Greed for the Spheres: A Signed Distance Interpolation Method
For computer graphics and geometry processing tasks requiring consistent SDF interpolation, this method provides a guaranteed-consistent alternative to existing techniques that lack such guarantees.
The paper introduces a greedy algorithm for interpolating Signed Distance Function (SDF) data that guarantees consistency with input samples, enabling applications like global SDF refinement, mesh reconstruction, and pseudo-SDF repair. The method outperforms prior work by ensuring the interpolated SDF corresponds to a realizable surface.
We propose a method to interpolate Signed Distance Function (SDF) data from a discrete set of samples. Unlike prior work, our approach ensures that the new SDF data values are fully consistent with the input and each other, such that the augmented data still corresponds to a geometrically realizable surface. We express the theoretical properties of SDFs as hard geometric constraints, and construct an efficient greedy algorithm for consistent SDF interpolation that is made even faster with powerful parallelized GPU preprocessing. We exemplify the usefulness of our method by evaluating it on three practical applications: global SDF refinement, in which the SDF data is upsampled without knowledge of the ground truth; mesh reconstruction, where our method can reconstruct highly detailed surfaces using global information from coarse input SDFs; and repair of pseudo-SDFs, which result from many pipelines such as CSG Boolean operations and must be turned into valid SDFs for downstream processing tasks. Our refined SDFs are guaranteed to be consistent with the input, where previous methods have no such guarantee.