Instant Self-Intersection Repair for 3D Meshes

Self-intersection repair in static 3D surface meshes presents unique challenges due to the absence of temporal motion and penetration depth information—two critical elements typically leveraged in physics-based approaches. We introduce a novel framework that transforms local contact handling into a global repair strategy through a combination of local signed tangent-point energies and their gradient diffusion. At the heart of our method is a key insight: rather than computing expensive global repulsive potentials, we can effectively approximate long-range interactions by diffusing energy gradients from local contacts throughout the mesh surface. In turn, resolving complex self-intersections reduces to simply propagating local repulsive energies through standard diffusion mechanics and iteratively solving tractable local optimizations. We further accelerate convergence through our momentum-based optimizer, which adaptively regulates momentum based on gradient statistics to prevent overshooting while maintaining rapid intersection repair. The resulting algorithm handles a variety of challenging scenarios, from shallow contacts to deep penetrations, while providing computational efficiency suitable for interactive applications.