Generating various flow fields using principal component analysis

The visual simulation of fluids has become an important element in many applications, such as movies and computer games. In these applications, large-scale fluid scenes, such as fire in a village, are often simulated by repeatedly rendering multiple fluid flows. In these cases, animators are requested to generate many variations of a fluid flow. Previously, we developed a method to help animators meet such requirements [Sato et al. 2013]. However, the method was limited to 2D fluid simulation. In the previous method [Sato et al. 2013], we use Laplacian eigenfunctions as the basis functions. However, Laplacian eigenfunctions are too expensive in computation and storage costs for 3D fluid simulation. Furthermore, Laplacian eignfunctions force us to use slip boundary conditions and this makes the method less practical. In order to address these problems, we introduce Principal Component Analysis (PCA) for the basis functions. In generating the principal components of the input velocity fields, we use a subspace approach [Treuille et al. 2006; Kim and Delaney 2013]. The variations are generated by modulating the coefficient of each principal component.