Efficient and Accurate Spatial Queries Using Lossy Compressed 3D Geometry Data

3D spatial data management is increasingly vital across various application scenarios, such as GIS, digital twins, human atlases, and tissue imaging. However, the inherent complexity of 3D spatial data, primarily represented by 3D geometries in real-world applications, hinders the efficient evaluation of spatial relationships through resource-intensive geometric computations. Geometric simplification algorithms have been developed to reduce the complexity of 3D representations, albeit at the cost of querying accuracy. Previous work has aimed to address precision loss by leveraging the spatial relationship between the simplified and original 3D object representations. However, this approach relied on specialized geometric simplification algorithms tailored to regions with specific criteria. In this paper, we introduce a novel approach to achieve highly efficient and accurate 3D spatial queries, incorporating geometric computation and simplification. We present a generalized progressive refinement methodology applicable to general geometric simplification algorithms, involving accurate querying of 3D geometry data using low-resolution representations and simplification extents quantified using Hausdorff distances at the facet level. Additionally, we propose techniques for calculating and storing Hausdorff distances efficiently. Extensive experimental evaluations validate the effectiveness of the proposed method which outperforms state-of-the-art systems by a factor of 4 while minimizing computational and storage overhead.