ℓ ₁ -Based Construction of Polycube Maps from Complex Shapes

Abstract

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 control a low-distortion polycube from a detailed surface remains challenging in practice. We propose a variational method for deforming an input triangle 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.

Robust edge-preserving surface mesh polycube deformation

“…Therefore, the value of the 1 -norm of every unit face normal of the polycube shape is equal to 1 [17]. Based on this observation, Ref.…”

“…[7,[16][17][18]. The authors use a segmentation method to patch the input mesh, then use box-primitives to approximate it coarsely in Ref.…”

“…While the algorithms in Refs. [7,17] are volume-mesh-based, they look for the specific polycube which minimizes the distortion of the volumetric map.…”

“…Based on this observation, Ref. [17] defines an 1 -norm energy which is weighted by triangle area, then proposes a variational method to deform an input triangle mesh into a polycube shape by minimization of this energy. The 1 -norm term of the mesh's face normals, and the weight term of triangle areas are both non-linear in mesh position.…”

“…Finally, a complicated numerical method is resorted to solve the minimization problem in Ref. [17]. To decrease distortion, a volumetric mesh is created from the surface mesh, then an as-rigidas-possible volumetric distortion energy [19] is used to regularize the system.…”