  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.
