GASP: Gaussian Splatting for Physic-Based Simulations

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.

Gaussian Splatting with NeRF-based Color and Opacity

Neural Radiance Fields (NeRFs) have demonstrated the remarkable potential of neural networks to capture the intricacies of 3D objects. By encoding the shape and color information within neural network weights, NeRFs excel at producing strikingly sharp novel views of 3D objects. Recently, numerous generalizations of NeRFs utilizing generative models have emerged, expanding its versatility. In contrast, Gaussian Splatting (GS) offers a similar renders quality with faster training and inference as it does not need neural networks to work. We encode information about the 3D objects in the set of Gaussian distributions that can be rendered in 3D similarly to classical meshes. Unfortunately, GS are difficult to condition since they usually require circa hundred thousand Gaussian components. To mitigate the caveats of both models, we propose a hybrid model that uses GS representation of the 3D object's shape and NeRF-based encoding of color and opacity. Our model uses Gaussian distributions with trainable positions (i.e. means of Gaussian), shape (i.e. covariance of Gaussian), color and opacity, and neural network, which takes parameters of Gaussian and viewing direction to produce changes in color and opacity. Consequently, our model better describes shadows, light reflections, and transparency of 3D objects.