All-Hex Meshing using Closed-Form Induced Polycube

The polycube-based hexahedralization methods are robust to generate all-hex meshes without internal singularities. They avoid the difficulty to control the global singularity structure for a valid hexahedralization in frame-field based methods. To thoroughly utilize this advantage, we propose to use a frame field without internal singularities to guide the polycube construction. Theoretically, our method extends the vector fields associated with the polycube from exact forms to closed forms, which are curl free everywhere but may be not globally integrable. The closed forms give additional degrees of freedom to deal with the topological structure of high-genus models, and also provide better initial axis alignment for subsequent polycube generation. We demonstrate the advantages of our method on various models, ranging from genus-zero models to high-genus ones, and from single-boundary models to multipleboundary ones.