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.

翻译：我们提出了一种从离散样本集合插值有符号距离函数（SDF）数据的方法。与先前工作不同，我们的方法确保新生成的SDF数据值与输入数据及彼此之间完全一致，从而使得扩充后的数据仍对应一个几何上可实现的表面。我们将SDF的理论性质表达为硬性几何约束，并构建了一种高效的贪心算法用于一致SDF插值，该算法通过强大的并行化GPU预处理进一步加速。我们通过三个实际应用评估了该方法的有用性：全局SDF细化——在无真实值知识的情况下对SDF数据进行上采样；网格重建——利用粗粒度输入SDF的全局信息重建高细节表面；以及伪SDF修复——这类数据源自CSG布尔运算等众多流程，需转化为有效SDF以进行下游处理。我们细化的SDF保证与输入一致，而先前方法无法提供此类保证。