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.

翻译：本文提出拓扑偏移，一种生成流形且无自交偏移曲面的新方法，该曲面在拓扑上等价于无限接近原始曲面的偏移。我们的方法通过构造生成严格包围输入模型的流形、水密且无自交的偏移曲面，同时最大程度地使其移动到用户指定的距离。与现有方法不同，我们将输入模型嵌入体网格中，并通过纯组合操作在网格周围插入拓扑偏移。随后对拓扑偏移进行膨胀/收缩以匹配用户指定距离，同时确保不引入任何相交或非流形结构。我们在Thingi10k数据集的非相交子集上评估了方法的有效性和鲁棒性，并证明拓扑偏移在多种图形应用中具有优势，包括：(1) 将非流形曲面转换为流形曲面，(2) 创建嵌套笼结构/分层偏移，以及(3) 可靠计算有限距离偏移。