`1-based Construction of Polycube Maps from Complex Shapes

Polycube maps of triangle meshes have proved useful in a wide range of applications including texture mapping and hexahedral mesh generation. However, constructing either fully automatically or with limited user con-trol a low-distortion polycube from a detailed surface remains challenging in practice. We propose a variational method for deforming an input trian-gle mesh into a polycube shape through minimization of the `1-norm of the mesh normals, regularized via an as-rigid-as-possible volumetric distortion energy. Unlike previous work, our approach makes no assumption on the orientation, or on the presence of features in the input model. User-guided control over the resulting polycube map is also offered to increase design flexibility. We demonstrate the robustness, efficiency and controllability of our method on a variety of examples, and explore applications in hexahedral remeshing and quadrangulation