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This paper presents a particle-based model for preserving fluid sheets of animated liquids with an adaptively sampled Fluid-Implicit-Particle (FLIP) method. In our method, we preserve fluid sheets by filling the breaking sheets with particle splitting in the thin regions, and by collapsing them in the deep water. To identify the critically thin parts, we compute the anisotropy of the particle neighborhoods, and use this information as a resampling criterion to reconstruct thin liquid surfaces. Unlike previous approaches, our method does not suffer from diffusive surfaces or complex remeshing operations, and robustly handles topology changes with the use of a meshless representation. We extend the underlying FLIP model with an anisotropic position correction to improve the particle spacing, and adaptive sampling to efficiently perform simulations of larger volumes. Due to the Lagrangian nature of our method, it can be easily implemented and efficiently parallelized. The results show that our method can produce visually complex liquid animations with thin structures and vivid motions.