Optimal representation of time-dependent spherical geometries

Applications in fields such as fluid mechanics, video games and image processing frequently involve the simulation of 3D objects with spherical topology, with a surface quantity that varies with the geometry and/or according to some surface partial differential equation. However, when the geometry undergoes continuous deformations, significant distortions in the surface point distribution may arise. This can lead to aliasing effects and numerical instability, reducing the overall accuracy of the simulation. To address this issue, we introduce a novel tool to improve the efficiency of a spectral reparametrization procedure able to ensure the optimal representation of such 3D objects and surface quantities, even when dealing with long time simulations. This new strategy makes the reparametrization technique fully adaptive, selecting only the frequencies that are needed to represent a given surface, improving the efficiency of the algorithm, preventing degradation in the quality of the simulation and enhancing the overall stability.