Enhancing Digital Twin Fidelity Through Low-Discrepancy Sequence and Hilbert Curve-Driven Point Cloud Down-Sampling

This paper addresses the critical challenge of point cloud down-sampling for digital twin creation, where reducing data volume while preserving geometric fidelity remains an ongoing research problem. We propose a novel down-sampling approach that combines Low-Discrepancy Sequences (LDS) with Hilbert curve ordering to create a method that preserves both global distribution characteristics and local geometric features. Unlike traditional methods that impose uniform density or rely on computationally intensive feature detection, our LDS-Hilbert approach leverages the complementary mathematical properties of Low-Discrepancy Sequences and space-filling curves to achieve balanced sampling that respects the original density distribution while ensuring comprehensive coverage. Through four comprehensive experiments covering parametric surface fitting, mesh reconstruction from basic closed geometries, complex CAD models, and real-world laser scans, we demonstrate that LDS-Hilbert consistently outperforms established methods, including Simple Random Sampling (SRS), Farthest Point Sampling (FPS), and Voxel Grid Filtering (Voxel). Results show parameter recovery improvements often exceeding 50% for parametric models compared to the FPS and Voxel methods, nearly 50% better shape preservation as measured by the Point-to-Mesh Distance (than FPS) and up to 160% as measured by the Viewpoint Feature Histogram Distance (than SRS) on complex real-world scans. The method achieves these improvements without requiring feature-specific calculations, extensive pre-processing, or task-specific training data, making it a practical advance for enhancing digital twin fidelity across diverse application domains.