We propose an analytic construction of the geometry required for free-surface fluid simulations and deformation mechanics based on partial optimal transport such as the Gallouët-Mérigot's scheme or the Power Particles method. Such methods previously relied on a discretization of the cells by leveraging a classical convex cell clipping algorithm. However, this results in a heavy computational cost and a coarse approximation of the evaluated quantities. In contrast, our algorithm efficiently computes the generalized Laguerres cells, that is, intersections between Laguerre cells and spheres. This makes it possible to more precisely compute the volume and the area of the facets as well as strongly reducing the number of operations required to obtain the geometry. Additionally, we provide a dedicated rendering framework solely based on the computed volumetric structure.

翻译：我们提出了一种基于部分最优输运（如Gallouët-Mérigot方案或Power Particles方法）的自由表面流体模拟与变形力学所需几何结构的解析构造方法。此类方法先前依赖于利用经典凸单元裁剪算法对单元进行离散化。然而，这导致了高昂的计算成本和被评估物理量的粗略近似。相比之下，我们的算法能高效计算广义Laguerre单元，即Laguerre单元与球体的交集。这使得能够更精确地计算体积和面片面积，并大幅减少获取几何结构所需的操作次数。此外，我们提供了一个完全基于所计算体积结构的专用渲染框架。