MCHex: Marching Cubes Based Adaptive Hexahedral Mesh Generation with Guaranteed Positive Jacobian

📝 Original Info

• Title: MCHex: Marching Cubes Based Adaptive Hexahedral Mesh Generation with Guaranteed Positive Jacobian
• ArXiv ID: 2511.02064
• Date: 2025-11-03
• Authors: ** 논문에 명시된 저자 정보가 제공되지 않았습니다. (저자명 미상) **

📝 Abstract

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).

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