We present a robust technique to build a topologically optimal all-hexahedral layer on the boundary of a model with arbitrarily complex ridges and corners. The generated boundary layer mesh strictly respects the geometry of the input surface mesh, and it is optimal in the sense that the hexahedral valences of the boundary edges are as close as possible to their ideal values (local dihedral angle divided by 90°). Starting from a valid watertight surface mesh (all-quad in practice), we build a global optimization integer programming problem to minimize the mismatch between the hexahedral valences of the boundary edges and their ideal values. The formulation of the integer programming problem relies on the duality between boundary hexahedral configurations and triangulations of the disk, which we reframe in terms of integer constraints. The global problem is solved efficiently by performing combinatorial branch-and-bound searches on a series of sub-problems defined in the vicinity of complicated ridges/corners, where the local mesh topology is necessarily irregular because of the inherent constraints in hexahedral meshes. From the integer solution, we build the topology of the all-hexahedral layer, and the mesh geometry is computed by untangling/smoothing. Our approach is fully automated, topologically robust, and fast.

我们提出了一种稳健的技术，可以在具有任意复杂的脊和角的模型的边界上构建拓扑最优的全六面体层。生成的边界层网格严格遵守输入表面网格的几何形状，并且在边界边的六面体价尽可能接近其理想值（局部二面角除以 90°）的意义上是最优的。从有效的水密表面网格（实际上是全四边形）开始，我们构建了一个全局优化整数规划问题，以最小化边界边的六面体价与其理想值之间的不匹配。整数规划问题的公式化依赖于边界六面体构型和圆盘三角剖分之间的对偶性，我们根据整数约束对其进行重构。通过对在复杂脊/角附近定义的一系列子问题执行组合分支定界搜索，可以有效地解决全局问题，由于六面体网格的固有约束，局部网格拓扑必然是不规则的。从整数解，我们构建全六面体层的拓扑结构，并通过解开/平滑计算网格几何形状。我们的方法是完全自动化的、拓扑稳健且快速的。并且网格几何形状是通过解开/平滑计算的。我们的方法是完全自动化的、拓扑稳健且快速的。并且网格几何形状是通过解开/平滑计算的。我们的方法是完全自动化的、拓扑稳健且快速的。