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

TL;DR

MCHex introduces a Marching Cubes based method for adaptive hexahedral mesh generation that improves boundary accuracy and guarantees positive Jacobian, enhancing grid quality over traditional approaches.

Contribution

The paper proposes MCHex, a novel Marching Cubes based approach that replaces the traditional outside element removal, ensuring better boundary fit and guaranteed positive Jacobian.

Findings

MCHex achieves higher IoU and lower Hausdorff distance ratio.

MCHex guarantees a positive minimum scaled Jacobian, outperforming traditional methods.

Comparable runtime with improved mesh quality.

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).