Physics simulation is paramount for modeling and utilizing 3D scenes in various real-world applications. However, integrating with state-of-the-art 3D scene rendering techniques such as Gaussian Splatting (GS) remains challenging. Existing models use additional meshing mechanisms, including triangle or tetrahedron meshing, marching cubes, or cage meshes. Alternatively, we can modify the physics-grounded Newtonian dynamics to align with 3D Gaussian components. Current models take the first-order approximation of a deformation map, which locally approximates the dynamics by linear transformations. In contrast, our GS for Physics-Based Simulations (GASP) pipeline uses parametrized flat Gaussian distributions. Consequently, the problem of modeling Gaussian components using the physics engine is reduced to working with 3D points. In our work, we present additional rules for manipulating Gaussians, demonstrating how to adapt the pipeline to incorporate meshes, control Gaussian sizes during simulations, and enhance simulation efficiency. This is achieved through the Gaussian grouping strategy, which implements hierarchical structuring and enables simulations to be performed exclusively on selected Gaussians. The resulting solution can be integrated into any physics engine that can be treated as a black box. As demonstrated in our studies, the proposed pipeline exhibits superior performance on a diverse range of benchmark datasets designed for 3D object rendering. The project webpage, which includes additional visualizations, can be found at https://waczjoan.github.io/GASP.

翻译：物理仿真在各类现实应用中对三维场景的建模与利用至关重要。然而，将其与前沿的三维场景渲染技术（如高斯泼溅（GS））相结合仍具挑战性。现有模型采用额外的网格化机制，包括三角形或四面体网格划分、行进立方体或笼状网格。作为替代方案，我们可以修改基于物理的牛顿动力学以匹配三维高斯分量。现有模型采用变形映射的一阶近似，通过线性变换局部逼近动力学。相比之下，我们提出的基于物理仿真的高斯泼溅（GASP）流程采用参数化的扁平高斯分布。因此，利用物理引擎建模高斯分量的问题被简化为处理三维点集。在本研究中，我们提出了操作高斯的附加规则，展示了如何调整流程以整合网格、在仿真过程中控制高斯尺寸并提升仿真效率。这通过高斯分组策略实现，该策略实施分层结构，使得仿真仅需在选定的高斯上进行。所得解决方案可集成至任何可视为黑箱的物理引擎中。如我们的研究所展示，该流程在专为三维物体渲染设计的多种基准数据集上表现出优越性能。包含额外可视化内容的项目网页位于 https://waczjoan.github.io/GASP。