This paper describes a novel method of generating hex-dominant meshes using pre-computed optimal subdivisions of the unit cube in a grid-based approach. Our method addresses geometries that are standard in mechanical engineering and often must comply with the restrictions of subtractive manufacturability. A central component of our method is the set of subdivisions we pre-compute with Answer Set Programming. Despite being computationally expensive, we obtain optimal meshes of up to 35 nodes available to our method in a template fashion. The first step in our grid-based method generates a coarse Precursor Mesh for meshing complete parts representing the bar stock. Then, the resulting mesh is generated in a subtractive manner by inserting and fitting the pre-generated subdivisions into the Precursor Mesh. This step guarantees that the elements are of good quality. In the final stage, the mesh nodes are mapped to geometric entities of the target geometry to get an exact match. We demonstrate our method with multiple examples showing the strength of this approach.

翻译：本文描述了一种新颖的六面体主导网格生成方法，该方法基于预计算的单位立方体最优细分，采用网格化策略。我们的方法针对机械工程中常见的几何形状，这些形状通常需满足减材制造的限制条件。方法的核心组件是通过回答集编程预计算的一组细分方案。尽管计算成本较高，我们仍能以模板化方式获得包含多达35个节点的最优网格。在网格化方法的第一步中，我们生成粗粒度前驱网格，用于完整表示棒料零件的网格划分。随后，通过将预生成的细分方案插入并适配到前驱网格中，以减材方式生成最终网格。此步骤确保单元质量优良。最后阶段，网格节点映射至目标几何实体以实现精确匹配。我们通过多个示例展示了该方法的优势。