Wave Curves: Simulating Lagrangian water waves on dynamically deforming surfaces

representative image




ACM Transactions on Graphics (SIGGRAPH 2020)


We propose a method to enhance the visual detail of a water surface simulation. Our method works as a post-processing step which takes a simulation as input and increases its apparent resolution by simulating many detailed Lagrangian water waves on top of it. We extend linear water wave theory to work in non-planar domains which deform over time, and we discretize the theory using Lagrangian wave packets attached to spline curves. The method is numerically stable and trivially parallelizable, and it produces high frequency ripples with dispersive wave-like behaviors customized to the underlying fluid simulation.

Supplementary video


Please note that one of the test scenes in the original publication used an incorrect parameter setting. We correct this error and clarify some mathematical notation in the “errata” document below.


We wish to thank the anonymous reviewers and the members of the Visual Computing Group at IST Austria for their valuable feedback. This research was supported by the Scientific Service Units (SSU) of IST Austria through resources provided by Scientific Computing. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme under grant agreements No 638176 and Marie Sklodowska-Curie Grant Agreement No. 665385W.