Quality-Constrained Predictive Anisotropic Grid Warping for FLIP Liquids

Abstract We propose a \textit{quality-constrained predictive anisotropic grid warping} method for FLIP-based liquid simulation. Dynamic grid warping can concentrate resolution near important flow regions, but strong deformation may introduce local compression, shear, and poor cell aspect ratios. Our objective is to preserve substantial adaptive grid motion while explicitly controlling local cell quality. The method predicts near-future particle motion and estimates local velocity gradients to construct a directional anisotropic metric. A determinant-normalized metric redistributes resolution according to predicted deformation without uniformly shrinking the grid. During warping, Jacobian-based regularization and acceptance constraints on the determinant and condition number limit local volume and shape distortion while permitting coherent large-scale grid motion. A metric-change-guided tracking strategy reduces repeated optimization when the target metric varies slowly. We compare the method with Uniform FLIP, conventional scalar dynamic warping, and reactive anisotropic warping without future prediction. Across free-surface deformation, impact, thin-sheet, rotational, and repeated-wall-interaction scenes, the proposed method reduces local grid distortion and post-projection divergence while maintaining comparable or greater warp displacement than conventional warping. The results indicate that predictive directional adaptation can be combined with explicit local quality control in a structured warped-grid FLIP solver.