Topological Offsets

We introduce Topological Offsets, a novel approach to generate manifold and self-intersection-free offset surfaces that are topologically equivalent to an offset infinitesimally close to the surface. Our approach, by construction, creates a manifold, watertight, and self-intersection-free offset surface strictly enclosing the input, while doing a best effort to move it to a prescribed distance from the input. Differently from existing approaches, we embed the input in a volumetric mesh, and insert a topological offset around the mesh with purely combinatorial operations. The topological offset is then inflated/deflated to match the user-prescribed distance, while enforcing that no intersections or non-manifold configurations are introduced. We evaluate the effectiveness and robustness of our approach on the non-intersecting subset of Thingi10k, and show that topological offsets are beneficial in multiple graphics applications, including (1) converting non-manifold surfaces to manifold ones, (2) creation of nested cages/layered offsets, and (3) reliably computing finite offsets.