This paper presents a geometry-driven framework for temporally stable 2D isoline reconstruction from particle-based simulation data. Unlike conventional Marching Squares methods, which assume grid-aligned scalar fields and often suffer from boundary jitter and flickering when applied to unstructured particle distributions, the proposed method constructs a continuous scalar field using an SPH kernel and estimates stabilized normals from level-set gradients at cell-level representative positions. Instead of relying on explicit Quadratic Error Function (QEF) optimization, we introduce a virtual-plane projection strategy that determines isoline vertices using a local geometric constraint. This projection can be interpreted as a first-order geometric approximation of QEF minimization, enabling QEF-free vertex positioning while reducing sensitivity to noisy particle-derived normals. As a result, the proposed method improves robustness in sparse particle regions while preserving important geometric features. To further enhance computational efficiency, we integrate a boundary-aware greedy meshing scheme that merges redundant interior geometry while preserving isoline boundaries. Experimental results demonstrate that the proposed method improves boundary stability and area consistency, reduces temporal variation, and decreases triangle counts by up to 70–75% compared with Marching Squares (MS) and Extended Marching Cube (EMC)-based reconstruction. These results indicate that the proposed framework is suitable for efficient real-time visualization of dynamic particle-based simulations.
Kwon et al. (Tue,) studied this question.