Density-Normalized Contact Fields for Stable Collision Response in Gaussian Splatting

Abstract Gaussian Splatting represents complex three-dimensional scenes as a collection of continuous anisotropic Gaussian primitives, providing high rendering quality and an efficient scene representation. However, when such Gaussian representations are directly used for collision handling, the resulting collision boundary can vary with local Gaussian density, overlap, and opacity distribution even for identical or similar geometric surfaces. This density dependence can destabilize contact positions and normals, thereby reducing the consistency of rigid-body collision responses such as penetration correction, restitution, and rotational response. In this paper, we propose a density-normalized contact field for stable collision response in Gaussian Splatting scenes. The proposed method accumulates the local contribution of each Gaussian while simultaneously estimating the effective number of Gaussians influencing a given position, thereby normalizing the accumulation bias caused by local representation density. This enables the construction of a more stable continuous contact field under Gaussian duplication or changes in local sampling density. We further use an iso-surface of the proposed contact field as the collision boundary and compute continuous contact normals from its spatial gradient, allowing the resulting contact information to be directly incorporated into rigid-body position correction and impulse-based collision response. We compare the proposed method with existing Gaussian-primitive-based collision formulations and Gaussian-overlap-based approaches under varying Gaussian densities, duplication levels, surface curvatures, and complex three-dimensional scenes. The results show that existing methods can exhibit substantial changes in collision-boundary location and contact normal as the Gaussian distribution varies, whereas the proposed method maintains a more consistent contact boundary for the same underlying geometry. Rigid-body collision experiments further demonstrate that the proposed method reduces contact-normal variation and instability in rotational response, resulting in more stable repeated collisions. These results indicate that the proposed method provides a stable contact representation for physical interaction in Gaussian Splatting scenes without requiring explicit mesh reconstruction or signed-distance-field reconstruction.