to a dense grid of Ferguson-Hermite samples. Moreover, our construct requires smaller storage than traditional zero order trilinearly filtered fields of the same visual quality, at the expense of performance.