Abstract Inside–outside classification is widely used for geometry processing tasks such as surface reconstruction, geometry completion, and calculating signed distance fields. We introduce a new integral formulation of this problem, which assigns confidence scores that points are inside or outside, given incomplete boundary geometry. Even though our geometric construction does not appear in previous work, we show that it is unexpectedly linked to both the well‐established generalized winding number (GWN) and pseudonormal methods for geometry completion, and it provably reduces to either one of them for specific values of a control parameter. The results obtained with our method frequently outperform screened Poisson surface reconstruction (PSR), GWN, and the pseudonormal method in terms of quality, and are at least on par with them on all of our examples. Unlike these methods, our algorithm naturally extends to the multi‐label setting, in which regions with an arbitrary number of colors or physical materials can be reconstructed, and non‐manifold features such as T‐junctions may appear in the interface and boundary geometry.

We introduce a multi-material non-manifold mesh-based surface tracking algorithm that converts self-intersections into topological changes. Our algorithm generalizes prior work on manifold surface tracking with topological changes: it preserves surface features like mesh-based methods, and it robustly handles topological changes like level set methods. Our method also offers improved efficiency and robustness over the state of the art. We demonstrate the effectiveness of the approach on a range of examples, including complex soap film simulations with thousands of interacting bubbles, and boolean unions of non-manifold meshes consisting of millions of triangles.

Previous research on animations of soap bubbles, films, and foams largely focuses on the motion and geometric shape of the bubble surface. These works neglect the evolution of the bubble's thickness, which is normally responsible for visual phenomena like surface vortices, Newton's interference patterns, capillary waves, and deformation-dependent rupturing of films in a foam. In this paper, we model these natural phenomena by introducing the film thickness as a reduced degree of freedom in the Navier-Stokes equations and deriving their equations of motion. We discretize the equations on a non-manifold triangle mesh surface and couple it to an existing bubble solver. In doing so, we also introduce an incompressible fluid solver for 2.5D films and a novel advection algorithm for convecting fields across non-manifold surface junctions. Our simulations enhance state-of-the-art bubble solvers with additional effects caused by convection, rippling, draining, and evaporation of the thin film.