Explicit topology and connectivity constraints for 3D model repair

Designers often prioritize structural design over machinability, leading to various defects such as open boundaries, self-intersections, non-manifoldness, topological errors, and disconnected patches. This makes mesh repair a fundamental task in digital geometry processing. Despite significant progress in recent decades, topological and connectivity constraints continue to pose substantial challenges. In this paper, we propose a general integer programming framework to address the problem of mesh repair. We start by dividing the entire surface into topologically equivalent disk surface patches. Our formulation not only considers manifoldness and watertightness but also addresses connectivity constraints and user-specified topological constraints. First, topological constraints are defined based on Euler's characteristic formula. Second, we observe that in a connected graph with n nodes, a capacity configuration with n−1 ‘1’s and one ‘n−1’ leads to a non-vanishing flow plan, and thus allowing us to transform the connectivity requirements into a max-flow problem. In implementation, our method begins by identifying topological disk equivalent surface patches and assigning each surface patch a binary labeling variable to indicate whether it should be retained. To ensure the outcome closely resembles the original model, we also introduce the alpha-wrapping technique to extract the approximate outer layer, which helps define the adherence of surface patches. As the Fig. 1 demonstrates, our method can produce repaired models with genera of 0, 1, and 3, while maintaining a single component. We tested our method on a large set of defective models, demonstrating its advantages over state-of-the-art methods.