Drawing with water waves

The deterministic reproduction of complex 3D wave fields remains a significant challenge in ocean engineering. This study proposes a novel methodology for drawing arbitrary 2D curves and 3D volumetric shapes on a water surface using transient multi-directional focused waves. To overcome the limitations of conventional discrete-point focusing methods, our framework integrates B\'ezier curve parametrisation, equal arc-length sampling, and an Iterative Amplitude Correction (IAC) algorithm. This effectively mitigates wave height overshoot and enables precise spatial superposition of spectral components. The method's effectiveness was validated through linear wave theory and Smoothed Particle Hydrodynamics (SPH) simulations, successfully reproducing 2D characters and a 3D human face. Physical experiments in the FloWave circular wave basin further demonstrated target shape generation, such as a 2D star and 3D pyramid. Although further integration of nonlinear wave theories is necessary for high-amplitude accuracy, this technique establishes a deterministic methodology for creating arbitrary 2D and 3D surface geometries. It represents a significant advantage in wave field control for ocean engineering applications.