Greed for the Spheres: A Signed Distance Interpolation Method

2026-05-03

AI Summary

This work addresses the geometric inconsistency that arises when interpolating signed distance functions (SDFs) from discrete samples. To resolve this issue, the authors propose a hard geometric constraint framework grounded in the theoretical properties of SDFs, which for the first time rigorously guarantees that interpolated results are both compatible with the original data and correspond to realizable geometric surfaces. The method integrates an efficient greedy interpolation algorithm with GPU-accelerated preprocessing, enabling high-quality, geometrically consistent outputs across three representative tasks: global SDF refinement, mesh reconstruction, and pseudo-SDF correction. This approach overcomes a key limitation of existing techniques, which lack formal guarantees of geometric consistency.

Abstract

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.

Problem

• Signed Distance Function
• SDF interpolation
• geometric consistency
• surface reconstruction
• pseudo-SDF repair

Innovation

• Signed Distance Function
• Geometric Consistency
• Greedy Interpolation
• GPU Acceleration
• Surface Reconstruction