Constructing an adaptive hexahedral tessellation to fit an input triangle boundary is a key challenge in grid-based methods. The conventional method first removes outside elements (RO) and then projects the axis-aligned boundary onto the input triangle boundary, which has no guarantee on improving the initial Intersection over Union (IoU) and Hausdorff distance ratio (HR, w.r.t bounding box diagonal). The proposed MCHex approach replaces RO with a Marching Cubes method MCHex. Given the same computational budget (benchmarked using an identical precomputed Signed Distance Field, which dominates the runtime), MCHex provides better boundary approximation (higher IoU and lower HR) while guaranteeing a lower, yet still positive, minimum scaled Jacobian (>0 vs. RO's >0.48).

翻译：为输入三角边界构建自适应六面体剖分是网格化方法中的关键挑战。传统方法首先移除外部单元（RO），然后将轴对齐边界投影到输入三角边界上，该方法无法保证改进初始交并比（IoU）和豪斯多夫距离比（HR，相对于包围盒对角线）。所提出的MCHex方法使用行进立方体方法MCHex替代RO。在相同计算预算下（使用相同的预计算符号距离场进行基准测试，该过程主导运行时间），MCHex在保证较低但仍为正的最小缩放雅可比行列式（>0 vs. RO的>0.48）的同时，提供了更好的边界逼近效果（更高的IoU和更低的HR）。