Hist2Hex: Construction-History-Guided CAD Decomposition with a Language Model for Hexahedral Meshing

Hexahedral meshing of CAD models is central to simulation-driven design. It requires first decomposing the solid into hex-meshable blocks, which remains a long-standing bottleneck. Existing methods operate on the final boundary representation. This representation omits the construction history and the feature boundaries it records. We observe that replaying the Boolean construction history deterministically associates each final body with its body-specific construction subsequence. We present Hist2Hex, a two-stage framework that exploits this structure for hexahedral meshing. In the first stage, deterministic history replay reconstructs the final bodies and establishes these associations between geometry and history without learning. In the second stage, a language model decomposes each sub-solid into hex-meshable leaf blocks. It selects cut planes conditioned on three sources of information: the serialized history, the boundary-representation (B-rep) geometry, and a table of enumerated candidates. Hist2Hex achieves the highest final-mesh success rates across all three datasets, while a controlled Fusion360 ablation shows that serialized history improves candidate selection with Stage 1 and the candidate pool fixed.