Physics simulation is paramount for modeling and utilization of 3D scenes in various real-world applications. However, its integration 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. As an alternative, 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 Gaussian Splatting for Physics-Based Simulations (GASP) model uses such a map (without any modifications) and flat Gaussian distributions, which are parameterized by three points (mesh faces). Subsequently, each 3D point (mesh face node) is treated as a discrete entity within a 3D space. Consequently, the problem of modeling Gaussian components is reduced to working with 3D points. Additionally, the information on mesh faces can be used to incorporate further properties into the physics model, facilitating the use of triangles. Resulting solution can be integrated into any physics engine that can be treated as a black box. As demonstrated in our studies, the proposed model exhibits superior performance on a diverse range of benchmark datasets designed for 3D object rendering.
物理仿真在各种实际应用中对3D场景的建模和利用至关重要。然而，将其与最新的3D场景渲染技术（如高斯分裂，GS）结合仍然充满挑战。现有模型通常使用额外的网格化机制，包括三角形或四面体网格、Marching Cubes算法或笼型网格。作为替代方案，我们可以修改基于物理的牛顿力学，使其与3D高斯组件对齐。目前的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，我们的基于物理仿真的高斯分裂模型（GASP）使用这样的映射（无需任何修改）和由三点（网格面）参数化的平面高斯分布。随后，每个3D点（网格面节点）被视为3D空间中的一个离散实体。这样，建模高斯组件的问题简化为处理3D点。此外，网格面上的信息可以用于将更多属性整合到物理模型中，从而促进三角形的使用。最终的解决方案可以集成到任何可作为黑箱处理的物理引擎中。正如我们的研究所示，所提出的模型在设计用于3D对象渲染的多种基准数据集上表现出卓越的性能。