Stylizing 2D & 3D liquid animations through adaptive particle-based implicit fields

Combining physically-based simulation with stylized visual effects not only requires changing the appearance of surfaces, but their shapes as well. We describe a new expressive rendering method for liquid animations, which can be used on top of any preexisting particle-based simulation. Our solution builds on visual particles that carry both water and air distributions, both evolving through particle history based on kinematic information from the simulation. These density fields are combined at each frame to create the implicit iso-surface of interest, rendered in an adapted style. By defining a series of visual particle states, we parametrize this model to capture the typical stylized geometry of water bodies used to highlight dynamic motion in paintings and cartoons, such as elongating droplets, concavities carved at the crest of breaking waves, and stylized air–water mixtures such as bubbles and foam, which we further enhance in 3D scenes using a dedicated stylized surface-color pattern. Regardless of the 2D or 3D nature of the input simulation, our solution maintains temporal coherence and ensures that water bodies keep an approximately constant surface in 2D, resp. volume in 3D, over time. Finally, we conducted a user study to show the effectiveness of our method against state-of-the-art AI-based tools and a hands-on evaluation with a professional artist, in a variety of animation scenarios where stylized shapes are needed. This is an extension of our previous work presented at STAG 2025. It introduces new material, including a refined blending operator, a stylized surface-color pattern, performance metrics, and artist evaluations.