Designing Vector Fields on Smoothed Particle Hydrodynamics Using Divergence-Constrained Moving Least Squares

This study proposes a novel method for effectively visualizing various vector field patterns based on Smoothed Particle Hydrodynamics (SPH) particle data. The proposed approach utilizes the Moving Least Squares (MLS) technique, a polynomial interpolation method widely used in physics-based simulations. However, conventional MLS assumes a structured grid and relies on vector-based constraints for higher-order interpolation, making it difficult to apply directly to unstructured particle data such as SPH. To address this limitation, we incorporate SPH kernel-based anisotropic weighting to estimate particle density and integrate it into the MLS framework, taking into account the irregular spatial distribution of particles. The resulting algorithm is designed to accurately represent a wide range of vector field structures within particle-based datasets. Experimental results demonstrate that our method effectively captures fine vector field details that are challenging to express using traditional grid-based MLS or divergence-constrained MLS techniques.