Constructing hexahedral shell meshes via volumetric polycube maps

Shells are three-dimensional structures. One dimension, the thickness, is much smaller than the other two dimensions. Shell structures can be widely found in many real-world objects. This paper presents a method to construct a layered hexahedral mesh for shell objects. Given a closed 2-manifold and the user-specified thickness, we construct the shell space using the distance field and then parameterize the shell space to a polycube domain. The volume parameterization induces the hexahedral tessellation in the object shell space. As a result, the constructed mesh is an all-hexahedral mesh in which most of the vertices are regular, i.e., the valence is 6 for interior vertices and 5 for boundary vertices. The mesh also has a layered structure, so that all layers have exactly the same tessellation. We prove that our parameterization is guaranteed to be bijective. As a result, the constructed hexahedral mesh is free of degeneracy, such as self-intersection, flip-over, etc. We also show that the iso-parametric line (in the thickness dimension) is orthogonal to the other two iso-parametric lines. We apply our algorithm to numerous real-world models of various geometry and topology. The promising experimental results demonstrate the efficacy of our algorithm. Although our main focus is to construct a hexahedral mesh by using volumetric polycube parameterization, the proposed framework is general that can be applied to other regular domains, such as cylinder and sphere, which is also demonstrated in the paper.