From Blobs to Spokes: High-Fidelity Surface Reconstruction via Oriented Gaussians

3D Gaussian Splatting (3DGS) has revolutionized fast novelview synthesis, yet its opacity-based formulation makes surface extrac-tion fundamentally difficult. Unlike implicit methods built on SignedDistance Fields or occupancy, 3DGS lacks a global geometric field, forc-ing existing approaches to resort to heuristics such as TSDF fusion ofblended depth maps. Inspired by the Objects as Volumes framework [38],we derive a principled occupancy field for Gaussian Splatting and showhow it can be used to extract highly accurate watertight meshes of com-plex scenes. Our key contribution is to introduce a learnable orientednormal at each Gaussian element and to define an adapted attenuationformulation, which leads to closed-form expressions for both the normaland occupancy fields at arbitrary locations in space. We further intro-duce a novel consistency loss and a dedicated densification strategy toenforce Gaussians to wrap the entire surface by closing geometric holes,ensuring a complete shell of oriented primitives. We modify the differen-tiable rasterizer to output depth as an isosurface of our continuous model,and introduce Primal Adaptive Meshing for Region-of-Interest mesh-ing at arbitrary resolution. We additionally expose fundamental biasesin standard surface evaluation protocols and propose two more rigor-ous alternatives. Overall, our method Gaussian Wrapping sets a newstate-of-the-art on DTU and Tanks and Temples, producing complete,watertight meshes at a fraction of the size of concurrent work—recoveringthin structures such as the notoriously elusive bicycle spokes. Our projectpage is available here.