Polycube Segmentations via Dual Loops

Polycube segmentations for 3D models effectively support a wide variety of applications such as hexahedral mesh construction, seamless texture mapping, spline fitting, and multi-block grid generation. However, the automated construction of valid polycube segmentations suffers from robustness issues: state-of-the-art methods are not guaranteed to find a valid solution. In this paper we present an iterative algorithm which is guaranteed to return a valid polycube segmentation for 3D models of any genus. Our algorithm is based on a novel dual representation of polycubes [Snoep, Speckmann, & Verbeek, 2025]. Starting from an initial simple polycube of the correct genus, together with the corresponding dual loop structure and polycube segmentation, we iteratively refine the polycube, loop structure, and segmentation, while maintaining the correctness of the solution. Our algorithm is robust by construction: at any point during the iterative process the current segmentation is valid. Furthermore, the iterative nature of our algorithm facilitates a seamless trade-off between quality and complexity of the solution.