MCHex: marching cubes based adaptive hexahedral mesh generation with guaranteed positive Jacobian

Grid-based methods are robust for automatic hexahedral (hex) meshing, but struggle with boundary fidelity and element quality. Conventional pipelines remove outside elements, yielding axis-aligned surfaces converging to the input geometry at first order; subsequent padding and projection are heuristic, offering no guarantees on final boundary fidelity or mesh quality. This paper introduces MCHex, a fundamental reformulation of boundary and mesh-quality handling in grid-based hex meshing. MCHex applies marching cubes (MC) inside each grid cell, ensuring the mesh boundary is an MC surface. The key insight is that constraining cut-cell configurations to 3-regular polyhedra and applying midpoint subdivision produces an all-hex mesh with guaranteed positive Jacobian for every element. MCHex provides three advantages: (1) theoretical positive-Jacobian guarantee for every element; (2) boundary convergence matching MC’s approximation rate, via a non-heuristic algorithm with well-bounded time complexity and the fastest wall-clock time among existing methods; and (3) manifold surfaces for arbitrary geometries plus a natural padded layer. Extensive evaluation on 202 benchmark geometries, using a slightly smaller element budget, compares MCHex with previous state-of-the-art methods; it consistently yields positive-Jacobian meshes with similar boundary fidelity while running significantly faster. It integrates seamlessly with post-processing such as smoothing and simplification, and is suitable for simulation.